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÷ü ø3[#CC.1.OA.8 Work with addition and subtraction equations. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ?’ 3, 6 + 6 = ?’. NBT½CC.1.NBT.1 Extend the counting sequence. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.by end of 2nd to 100kCC.1.MD.3 Tell and write time. Tell and write time in hours and halfhours using analog and digital clocks.SD.1.M.1.1 (Knowledge) Students are able to tell time to the halfhour using digital and analog clocks and order a sequence of events with respect to time.CC.1.MD.4 Represent and interpret data. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.SD.1.S.1.1 (Application) Students are able to display data in simple picture graphs with units of one and bar graphs with intervals of one.SUSD.1.S.1.2 (Comprehension) Students are able to answer questions from organized data.%CC.2.OA.3 Work with equal groups of objects to gain foundations for multiplication. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.uSD.2.A.4.1 (Comprehension) Students are able to find and extend growing patterns using symbols, objects, and numbers.4.1VCC.2.NBT.2 Understand place value. Count within 1000; skipcount by 5s, 10s, and 100s.ūCC.2.NBT.5 Use place value understanding and properties of operations to add and subtract. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. ©SD.2.N.2.1 (Application) Students are able to solve twodigit addition and subtraction problems written in horizontal and vertical formats using a variety of strategies.SD does not mention strategiesĀCC.2.MD.1 Measure and estimate lengths in standard units. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. SD.5.M.1.4 (Application) Students are able to use appropriate tools to measure length, weight, temperature, and area in problem solving.1.4SD.1.M.1.5 (Knowledge) Students are able to identify appropriate measuring tools for length, weight, capacity, and temperature.CC.2.MD.7 Work with time and money. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. SD.2.M.1.1 (Knowledge) Students are able to tell time to the minute using digital and analog clocks and relate time to daily events.SD does not require am or pmSD.3.M.1.1 (Knowledge) Students are able to read and tell time before and after the hour within fiveminute intervals on an analog clock.öCC.2.MD.8 Work with time and money. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ (dollars) and ¢ (cents) symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? SD.2.M.1.4 (Knowledge) Students are able to represent and write the value of money using the "¢" sign and in decimal form using the "$" sign.
by end of 3rdSD.2.M.1.3 (Application) Students are able to determine the value of a collection of like and unlike coins with a value up to $1.00.1.3wSD.3.M.1.2 (Application) Students are able to count, compare, and solve problems using a collection of coins and bills.SD.1.M.1.3 (Application) Students are able to use different combinations of pennies, nickels, and dimes to represent money amounts to 25 cents.10CC.2.MD.10 Represent and interpret data. Draw a picture graph and a bar graph (with singleunit scale) to represent a data set with up to four categories. Solve simple puttogether, takeapart, and compare problems using information presented in a bar graph. WSD.2.S.1.2 (Application) Students are able to represent data sets in more than one way.SD.3.S.1.1 (Application) Students are able to ask and answer questions from data represented in bar graphs, pictographs and tally charts.6CC.2.G.1 Reason with shapes and their attributes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. (Sizes are compared directly or visually, not compared by measuring.)SD.4.G.1.1 (Knowledge) Students are able to identify the following plane and solid figures: pentagon, hexagon, octagon, pyramid, rectangular prism, and cone.
by end of 4th%CC.3.OA.1 Represent and solve problems involving multiplication and division. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. vSD.3.A.1.1 (Comprehension) Students are able to explain the relationship between repeated addition and multiplication.?CC.3.OA.3 Represent and solve problems involving multiplication and division. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. SD.4.A.3.1 (Application) Students are able to write and solve number sentences that represent onestep word problems using whole numbers.dCC.3.OA.5 Understand properties of multiplication and the relationship between multiplication and division. Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15 then 15 × 2 = 30, or by 5 × 2 = 10 then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) (Students need not use formal terms for these properties.)PSD.3.G.1.2 Students are able to identify points, lines, line segments, and rays.eSD.4.G.1.2 (Knowledge) Students are able to identify parallel, perpendicular, and intersecting lines.PCC.4.G.2 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.SD.5.G.1.1 (Knowledge) Students are able to describe and identify isosceles and equilateral triangles, pyramids, rectangular prisms, and cones.BCC.4.G.3 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry.rSD.5.G.2.1 (Comprehension) Students are able to determine lines of symmetry in rectangles, squares, and triangles. CC.5.OA.1 Write and interpret numerical expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.SD.6.A.1.1 (Application) Students are able to use order of operations, excluding nested parentheses and exponents, to simplify whole number expressions.CC.5.OA.2 Write and < interpret numerical expressions. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation add 8 and 7, then multiply by 2 as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.HCC.5.OA.3 Analyze patterns and relationships. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. nSD.5.A.4.1 (Application) Students are able to solve problems using patterns involving more than one operation._CC.5.NBT.3 Understand the place value system. Read, write, and compare decimals to thousandths.sSD.5.N.1.1 (Comprehension) Students are able to read, write, order, and compare numbers from .001 to 1,000,000,000.ĮCC.5.NBT.3a Read and write decimals to thousandths using baseten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). CC.5.NBT.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.^CC.7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. CC.7.NS.2 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. `CC.7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.(SD standards require positive fractions Grade DifferenceDegree of MatchNotesCC1VCC.K.CC.1 Know number names and the count sequence. Count to 100 by ones and by tens. K`SD.K.N.1.1 (Comprehension) Students are able to read, write, count, and sequence numerals to 20.N1.103 = Excellent match between the two documents:only to 50 in SD standards read, write, count and sequnce]SD.1.N.1.1 (Comprehension) Students are able to read, write, count, and order numerals to 50.12aSD.2.N.1.1 (Comprehension) Students are able to read, write, count, and sequence numerals to 100.23¶CC.K.CC.3 Know number names and the count sequence. Write numbers from 0 to 20. Represent a number of objects with a written numeral 020 (with 0 representing a count of no objects).<2 = Good match, with minor aspects of the CCSS not addressedSD standards numerals to 205CC.K.CC.5 Count to tell the number of objects. Count to answer how many? questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 120, count out that many objects.6łCC.K.CC.6 Compare numbers. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. (Include groups with up to ten objects.)SD.K.A.2.1 (Comprehension) Students are able to compare collections of objects to determine more, less, and equal (greater than and less than).A2.17^CC.K.CC.7 Compare numbers. Compare two numbers between 1 and 10 presented as written numerals.ŖSD.1.A.2.1 (Comprehension) Students are able to use the concepts and language of more, less, and equal (greater than and less than) to compare numbers and sets (0 to 20).71 = Weak match, major aspects of the CCSS not addressed 1st they go to 20OACC.K.OA.1 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Represent addition and subtraction with objects, fingers, mental images, drawings (drawings need not show details, but should show the mathematics in the problem), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. qSD.K.A.3.1 (Knowledge) Students are able to use concrete objects to model the meaning of the "+" and "" symbols.3.1CC.K.OA.2 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.jSD.K.N.3.1 (Application) Students are able to solve addition and subtraction problems up to 10 in context.MD¶CC.K.MD.1 Describe and compare measurable attributes. Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.qSD.K.M.1.5 (Comprehension) Students are able to compare and order concrete objects by length, height, and weight.M1.55CC.K.MD.2 Describe and compare measurable attributes. Directly compare two objects with a measurable attribute in common, to see which object has more of / less of the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.üCC.K.MD.3 Classify objects and count the number of objects in each category. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. (Limit category counts to be less than or equal to 10.)eSD.K.A.4.2 (Comprehension) Students are able to sort and classify objects according to one attribute.4.2G<CC.K.G.1 Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.iSD.K.G.2.1 (Comprehension) Students are able to describe the position of twodimensional (plane) figures.
by end of 1stWSD.1.G.2.1 (Comprehension) Students are able to describe proximity of objects in space.[SD.K.G.1.1 (Knowledge) Students are able to identify basic twodimensional (plane) figures.ZSD.1.G.1.1 (Comprehension) Students are able to describe characteristics of plane figures.< ŠCC.K.G.2 Identify and describe shapes (such as squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Correctly name shapes regardless of their orientations or overall size.
by end of 2ndUSD.1.G.1.2 (Comprehension) Students are able to sort basic threedimensional figures.1.2wSD.2.G.2.1 (Knowledge) Students are able to identify geometric figures regardless of position and orientation in space.ęCC.K.G.3 Identify and describe shapes (such as squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Identify shapes as twodimensional (lying in a plane, flat ) or threedimensional ( solid ).even by end of 1st weak4GCC.K.G.4 Analyze, compare, create, and compose shapes. Analyze and compare two and threedimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/ corners ) and other attributes (e.g., having sides of equal length).ÆSD.3.G.1.1 (Comprehension) Students are able to recognize and compare the following plane and solid geometric figures: square, rectangle, triangle, cube, sphere, and cylinder.3by end of 3rd they compareSD.2.G.1.1 (Comprehension) Students are able to use the terms side and vertex (corners) to identify plane and solid figures.wCC.1.OA.1 Represent and solve problems involving addition and subtraction. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. “SD.1.N.2.1 (Application) Students are able to solve addition and subtraction problems with numbers 0 to 20 written in horizontal and vertical formats using a variety of strategies.jSD.1.N.3.1 (Application) Students are able to solve addition and subtraction problems up to 20 in context.SD.1.A.2.2 (Application) Students are able to solve open addition and subtraction sentences with one unknown (c) using numbers equal to or less than 10.2.2ķCC.8.NS.2 Know that there are numbers that are not rational, and approximate them by rational numbers. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., Ą^2). For example, by truncating the decimal expansion of "2 (square root of 2), show that "2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.SD.912.N.1.2A (Application) Students are able to apply properties and axioms of the real number system to various subsets, e.g., axioms of order, closure.1.2A'SD only compart rational and irrationalÉCC.8.EE.1 Work with radicals and integer exponents. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 × 3^( 5) = 3^( 3) = 1/(3^3) = 1/27.SD.912.N.2.1 (Comprehension) Students are able to add, subtract, multiply, and divide real numbers including integral exponents.°CC.8.EE.4 Work with radicals and integer exponents. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.SD.912.N.1.2 (Comprehension) Students are able to apply the concept of place value, magnitude, and relative magnitude of real numbers.CC.8.EE.5 Understand the connections between proportional relationships, lines, and linear equations. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distancetime graph to a distancetime equation to determine which of two moving objects has greater speed.`SD.K.M.1.4 (Knowledge) Students are able to estimate length using nonstandard units of measure.^SD.K.N.1.2 (Knowledge) Students are able to use fraction models to create one half of a whole.SD.K.S.1.1 (Knowledge) Students are able to describe data represented in simple graphs (using real objects) and pictographs.SD.1.A.3.1 (Application) Students are able to write number sentences from problem situations using "+" or "", and "=" with numbers to ten.SD.1.A.4.1 (Comprehension) Students are able to identify and extend repeating patterns containing multiple elements using objects and pictures.SD.1.A.4.2 (Comprehension) Students are able to determine common attributes in a given group and identify those objects that do not belong.5SD.1.M.1.2 (Application) Find a date on the calendar.dSD.1.M.1.4 (Comprehension) Students are able to estimate weight using nonstandard units of measure.1.6oSD.1.M.1.6 (Comprehension) Students are able to compare and order concrete objects by temperature and capacity.`SD.1.N.1.2 (Knowledge) Students are able to use unit fraction models to create parts of a whole.zSD.1.S.2.1 (Comprehension) Students are able to recognize whether the outcome of a simple event is possible or impossible.SD.2.A.2.1 (Comprehension) Students are able to use concepts of equal to, greater than, and less than to compare numbers (0100).bSD.2.A.3.1 (Application) Students are able to write and solve number sentences from word problems.bSD.2.A.4.2 (Comprehension) Students are able to determine likenesses and differences between sets.QSD.2.M.1.2 (Application) Students are able to use the calendar to solve problems.SD.2.M.1.5 (Comprehension) Students are able to use whole number approximations for capacity using nonstandard units of measure.xSD.2.M.1.6 (Comprehension) Students are able to solve everyday problems by measuring length to the nearest inch or foot.eSD.2.N.1.2 (Comprehension) Students are able to identify and represent fractions as parts of a group.kSD.2.N.3.1 (Application) Students are able to solve addition and subtraction problems up to 100 in context.iSD.2.S.1.1 (Comprehension) Students are able to use interviews, surveys, and observations to gather data.SD.2.S.1.3 (Comprehension) Students are able to answer questions about and generate explanations of data given in tables and graphs. SD.2.S.2.1 (Application) Students are able to list possible outcomes of a simple event and make predictions about which outcome is more or less likely to occur.sSD.3.A.2.1 (Comprehension) Students are able to select appropriate relational symbols (<, >, =) to compare numbers.SD.3.N.1.1 (Comprehension) Students are able to place in order and compare whole < numbers less than 10,000, using appropriate words and symbols.]SD.3.N.1.2 (Comprehension) Students are able to find multiples of whole numbers 2, 5, and 10.YSD.3.S.2.1 (Comprehension) Students are able to describe events as certain or impossible.SD.4.A.1.1 (Comprehension) Students are able to simplify whole number expressions involving addition, subtraction, multiplication, and division._SD.4.A.2.2 (Application) Students are able to simplify a twostep equation using whole numbers.]SD.4.G.2.2 (Knowledge) Students are able to identify a slide (translation) of a given figure.YSD.4.N.1.4 (Application) Students are able to interpret negative integers in temperature.¤SD.4.S.1.2 (Knowledge) Given a small ordered data set of whole number data points (odd number of points), students are able to identify the median, mode, and range.SD.4.S.2.1 (Comprehension) Students are able to determine the probability of simple events limited to equally likely and not equally likely outcomes.oSD.5.G.2.2 (Knowledge) Students are able to identify a turn or flip (rotation or reflection) of a given figure.ZSD.5.N.1.4 (Comprehension) Students are able to locate negative integers on a number line.XSD.5.N.1.5 (Comprehension) Students are able to determine the squares of numbers 1  12.SD.5.S.2.1 (Application) Students are able to classify probability of simple events as certain, likely, unlikely, or impossible.VSD.5.S.2.2 (Application) Students are able to use models to display possible outcomes.SD.6.A.4.1 (Comprehension) Students are able to use concrete materials, graphs and algebraic statements to represent problem situations.zSD.6.G.1.1 (Comprehension) Students are able to identify and describe the characteristics of triangles and quadrilaterals.MSD.6.G.1.2 (Comprehension) Students are able to identify and describe angles.aSD.6.G.2.1 (Application) Students are able to use basic shapes to demonstrate geometric concepts.
SD.6.N.3.1 (Application) Students are able to use various strategies to solve one and twostep problems involving positive decimals.SD.6.S.1.2 (Application) Students are able to display data using bar and line graphs and draw conclusions from data displayed in a graph.SSD.6.S.2.1 (Knowledge) Students are able to find the probability of a simple event.`SD.7.G.1.2 (Knowledge) Students are able to identify and describe elements of geometric figures.^SD.7.G.2.1 (Application) Students are able to demonstrate ways that shapes can be transformed.£SD.7.M.1.1 (Comprehension) Students are able to select, use, and convert appropriate units of measurement for a situation including capacity and angle measurement.iSD.7.N.1.2 (Application) Students are able to find and use common multiples and factors of whole numbers.SD.8.G.2.1 (Application) Students are able to write and solve proportions that express the relationships between corresponding parts of similar quadrilaterals and triangles.SD.8.S.2.1 (Comprehension) Students are able to find the sample space and compute probability for two simultaneous independent events.SD.912.N.3.1 Students are able to use estimation strategies in problem situations to predict results and to check the reasonableness of results.SD.912.N.3.2 (Comprehension) Students are able to select alternative computational strategies and explain the chosen strategy.RSD.912.S.1.1 (Analysis) Students are able to draw conclusions from a set of data.lSD.912.S.2.1 (Knowledge) Students are able to distinguish between experimental and theoretical probability.{SD.912.S.2.2 (Comprehension) Students are able to predict outcomes of simple events using given theoretical probabilities.2.3AcSD.912.A.2.3A (Application) Students are able to determine solutions to absolute value statements.{SD.912.M.1.2A (Analysis) Students are able to use indirect measurement in problem situations that defy direct measurement.SD.912.S.2.3A (Analysis) Students are able to generate data and use the data to determine empirical (experimental) probabilities. SD Strand
SD Standard #SD StandardSD GradeCC Matched GradeCC Matched Standard CC Strand
CC Standard # SD Grade
SD StrandCC StandardCC GradeSD Matched GradeSD Matched StandardSD.8.A.4.1 Students are able to create rules to explain the relationship between numbers when a change in the first variable affects the second variable.SD requires the synthesis levelECC.6.G.4 Solve realworld and mathematical problems involving area, surface area, and volume. Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems.jSD.8.G.1.1 (Application) Students are able to describe and classify prisms, pyramids, cylinders, and cone.(SD adds nets as an enabling skill for HSSPŁCC.6.SP.2 Develop understanding of statistical variability. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.SD.8.S.1.2 (Application) Students are able to use a variety of visual representations to display data to make comparisons and predictions.CC.6.SP.4 Summarize and describe distributions. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. ©SD.7.S.1.2 (Application) Students are able to display data, using frequency tables, line plots, stemandleaf plots, and make predictions from data displayed in a graph.1not all representaions are listed in SD standardsSD.4.N.2.1 (Application) Students are able to find the products of twodigit factors and quotient of two natural numbers using a onedigit divisor.:CC.4.NBT.6 Use place value understanding and properties of operations to perform multidigit arithmetic. Find wholenumber quotients and remainders with up to fourdigit dividends and onedigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.)ŻCC.4.NF.1 Extend understanding of fraction equivalence and ordering. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)SD.5.A.3.1 (Application) Students are able to, using whole numbers, write and solve number sentences that represent twostep word problems.SD.4.N.3.1 (Application) Students are able to estimate sums and differences in whole numbers and money to determine if a given answer is reasonable.9CC.3.OA.9 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. GSD.3.A.4.1 (Comprehension) Students are able to extend linear patterns.øCC.3.NBT.1 Use place value understanding and properties of operations to perform multidigit arithmetic. Use place value understanding to round whole numbers to the nearest 10 or 100.SD.3.N.3.1 (Application) Students are able to round twodigit whole numbers to the nearest tens, and threedigit whole numbers to the nearest hundreds.=CC.3.NBT.2 Use place value understanding and properties of operations to perform multidigit arithmetic. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of oper< ations, and/or the relationship between addition and subtraction. (A range of algorithms may be used.)/CC.3.NBT.3 Use place value understanding and properties of operations to perform multidigit arithmetic. Multiply onedigit whole numbers by multiples of 10 in the range 1090 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. (A range of algorithms may be used.)NFQCC.3.NF.1 Develop understanding of fractions as numbers. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)aSD.3.N.1.3 (Knowledge) Students are able to name and write fractions from visual representations.CC.3.NF.2 Develop understanding of fractions as numbers. Understand a fraction as a number on the number line; represent fractions on a number line diagram. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)SD.4.N.1.3 (Comprehension) Students are able to use a number line to compare numerical value of fractions or mixed numbers (fourths, halves, and thirds).3aŻCC.3.NF.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)3bCC.3.NF.3b Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3), Explain why the fractions are equivalent, e.g., by using a visual fraction model. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)]CC.3.MD.1 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
cSD.4.M.1.1 (Knowledge) Students are able to identify equivalent periods of time and solve problems.CC.3.MD.2 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems (problems involving notions of times as much. )SD.3.M.1.3 (Knowledge) Students are able to identify U.S. Customary units of length (feet), weight (pounds), and capacity (gallons).fSD.4.M.1.3 (Application) Students are able to use scales of length, temperature, capacity, and weight.^CC.3.MD.3 Represent and interpret data. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep how many more and how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.ySD.3.S.1.2 (Application) Students are able to gather data and use the information to complete a scaled and labeled graph.CC.3.MD.4 Represent and interpret data. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters.QSD.3.M.1.5 (Knowledge) Students are able to measure length to the nearest ½ inch.[SD.4.M.1.4 (Comprehension) Students are able to measure length to the nearest quarter inch.CC.3.MD.7 Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Relate area to the operations of multiplication and addition.SD.6.M.1.2 (Comprehension) Students are able to find the perimeter and area of squares and rectangles (whole number measurements). CC.3.MD.8 Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different area or with the same area and different perimeter.°CC.3.G.1 Reason with shapes and their attributes. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.zSD.3.G.2.1 (Comprehension) Students are able to demonstrate relationships between figures using similarity and congruence.
SD.4.G.2.1 (Comprehension) Students are able to compare geometric figures using size, shape, orientation, congruence, and similarity.CC.3.G.2 Reason with shapes and their attributes. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part is 1/4 of the area of the shape.»CC.4.OA.3 Use the four operations with whole numbers to solve problems. Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.IF.8aÄCC.912.F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. IF.8b%CC.912.F.IF.8b Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as representing exponential growth and decay.SD.912.A.4.4A (Application) Students are able to apply properties and definitions of trigonometric, exponential, and logarithmic expressions.4.4ABF.1CC.912.F.BF.1 Build a function that models < a relationship between two quantities. Write a function that describes a relationship between two quantities.* BF.1apCC.912.F.BF.1a Determine an explicit expression, a recursive process, or steps for calculation from a context. BF.1būCC.912.F.BF.1b Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. BF.2īCC.912.F.BF.2 Build a function that models a relationship between two quantities. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*_SD.912.A.3.3A (Analysis) Students are able to use sequences and series to model relationships.3.3ABF.3¦CC.4.NBT.2 Generalize place value understanding for multidigit whole numbers. Read and write multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)SD.2.A.2.2 (Application) Students are able to solve open addition and subtraction sentences with one unknown (c) using numbers equal to or less than 20."CC.1.OA.2 Represent and solve problems involving addition and subtraction. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.*SD does not require unknown with 3 numbersŲCC.1.OA.3 Understand and apply properties of operations and the relationship between addition and subtraction. Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) (Students need not use formal terms for these properties.)=associative property is in 5th commutative property is in 4thCC.1.OA.6 Add and subtract within 20. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 4 = 13 3 1 = 10 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).2CC.1.OA.7 Work with addition and subtraction equations. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.tSD.2.A.2.3 (Application) Students are able to balance simple addition and subtraction equations using sums up to 20.2.38eCC.912.F.TF.3 (+) Extend the domain of trigonometric functions using the unit circle. Use special triangles to determine geometrically the values of sine, cosine, tangent for Ą/3, Ą/4 and Ą/6, and use the unit circle to express the values of sine, cosine, and tangent for Ą  x, Ą + x, and 2Ą  x in terms of their values for x, where x is any real number.SD.912.G.1.2A (Application) Students are able to determine the values of the sine, cosine, and tangent ratios of right triangles.TF.5“CC.912.F.TF.5 Model periodic phenomena with trigonometric functions. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* CO.2CC.912.G.CO.2 Experiment with transformations in the plane. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).SD.912.G.2.2 (Application) Students are able to reflect across vertical or horizontal lines, and translate twodimensional figures.CO.3æCC.912.G.CO.3 Experiment with transformations in the plane. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.CO.4ŃCC.912.G.CO.4 Experiment with transformations in the plane. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.CO.5CC.4.NF.5 Understand decimal notation for fractions, and compare decimal fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100 and add 3/10 + 4/100 = 34/100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)SD.5.N.1.3 (Knowledge) Students are able to identify alternative representations of fractions and decimals involving tenths, fourths, halves, and hundredths.uCC.4.NF.6 Understand decimal notation for fractions, and compare decimal fractions. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)åCC.4.NF.7 Understand decimal notation for fractions, and compare decimal fractions. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons comparisons are valid only when two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)^CC.4.MD.1 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn < table. For example: Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), & . ¾SD.3.M.1.4 (Application) Students are able to select appropriate units to measure length (inch, foot, mile, yard); weight (ounces, pounds, tons); and capacity (cups, pints, quarts, gallons).SD.5.M.1.3 (Application) Students are able to use and convert U.S. Customary units of length (inches, feet, yard), and weight (ounces, pounds).CC.4.MD.2 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.gSD.4.M.1.2 (Application) Students are able to solve problems involving money including unit conversion.ySD.5.M.1.1 (Comprehension) Students are able to determine elapsed time within an a.m. or p.m. period on the quarterhour.eSD.5.M.1.2 (Application) Students are able to solve problems involving money including making change.CC.4.MD.3 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. very weakCC.4.MD.4 Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.qSD.4.S.1.1 (Application) Students are able to interpret data from graphical representations and draw conclusions.CC.4.MD.5 Geometric measurement: understand concepts of angle and measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
 a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a onedegree angle, and can be used to measure angles.
 b. An angle that turns through n onedegree angles is said to have an angle measure of n degrees.USD.5.G.1.2 (Knowledge) Students are able to identify acute, obtuse, and right angles."very weak,practically non existentCC.4.G.1 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.CC.912.S.ID.2 Summarize, represent, and interpret data on a single count or measurement variable. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.* SD.912.S.1.2 (Comprehension) Students are able to compare multiple onevariable data sets, using range, interquartile range, mean, mode, and median.~SD.912.S.1.3A (Analysis) Students are able to compare multiple onevariable data sets, using standard deviation and variance.ID.3ūCC.912.S.ID.3 Summarize, represent, and interpret data on a single count or measurement variable. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).* SD doesn't mention outliersID.4CC.912.S.ID.4 Summarize, represent, and interpret data on a single count or measurement variable. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.*kSD.912.S.1.4A (Application) Students are able to describe the normal curve and use it to make predictions.ID.5gCC.912.S.ID.5 Summarize, represent, and interpret data on two categorical and quantitative variables. Summarize categorical data for two categories in twoway frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.*ID.6ÓCC.912.S.ID.6 Summarize, represent, and interpret data on two categorical and quantitative variables. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.*ID.6aØCC.5.NBT.5 Perform operations with multidigit whole numbers and with decimals to hundredths. Fluently multiply multidigit whole numbers using the standard algorithm. ©CC.5.NBT.6 Perform operations with multidigit whole numbers and with decimals to hundredths. Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. jSD.5.N.2.1 (Application) Students are able to find the quotient of whole numbers using twodigit divisors.}CC.5.NBT.7 Perform operations with multidigit whole numbers and with decimals to hundredths. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.oSD.4.N.2.2 (Application) Students are able to add and subtract decimals with the same number of decimal places.fSD.5.N.2.3 (Application) Students are able to multiply and divide decimals by natural numbers (1  9).CC.5.MD.1 Convert like measurement units within a given measurement system. Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep real world problems.SD does not include metric³CC.5.MD.2 Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were< redistributed equally.BSD.5.S.1.1 Students are able to gather, graph, and interpret data.eSD.5.S.1.2 (Application) Students are able to calculate and explain mean for a whole number data set.5aCC.5.MD.5a Find the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication.sSD.8.M.1.2 (Comprehension) Students are able to find area, volume, and surface area with whole number measurements.5bÜCC.5.MD.5b Apply the formulas V =(l)(w)(h) and V = (b)(h) for rectangular prisms to find volumes of right rectangular prisms with wholenumber edge lengths in the context of solving real world and mathematical problems. cSD.5.A.3.2 (Application) Students are able to identify information and apply it to a given formula.3.2ĀCC.5.G.1 Graph points on the coordinate plane to solve realworld and mathematical problems. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate).
SD.5.G.2.3 (Application) Students are able to use twodimensional coordinate grids to find locations and represent points and simple figures.KCC.5.G.3 Classify twodimensional figures into categories based on their properties. Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.CC.5.G.4 Classify twodimensional figures into categories based on their properties. Classify twodimensional figures in a hierarchy based on properties.RPCC.6.RP.1 Understand ratio concepts and use ratio reasoning to solve problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. For every vote candidate A received, candidate C received nearly three votes. aSD.6.A.3.2 (Application) Students are able to solve onestep problems involving ratios and rates.8SD standard does not state understand SD states one stepCC.6.RP.2 Understand ratio concepts and use ratio reasoning to solve problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b `" 0 (b not equal to zero), and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." (Expectations for unit rates in this grade are limited to noncomplex fractions.)aSD standards do not state understand and limits to one step rate is not addressed in SD standards
CC.6.RP.3 Understand ratio concepts and use ratio reasoning to solve problems. Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.SD standards limit to one stepÖCC.6.RP.3a Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.®SD.7.A.4.1 (Application) Students are able to recognize onestep patterns using tables, graphs, and models and create onestep algebraic expressions representing the pattern.3cqSD.3.A.2.2 (Application) Students are able to solve problems involving addition and subtraction of whole numbers.]SD.5.A.1.1 (Application) Students are able to use a variable to write an addition expression.SD.5.A.2.1 (Application) Students are able to write onestep first degree equations using the set of whole numbers and find a solution.±SD.5.N.3.1 (Application) Students are able to use different estimation strategies to solve problems involving whole numbers, decimals, and fractions to the nearest whole number.mCC.4.OA.4 Gain familiarity with factors and multiples. Find all factor pairs for a whole number in the range 1100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1100 is a multiple of a given onedigit number. Determine whether a given whole number in the range 1100 is prime or composite.[SD.4.N.1.2 (Comprehension) Students are able to find multiples of whole numbers through 12.qSD.5.N.1.2 (Comprehension) Students are able to find prime, composite, and factors of whole numbers from 1 to 50.¼CC.4.OA.5 Generate and analyze patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule Add 3 and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. ySD.4.A.4.1 (Application) Students are able to solve problems involving pattern identification and completion of patterns.ČCC.K.G.2 Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Correctly name shapes regardless of their orientations or overall size.ŽCC.K.G.3 Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Identify shapes as twodimensional (lying in a plane, flat ) or threedimensional ( solid ).sSD.K.A.4.1 (Knowledge) Students are able to identify and extend twopart repeating patterns using concrete objects.gSD.K.M.1.1 (Knowledge) Students are able tell time to the nearest hour using digital and analog clocks.FSD.K.M.1.2 (Kn< owledge) Students are able to name the days of the week.nSD.K.M.1.3 (Knowledge) Students are able to identify pennies, nickels, dimes, and quarters using money models.XSD.6.N.1.2 (Knowledge) Students are able to find factors and multiples of whole numbers.SD doesn't require fluencyĶCC.6.NS.3 Compute fluently with multidigit numbers and find common factors and multiples. Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation.]SD.6.N.2.1 (Comprehension) Students are able to add, subtract, multiply, and divide decimals.SD allows calculatorsĀCC.6.NS.4 Compute fluently with multidigit numbers and find common factors and multiples. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1 100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).*SD does not require fluency or GCF and LCM×CC.6.NS.5 Apply and extend previous understandings of numbers to the system of rational numbers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in realworld contexts, explaining the meaning of 0 in each situation.«SD.7.N.1.1 (Comprehension) Students are able to represent numbers in a variety of forms by describing, ordering, and comparing integers, decimals, percents, and fractions.+SD does not require an explaination of zero
SD.8.N.1.1 (Comprehension) Students are able to represent numbers in a variety of forms and identify the subsets of rational numbers.6ašCC.6.NS.6a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., ( 3) = 3, and that 0 is its own opposite.*SD does not require in depth understanding6bCC.6.NS.6b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. qSD.6.A.3.1 (Knowledge) Students are able to identify and graph ordered pairs in Quadrant I on a coordinate plane.MSD limits to one guadrant SD doesn't include location or reflections of pointSD.7.A.3.1 (Application) Students are able to identify and graph ordered pairs on a coordinate plane and inequalities on a number line.6cĒCC.6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.:SD doesn't require finding or positioning on a number lineCC.6.NS.7 Apply and extend previous understandings of numbers to the system of rational numbers. Understand ordering and absolute value of rational numbers. 7aCC.6.NS.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret 3 > 7 as a statement that 3 is located to the right of 7 on a number line oriented from left to right.SD has identify 7c?CC.6.NS.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a realworld situation. For example, for an account balance of 30 dollars, write  30 = 30 to describe the size of the debt in dollars.(Not in SD standards, shown as an exampleZCC.6.NS.8 Apply and extend previous understandings of numbers to the system of rational numbers. Solve realworld and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.1SD only addresses second sentence in CC standardsEE¦CC.6.EE.1 Apply and extend previous understandings of arithmetic to algebraic expressions. Write and evaluate numerical expressions involving wholenumber exponents.SD.6.A.1.2 (Application) Students are able to write algebraic expressions involving addition or multiplication using whole numbers.HSD does not require exponents in 6th 7th shows exponents in the examplesvSD.7.A.1.1 (Application) Students are able to write and evaluate algebraic expressions using the set of whole numbers.„CC.6.EE.2 Apply and extend previous understandings of arithmetic to algebraic expressions. Write, read, and evaluate expressions in which letters stand for numbers.TSD does not use language of letters standing for numbers, we show it in the examples2a«CC.6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5 y. SD only allows for addition or multiplication2cĖCC.6.EE.2c Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in realworld problems. Perform arithmetic operations, including those involving wholenumber exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = 1/2. 5SD does not require real world except in the examplesŚCC.6.EE.3 Apply and extend previous understandings of arithmetic to algebraic expressions. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.SD.7.A.1.2 (Knowledge) Students are able to identify associative, commutative, distributive, and identity properties involving algebraic expressions.SD not require application6CC.6.EE.6 Reason about and solve onevariable equations and inequalities. Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in< a specified set.øSD.8.A.2.1 (Application) Students are able to write and solve twostep 1st degree equations, with one variable, and onestep inequalities, with one variable, using the set of integers.!SD does not require understanding½CC.6.EE.9 Represent and analyze quantitative relationships between dependent and independent variables. Use variables to represent two quantities in a realworld problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.OCC.3.NF.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)±CC.3.NF.3d Compare two fractions with the same numerator or the same denominator, by reasoning about their size, Recognize that valid comparisons rely on the two fractions referring to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)ßCC.3.MD.5 Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Recognize area as an attribute of plane figures and understand concepts of area measurement.
 a. A square with side length 1 unit, called a unit square, is said to have one square unit of area, and can be used to measure area.
 b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. ŚCC.3.MD.6 Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). ŖCC.3.MD.7a Find the area of a rectangle with wholenumber side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.šCC.3.MD.7b Multiply side lengths to find areas of rectangles with wholenumber side lengths in the context of solving real world and mathematical problems, and represent wholenumber products as rectangular areas in mathematical reasoning. SD.5.N.2.2 (Application) Students are able to determine equivalent fractions including simplification (lowest terms of fractions).HCC.4.NF.2 Extend understanding of fraction equivalence and ordering. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)CC.7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.9SD does not require proprtionality or verbal descriptions=CC.7.RP.3 Analyze proportional relationships and use them to solve realworld and mathematical problems. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.TSD.7.A.3.2 Students are able to model and solve multistep problems involving rates.BSD does not require proportional relationships or percent problemsHCC.7.NS.1 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.rSD.7.N.2.1 (Application) Students are able to add, subtract, multiply, and divide integers and positive fractions.FSD only require positive fractions; does not talk about representation1d/CC.4.NF.3b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.ćCC.4.NF.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.×CC.4.NF.3d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. YCC.4.NF.4 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)ÉCC.4.NF.4a Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). CC.4.NF.4b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)CC.4.NF.4c Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? RCC.7.NS.3 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Solve realworld and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
#SD only requires positive fractionszCC.7.EE.3 Solve reallife and mathematical problems using numerical and algebraic expressions and equations. Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her < salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.}SD.8.N.3.1 (Application) Students are able to use various strategies to solve multistep problems involving rational numbers. CC.7.EE.4 Solve reallife and mathematical problems using numerical and algebraic expressions and equations. Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.lack of depth of inequalitieslSD.8.A.4.2 (Analysis) Students are able to describe and represent relations using tables, graphs, and rules.4aCC.7.EE.4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?,SD does not mention context or word problemsCC.7.G.1 Draw, construct, and describe geometrical figures and describe the relationships between them. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.nSD.7.G.1.1 (Application) Students are able to identify, describe, and classify polygons having up to 10 sides.USD does not construct or solve problems to produce scale drawing at a different scalezCC.7.G.2 Draw, construct, and describe geometrical figures and describe the relationships between them. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.)CC.7.G.4 Solve reallife and mathematical problems involving angle measure, area, surface area, and volume. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.ÄSD.7.M.1.2 (Comprehension) Students, when given the formulas, are able to find circumference, perimeter, and area of circles, parallelograms, triangles, and trapezoids (whole number measurements).CC.7.SP.4 Draw informal comparative inferences about two populations. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventhgrade science book are generally longer than the words in a chapter of a fourthgrade science book.)SD does not require visual representationæCC.7.SP.5 Investigate chance processes and develop, use, and evaluate probability models. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.rSD.7.S.2.1 (Comprehension) Students are able, given a sample space, to find the probability of a specific outcome.SD does not mention 0 or 1CC.8.NS.1. Know that there are numbers that are not rational, and approximate them by rational numbers. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.912fSD.912.N.1.1 (Comprehension) Students are able to identify multiple representations of a real number.1 to 47CC.5.NF.7b Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5) and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.{CC.5.NF.7c Solve realworld problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3cup servings are in 2 cups of raisins? åCC.5.MD.3 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
 a. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume.
 b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.ÕCC.5.MD.4 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.ōCC.5.MD.5 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
5céCC.5.MD.5c Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real world problems.CC.5.G.2 Graph points on the coordinate plane to solve realworld and mathematical problems. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
graphing onlyfSD.912.A.3.1 (Application) Students are able to create linear models to represent problem situations.CC.8.EE.7 Analyze and solve linear equations and pairs of simultaneous linear equations. Solve linear equations in one variable.¬SD.6.A.2.1 (Application) Students are able to write and solve onestep 1st degree equations, with one variable, involving inverse operations using the set of whole numbers.ĪSD.7.A.2.1 (Application) Students are able to write and solve onestep 1st degree equations, with one variable, using the set of integers and inequalities, with one variable, using the set of whole numbers.\CC.8.EE.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).7bĮCC.8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.SD.8.A.1.1 (Application) Students are able to use properties to expand, combine, and simplify 1st degree algebraic expressions with the set of integers.SD.912.A.1.1A (< Application) Students are able to write equivalent forms of rational algebraic expressions using properties of real numbers.1.1ACC.8.EE.8 Analyze and solve linear equations and pairs of simultaneous linear equations. Analyze and solve pairs of simultaneous linear equations.ZSD.912.A.2.1A (Analysis) Students are able to determine solutions of quadratic equations.2.1Ano analyze
8bCC.8.EE.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.}SD.912.A.2.2A (Application) Students are able to determine the solution of systems of equations and systems of inequalities.2.2AńCC.8.G.5 Understand congruence and similarity using physical models, transparencies, or geometry software. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angleangle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the three angles appear to form a line, and give an argument in terms of transversals why this is so.bSD.912.G.1.2 (Application) Students are able to identify and apply relationships among triangles.YSD.912.G.1.1A (Evaluation) Students are able to justify properties of geometric figures.ĻCC.8.G.7 Understand and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions.SD.8.G.1.2 (Application) Students, when given any two sides of an illustrated right triangle, are able to use the Pythagorean Theorem to find the third side.CC.8.G.8 Understand and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.SD.912.G.2.1 (Analysis) Students are able to recognize the relationship between a threedimensional figure and its twodimensional representation.ćCC.8.G.9 Solve realworld and mathematical problems involving volume of cylinders, cones and spheres. Know the formulas for the volume of cones, cylinders, and spheres and use them to solve realworld and mathematical problems.SD.912.G.1.4A (Analysis) Students are able to use formulas for surface area and volume to solve problems involving threedimensional figures.1.4AECC.8.SP.1 Investigate patterns of association in bivariate data. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.aSD.912.S.1.2A (Evaluation) Students are able to analyze and evaluate graphical displays of data.SD.912.S.1.5A (Application) Students are able to use scatterplots, bestfit lines, and correlation coefficients to model data and support conclusions.1.5AVCC.8.SP.2 Investigate patterns of association in bivariate data. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.fSD.912.S.1.3 (Analysis) Represent a set of data in a variety of graphical forms and draw conclusions.RN.1£CC.912.N.RN.1 Extend the properties of exponents to rational exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want [5^(1/3)]^3 = 5^[(1/3) x 3] to hold, so [5^(1/3)]^3 must equal 5.SD.912.N.2.1A (Application) Students are able to add, subtract, multiply, and divide real numbers including rational exponents.<SD standards only require add, subtract, multiply and divideRN.3%CC.912.N.RN.3 Use properties of rational and irrational numbers. Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.#SD does not require an explainationQ.1"CC.912.N.Q.1 Reason quantitatively and use units to solve problems. Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.*gSD.912.M.1.1 (Comprehension) Students are able to choose appropriate unit label, scale, and precision.BSD does not address choose and interpret scale or origin in graphseSD.912.M.1.2 (Comprehension) Students are able to use suitable units when describing rate of change.SD.912.M.1.1A (Application) Students are able to use dimensional analysis to check answers and determine units of a problem solution.Q.2CC.912.N.Q.2 Reason quantitatively and use units to solve problems. Define appropriate quantities for the purpose of descriptive modeling.*Q.3„CC.912.N.Q.3 Reason quantitatively and use units to solve problems. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.*CN.1¹CC.912.N.CN.1 Perform arithmetic operations with complex numbers. Know there is a complex number i such that i^2 = "1, and every complex number has the form a + bi with a and b real.
SD.912.N.1.1A (Comprehension) Students are able to describe the relationship of the real number system to the complex number system.CN.2ŹCC.912.N.CN.2 Perform arithmetic operations with complex numbers. Use the relation i^2 = 1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.”SD.3.A.1.2 (Knowledge) Students are able to identify special properties of 0 and 1 with respect to arithmetic operations (addition, subtraction, multiplication).SD.3.A.3.1 (Application) Students are able to use the relationship between multiplication and division to compute and check results.xSD.4.A.1.2 (Application) Students are able to recognize and use the commutative property of addition and multiplication.ōCC.3.OA.6 Understand properties of multiplication and the relationship between multiplication and division. Understand division as an unknownfactor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. SD.4.A.1.3 (Application) Students are able to relate the concepts of addition, subtraction, multiplication, and division to one another.>CC.3.OA.7 Multiply and divide within 100. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of onedigit numbers.[SD.3.A.4.2 Students are able to use number patterns and relationships to learn basic facts.
SD.3.N.2.1 (Application) Students are able to add and subtract whole numbers up to three digits and multiply two digits by one digit.cCC.3.OA.8 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Solve twostep word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strat< egies including rounding. (This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).)SD.912.A.4.2A (Analysis) Students are able to describe the behavior of a polynomial, given the leading coefficient, roots, and degree4.2AAPR.6]CC.912.A.APR.6 Rewrite rational expressions. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.CC standard is poorly wordedCED.1CC.912.A.CED.1 Create equations that describe numbers or relationship. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.*(SD address one variable linear equationsCED.2ÜCC.912.A.CED.2 Create equations that describe numbers or relationship. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*SD.912.A.3.2A (Synthesis) Students are able to create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential.3.2AqSD.912.A.4.1 (Application) Students are able to use graphs, tables, and equations to represent linear functions.CED.4õCC.912.A.CED.4 Create equations that describe numbers or relationship. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm s law V = IR to highlight resistance R.*SD.912.A.2.1 (Comprehension) Students are able to use algebraic properties to transform multistep, singlevariable, firstdegree equations.*SD only asks for single variable equationsREI.3¹CC.912.A.REI.3 Solve equations and inequalities in one variable. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. ŗSD.912.A.2.2 (Application) Students are able to use algebraic properties to transform multistep, singlevariable, firstdegree inequalities and represent solutions using a number line.REI.4mCC.912.A.REI.4 Solve equations and inequalities in one variable. Solve quadratic equations in one variable. REI.4a×CC.912.A.REI.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p)^2 = q that has the same solutions. Derive the quadratic formula from this form. LSD does not require completing the square or to derive the quadratic formulaREI.4bCCC.912.A.REI.4b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.REI.5ćCC.912.A.REI.5 Solve systems of equations. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.SD does not require proffREI.6µCC.912.A.REI.6 Solve systems of equations. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.REI.10öCC.912.A.REI.10 Represent and solve equations and inequalities graphically. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).REI.11ōCC.912.A.REI.11 Represent and solve equations and inequalities graphically. Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*REI.12ZCC.912.A.REI.12 Represent and solve equations and inequalities graphically. Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding halfplanes.YSD.912.A.4.6A (Application) Students are able to graph solutions to linear inequalities.4.6AFIF.1 CC.912.F.IF.1 Understand the concept of a function and use function notation. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).iSD.912.A.4.1A (Analysis) Students are able to determine the domain, range, and intercepts of a function.4.1AIF.2ąCC.912.F.IF.2 Understand the concept of a function and use function notation. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.IF.4ōCC.912.F.IF.4 Interpret functions that arise in applications in terms of the context. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*IF.5CC.912.F.IF.5 Interpret functions that arise in applications in terms of the context. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*IF.7ÖCC.912.F.IF.7 Analyze functions using different representations. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*IF.7a^CC.912.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.*IF.7c
CC.912.F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.* IF.7e§CC.912.F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.*mSD.912.A.4.5A (Analysis) Students are able to describe characteristics of nonlinear functions and relations.4.5AhSD.912.A.4.3A (Analysis) Students are able to apply transformations to graphs and describe the results.4.3AIF.8ŹCC.912.F.IF.8 Analyze functions using different representations. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. pCC.8.G.2 Understand congruence and similarity using physical m< odels, transparencies, or geometry software. Understand that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.ćCC.8.G.3 Understand congruence and similarity using physical models, transparencies, or geometry software. Describe the effect of dilations, translations, rotations and reflections on twodimensional figures using coordinates.CC.8.G.4 Understand congruence and similarity using physical models, transparencies, or geometry software. Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them.uCC.8.G.6 Understand and apply the Pythagorean Theorem. Explain a proof of the Pythagorean Theorem and its converse. CC.8.SP.3 Investigate patterns of association in bivariate data. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.·CC.912.F.BF.3 Build new functions from existing functions. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.BF.5~SD.4.A.2.1 (Comprehension) Students are able to select appropriate relational symbols (<, >, =) to make number sentences true.nSD.4.N.1.1 (Comprehension) Students are able to read, write, order, and compare numbers from .01 to 1,000,000.CC.4.NBT.3 Generalize place value understanding for multidigit whole numbers. Use place value understanding to round multidigit whole numbers to any place. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)BCC.4.NBT.4 Use place value understanding and properties of operations to perform multidigit arithmetic. Fluently add and subtract multidigit whole numbers using the standard algorithm. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.)
CC.4.NBT.5 Use place value understanding and properties of operations to perform multidigit arithmetic. Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.)xSD.5.A.1.2 (Application) Students are able to recognize and use the associative property of addition and multiplication.CC.912.F.LE.4 Construct and compare linear, quadratic, and exponential models and solve problems. For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.*TF.3»CC.912.N.VM.2 (+) Represent and model with vector quantities. Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.VM.3CC.912.N.VM.3 (+) Represent and model with vector quantities. Solve problems involving velocity and other quantities that can be represented by vectors.VM.4LCC.912.N.VM.4 (+) Perform operations on vectors. Add and subtract vectors.
VM.4a¼CC.912.N.VM.4a (+) Add vectors endtoend, componentwise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.VM.4b{CC.912.N.VM.4b (+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. VM.4c;CC.912.N.VM.4c (+) Understand vector subtraction v w as v + ( w), where ( w) is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction componentwise.VM.5PCC.912.N.VM.5 (+) Perform operations on vectors. Multiply a vector by a scalar.VM.5aįCC.912.N.VM.5a (+) Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication componentwise, e.g., as c(v(sub x), v(sub y)) = (cv(sub x), cv(sub y)).VM.5b/CC.912.G.CO.5 Experiment with transformations in the plane. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.SD does not include rotationCO.7CC.912.G.CO.7 Understand congruence in terms of rigid motions. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.CO.8ČCC.912.G.CO.8 Understand congruence in terms of rigid motions. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.CO.9lCC.912.G.CO.9 Prove geometric theorems. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints.CO.10bCC.912.G.CO.10 Prove geometric theorems. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.CO.11CC.912.G.CO.11 Prove geometric theorems. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.SRT.2CC.912.G.SRT.2 Understand similarity in terms of similarity transformations. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.SRT.3¾CC.912.G.SRT.3 Understand similarity in terms of similarity transformations. Use the properties of similarity transformations to establish the AA criterion for two triangles t< o be similar.SRT.4CC.912.G.SRT.4 Prove theorems involving similarity. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.SRT.5¬CC.912.G.SRT.5 Prove theorems involving similarity. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.SD.912.G.1.1 (Application) Students are able to apply the properties of triangles and quadrilaterals to find unknown parts.SSD.912.G.2.3 (Application) Students are able to use proportions to solve problems.SRT.8¼CC.912.G.SRT.8 Define trigonometric ratios and solve problems involving right triangles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.C.1^CC.912.G.C.1 Understand and apply theorems about circles. Prove that all circles are similar.C.2hCC.912.G.C.2 Understand and apply theorems about circles. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.[SD.912.G.1.3A (Application) Students are able to apply properties associated with circles.1.3AGPE.1CC.912.G.GPE.1 Translate between the geometric description and the equation for a conic section. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.GPE.2 CC.912.G.GPE.2 Translate between the geometric description and the equation for a conic section. Derive the equation of a parabola given a focus and directrix.GPE.3÷CC.912.G.GPE.3 (+) Translate between the geometric description and the equation for a conic section. Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.GPE.47CC.912.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, "3) lies on the circle centered at the origin and containing the point (0, 2).iSD.912.G.2.1A (Synthesis) Students are able to use Cartesian coordinates to verify geometric properties.GPE.5)CC.912.G.GPE.5 Use coordinates to prove simple geometric theorems algebraically. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).GPE.7ĶCC.912.G.GPE.7 Use coordinates to prove simple geometric theorems algebraically. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*SD.912.M.1.3 (Application) Students are able to use formulas to find perimeter, circumference, and area to solve problems involving common geometric figures.GMD.3CC.912.G.GMD.3 Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*ID.1¾CC.912.S.ID.1 Summarize, represent, and interpret data on a single count or measurement variable. Represent data with plots on the real number line (dot plots, histograms, and box plots).* ID.2\CC.912.A.REI.1 Understand solving equations as a process of reasoning and explain the reasoning. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.REI.2ÜCC.912.A.REI.2 Understand solving equations as a process of reasoning and explain the reasoning. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.REI.7CC.912.A.REI.7 Solve systems of equations. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = 3x and the circle x^2 + y^2 = 3.REI.8CC.912.A.REI.8 (+) Solve systems of equations. Represent a system of linear equations as a single matrix equation in a vector variable.REI.9ČCC.912.A.REI.9 (+) Solve systems of equations. Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).IF.3RCC.912.F.IF.3 Understand the concept of a function and use function notation. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n1) for n e" 1 (n is greater than or equal to 1).IF.6CC.912.F.IF.6 Interpret functions that arise in applications in terms of the context. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*IF.7bCC.912.F.IF.7b Graph square root, cube root, and piecewisedefined functions, including step functions and absolute value functions.* IF.7dļCC.912.S.ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.*ID.6b_CC.912.S.ID.6b Informally assess the fit of a function by plotting and analyzing residuals.* ID.6c]CC.912.S.ID.6c Fit a linear function for a scatter plot that suggests a linear association.*ID.7CC.912.S.ID.7 Interpret linear models. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.*ID.8~CC.912.S.ID.8 Interpret linear models. Compute (using technology) and interpret the correlation coefficient of a linear fit.*USD verb is use correlation coefficients, not interpret SD does not require technologyIC.1ąCC.912.S.IC.1 Understand and evaluate random processes underlying statistical experiments. Understand statistics as a process for making inferences about population parameters based on a random sample from that population.*lSD.912.S.1.1A (Evaluation) Students are able to analyze and evaluate the design of surveys and experiments.IC.3CC.912.S.IC.3 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.*CP.1/CC.912.S.CP.1 Understand independence and conditional probability and use them to interpret data. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or < categories) of the outcomes, or as unions, intersections, or complements of other events ( or, and, not ).*SD.912.S.2.2A (Application) Students are able to determine probability of compound, complementary, independent, and mutually exclusive events.CP.22CC.912.S.CP.2 Understand independence and conditional probability and use them to interpret data. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.*CP.3CC.912.S.CP.3 Understand independence and conditional probability and use them to interpret data. Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.*CP.7ēCC.912.S.CP.7 Use the rules of probability to compute probabilities of compound events in a uniform probability model. Apply the Addition Rule, P(A or B) = P(A) + P(B) P(A and B), and interpret the answer in terms of the model.*CP.8!CC.912.S.CP.8 (+) Use the rules of probability to compute probabilities of compound events in a uniform probability model. Apply the general Multiplication Rule in a uniform probability model, P(A and B) = [P(A)]x[P(BA)] =[P(B)]x[P(AB)], and interpret the answer in terms of the model.*CP.9ŽCC.912.S.CP.9 (+) Use the rules of probability to compute probabilities of compound events in a uniform probability model. Use permutations and combinations to compute probabilities of compound events and solve problems.*VSD.912.S.2.1A (Application) Students are able to use probabilities to solve problems.MD.6ŖCC.912.S.MD.6 (+) Use probability to evaluate outcomes of decisions. Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).* CC.K.CC.2 Know number names and the count sequence. Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
CC.K.CC.4 Count to tell the number of objects. Understand the relationship between numbers and quantities; connect counting to cardinality. ¶CC.K.CC.4a When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.4bÄCC.K.CC.4b Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.4c`CC.K.CC.4c Understand that each successive number name refers to a quantity that is one larger. ECC.K.OA.3 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). ,CC.K.OA.4 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. CC.K.OA.5 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Fluently add and subtract within 5.CC.K.NBT.1 Work with numbers 1119 to gain foundations for place value. Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. „CC.K.G.5 Analyze, compare, create, and compose shapes. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.ĮCC.K.G.6 Analyze, compare, create, and compose shapes. Compose simple shapes to form larger shapes. For example, "can you join these two triangles with full sides touching to make a rectangle? öCC.1.OA.4 Understand and apply properties of operations and the relationship between addition and subtraction. Understand subtraction as an unknownaddend problem. For example, subtract 10 8 by finding the number that makes 10 when added to 8. tCC.1.OA.5 Add and subtract within 20. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).öCC.1.NBT.2 Understand place value. Understand that the two digits of a twodigit number represent amounts of tens and ones. Understand the following as special cases:
 a. 10 can be thought of as a bundle of ten ones called a ten.
 b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
 c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).³CC.1.NBT.3 Understand place value. Compare two twodigit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. BCC.1.NBT.4 Use place value understanding and properties of operations to add and subtract. Add within 100, including adding a twodigit number and a onedigit number, and adding a twodigit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding twodigit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. ½CC.6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole given a part and the percent.øSD.6.N.1.1 (Comprehension) Students are able to represent fractions in equivalent forms and convert between fractions, decimals, and percents using halves, fourths, tenths, hundredths.7SD restricts to halves, fourthes, tenths and hundredths3dCC.6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.ySD.6.M.1.1 (Comprehension) Students are able to select, use, and convert appropriate unit of measurement for a situation.SD does not use ratio reasoningNS!CC.6.NS.1 Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Interpret and compute quotients of fractions, and solve word pr< oblems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?mSD.8.N.2.1 (Application) Students are able to read, write, and compute within any subset of rational numbers.SD doesn't generalizeSD.7.N.3.1 (Application) Students are able to use various strategies to solve one and twostep problems involving positive fractions and integers.CC.6.NS.2 Compute fluently with multidigit numbers and find common factors and multiples. Fluently divide multidigit numbers using the standard algorithm. °CC.1.G.2 Reason with shapes and their attributes. Compose twodimensional shapes (rectangles, squares, trapezoids, triangles, halfcircles, and quartercircles) or threedimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as right rectangular prism. )CC.1.G.3 Reason with shapes and their attributes. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. CC.2.OA.1 Represent and solve problems involving addition and subtraction. Use addition and subtraction within 100 to solve one and twostep word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. ŖCC.2.OA.2 Add and subtract within 20. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two onedigit numbers. CC.2.OA.4 Work with equal groups of objects to gain foundations for multiplication. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.×CC.2.NBT.1 Understand place value. Understand that the three digits of a threedigit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
 a. 100 can be thought of as a bundle of ten tens called a hundred.
 b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).{CC.2.NBT.3 Understand place value. Read and write numbers to 1000 using baseten numerals, number names, and expanded form.¼CC.2.NBT.4 Understand place value. Compare two threedigit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.æCC.2.NBT.6 Use place value understanding and properties of operations to add and subtract. Add up to four twodigit numbers using strategies based on place value and properties of operations.
CC.2.NBT.7 Use place value understanding and properties of operations to add and subtract. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting threedigit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.ÉCC.2.NBT.8 Use place value understanding and properties of operations to add and subtract. Mentally add 10 or 100 to a given number 100900, and mentally subtract 10 or 100 from a given number 100900.žCC.2.NBT.9 Use place value understanding and properties of operations to add and subtract. Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.) ģCC.2.MD.2 Measure and estimate lengths in standard units. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. CC.2.MD.3 Measure and estimate lengths in standard units. Estimate lengths using units of inches, feet, centimeters, and meters.æCC.2.MD.4 Measure and estimate lengths in standard units. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.)CC.2.MD.5 Relate addition and subtraction to length. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.CC.2.MD.6 Relate addition and subtraction to length. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, & , and represent wholenumber sums and differences within 100 on a number line diagram. (CC.2.MD.9 Represent and interpret data. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in wholenumber units.CC.2.G.2 Reason with shapes and their attributes. Partition a rectangle into rows and columns of samesize squares and count to find the total number of them. YCC.2.G.3 Reason with shapes and their attributes. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. ĮCC.3.OA.2 Represent and solve problems involving multiplication and division. Interpret wholenumber quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of sh< ares or a number of groups can be expressed as 56 ÷ 8.;CC.3.OA.4 Represent and solve problems involving multiplication and division. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = __÷ 3, 6 × 6 = ?.yCC.3.NF.2a Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.):CC.3.NF.2b Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)CC.3.NF.3 Develop understanding of fractions as numbers. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)\CC.K12.MP.3 Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and if there is a flaw in an argument explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. źCC.3.MD.7c Use tiling to show in a concrete case that the area of a rectangle with wholenumber side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. 7déCC.3.MD.7d Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve real world problems. ķCC.6.SP.5 Summarize and describe distributions. Summarize numerical data sets in relation to their context, such as by:
 a. Reporting the number of observations.
 b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
 c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data was gathered.
 d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered.rSD.6.S.1.1 (Comprehension) Students are able to find the mean, mode, and range of an ordered set of positive data.hSD.7.S.1.1 (Comprehension) Students are able to find the mean, median, mode, and range of a set of data.SD.8.S.1.1 (Comprehension) Students are able to find the mean, median, mode, and range of a data set from a stemandleaf plot and a line plot.ÆCC.7.RP.2 Analyze proportional relationships and use them to solve realworld and mathematical problems. Recognize and represent proportional relationships between quantities.SD.8.M.1.1 (Application) Students are able to apply proportional reasoning to solve measurement problems with rational number measurements.SD applies doesn't analyzeēCC.7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.\SD.8.A.3.1 (Comprehension) Students are able to describe and determine linear relationships.7SD does not mention tables or graphing as straight line2bCC.K12.MP.5 Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. °CC.4.MD.6 Geometric measurement: understand concepts of angle and measure angles. Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure.¹CC.4.MD.7 Geometric measurement: understand concepts of angle and measure angles. Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on< a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.ėCC.5.NBT.1 Understand the place value system. Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 7CC.5.NBT.2 Understand the place value system. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10.kCC.5.NBT.4 Understand the place value system. Use place value understanding to round decimals to any place.CC.5.NF.1 Use equivalent fractions as a strategy to add and subtract fractions. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) óCC.5.NF.2 Use equivalent fractions as a strategy to add and subtract fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 by observing that 3/7 < 1/2. ųCC.5.NF.3 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3 and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?ęCC.5.NF.4 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. ]CC.5.NF.4a Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) \CC.5.NF.4b Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.CC.5.NF.5 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret multiplication as scaling (resizing) by:
 a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
 b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a) / (n×b) to the effect of multiplying a/b by 1.CC.5.NF.6 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.öCC.5.NF.7 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.)DCC.5.NF.7a Interpret division of a unit fraction by a nonzero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.CC.912.G.GMD.4 Visualize relationships between twodimensional and threedimensional objects. Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects.MG.1ĶCC.912.G.MG.1 Apply geometric concepts in modeling situations. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*MG.2ĮCC.912.G.MG.2 Apply geometric concepts in modeling situations. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).*MG.3CC.912.G.MG.3 Apply geometric concepts in modeling situations. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).*ID.9WCC.912.S.ID.9 Interpret linear models. Distinguish between correlation and causation.*IC.2eCC.912.S.IC.2 Understand and evaluate random processes underlying statistical experiments. Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0. 5. Would a result of 5 tails in a row cause you to question the model?*IC.4CC.912.S.IC.4 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.*IC.5CC.912.S.IC.5 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.*IC.6ńCC.6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed. For example, If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?>CC.6.NS.6 Apply and extend previous understandings of numbers to the system of rational numbers. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. »CC.6.NS.7b Write, interpret, and explain statements of order for rational numbers in realworld contexts. For example, write 3°C > 7°C to express the fact that 3°C is warmer than 7°C.ĮCC.6.NS.7d Distinguish< comparisons of absolute value from statements about order. For example, recognize that an account balance less than 30 dollars represents a debt greater than 30 dollars.=CC.6.EE.2b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. yCC.6.EE.4 Apply and extend previous understandings of arithmetic to algebraic expressions. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.[CC.6.EE.5 Reason about and solve onevariable equations and inequalities. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.śCC.6.EE.7 Reason about and solve onevariable equations and inequalities. Solve realworld and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.aCC.6.EE.8 Reason about and solve onevariable equations and inequalities. Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.UCC.6.G.1 Solve realworld and mathematical problems involving area, surface area, and volume. Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems.CC.6.G.2 Solve realworld and mathematical problems involving area, surface area, and volume. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems.yCC.6.G.3 Solve realworld and mathematical problems involving area, surface area, and volume. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving realworld and mathematical problems.CC.6.SP.1 Develop understanding of statistical variability. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, How old am I? is not a statistical question, but How old are the students in my school? is a statistical question because one anticipates variability in students ages.üCC.6.SP.3 Develop understanding of statistical variability. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. CC.7.RP.1 Analyze proportional relationships and use them to solve realworld and mathematical problems. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.CC.7.RP.2c Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.2dÄCC.7.RP.2d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.1a®CC.7.NS.1a Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. 1b1CC.7.NS.1b Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing realworld contexts.1c
CC.7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p q = p + ( q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in realworld contexts.pCC.7.NS.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as ( 1)( 1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing realworld contexts.)CC.7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with nonzero divisor) is a rational number. If p and q are integers then (p/q) = ( p)/q = p/( q). Interpret quotients of rational numbers by describing realworld contexts.CC.7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.ĖCC.7.EE.1 Use properties of operations to generate equivalent expressions. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.SD.912.A.1.2A (Application) Students are able to extend the use of real number properties to expressions involving complex numbers.CN.3®CC.912.N.CN.3 (+) Perform arithmetic operations with complex numbers. Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.< *SD does not identify the conjugate by nameCN.7CC.912.N.CN.7 Use complex numbers in polynomial identities and equations. Solve quadratic equations with real coefficients that have complex solutions.SSE.2
CC.912.A.SSE.2 Interpret the structure of expressions. Use the structure of an expression to identify ways to rewrite it. For example, see x^4 y^4 as (x^2)^2 (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 y^2)(x^2 + y^2).SD.912.A.1.1 (Comprehension) Students are able to write equivalent forms of algebraic expressions using properties of the set of real numbers.#SD has students simplify and factorSSE.3ŃCC.912.A.SSE.3 Write expressions in equivalent forms to solve problems. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*(SD does not address exponential functionSSE.3a_CC.912.A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.*SSE.3bCC.912.A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.*>SD does not ask for completing the square or factoring by nameSSE.4ųCC.912.A.SSE.4 Write expressions in equivalent forms to solve problems. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.*SD.912.A.3.1A (Analysis) Students are able to distinguish between linear, quadratic, inverse variation, and exponential models.3.1A*SD does not ask them to derive the formulaAPR.3÷CC.912.A.APR.3 Understand the relationship between zeros and factors of polynomials. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.>CC.7.SP.3 Draw informal comparative inferences about two populations. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.ĘCC.7.SP.6 Investigate chance processes and develop, use, and evaluate probability models. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.)CC.7.SP.7 Investigate chance processes and develop, use, and evaluate probability models. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. 6CC.7.SP.7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.tCC.7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land openend down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?½CC.7.SP.8 Investigate chance processes and develop, use, and evaluate probability models. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.8a°CC.7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.CC.7.SP.8b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes ), identify the outcomes in the sample space which compose the event.8c2CC.7.SP.8c Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?7CC.8.EE.2 Work with radicals and integer exponents. Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that "2 is irrational.«CC.8.EE.3 Work with radicals and integer exponents. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 10^8 and the population of the world as 7 × 10^9, and determine that the world population is more than 20 times larger.vCC.8.EE.6 Understand the connections between proportional relationships, lines, and linear equations. Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane; derive the equation y =mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.ÕCC.8.EE.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.CC.8.EE.8c Solve realworld and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.CC.8.F.1 Define, evaluate, and compare functions. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.)CC.8.F.2 Define, evaluate, and compare functions. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. CC.8.F.3 Define, evaluate, and compare functions. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of function< s that are not linear. For example, the function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.ŪCC.8.F.4 Use functions to model relationships between quantities. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.SCC.8.F.5 Use functions to model relationships between quantities. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.CC.8.G.1 Understand congruence and similarity using physical models, transparencies, or geometry software. Verify experimentally the properties of rotations, reflections, and translations:
 a. Lines are taken to lines, and line segments to line segments of the same length.
 b. Angles are taken to angles of the same measure.
 c. Parallel lines are taken to parallel lines. °CC.K12.MP.4 Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, twoway tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. øCC.8.SP.4 Investigate patterns of association in bivariate data. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?RN.2§CC.912.F.BF.5 (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.LE.1ĢCC.912.F.LE.1 Construct and compare linear, quadratic, and exponential models and solve problems. Distinguish between situations that can be modeled with linear functions and with exponential functions.*cSD.912.A.3.2 (Comprehension) Students are able to distinguish between linear and nonlinear models.LE.1b~CC.912.F.LE.1b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.*LE.1cCC.912.F.LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.*LE.2CC.912.F.LE.2 Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table).*LE.3CC.912.F.LE.3 Construct and compare linear, quadratic, and exponential models and solve problems. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.*LE.4CN.9§CC.912.N.CN.9 (+) Use complex numbers in polynomial identities and equations. Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.VM.1 CC.912.N.VM.1 (+) Represent and model with vector quantities. Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v(bold), v, v, v(not bold)).VM.2CC.912.S.IC.6 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Evaluate reports based on data.*CP.4¢CC.912.S.CP.4 Understand independence and conditional probability and use them to interpret data. Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.*CP.5eCC.912.S.CP.5 Understand independence and conditional probability and use them to interpret data. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.*CP.6
CC.912.S.CP.6 Use the rules of probability to compute probabilities of compound events in a uniform probability model. Find the conditional probability of A given B as the fraction of B s outcomes that also belong to A, and interpret the answer in terms of the model.*MD.1/CC.912.S.MD.1 (+) Calculate expected values and use them to solve problems. Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.*MD.2»CC.912.S.MD.2 (+) Calculate expected values and use them to solve problems. Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.* MD.3óCC.912.S.MD.3 (+) Calculate expected values and use them to solve problems. Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiplechoice test where each question has four choices, and find the expected grade under various grading schemes.*MD.4ŽCC.912.S.MD.4 (+) Calculate expected values and use them to solve problems. Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected < value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?*MD.5¹CC.912.S.MD.5 (+) Use probability to evaluate outcomes of decisions. Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.*MD.5a¬CC.912.S.MD.5a (+) Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fastfood restaurant.*MD.5b’CC.912.S.MD.5b (+) Evaluate and compare strategies on the basis of expected values. For example, compare a highdeductible versus a lowdeductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.*MD.7ŚCC.912.S.MD.7 (+) Use probability to evaluate outcomes of decisions. Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).*K12MPCC.K12.MP.1 Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, Does this make sense? They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. CC.K12.MP.2 Reason abstractly and quantitatively. Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. @CC.7.EE.2 Use properties of operations to generate equivalent expressions. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that increase by 5% is the same as multiply by 1.05. ¼CC.7.EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example, As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.CC.7.G.3 Draw, construct, and describe geometrical figures and describe the relationships between them. Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. CC.7.G.5 Solve reallife and mathematical problems involving angle measure, area, surface area, and volume. Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. 0CC.7.G.6 Solve reallife and mathematical problems involving angle measure, area, surface area, and volume. Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. CC.7.SP.1 Use random sampling to draw inferences about a population. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.CC.7.SP.2 Use random < sampling to draw inferences about a population. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.CC.912.F.IF.7d (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.* IF.9YCC.912.F.IF.9 Analyze functions using different representations. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.BF.1cCC.912.F.BF.1c (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.BF.4TCC.912.F.BF.4 Build new functions from existing functions. Find inverse functions. BF.4aŚCC.912.F.BF.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2(x^3) or f(x) = (x+1)/(x1) for x `" 1 (x not equal to 1). BF.4bWCC.912.F.BF.4b (+) Verify by composition that one function is the inverse of another. BF.4cwCC.912.F.BF.4c (+) Read values of an inverse function from a graph or a table, given that the function has an inverse.BF.4dlCC.912.F.BF.4d (+) Produce an invertible function from a noninvertible function by restricting the domain.LE.1a¦CC.912.F.LE.1a Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.*LE.5·CC.912.F.LE.5 Construct and compare linear, quadratic, and exponential models and solve problems. Interpret the parameters in a linear or exponential function in terms of a context.*TF.1¼CC.912.F.TF.1 Extend the domain of trigonometric functions using the unit circle. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.TF.2(CC.912.F.TF.2 Extend the domain of trigonometric functions using the unit circle. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.TF.4¹CC.912.F.TF.4 (+) Extend the domain of trigonometric functions using the unit circle. Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.TF.6ęCC.912.F.TF.6 (+) Model periodic phenomena with trigonometric functions. Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.TF.7÷CC.912.F.TF.7 (+) Model periodic phenomena with trigonometric functions. Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.*TF.8ŁCC.912.F.TF.8 Prove and apply trigonometric identities. Prove the Pythagorean identity (sin A)^2 + (cos A)^2 = 1 and use it to find sin A, cos A, or tan A, given sin A, cos A, or tan A, and the quadrant of the angle.TF.9¦CC.912.F.TF.9 (+) Prove and apply trigonometric identities. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.CO.1CC.912.G.CO.1 Experiment with transformations in the plane. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.CO.64CC.912.G.CO.6 Understand congruence in terms of rigid motions. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.CO.12ŲCC.912.G.CO.12 Make geometric constructions. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.CO.13CC.912.G.CO.13 Make geometric constructions. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.SRT.1¦CC.912.G.SRT.1 Understand similarity in terms of similarity transformations. Verify experimentally the properties of dilations given by a center and a scale factor:
 a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
 b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.SRT.6CC.912.G.SRT.6 Define trigonometric ratios and solve problems involving right triangles. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.SRT.7ÆCC.912.G.SRT.7 Define trigonometric ratios and solve problems involving right triangles. Explain and use the relationship between the sine and cosine of complementary angles.SRT.9ĶCC.912.G.SRT.9 (+) Apply trigonometry to general triangles. Derive the formula A = (1/2)ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.SRT.10CC.912.G.SRT.10 (+) Apply trigonometry to general triangles. Prove the Laws of Sines and Cosines and use them to solve problems.SRT.11ēCC.912.G.SRT.11 (+) Apply trigonometry to general triangles. Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces).C.3ÅCC.912.G.C.3 Understand and apply theorems about circles. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.C.4CC.912.G.C.4 (+) Understand and apply theorems about circles. Construct a tangent line from a point outside a given circle to the circle.C.5.CC.912.G.C.5 Find arc lengths and areas of sectors of circles. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.GPE.6ĀCC.912.G.GPE.6 Use coordinates to prove simple geometric theorems algebraically. Find the point on a directed line segment between two given points that partitions the segment in a given ratio.GMD.1CC.912.G.GMD.1 Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection argument< s, Cavalieri s principle, and informal limit arguments.GMD.2ĘCC.912.G.GMD.2 (+) Explain volume formulas and use them to solve problems. Give an informal argument using Cavalieri s principle for the formulas for the volume of a sphere and other solid figures.GMD.4ŪCC.1.NBT.5 Use place value understanding and properties of operations to add and subtract. Given a twodigit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.³CC.1.NBT.6 Use place value understanding and properties of operations to add and subtract. Subtract multiples of 10 in the range 1090 from multiples of 10 in the range 1090 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. ŖCC.1.MD.1 Measure lengths indirectly and by iterating length units. Order three objects by length; compare the lengths of two objects indirectly by using a third object. ĪCC.1.MD.2 Measure lengths indirectly and by iterating length units. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of samesize length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.#CC.1.G.1 Reason with shapes and their attributes. Distinguish between defining attributes (e.g., triangles are closed and threesided) versus nondefining attributes (e.g., color, orientation, overall size); for a wide variety of shapes; build and draw shapes to possess defining attributes.©CC.912.N.RN.2 Extend the properties of exponents to rational exponents. Rewrite expressions involving radicals and rational exponents using the properties of exponents.CN.41CC.912.N.CN.4 (+) Represent complex numbers and their operations on the complex plane. Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.CN.5XCC.912.N.CN.5 (+) Represent complex numbers and their operations on the complex plane. Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (1 + "3i)^3 = 8 because (1 + "3i) has modulus 2 and argument 120°.CN.6CC.912.N.CN.6 (+) Represent complex numbers and their operations on the complex plane. Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.CN.8µCC.912.N.CN.8 (+) Use complex numbers in polynomial identities and equations. Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x 2i).CC.K12.MP.6 Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.0CC.K12.MP.7 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x^2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 3(x y)^2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. ŪCC.K12.MP.8 Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y 2)/(x 1) = 3. Noticing the regularity in the way terms cancel when expanding (x 1)(x + 1), (x 1)(x^2 + x + 1), and (x <Y 1)(x^3 + x^2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. ŪCC.912.N.VM.5b (+) Compute the magnitude of a scalar multiple cv using cv = cv. Compute the direction of cv knowing that when cv =8 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).VM.6ĒCC.912.N.VM.6 (+) Perform operations on matrices and use matrices in applications. Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. VM.7ĀCC.912.N.VM.7 (+) Perform operations on matrices and use matrices in applications. Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. VM.8CC.912.N.VM.8 (+) Perform operations on matrices and use matrices in applications. Add, subtract, and multiply matrices of appropriate dimensions.VM.9CC.912.N.VM.9 (+) Perform operations on matrices and use matrices in applications. Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. VM.10PCC.912.N.VM.10 (+) Perform operations on matrices and use matrices in applications. Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. VM.11żCC.912.N.VM.11 (+) Perform operations on matrices and use matrices in applications. Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.VM.12ÕCC.912.N.VM.12 (+) Perform operations on matrices and use matrices in applications. Work with 2 X 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. SSE.1CC.912.A.SSE.1 Interpret the structure of expressions. Interpret expressions that represent a quantity in terms of its context.*SSE.1a]CC.912.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.*SSE.1bĀCC.912.A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P.*SSE.3cCC.912.A.SSE.3c Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15^t can be rewritten as [1.15^(1/12)]^(12t) H" 1.012^(12t) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.*APR.1CC.912.A.APR.1 Perform arithmetic operations on polynomials. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.APR.2CC.912.A.APR.2 Understand the relationship between zeros and factors of polynomial. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x a is p(a), so p(a) = 0 if and only if (x a) is a factor of p(x).APR.4CC.912.A.APR.4 Use polynomial identities to solve problems. Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)^2 = (x^2 y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples.APR.5vCC.912.A.APR.5 (+) Use polynomial identities to solve problems. Know and apply that the Binomial Theorem gives the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal s Triangle. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.)APR.7$CC.912.A.APR.7 (+) Rewrite rational expressions. Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.CED.3pCC.912.A.CED.3 Create equations that describe numbers or relationship. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.*REI.17CC.4.OA.1 Use the four operations with whole numbers to solve problems. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.?CC.4.OA.2 Use the four operations with whole numbers to solve problems. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. CC.4.NBT.1 Generalize place value understanding for multidigit whole numbers. Recognize that in a multidigit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)4CC.4.NF.3 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)xCC.4.NF.3a Understand addition and subtraction of fractions as joining and
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¼’’’’’’’’’’’’’’’’@ @ Grade Difference;F^e żĄ ’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ż’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ż’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ż’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ż’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’arial ’’’’’’’’’’’’’’’’’’’’(żĄ arial~ŗ»
¼’’’’’’’’’’’’’’’’@ @ Degree of Match;<Jf
żÄ arial ’’’’’’’’’’’’’’’’’’’’(żÄ arial~ŗ»
¼’’’’’’’’’’’’’’’’pwNotesJ¦¬ ’żĄ ariall ’’’’’’’’’’’’’’’’ ww;MDgżĄ (żĄ @ @ CC;LBhżĄ (żĄ @ @ 1;”ģiżĄ (żĄ @ @ VCC.K.CC.1 Know number names and the count sequence. Count to 100 by ones and by tens. J06łĄ @ @ ;LBjżĄ (żĄ @ @ K;«kżĄ (żĄ @ @ `SD.K.N.1.1 (Comprehension) Students are able to read, write, count, and sequence numerals to 20.;LBlżĄ (żĄ @ @ N;NFmżĄ (żĄ @ @ 1.1;LBnżĄ (żĄ @ @ 0;xo żĄ (żĄ @ @ 3 = Excellent match between the two documents;
“p
żÄ (ĄżÄ pw:only to 50 in SD standards read, write, count and sequnceJ06 ’żĄ ww;MDqżĄ (żĄ @@ @ CC;LBrżĄ (%nżĄ @ @ 1;”ģsżĄ (żĄ @ @ VCC.K.CC.1 Know number names and the count sequence. Count to 100 by ones and by tens. J06łĄ @ @ ;LBtżĄ (żĄ @ @ 1;ØśużĄ (żĄ @ @ ]SD.1.N.1.1 (Comprehension) Students are able to read, write, count, and order numerals to 50.;LBvżĄ (żĄ @ @ N;NFwżĄ (żĄ @ @ 1.1;MDxżĄ (żĄ @ @ 1J06 żĄ @ @ ;
“y
żÄ (żÄ pw:only to 50 in SD standards read, write, count and sequnceJ06 ’żĄ ww;MDzżĄ (żĄ @ @ CC;LB{żĄ (żĄ @ @ 1;”ģżĄ (żĄ @ @ VCC.K.CC.1 Know number names and the count sequence. Count to 100 by ones and by tens. J06łĄ @ @ ;LB}żĄ (żĄ @ @ 2;¬~żĄ (żĄ @ @ aSD.2.N.1.1 (Comprehension) Students are able to read, write, count, and sequence numerals to 100.;LBżĄ (żĄ @ @ N;NFżĄ (żĄ @ @ 1.1;MDżĄ (żĄ @ @ 2J06 żĄ @ @ ;
“
żÄ (żÄ pw:only to 50 in SD standards read, write, count and sequnceJ06 ’żĄ ww;MDżĄ (żĄ @ @ CC;LBżĄ (żĄ @ @ 3;¬
żĄ (ttżĄ @ @ ¶CC.K.CC.3 Know number names and the count sequence. Write numbers from 0 to 20. Represent a number of objects with a written numeral 020 (with 0 representing a count of no objects).J06łĄ @ @ ;LBżĄ (żĄ @ @ K;«żĄ (żĄ @ @ `SD.K.N.1.1 (Comprehension) Students are able to read, write, count, and sequence numerals to 20.;LBżĄ (żĄ @ @ N;NFżĄ (żĄ @ @ 1.1;LBżĄ (żĄ @ @ 0;ø żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;fv
żÄ (żÄ pwSD standards numerals to 20J06 ’żĄ ww;MDżĄ (żĄ @ @ CC;LBżĄ (żĄ @ @ 5;odżĄ (żĄ @ @ CC.K.CC.5 Count to tell the number of objects. Count to answer how many? questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ABCDEFGž’’’IJKLMNOž’’’ż’’’ż’’’ż’’’ż’’’ż’’’ż’’’ż’’’ż’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’; given a number from 120, count out that many objects.J06łĄ @ @ ;LBżĄ (żĄ @ @ K;«żĄ (żĄ @ @ `SD.K.N.1.1 (Comprehension) Students are able to read, write, count, and sequence numerals to 20.;LBżĄ (żĄ @ @ N;NFżĄ (żĄ @ @ 1.1;LBżĄ (żĄ @ @ 0;ø żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@
żÄ (żÄ pwJ06 ’żĄ ww;MDżĄ (żĄ @ @ CC;LBżĄ (żĄ @ @ 6;D2żĄ (żĄ @ @ łCC.K.CC.6 Compare numbers. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. (Include groups with up to ten objects.)J06łĄ @ @ ;LBżĄ (żĄ @ @ K;Ś^żĄ (żĄ @ @ SD.K.A.2.1 (Comprehension) Students are able to compare collections of objects to determine more, less, and equal (greater than and less than).;LBżĄ (żĄ @ @ A;NFżĄ (żĄ @ @ 2.1;LBżĄ (żĄ @ @ 0;x żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@
żÄ (żÄ pwJ06 ’żĄ ww;MD”żĄ (żĄ @ @ CC;LB¢żĄ (żĄ @ @ 7;©ü£żĄ (żĄ @ @ ^CC.K.CC.7 Compare numbers. Compare two numbers between 1 and 10 presented as written numerals.J06łĄ @ @ ;LB¤żĄ (żĄ @ @ 1;õ„żĄ (żĄ @ @ ŖSD.1.A.2.1 (Comprehension) Students are able to use the concepts and language of more, less, and equal (greater than and less than) to compare numbers and sets (0 to 20).;LB¦żĄ (żĄ @ @ A;NF§żĄ (żĄ @ @ 2.1;MDØżĄ (żĄ @ @ 1;®© żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;]dŖ
żÄ (żÄ pw 1st they go to 20J06 ’żĄ ww;MD«żĄ (żĄ @ @ OA;LB¬żĄ (żĄ @ @ 1;Ė@żĄ (żĄ @ @ CC.K.OA.1 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Represent addition and subtraction with objects, fingers, mental images, drawings (drawings need not show details, but should show the mathematics in the problem), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. J06łĄ @ @ ;LB®żĄ (żĄ @ @ K;¼"ÆżĄ (żĄ @ @ qSD.K.A.3.1 (Knowledge) Students are able to use concrete objects to model the meaning of the "+" and "" symbols.;LB°żĄ (żĄ @ @ A;NF±żĄ (żĄ @ @ 3.1;LB²żĄ (żĄ @ @ 0;ø³ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@“
żÄ (żÄ pwJ06 ’żĄ ww;MDµ żĄ (żĄ @ @ OA;LB¶ żĄ (żĄ @ @ 2;RN· żĄ (żĄ @ @ CC.K.OA.2 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.J06 łĄ @ @ ;LBø żĄ (żĄ @ @ K;µ¹ żĄ (żĄ @ @ jSD.K.N.3.1 (Application) Students are able to solve addition and subtraction problems up to 10 in context.;LBŗ żĄ (żĄ @ @ N;NF» żĄ (żĄ @ @ 3.1;LB¼ żĄ (żĄ @ @ 0;x½ żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@¾
żÄ (żÄ pwJ06 ’żĄ ww;MDæ
żĄ (żĄ @ @ OA;LBĄ
żĄ (żĄ @ @ 2;RNĮ
żĄ (żĄ @ @ CC.K.OA.2 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.J06
łĄ @ @ ;LBĀ
żĄ (żĄ @ @ K;¼"Ć
żĄ (żĄ @ @ qSD.K.A.3.1 (Knowledge) Students are able to use concrete objects to model the meaning of the "+" and "" symbols.;LBÄ
żĄ (ž’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’7AøąMicūģÄLZ¶¶7Ū%
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;@R_żĄ arial’’’’’’’’’’’’’’’’’’’’(żĄ arial~ŗ»
¼’’’’’’’’’’’’’’’’@ @ CC Strand;DZ`żĄ arial’’’’’’’’’’’’’’’’’’’’(żĄ arial~ŗ»
¼’’’’’’’’’’’’’’’’@ @
CC Standard #;BVażĄ arial’’’’’’’’’’’’’’’’’’’’(żĄ arial~ŗ»
¼’’’’’’’’’’’’’’’’@ @ CC StandardJ¦¬łĄ ariall ¼’’’’’’’’’’’’’’’’@ @ J¦¬żĄ ariall ¼’’’’’’’’’’’’’’’’@ @ J¦¬żĄ ariall ¼’’’’’’’’’’’’’’’’@ @ ;@RbżĄ arial ’’’’’’’’’’’’’’’’’’’’(żĄ arial~ŗ»
¼’’’’’’’’’’’’’’’’@ @ SD Strand;DZcżĄ arial ’’’’’’’’’’’’’’’’’’’’(żĄ arial~ŗ»
¼’’’’’’’’’’’’’’’’@ @
SD Standard #;G`dżĄ arial ’’’’’’’’’’’’’’’’’’’’(żĄ arial~ŗ»
¼’’’’’’’’’’’’’’’’@ @ Grade Difference;F^e żĄ arial ’’’’’’’’’’’’’’’’’’’’(żĄ arial~ŗ»
¼’’’’’’’’’’’’’’’’@ @ Degree of Match;<Jf
żÄ arial ’’’’’’’’’’’’’’’’’’’’(żÄ arial~ŗ»
¼’’’’’’’’’’’’’’’’pwNotesJ¦¬ ’żĄ ariall ’’’’’’’’’’’’’’’’ ww;MDgżĄ (żĄ @ @ CC;LBhżĄ (żĄ @ @ 1;”ģiżĄ (żĄ @ @ VCC.K.CC.1 Know number names and the count sequence. Count to 100 by ones and by tens. J06łĄ @ @ ;LBjżĄ (żĄ @ @ K;«kżĄ (żĄ @ @ `SD.K.N.1.1 (Comprehension) Students are able to read, write, count, and sequence numerals to 20.;LBlżĄ (żĄ @ @ N;NFmżĄ (żĄ @ @ 1.1;LBnżĄ (żĄ @ @ 0;xo żĄ (żĄ @ @ 3 = Excellent match between the two documents;
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żÄ (ĄżÄ pw:only to 50 in SD standards read, write, count and sequnceJ06 ’żĄ ww;MDqżĄ (żĄ @@ @ CC;LBrżĄ (%nżĄ @ @ 1;”ģsżĄ (żĄ @ @ VCC.K.CC.1 Know number names and the count sequence. Count to 100 by ones and by tens. J06łĄ @ @ ;LBtżĄ (żĄ @ @ 1;ØśużĄ (żĄ @ @ ]SD.1.N.1.1 (Comprehension) Students are able to read, write, count, and order numerals to 50.;LBvżĄ (żĄ @ @ N;NFwżĄ (żĄ @ @ 1.1;MDxżĄ (żĄ @ @ 1J06 żĄ @ @ ;
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żÄ (żÄ pw:only to 50 in SD standards read, write, count and sequnceJ06 ’żĄ ww;MDzżĄ (żĄ @ @ CC;LB{żĄ (żĄ @ @ 1;”ģżĄ (żĄ @ @ VCC.K.CC.1 Know number names and the count sequence. Count to 100 by ones and by tens. J06łĄ @ @ ;LB}żĄ (żĄ @ @ 2;¬~żĄ (żĄ @ @ aSD.2.N.1.1 (Comprehension) Students are able to read, write, count, and sequence numerals to 100.;LBżĄ (żĄ @ @ N;NFżĄ (żĄ @ @ 1.1;MDżĄ (żĄ @ @ 2J06 żĄ @ @ ;
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żÄ (żÄ pw:only to 50 in SD standards read, write, count and sequnceJ06 ’żĄ ww;MDżĄ (żĄ @ @ CC;LBżĄ (żĄ @ @ 3;¬
żĄ (ttżĄ @ @ ¶CC.K.CC.3 Know number names and the count sequence. Write numbers from 0 to 20. Represent a number of objects with a written numeral 020 (with 0 representing a count of no objects).J06łĄ @ @ ;LBżĄ (żĄ @ @ K;«żĄ (żĄ @ @ `SD.K.N.1.1 (Comprehension) Students are able to read, write, count, and sequence numerals to 20.;LBżĄ (żĄ @ @ N;NFżĄ (żĄ @ @ 1.1;LBżĄ (żĄ @ @ 0;ø żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;fv
żÄ (żÄ pwSD standards numerals to 20J06 ’żĄ ww;MDżĄ (żĄ @ @ CC;LBżĄ (żĄ @ @ 5;odżĄ (żĄ @ @ CC.K.CC.5 Count to tell the number of objects. Count to answer how many? questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 120, count out that many objects.J06łĄ @ @ ;LBżĄ (żĄ @ @ K;«żĄ (żĄ @ @ `SD.K.N.1.1 (Comprehension) Students are able to read, write, count, and sequence numerals to 20.;LBżĄ (żĄ @ @ N;NFżĄ (żĄ @ @ 1.1;LBżĄ (żĄ @ @ 0;ø żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@
żÄ (żÄ pwJ06 ’żĄ ww;MDżĄ (żĄ @ @ CC;LBżĄ (żĄ @ @ 6;D2żĄ (żĄ @ @ łCC.K.CC.6 Compare numbers. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. (Include groups with up to ten objects.)J06łĄ @ @ ;LBżĄ (żĄ @ @ K;Ś^żĄ (żĄ @ @ SD.K.A.2.1 (Comprehension) Students are able to compare collections of objects to determine more, less, and equal (greater than and less than).;LBżĄ (żĄ @ @ A;NFżĄ (żĄ @ @ 2.1;LBżĄ (żĄ @ @ 0;x żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@
żÄ (żÄ pwJ06 ’żĄ ww;MD”żĄ (żĄ @ @ CC;LB¢żĄ (żĄ @ @ 7;©ü£żĄ (żĄ @ @ ^CC.K.CC.7 Compare numbers. Compare two numbers between 1 and 10 presented as written numerals.J06łĄ @ @ ;LB¤żĄ (żĄ @ @ 1;õ„żĄ (żĄ @ @ ŖSD.1.A.2.1 (Comprehension) Students are able to use the concepts and language of more, less, and equal (greater than and less than) to compare numbers and sets (0 to 20).;LB¦żĄ (żĄ @ @ A;NF§żĄ (żĄ @ @ 2.1;MDØżĄ (żĄ @ @ 1;®© żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;]dŖ
żÄ (żÄ pw 1st they go to 20J06 ’żĄ ww;MD«żĄ (żĄ @ @ OA;LB¬żĄ (żĄ @ @ 1;Ė@żĄ (żĄ @ @ CC.K.OA.1 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Represent addition and subtraction with objects, fingers, mental images, drawings (drawings need not show details, but should show the mathematics in the problem), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. J06łĄ @ @ ;LB®żĄ (żĄ @ @ K;¼"ÆżĄ (żĄ @ @ qSD.K.A.3.1 (Knowledge) Students are able to use concrete objects to model the meaning of the "+" and "" symbols.;LB°żĄ (żĄ @ @ A;NF±żĄ (żĄ @ @ 3.1;LB²żĄ (żĄ @ @ 0;ø³ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@“
żÄ (żÄ pwJ06 ’żĄ ww;MDµ żĄ (żĄ @ @ OA;LB¶ żĄ (żĄ @ @ 2;RN· żĄ (żĄ @ @ CC.K.OA.2 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.J06 łĄ @ @ ;LBø żĄ (żĄ @ @ K;µ¹ żĄ (żĄ @ @ jSD.K.N.3.1 (Application) Students are able to solve addition and subtraction problems up to 10 in context.;LBŗ żĄ (żĄ @ @ N;NF» żĄ (żĄ @ @ 3.1;LB¼ żĄ (żĄ @ @ 0;x½ żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@¾
żÄ (żÄ pwJ06 ’żĄ ww;MDæ
żĄ (żĄ @ @ OA;LBĄ
żĄ (żĄ @ @ 2;RNĮ
żĄ (żĄ @ @ CC.K.OA.2 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.J06
łĄ @ @ ;LBĀ
żĄ (żĄ @ @ K;¼"Ć
żĄ (żĄ @ @ qSD.K.A.3.1 (Knowledge) Students are able to use concrete objects to model the meaning of the "+" and "" symbols.;LBÄ
żĄ (olve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.J06
łĄ @ @ ;LBĀ
żĄ (żĄ @ @ K;¼"Ć
żĄ (żĄ @ @ qSD.K.A.3.1 (Knowledge) Students are able to use concrete objects to model the meaning of the "+" and "" symbols.;LBÄ
żĄ (żĄ @ @ A;NFÅ
żĄ (żĄ @ @ 3.1;LBĘ
żĄ (żĄ @ @ 0J06
żĄ @ @ ;K@Ē
żÄ (żÄ pwJ06
’żĄ ww;MDČżĄ (żĄ @ @ MD;LBÉżĄ (żĄ ’’’’’’’’’’’’’’’’’’’’ž’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’@ @ 1;¬ŹżĄ (żĄ @ @ ¶CC.K.MD.1 Describe and compare measurable attributes. Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.J06łĄ @ @ ;LBĖżĄ (żĄ @ @ K;¼"ĢżĄ (żĄ @ @ qSD.K.M.1.5 (Comprehension) Students are able to compare and order concrete objects by length, height, and weight.;LBĶżĄ (żĄ @ @ M;NFĪżĄ (żĄ @ @ 1.5;LBĻżĄ (żĄ @ @ 0;®Š żĄ (X`żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@Ń
żÄ (żÄ pwJ06 ’żĄ ww;MDŅżĄ (żĄ @ @ MD;LBÓżĄ (żĄ @ @ 2;µŖŌżĄ (żĄ @ @ 5CC.K.MD.2 Describe and compare measurable attributes. Directly compare two objects with a measurable attribute in common, to see which object has more of / less of the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.J06łĄ @ @ ;LBÕżĄ (żĄ @ @ K;¼"ÖżĄ (żĄ @ @ qSD.K.M.1.5 (Comprehension) Students are able to compare and order concrete objects by length, height, and weight.;LB×żĄ (żĄ @ @ M;NFŲżĄ (żĄ @ @ 1.5;LBŁżĄ (żĄ @ @ 0;øŚ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@Ū
żÄ (żÄ pwJ06 ’żĄ ww;MDÜ
żĄ (żĄ @ @ MD;LBŻ
żĄ (żĄ @ @ 3;G8Ž
żĄ (żĄ @ @ üCC.K.MD.3 Classify objects and count the number of objects in each category. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. (Limit category counts to be less than or equal to 10.)J06
łĄ @ @ ;LBß
żĄ (żĄ @ @ K;°
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żĄ (żĄ @ @ eSD.K.A.4.2 (Comprehension) Students are able to sort and classify objects according to one attribute.;LBį
żĄ (żĄ @ @ A;NFā
żĄ (żĄ @ @ 4.2;LBć
żĄ (żĄ @ @ 0;øä
żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@å
żÄ (żÄ pwJ06
’żĄ ww;LBężĄ (żĄ @ @ G;LBēżĄ (żĄ @ @ 1;øčżĄ (żĄ @ @ <CC.K.G.1 Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.J06łĄ @ @ ;LBéżĄ (żĄ @ @ K;“źżĄ (żĄ @ @ iSD.K.G.2.1 (Comprehension) Students are able to describe the position of twodimensional (plane) figures.;LBėżĄ (żĄ @ @ G;NFģżĄ (żĄ @ @ 2.1;LBķżĄ (żĄ @ @ 0;xī żĄ (żĄ @ @ 3 = Excellent match between the two documents;XZļ
żÄ (żÄ pw
by end of 1stJ06 ’żĄ ww;LBšżĄ (żĄ @ @ G;LBńżĄ (żĄ @ @ 1;øņżĄ (żĄ @ @ <CC.K.G.1 Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.J06łĄ @ @ ;LBóżĄ (żĄ @ @ 1;¢īōżĄ (żĄ @ @ WSD.1.G.2.1 (Comprehension) Students are able to describe proximity of objects in space.;LBõżĄ (żĄ @ @ G;NFöżĄ (żĄ @ @ 2.1;MD÷żĄ (żĄ @ @ 1J06 żĄ @ @ ;XZų
żÄ (żÄ pw
by end of 1stJ06 ’żĄ ww;LBłżĄ (żĄ @ @ G;LBśżĄ (żĄ @ @ 1;øūżĄ (żĄ @ @ <CC.K.G.1 Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.J06łĄ @ @ ;LBüżĄ (żĄ @ @ K;¦öżżĄ (żĄ @ @ [SD.K.G.1.1 (Knowledge) Students are able to identify basic twodimensional (plane) figures.;LBžżĄ (żĄ @ @ G;NF’żĄ (żĄ @ @ 1.1;LBżĄ (żĄ @ @ 0J06 żĄ @ @ ;XZ
żÄ (żÄ pw
by end of 1stJ06 ’żĄ ww;LBżĄ (żĄ @ @ G;LBżĄ (żĄ @ @ 1;øżĄ (żĄ @ @ <CC.K.G.1 Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.J06łĄ @ @ ;LBżĄ (żĄ @ @ 1;„ōżĄ (żĄ @ @ ZSD.1.G.1.1 (Comprehension) Students are able to describe characteristics of plane figures.;LBżĄ (żĄ @ @ G;NFżĄ (żĄ @ @ 1.1;MD żĄ (żĄ @ @ 1J06 żĄ @ @ ;XZ
żÄ (żÄ pw
by end of 1stJ06 ’żĄ ww;LBżĄ (żĄ @ @ G;LBżĄ (żĄ @ @ 2;ą
żĄ (żĄ @ @ ŠCC.K.G.2 Identify and describe shapes (such as squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Correctly name shapes regardless of their orientations or overall size.J06łĄ @ @ ;LBżĄ (żĄ @ @ K;¦öżĄ (żĄ @ @ [SD.K.G.1.1 (Knowledge) Students are able to identify basic twodimensional (plane) figures.;LBżĄ (żĄ @ @ G;NFżĄ (żĄ @ @ 1.1;LBżĄ (żĄ @ @ 0;x żĄ (żĄ @ @ 3 = Excellent match between the two documents;XZ
żÄ (żÄ pw
by end of 2ndJ06 ’żĄ ww;LBżĄ (żĄ @ @ G;LBżĄ (żĄ @ @ 2;ążĄ (żĄ @ @ ŠCC.K.G.2 Identify and describe shapes (such as squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Correctly name shapes regardless of their orientations or overall size.J06łĄ @ @ ;LBżĄ (żĄ @ @ 1; źżĄ (żĄ @ @ USD.1.G.1.2 (Comprehension) Students are able to sort basic threedimensional figures.;LBżĄ (żĄ @ @ G;NFżĄ (żĄ @ @ 1.2;MDżĄ (żĄ @ @ 1J06 żĄ @ @ ;XZ
żÄ (żÄ pw
by end of 2ndJ06 ’żĄ ww;LBżĄ (żĄ @ @ G;LBżĄ (żĄ @ @ 2;ą żĄ (żĄ @ @ ŠCC.K.G.2 Identify and describe shapes (such as squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Correctly name shapes regardless of their orientations or overall size.J06łĄ @ @ ;LB!żĄ (żĄ @ @ 1;¢ī"żĄ (żĄ @ @ WSD.1.G.2.1 (Comprehension) Students are able to describe proximity of objects in space.;LB#żĄ (żĄ @ @ G;NF$żĄ (żĄ @ @ 2.1;MD%żĄ (żĄ @ @ 1J06 żĄ @ @ ;XZ&
żÄ (żÄ pw
by end of 2ndJ06 ’żĄ ww;LB'żĄ (żĄ @ @ G;LB(żĄ (żĄ @ @ 2;ą)żĄ (żĄ @ @ ŠCC.K.G.2 Identify and describe shapes (such as squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Correctly name shapes regardless of their orientations or overall size.J06łĄ @ @ ;LB*żĄ (żĄ @ @ 2;Ā.+żĄ (żĄ @ @ wSD.2.G.2.1 (Knowledge) Students are able to identify geometric figures regardless of position and orientation in space.;LB,żĄ (żĄ @ @ G;NFżĄ (żĄ @ @ 2.1;MD.żĄ (żĄ @ @ 2J06 żĄ @ @ ;XZ/
żÄ (żÄ pw
by end of 2ndJ06 ’żĄ ww;LB0żĄ (żĄ @ @ G;LB1żĄ (żĄ @ @ 3;2żĄ (żĄ @ @ ęCC.K.G.3 Identify and describe shapes (such as squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Identify shapes as twodimensional (lying in a plane, flat ) or threedimensional ( solid ).J06łĄ @ @ ;LB3żĄ (żĄ @ @ 1;„ō4żĄ (żĄ @ @ ZSD.1.G.1.1 (Comprehension) Students are able to describe characteristics of plane figures.;LB5żĄ (żĄ @ @ G;NF6żĄ (żĄ @ @ 1.1;MD7żĄ (żĄ @ @ 1;®8 żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;bn9
żÄ (żÄ pweven by end of 1st weakJ06 ’żĄ ww;LB:żĄ (żĄ @ @ G;LB;żĄ (żĄ @ @ 3;<żĄ (żĄ @ @ ęCC.K.G.3 Identify and describe shapes (such as squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Identify shapes as twodimensional (lying in a plane, flat ) or threedimensional ( solid ).J06łĄ @ @ ;LB=żĄ (żĄ @ @ 1; ź>żĄ (żĄ @ @ USD.1.G.1.2 (Comprehension) Students are able to sort basic threedimensional figures.;LB?żĄ (żĄ @ @ G;NF@żĄ (żĄ @ @ 1.2;MDAżĄ (żĄ @ @ 1J06 żĄ @ @ ;bnB
żÄ (żÄ pweven by end of 1st weakJ06 ’żĄ ww;LBCżĄ (żĄ @ @ G;LBDżĄ (żĄ @ @ 4;ŁĪEżĄ (żĄ @ @ GCC.K.G.4 Analyze, compare, create, and compose shapes. Analyze and compare two and threedimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/ corners ) and other attributes (e.g., having sides of equal length).J06łĄ @ @ ;LBFżĄ (żĄ @ @ 3;śGżĄ (żĄ @ @ ÆSD.3.G.1.1 (Comprehension) Students are able to recognize and compare the following plane and solid geometric figures: square, rectangle, triangle, cube, sphere, and cylinder.;LBHżĄ (żĄ @ @ G;NFIżĄ (żĄ @ @ 1.1;MDJżĄ (żĄ @ @ 3;®K żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;etL
żÄ (żÄ pwby end of 3rd they compareJ06 ’żĄ ww;LBMżĄ (żĄ @ @ G;LBNżĄ (żĄ @ @ 4;ŁĪOżĄ (żĄ @ @ GCC.K.G.4 Analyze, compare, create, and compose shapes. Analyze and compare two and threedimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/ corners ) and other attributes (e.g., having sides of equal length).J06łĄ @ @ ;LBPżĄ (żĄ @ @ 2;Ē8QżĄ (żĄ @ @ SD.2.G.1.1 (Comprehension) Students are able to use the terms side and vertex (corners) to identify plane and solid figures.;LBRżĄ (żĄ @ @ G;NFSżĄ (żĄ @ @ 1.1;MDTżĄ (żĄ @ @ 2J06 żĄ @ @ ;etU
żÄ (żÄ pwby end of 3rd they compareJ06 ’żĄ ww;LBVżĄ (żĄ @ @ G;LBWżĄ (żĄ @ @ 4;ŁĪXżĄ (żĄ @ @ GCC.K.G.4 Analyze, compare, create, and compose shapes. Analyze and compare two and threedimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/ corners ) and other attributes (e.g., having sides of equal length).J06łĄ @ @ ;LBYżĄ (żĄ @ @ 1;„ōZżĄ (żĄ @ @ ZSD.1.G.1.1 (Comprehension) Students are able to describe characteristics of plane figures.;LB[żĄ (żĄ @ @ G;NF\żĄ (żĄ @ @ 1.1;MD]żĄ (żĄ @ @ 1J06 żĄ @ @ ;et^
żÄ (żÄ pwby end of 3rd they compareJ06 ’żĄ ww;MD_żĄ (żĄ @ @ OA;LB`żĄ (żĄ @ @ 1;Ā.ażĄ (żĄ @ @ wCC.1.OA.1 Represent and solve problems involving addition and subtraction. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. J06łĄ @ @ ;LBbżĄ (żĄ @ @ 1;’ØcżĄ (żĄ @ @ “SD.1.N.2.1 (Application) Students are able to solve addition and subtraction problems with numbers 0 to 20 written in horizontal and vertical formats using a variety of strategies.;LBdżĄ (żĄ @ @ N;NFeżĄ (żĄ @ @ 2.1;LBfżĄ (żĄ @ @ 0;xg żĄ (żĄ @ @ 3 = Excellent match between the two documents;XZh
żÄ (żÄ pw
by end of 2ndJ06 ’żĄ ww;MDiżĄ (żĄ @ @ OA;LBjżĄ (żĄ @ @ 1;Ā.kżĄ (żĄ @ @ wCC.1.OA.1 Represent and solve problems involving addition and subtraction. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. J06łĄ @ @ ;LBlżĄ (żĄ @ @ 1;µmżĄ (żĄ @ @ jSD.1.N.3.1 (Application) Students are able to solve addition and subtraction problems up to 20 in context.;LBnżĄ (żĄ @ @ N;NFożĄ (żĄ @ @ 3.1;LBpżĄ (żĄ @ @ 0J06 żĄ @ @ ;XZq
żÄ (żÄ pw
by end of 2ndJ06 ’żĄ ww;MDrżĄ (żĄ @ @ OA;LBsżĄ (żĄ @ @ 1;Ā.tżĄ (żĄ @ @ wCC.1.OA.1 Represent and solve problems involving addition and subtraction. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. J06łĄ @ @ ;LBużĄ (żĄ @ @ 1;ćpvżĄ (żĄ @ @ SD.1.A.2.2 (Application) Students are able to solve open addition and subtraction sentences with one unknown (c) using numbers equal to or less than 10.;LBwżĄ (żĄ @ @ A;NFxżĄ (żĄ @ @ 2.2;LByżĄ (żĄ @ @ 0J06 żĄ @ @ ;XZz
żÄ (żÄ pw
by end of 2ndJ06 ’żĄ ww;MD{żĄ (żĄ @ @ OA;LBżĄ (żĄ @ @ 1;Ā.}żĄ (żĄ @ @ wCC.1.OA.1 Represent and solve problems involving addition and subtraction. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. J06łĄ @ @ ;LB~żĄ (żĄ @ @ 2;ćpżĄ (żĄ @ @ SD.2.A.2.2 (Application) Students are able to solve open addition and subtraction sentences with one unknown (c) using numbers equal to or less than 20.;LBżĄ (żĄ @ @ A;NFżĄ (żĄ @ @ 2.2;MDżĄ (żĄ @ @ 1J06 żĄ @ @ ;XZ
żÄ (żÄ pw
by end of 2ndJ06 ’żĄ ww;MDżĄ (żĄ @ @ OA;LB
żĄ (żĄ @ @ 2;mżĄ (żĄ @ @ "CC.1.OA.2 Represent and solve problems involving addition and subtraction. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.J06łĄ @ @ ;LBżĄ (żĄ @ @ 1;µżĄ (żĄ @ @ jSD.1.N.3.1 (Application) Students are able to solve addition and subtraction problems up to 20 in context.;LBżĄ (żĄ @ @ N;NFżĄ (żĄ @ @ 3.1;LBżĄ (żĄ @ @ 0;® żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;u
żÄ (żÄ pw*SD does not require unknown with 3 numbersJ06 ’żĄ ww;MD żĄ (żĄ @ @ OA;LB żĄ (żĄ @ @ 3;#š żĄ (żĄ @ @ ŲCC.1.OA.3 Understand and apply properties of operations and the relationship between addition and subtraction. Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) (Students need not use formal terms for these properties.)J06 łĄ @ @ ;LB żĄ (żĄ @ @ 1;’Ø żĄ (żĄ @ @ “SD.1.N.2.1 (Application) Students are able to solve addition and subtraction problems with numbers 0 to 20 written in horizontal and vertical formats using a variety of strategies.;LB żĄ (żĄ @ @ N;NF żĄ (żĄ @ @ 2.1;LB żĄ (żĄ @ @ 0;® żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;ŗ
żÄ (żÄ pw=associative property is in 5th commutative property is in 4thJ06 ’żĄ ww;MD!żĄ (żĄ @ @ OA;LB!żĄ (żĄ @ @ 6;yn!żĄ (żĄ @ @ CC.1.OA.6 Add and subtract within 20. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 4 = 13 3 1 = 10 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).J06!!łĄ @ @ ;LB!żĄ (żĄ @ @ 1;’Ø!żĄ (żĄ @ @ “SD.1.N.2.1 (Application) Students are able to solve addition and subtraction problems with numbers 0 to 20 written in horizontal and vertical formats using a variety of strategies.;LB!żĄ (żĄ @ @ N;NF!żĄ (żĄ @ @ 2.1;LB!żĄ (żĄ @ @ 0;® ! żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@”!
żÄ (żÄ pwJ06 !!’żĄ ww;MD¢"żĄ (żĄ @ @ OA;LB£"żĄ (żĄ @ @ 7;Æ¤¤"żĄ (żĄ @ @ 2CC.1.OA.7 Work with addition and subtraction equations. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.J06""łĄ @ @ ;LB„"żĄ (żĄ @ @ 1;ćp¦"żĄ (żĄ @ @ SD.1.A.2.2 (Application) Students are able to solve open addition and subtraction sentences with one unknown (c) using numbers equal to or less than 10.;LB§"żĄ (żĄ @ @ A;NFØ"żĄ (żĄ @ @ 2.2;LB©"żĄ (żĄ @ @ 0;øŖ" żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@«"
żÄ (żÄ pwJ06 ""’żĄ ww;MD¬#żĄ (żĄ @ @ OA;LB#żĄ (żĄ @ @ 7;Æ¤®#żĄ (żĄ @ @ 2CC.1.OA.7 Work with addition and subtraction equations. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.J06##łĄ @ @ ;LBÆ#żĄ (żĄ @ @ 2;æ(°#żĄ (żĄ @ @ tSD.2.A.2.3 (Application) Students are able to balance simple addition and subtraction equations using sums up to 20.;LB±#żĄ (żĄ @ @ A;NF²#żĄ (żĄ @ @ 2.3;MD³#żĄ (żĄ @ @ 1J06## żĄ @ @ ;K@“#
żÄ (żÄ pwJ06 ##’żĄ ww;9Dµ$üĄ VerdanażÄ pw132.A.2.3 (Application’’’’’’’’’’’’’’’’
*üĄ arialo 20.nderstand the meaning of’’’’’’’’’’’’’’’’@ @ OA;LB¶$żĄ (żĄ @ @ 8;·$żĄ (żĄ @ @ #CC.1.OA.8 Work with addition and subtraction equations. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ?’ 3, 6 + 6 = ?’. J06$$łĄ @ @ ;LBø$żĄ (żĄ @ @ 1;ćp¹$żĄ (żĄ @ @ SD.1.A.2.2 (Application) Students are able to solve open addition and subtraction sentences with one unknown (c) using numbers equal to or less than 10.;LBŗ$żĄ (żĄ @ @ A;NF»$żĄ (żĄ @ @ 2.2;LB¼$żĄ (żĄ @ @ 0;ø½$ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@¾$
żÄ (żÄ pwJ06 $$’żĄ ww;:Fæ%üĄ VerdanażÄ pw2 = Good match, with mi’’’’’’’’’’’’’’’’
*üĄ arial) using numbers equal to or less than 10.n whol’’’’’’’’’’’’’’’’@ @ NBT;LBĄ%żĄ (żĄ @ @ 1;ŗĮ%żĄ (żĄ @ @ ½CC.1.NBT.1 Extend the counting sequence. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.J06%%łĄ @ @ ;LBĀ%żĄ (żĄ @ @ 2;¬Ć%żĄ (żĄ @ @ aSD.2.N.1.1 (Comprehension) Students are able to read, write, count, and sequence numerals to 100.;LBÄ%żĄ (żĄ @ @ N;NFÅ%żĄ (żĄ @ @ 1.1;MDĘ%żĄ (żĄ @ @ 1;øĒ% żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;_hČ%
żÄ (żÄ pwby end of 2nd to 100J06 %%’żĄ ww;:FÉ&üĄ VerdanażÄ pwby end of 2nd to 100 mi’’’’’’’’’’’’’’’’
*üĄ ariald and write numerals and represent a number of objec’’’’’’’’’’’’’’’’@ @ NBT;LBŹ&żĄ (żĄ @ @ 1;ŗĖ&żĄ (żĄ @ @ ½CC.1.NBT.1 Extend the counting sequence. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.J06&&łĄ @ @ ;LBĢ&żĄ (żĄ @ @ 1;ØśĶ&żĄ (żĄ @ @ ]SD.1.N.1.1 (Comprehension) Students are able to read, write, count, and order numerals to 50.;LBĪ&żĄ (żĄ @ @ N;NFĻ&żĄ (żĄ @ @ 1.1;LBŠ&żĄ (żĄ @ @ 0J06&& żĄ @ @ ;_hŃ&
żÄ (żÄ pwby end of 2nd to 100J06 &&’żĄ ww;9DŅ'üĄ VerdanażÄ pwby end of 2nd to 100nsi’’’’’’’’’’’’’’’’
*üĄ ariald and write numerals and represent a number of objec’’’’’’’’’’’’’’’’@ @ MD;LBÓ'żĄ (żĄ @ @ 3;¶Ō'żĄ (żĄ ’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ż’’’ż’’’
!"#$%&'()*+,./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{}~@ @ kCC.1.MD.3 Tell and write time. Tell and write time in hours and halfhours using analog and digital clocks.J06''łĄ @ @ ;LBÕ'żĄ (żĄ @ @ 1;ęvÖ'żĄ (żĄ @ @ SD.1.M.1.1 (Knowledge) Students are able to tell time to the halfhour using digital and analog clocks and order a sequence of events with respect to time.;LB×'żĄ (żĄ @ @ M;NFŲ'żĄ (żĄ @ @ 1.1;LBŁ'żĄ (żĄ @ @ 0;xŚ' żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@Ū'
żÄ (żÄ pwJ06 ''’żĄ ww;9DÜ(üĄ VerdanażÄ pw3 = Excellent match bet’’’’’’’’’’’’’’’’
*üĄ arialr a sequence of events with respect to time.of objec’’’’’’’’’’’’’’’’@ @ MD;LBŻ(żĄ (żĄ @ @ 4;QLŽ(żĄ (żĄ @ @ CC.1.MD.4 Represent and interpret data. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.J06((łĄ @ @ ;LBß(żĄ (żĄ @ @ 1;ÖVą(żĄ (żĄ @ @ SD.1.S.1.1 (Application) Students are able to display data in simple picture graphs with units of one and bar graphs with intervals of one.;LBį(żĄ (żĄ @ @ S;NFā(żĄ (żĄ @ @ 1.1;LBć(żĄ (żĄ @ @ 0;øä( żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@å(
żÄ (żÄ pwJ06 ((’żĄ ww;9Dę)üĄ VerdanażÄ pw2 = Good match, with mi’’’’’’’’’’’’’’’’
*üĄ arialraphs with intervals of one. the total number of dat’’’’’’’’’’’’’’’’@ @ MD;LBē)żĄ (żĄ @ @ 4;QLč)żĄ (żĄ @ @ CC.1.MD.4 Represent and interpret data. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.J06))łĄ @ @ ;LBé)żĄ (żĄ @ @ 1; źź)żĄ (żĄ @ @ USD.1.S.1.2 (Comprehension) Students are able to answer questions from organized data.;LBė)żĄ (żĄ @ @ S;NFģ)żĄ (żĄ @ @ 1.2;LBķ)żĄ (żĄ @ @ 0J06)) żĄ @ @ ;K@ī)
żÄ (żÄ pwJ06 ))’żĄ ww;9Dļ*üĄ VerdanażÄ pw0.21.S.1.2 (Comprehensi’’’’’’’’’’’’’’’’
*üĄ arialk and answer questions about the total number of dat’’’’’’’’’’’’’’’’@ @ OA;LBš*żĄ (żĄ @ @ 3;pń*żĄ (żĄ @ @ %CC.2.OA.3 Work with equal groups of objects to gain foundations for multiplication. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.J06**łĄ @ @ ;LBņ*żĄ (żĄ @ @ 2;Ą*ó*żĄ (żĄ @ @ uSD.2.A.4.1 (Comprehension) Students are able to find and extend growing patterns using symbols, objects, and numbers.;LBō*żĄ (żĄ @ @ A;NFõ*żĄ (żĄ @ @ 4.1;LBö*żĄ (żĄ @ @ 0;®÷* żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@ų*
żÄ (żÄ pwJ06 **’żĄ ww;:Fł+üĄ VerdanażÄ pw1 = Weak match, major a’’’’’’’’’’’’’’’’
*üĄ arialmbers.cts (up to 20) has an odd or even number of me’’’’’’’’’’’’’’’’@ @ NBT;LBś+żĄ (żĄ @ @ 2;”ģū+żĄ (żĄ @ @ VCC.2.NBT.2 Understand place value. Count within 1000; skipcount by 5s, 10s, and 100s.J06++łĄ @ @ ;LBü+żĄ (żĄ @ @ 2;¬ż+żĄ (żĄ @ @ aSD.2.N.1.1 (Comprehension) Students are able to read, write, count, and sequence numerals to 100.;LBž+żĄ (żĄ @ @ N;NF’+żĄ (żĄ @ @ 1.1;LB+żĄ (żĄ @ @ 0;®+ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@+
żÄ (żÄ pwJ06 ++’żĄ ww;:F,üĄ VerdanażÄ pw1 = Weak match, major a’’’’’’’’’’’’’’’’
*üĄ arialmbers.cts (up to 20) has an odd or even number of me’’’’’’’’’’’’’’’’@ @ NBT;LB,żĄ (żĄ @ @ 5;F6,żĄ (żĄ @ @ ūCC.2.NBT.5 Use place value understanding and properties of operations to add and subtract. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. J06,,łĄ @ @ ;LB,żĄ (żĄ @ @ 2;ō,żĄ (żĄ @ @ ©SD.2.N.2.1 (Application) Students are able to solve twodigit addition and subtraction problems written in horizontal and vertical formats using a variety of strategies.;LB,żĄ (żĄ @ @ N;NF ,żĄ (żĄ @ @ 2.1;LB
,żĄ (żĄ @ @ 0;ø, żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;i,
żÄ (żÄ pwSD does not mention strategiesJ06 ,,’żĄ ww;9D
üĄ VerdanażÄ pwSD does not mention str’’’’’’’’’’’’’’’’
*üĄ arialzontal and vertical formats using a variety of strat’’’’’’’’’’’’’’’’@ @ MD;LBżĄ (żĄ @ @ 1;
ÄżĄ (żĄ @ @ ĀCC.2.MD.1 Measure and estimate lengths in standard units. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. J06łĄ @ @ ;LBżĄ (żĄ @ @ 5;ÓPżĄ (żĄ @ @ SD.5.M.1.4 (Application) Students are able to use appropriate tools to measure length, weight, temperature, and area in problem solving.;LBżĄ (żĄ @ @ M;NFżĄ (żĄ @ @ 1.4;MDżĄ (żĄ @ @ 3;ø żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@
żÄ (żÄ pwJ06 ’żĄ ww;MD.żĄ (żĄ @ @ MD;LB.żĄ (żĄ @ @ 1;
Ä.żĄ (żĄ @ @ ĀCC.2.MD.1 Measure and estimate lengths in standard units. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. J06..łĄ @ @ ;LB.żĄ (żĄ @ @ 1;Ź>.żĄ (żĄ @ @ SD.1.M.1.5 (Knowledge) Students are able to identify appropriate measuring tools for length, weight, capacity, and temperature.;LB.żĄ (żĄ @ @ M;NF.żĄ (żĄ @ @ 1.5;LB.żĄ (żĄ @ @ 1J06.. żĄ @ @ ;K@.
żÄ (żÄ pwJ06 ..’żĄ ww;MD /żĄ (żĄ @ @ MD;LB!/żĄ (żĄ @ @ 7;ÓP"/żĄ (żĄ @ @ CC.2.MD.7 Work with time and money. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. J06//łĄ @ @ ;LB#/żĄ (żĄ @ @ 2;ĻH$/żĄ (żĄ @ @ SD.2.M.1.1 (Knowledge) Students are able to tell time to the minute using digital and analog clocks and relate time to daily events.;LB%/żĄ (żĄ @ @ M;NF&/żĄ (żĄ @ @ 1.1;LB'/żĄ (żĄ @ @ 0;®(/ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;gx)/
żÄ (żÄ pwSD does not require am or pmJ06 //’żĄ ww;MD*0żĄ (żĄ @ @ MD;LB+0żĄ (żĄ @ @ 7;ÓP,0żĄ (żĄ @ @ CC.2.MD.7 Work with time and money. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. J0600łĄ @ @ ;LB0żĄ (żĄ @ @ 3;ŌR.0żĄ (żĄ @ @ SD.3.M.1.1 (Knowledge) Students are able to read and tell time before and after the hour within fiveminute intervals on an analog clock.;LB/0żĄ (żĄ @ @ M;NF00żĄ (żĄ @ @ 1.1;MD10żĄ (żĄ @ @ 1J0600 żĄ @ @ ;gx20
żÄ (żÄ pwSD does not require am or pmJ06 00’żĄ ww;MD31żĄ (żĄ @ @ MD;LB41żĄ (żĄ @ @ 8;A,51żĄ (żĄ @ @ öCC.2.MD.8 Work with time and money. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ (dollars) and ¢ (cents) symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? J0611łĄ @ @ ;LB61żĄ (żĄ @ @ 2;ŲZ71żĄ (żĄ @ @ SD.2.M.1.4 (Knowledge) Students are able to represent and write the value of money using the "¢" sign and in decimal form using the "$" sign.;LB81żĄ (żĄ @ @ M;NF91żĄ (żĄ @ @ 1.4;LB:1żĄ (żĄ @ @ 0;x;1 żĄ (żĄ @ @ 3 = Excellent match between the two documents;XZ<1
żÄ (żÄ pw
by end of 3rdJ06 11’żĄ ww;MD=2żĄ (żĄ @ @ MD;LB>2żĄ (żĄ @ @ 8;A,?2żĄ (żĄ @ @ öCC.2.MD.8 Work with time and money. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ (dollars) and ¢ (cents) symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? J0622łĄ @ @ ;LB@2żĄ (żĄ @ @ 2;ĻHA2żĄ (żĄ @ @ SD.2.M.1.3 (Application) Students are able to determine the value of a collection of like and unlike coins with a value up to $1.00.;LBB2żĄ (żĄ @ @ M;NFC2żĄ (żĄ @ @ 1.3;LBD2żĄ (żĄ @ @ 0J0622 żĄ @ @ ;XZE2
żÄ (żÄ pw
by end of 3rdJ06 22’żĄ ww;MDF3żĄ (żĄ @ @ MD;LBG3żĄ (żĄ @ @ 8;A,H3żĄ (żĄ @ @ öCC.2.MD.8 Work with time and money. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ (dollars) and ¢ (cents) symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? J0633łĄ @ @ ;LBI3żĄ (żĄ @ @ 3;Ā.J3żĄ (żĄ @ @ wSD.3.M.1.2 (Application) Students are able to count, compare, and solve problems using a collection of coins and bills.;LBK3żĄ (żĄ @ @ M;NFL3żĄ (żĄ @ @ 1.2;MDM3żĄ (żĄ @ @ 1J0633 żĄ @ @ ;XZN3
żÄ (żÄ pw
by end of 3rdJ06 33’żĄ ww;MDO4żĄ (żĄ @ @ MD;LBP4żĄ (żĄ @ @ 8;A,Q4żĄ (żĄ @ @ öCC.2.MD.8 Work with time and money. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ (dollars) and ¢ (cents) symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? J0644łĄ @ @ ;LBR4żĄ (żĄ @ @ 1;Ś^S4żĄ (żĄ @ @ SD.1.M.1.3 (Application) Students are able to use different combinations of pennies, nickels, and dimes to represent money amounts to 25 cents.;LBT4żĄ (żĄ @ @ M;NFU4żĄ (żĄ @ @ 1.3;LBV4żĄ (żĄ @ @ 1J0644 żĄ @ @ ;XZW4
żÄ (żÄ pw
by end of 3rdJ06 44’żĄ ww;MDX5żĄ (żĄ @ @ MD;MDY5żĄ (żĄ @ @ 10;OHZ5żĄ (żĄ @ @ CC.2.MD.10 Represent and interpret data. Draw a picture graph and a bar graph (with singleunit scale) to represent a data set with up to four categories. Solve simple puttogether, takeapart, and compare problems using information presented in a bar graph. J0655łĄ @ @ ;LB[5żĄ (żĄ @ @ 2;¢ī\5żĄ (żĄ @ @ WSD.2.S.1.2 (Application) Students are able to represent data sets in more than one way.;LB]5żĄ (żĄ @ @ S;NF^5żĄ (żĄ @ @ 1.2;LB_5żĄ (żĄ @ @ 0;®`5 żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;XZa5
żÄ (żÄ pw
by end of 3rdJ06 55’żĄ ww;MDb6żĄ (żĄ @ @ MD;MDc6żĄ (żĄ @ @ 10;OHd6żĄ (żĄ @ @ CC.2.MD.10 Represent and interpret data. Draw a picture graph and a bar graph (with singleunit scale) to represent a data set with up to four categories. Solve simple puttogether, takeapart, and compare problems using information presented in a bar graph. J0666łĄ @ @ ;LBe6żĄ (żĄ @ @ 3;ŌRf6żĄ (żĄ @ @ SD.3.S.1.1 (Application) Students are able to ask and answer questions from data represented in bar graphs, pictographs and tally charts.;LBg6żĄ (żĄ @ @ S;NFh6żĄ (żĄ @ @ 1.1;MDi6żĄ (żĄ @ @ 1J0666 żĄ @ @ ;XZj6
żÄ (żÄ pw
by end of 3rdJ06 66’żĄ ww;LBk7żĄ (żĄ @ @ G;LBl7żĄ (żĄ @ @ 1;¬m7żĄ (żĄ @ @ 6CC.2.G.1 Reason with shapes and their attributes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. (Sizes are compared directly or visually, not compared by measuring.)J0677łĄ @ @ ;LBn7żĄ (żĄ @ @ 4;ź~o7żĄ (żĄ @ @ SD.4.G.1.1 (Knowledge) Students are able to identify the following plane and solid figures: pentagon, hexagon, octagon, pyramid, rectangular prism, and cone. ;LBp7żĄ (żĄ @ @ G;NFq7żĄ (żĄ @ @ 1.1;MDr7żĄ (żĄ @ @ 2;øs7 żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;XZt7
żÄ (żÄ pw
by end of 4thJ06 77’żĄ ww;LBu8żĄ (żĄ @ @ G;LBv8żĄ (żĄ @ @ 1;¬w8żĄ (żĄ @ @ 6CC.2.G.1 Reason with shapes and their attributes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. (Sizes are compared directly or visually, not compared by measuring.)J0688łĄ @ @ ;LBx8żĄ (żĄ @ @ 2;Ā.y8żĄ (żĄ @ @ wSD.2.G.2.1 (Knowledge) Students are able to identify geometric figures regardless of position and orientation in space.;LBz8żĄ (żĄ @ @ G;NF{8żĄ (żĄ @ @ 2.1;LB8żĄ (żĄ @ @ 0J0688 żĄ @ @ ;XZ}8
żÄ (żÄ pw
by end of 4thJ06 88’żĄ ww;MD~9żĄ (żĄ @ @ OA;LB9żĄ (żĄ @ @ 1;p9żĄ (żĄ @ @ %CC.3.OA.1 Represent and solve problems involving multiplication and division. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. J0699łĄ @ @ ;LB9żĄ (żĄ @ @ 3;Į,9żĄ (żĄ @ @ vSD.3.A.1.1 (Comprehension) Students are able to explain the relationship between repeated addition and multiplication.;LB9żĄ (żĄ @ @ A;NF9żĄ (żĄ @ @ 1.1;LB
9żĄ (żĄ @ @ 0;®9 żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@9
żÄ (żÄ pwJ06 99’żĄ ww;MD:żĄ (żĄ @ @ OA;LB:żĄ (żĄ @ @ 3;¾:żĄ (żĄ @ @ ?CC.3.OA.3 Represent and solve problems involving multiplication and division. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. J06::łĄ @ @ ;LB:żĄ (żĄ @ @ 4;ŌR:żĄ (żĄ @ @ SD.4.A.3.1 (Application) Students are able to write and solve number sentences that represent onestep word problems using whole numbers.;LB:żĄ (żĄ @ @ A;NF:żĄ (żĄ @ @ 3.1;MD:żĄ (żĄ @ @ 1;®: żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@:
żÄ (żÄ pwJ06 ::’żĄ ww;MD;żĄ (żĄ @ @ OA;LB;żĄ (żĄ @ @ 5;Æ;żĄ (żĄ @ @ dCC.3.OA.5 Understand properties of multiplication and the relationship between multiplication and division. Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15 then 15 × 2 = 30, or by 5 × 2 = 10 then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) (Students need not use formal terms for these properties.)J06;;łĄ @ @ ;LB;żĄ (żĄ @ @ 3;ģ;żĄ (żĄ @ @ ”SD.3.A.1.2 (Knowledge) Students are able to identify special properties of 0 and 1 with respect to arithmetic operations (addition, subtraction, multiplication).;LB;żĄ (żĄ @ @ A;NF;żĄ (żĄ @ @ 1.2;LB;żĄ (żĄ @ @ 0;®; żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@;
żÄ (żÄ pwJ06 ;;’żĄ ww;MD<żĄ (żĄ @ @ OA;LB<żĄ (żĄ @ @ 5;Æ<żĄ (żĄ @ @ dCC.3.OA.5 Understand properties of multiplication and the relationship between multiplication and division. Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15 then 15 × 2 = 30, or by 5 × 2 = 10 then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) (Students need not use formal terms for these properties.)J06<<łĄ @ @ ;LB<żĄ (żĄ @ @ 3;ĻH <żĄ (żĄ @ @ SD.3.A.3.1 (Application) Students are able to use the relationship between multiplication and division to compute and check results.;LB”<żĄ (żĄ @ @ A;NF¢<żĄ (żĄ @ @ 3.1;LB£<żĄ (żĄ @ @ 0J06<< żĄ @ @ ;K@¤<
żÄ (żÄ pwJ06 <<’żĄ ww;MD„=żĄ (żĄ @ @ OA;LB¦=żĄ (żĄ @ @ 5;Æ§=żĄ (żĄ @ @ dCC.3.OA.5 Understand properties of multiplication and the relationship between multiplication and division. Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15 then 15 × 2 = 30, or by 5 × 2 = 10 then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) (Students need not use formal terms for these properties.)J06==łĄ @ @ ;LBØ=żĄ (żĄ @ @ 4;Ć0©=żĄ (żĄ @ @ xSD.4.A.1.2 (Application) Students are able to recognize and use the commutative property of addition and multiplication.;LBŖ=żĄ (żĄ @ @ A;NF«=żĄ (żĄ @ @ 1.2;MD¬=żĄ (żĄ @ @ 1J06== żĄ @ @ ;K@=
żÄ (żÄ pwJ06 ==’żĄ ww;MD®>żĄ (żĄ @ @ OA;LBÆ>żĄ (żĄ @ @ 6;?(°>żĄ (żĄ @ @ ōCC.3.OA.6 Understand properties of multiplication and the relationship between multiplication and division. Understand division as an unknownfactor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. J06>>łĄ @ @ ;LB±>żĄ (żĄ @ @ 3;ĻH²>żĄ (żĄ @ @ SD.3.A.3.1 (Application) Students are able to use the relationship between multiplication and division to compute and check results.;LB³>żĄ (żĄ @ @ A;NF“>żĄ (żĄ @ @ 3.1;LBµ>żĄ (żĄ @ @ 0;®¶> żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@·>
żÄ (żÄ pwJ06 >>’żĄ ww;MDø?żĄ (żĄ @ @ OA;LB¹?żĄ (żĄ @ @ 6;?(ŗ?żĄ (żĄ @ @ ōCC.3.OA.6 Understand properties of multiplication and the relationship between multiplication and division. Understand division as an unknownfactor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. J06??łĄ @ @ ;LB»?żĄ (żĄ @ @ 4;ÓP¼?żĄ (żĄ @ @ SD.4.A.1.3 (Application) Students are able to relate the concepts of addition, subtraction, multiplication, and division to one another.;LB½?żĄ (żĄ @ @ A;NF¾?żĄ (żĄ @ @ 1.3;MDæ?żĄ (żĄ @ @ 1J06?? żĄ @ @ ;K@Ą?
żÄ (żÄ pwJ06 ??’żĄ ww;MDĮ@żĄ (żĄ @ @ OA;LBĀ@żĄ (żĄ @ @ 7;¼Ć@żĄ (żĄ @ @ >CC.3.OA.7 Multiply and divide within 100. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of onedigit numbers.J06@@łĄ @ @ ;LBÄ@żĄ (żĄ @ @ 3;ĻHÅ@żĄ (żĄ @ @ SD.3.A.3.1 (Application) Students are able to use the relationship between multiplication and division to compute and check results.;LBĘ@żĄ (żĄ @ @ A;NFĒ@żĄ (żĄ @ @ 3.1;LBČ@żĄ (żĄ @ @ 0;®É@ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@Ź@
żÄ (żÄ pwJ06 @@’żĄ ww;MDĖAżĄ (żĄ @ @ OA;LBĢAżĄ (żĄ @ @ 7;¼ĶAżĄ (żĄ @ @ >CC.3.OA.7 Multiply and divide within 100. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of onedigit numbers.J06AAłĄ @ @ ;LBĪAżĄ (żĄ @ @ 3;¦öĻAżĄ (żĄ @ @ [SD.3.A.4.2 Students are able to use number patterns and relationships to learn basic facts.;LBŠAżĄ (żĄ @ @ A;NFŃAżĄ (żĄ @ @ 4.2;LBŅAżĄ (żĄ @ @ 0J06AA żĄ @ @ ;K@ÓA
żÄ (żÄ pwJ06 AA’żĄ ww;MDŌBżĄ (żĄ @ @ OA;LBÕBżĄ (żĄ @ @ 7;¼ÖBżĄ (żĄ @ @ >CC.3.OA.7 Multiply and divide within 100. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of onedigit numbers.J06BBłĄ @ @ ;LB×BżĄ (żĄ @ @ 3;ŠJŲBżĄ (żĄ @ @
SD.3.N.2.1 (Application) Students are able to add and subtract whole numbers up to three digits and multiply two digits by one digit.;LBŁBżĄ (żĄ @ @ N;NFŚBżĄ (żĄ @ @ 2.1;LBŪBżĄ (żĄ @ @ 0J06BB żĄ @ @ ;K@ÜB
żÄ (żÄ pwJ06 BB’żĄ ww;MDŻCżĄ (żĄ @ @ OA;LBŽCżĄ (żĄ @ @ 8;®ßCżĄ (żĄ @ @ cCC.3.OA.8 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Solve twostep word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).)J06CCłĄ @ @ ;LBąCżĄ (żĄ @ @ 5;ÖVįCżĄ (żĄ @ @ SD.5.A.3.1 (Application) Students are able to, using whole numbers, write and solve number sentences that represent twostep word problems.;LBāCżĄ (żĄ @ @ A;NFćCżĄ (żĄ @ @ 3.1;MDäCżĄ (żĄ @ @ 2;øåC żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@ęC
żÄ (żÄ pwJ06 CC’żĄ ww;MDēDżĄ (żĄ @ @ OA;LBčDżĄ (żĄ @ @ 8;®éDżĄ (żĄ @ @ cCC.3.OA.8 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Solve twostep word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).)J06DDłĄ @ @ ;LBźDżĄ (żĄ @ @ 4;ßhėDżĄ (żĄ @ @ SD.4.N.3.1 (Application) Students are able to estimate sums and differences in whole numbers and money to determine if a given answer is reasonable.;LBģDżĄ (żĄ @ @ N;NFķDżĄ (żĄ @ @ 3.1;MDīDżĄ (żĄ @ @ 1J06DD żĄ @ @ ;K@ļD
żÄ (żÄ pwJ06 DD’żĄ ww;MDšEżĄ (żĄ @ @ OA;LBńEżĄ (żĄ @ @ 9;ĻHņEżĄ (żĄ @ @ CC.3.OA.9 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. J06EEłĄ @ @ ;LBóEżĄ (żĄ @ @ 3;ĪōEżĄ (żĄ @ @ GSD.3.A.4.1 (Comprehension) Students are able to extend linear patterns.;LBõEżĄ (żĄ @ @ A;NFöEżĄ (żĄ @ @ 4.1;LB÷EżĄ (żĄ @ @ 0;®ųE żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@łE
żÄ (żÄ pwJ06 EE’żĄ ww;MDśFżĄ (żĄ @ @ OA;LBūFżĄ (żĄ @ @ 9;ĻHüFżĄ (żĄ @ @ CC.3.OA.9 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. J06FFłĄ @ @ ;LBżFżĄ (żĄ @ @ 3;¦öžFżĄ (żĄ @ @ [SD.3.A.4.2 Students are able to use number patterns and relationships to learn basic facts.;LB’FżĄ (żĄ @ @ A;NFFżĄ (żĄ @ @ 4.2;LBFżĄ (żĄ @ @ 0J06FF żĄ @ @ ;K@F
żÄ (żÄ pwJ06 FF’żĄ ww;NFGżĄ (żĄ @ @ NBT;LBGżĄ (żĄ @ @ 1;°GżĄ (żĄ @ @ øCC.3.NBT.1 Use place value understanding and properties of operations to perform multidigit arithmetic. Use place value understanding to round whole numbers to the nearest 10 or 100.J06GGłĄ @ @ ;LBGżĄ (żĄ @ @ 3;ānGżĄ (żĄ @ @ SD.3.N.3.1 (Application) Students are able to round twodigit whole numbers to the nearest tens, and threedigit whole numbers to the nearest hundreds.;LBGżĄ (żĄ @ @ N;NF GżĄ (żĄ @ @ 3.1;LB
GżĄ (żĄ @ @ 0;øG żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@G
żÄ (żÄ pwJ06 GG’żĄ ww;NF
HżĄ (żĄ @ @ NBT;LBHżĄ (żĄ @ @ 2;ŗHżĄ (żĄ @ @ =CC.3.NBT.2 Use place value understanding and properties of operations to perform multidigit arithmetic. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. (A range of algorithms may be used.)J06HHłĄ @ @ ;LBHżĄ (żĄ @ @ 3;ŠJHżĄ (żĄ @ @
SD.3.N.2.1 (Application) Students are able to add and subtract whole numbers up to three digits and multiply two digits by one digit.;LBHżĄ (żĄ @ @ N;NFHżĄ (żĄ @ @ 2.1;LBHżĄ (żĄ @ @ 0;®H żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@H
żÄ (żÄ pwJ06 HH’żĄ ww;NFIżĄ (żĄ @ @ NBT;LBIżĄ (żĄ @ @ 3;zIżĄ (żĄ @ @ /CC.3.NBT.3 Use place value understanding and properties of operations to perform multidigit arithmetic. Multiply onedigit whole numbers by multiples of 10 in the range 1090 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. (A range of algorithms may be used.)J06IIłĄ @ @ ;LBIżĄ (żĄ @ @ 3;ŠJIżĄ (żĄ @ @
SD.3.N.2.1 (Application) Students are able to add and subtract whole numbers up to three digits and multiply two digits by one digit.;LBIżĄ (żĄ @ @ N;NFIżĄ (żĄ @ @ 2.1;LBIżĄ (żĄ @ @ 0;®I żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@ I
żÄ (żÄ pwJ06 II’żĄ ww;MD!JżĄ (żĄ @ @ NF;LB"JżĄ (żĄ @ @ 1;ā#JżĄ (żĄ @ @ QCC.3.NF.1 Develop understanding of fractions as numbers. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)J06JJłĄ @ @ ;LB$JżĄ (żĄ @ @ 3;¬%JżĄ (żĄ @ @ aSD.3.N.1.3 (Knowledge) Students are able to name and write fractions from visual representations.;LB&JżĄ (żĄ @ @ N;NF'JżĄ (żĄ @ @ 1.3;LB(JżĄ (żĄ @ @ 0;®)J żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@*J
żÄ (żÄ pwJ06 JJ’żĄ ww;MD+KżĄ (żĄ @ @ NF;LB,KżĄ (żĄ @ @ 2;LBKżĄ (żĄ @ @ CC.3.NF.2 Develop understanding of fractions as numbers. Understand a fraction as a number on the number line; represent fractions on a number line diagram. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)J06KKłĄ @ @ ;LB.KżĄ (żĄ @ @ 4;är/KżĄ (żĄ @ @ SD.4.N.1.3 (Comprehension) Students are able to use a number line to compare numerical value of fractions or mixed numbers (fourths, halves, and thirds).;LB0KżĄ (żĄ @ @ N;NF1KżĄ (żĄ @ @ 1.3;MD2KżĄ (żĄ @ @ 1;ø3K żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@4K
żÄ (żÄ pwJ06 KK’żĄ ww;MD5LżĄ (żĄ @ @ NF;MD6LżĄ (żĄ @ @ 3a;(ś7LżĄ (żĄ @ @ ŻCC.3.NF.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)J06LLłĄ @ @ ;LB8LżĄ (żĄ @ @ 4;är9LżĄ (żĄ @ @ SD.4.N.1.3 (Comprehension) Students are able to use a number line to compare numerical value of fractions or mixed numbers (fourths, halves, and thirds).;LB:LżĄ (żĄ @ @ N;NF;LżĄ (żĄ @ @ 1.3;MD<LżĄ (żĄ @ @ 1;ø=L żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@>L
żÄ (żÄ pwJ06 LL’żĄ ww;MD?MżĄ (żĄ @ @ NF;MD@MżĄ (żĄ @ @ 3b;\bAMżĄ (żĄ @ @ CC.3.NF.3b Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3), Explain why the fractions are equivalent, e.g., by using a visual fraction model. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)J06MMłĄ @ @ ;LBBMżĄ (żĄ @ @ 3;¬CMżĄ (żĄ @ @ aSD.3.N.1.3 (Knowledge) Students are able to name and write fractions from visual representations.;LBDMżĄ (żĄ @ @ N;NFEMżĄ (żĄ @ @ 1.3;LBFMżĄ (żĄ @ @ 0;®GM żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@HM
żÄ (żÄ pwJ06 MM’żĄ ww;MDINżĄ (żĄ @ @ MD;LBJNżĄ (żĄ @ @ 1;ØśKNżĄ (żĄ @ @ ]CC.3.MD.1 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
J06NNłĄ @ @ ;LBLNżĄ (żĄ @ @ 3;ŌRMNżĄ (żĄ @ @ SD.3.M.1.1 (Knowledge) Students are able to read and tell time before and after the hour within fiveminute intervals on an analog clock.;LBNNżĄ (żĄ @ @ M;NFONżĄ (żĄ @ @ 1.1;LBPNżĄ (żĄ @ @ 0;®QN żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@RN
żÄ (żÄ pwJ06 NN’żĄ ww;MDSOżĄ (żĄ @ @ MD;LBTOżĄ (żĄ @ @ 1;ØśUOżĄ (żĄ @ @ ]CC.3.MD.1 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
J06OOłĄ @ @ ;LBVOżĄ (żĄ @ @ 4;®WOżĄ (żĄ @ @ cSD.4.M.1.1 (Knowledge) Students are able to identify equivalent periods of time and solve problems.;LBXOżĄ (żĄ @ @ M;NFYOżĄ (żĄ @ @ 1.1;MDZOżĄ (żĄ @ @ 1J06OO żĄ @ @ ;K@[O
żÄ (żÄ pwJ06 OO’żĄ ww;MD\PżĄ (żĄ @ @ MD;LB]PżĄ (żĄ @ @ 1;Øś^PżĄ (żĄ @ @ ]CC.3.MD.1 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
J06PPłĄ @ @ ;LB_PżĄ (żĄ @ @ 2;ĻH`PżĄ (żĄ @ @ SD.2.M.1.1 (Knowledge) Students are able to tell time to the minute using digital and analog clocks and relate time to daily events.;LBaPżĄ (żĄ @ @ M;NFbPżĄ (żĄ @ @ 1.1;LBcPżĄ (żĄ @ @ 1J06PP żĄ @ @ ;K@dP
żÄ (żÄ pwJ06 PP’żĄ ww;MDeQżĄ (żĄ @ @ MD;LBfQżĄ (żĄ @ @ 2;g\gQżĄ (żĄ @ @ CC.3.MD.2 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems (problems involving notions of times as much. )J06QQłĄ @ @ ;LBhQżĄ (żĄ @ @ 3;ĻHiQżĄ (żĄ @ @ SD.3.M.1.3 (Knowledge) Students are able to identify U.S. Customary units of length (feet), weight (pounds), and capacity (gallons).;LBjQżĄ (żĄ @ @ M;NFkQżĄ (żĄ @ @ 1.3;LBlQżĄ (żĄ @ @ 0;®mQ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@nQ
żÄ (żÄ pwJ06 QQ’żĄ ww;MDoRżĄ (żĄ @ @ MD;LBpRżĄ (żĄ @ @ 2;g\qRżĄ (żĄ @ @ CC.3.MD.2 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems (problems involving notions of times as much. )J06RRłĄ @ @ ;LBrRżĄ (żĄ @ @ 4;±sRżĄ (żĄ @ @ fSD.4.M.1.3 (Application) Students are able to use scales of length, temperature, capacity, and weight.;LBtRżĄ (żĄ @ @ M;NFuRżĄ (żĄ @ @ 1.3;MDvRżĄ (żĄ @ @ 1J06RR żĄ @ @ ;K@wR
żÄ (żÄ pwJ06 RR’żĄ ww;MDxSżĄ (żĄ @ @ MD;LBySżĄ (żĄ @ @ 2;g\zSżĄ (żĄ @ @ CC.3.MD.2 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ż’’’ż’’’
”¢£¤„¦§Ø©Ŗ«¬®Æ°±²³“µ¶·ø¹ŗ»¼½¾æĄĮĀĆÄÅĘĒČÉŹĖĢĶĪĻŠŃŅÓŌÕÖ×ŲŁŚŪÜŻŽßąįāćäåęēčéźėģķīļšńņóōõö÷ųłśūüżž’ the problem. (Excludes multiplicative comparison problems (problems involving notions of times as much. )J06SSłĄ @ @ ;LB{SżĄ (żĄ @ @ 5;ÓPSżĄ (żĄ @ @ SD.5.M.1.4 (Application) Students are able to use appropriate tools to measure length, weight, temperature, and area in problem solving.;LB}SżĄ (żĄ @ @ M;NF~SżĄ (żĄ @ @ 1.4;MDSżĄ (żĄ @ @ 2J06SS żĄ @ @ ;K@S
żÄ (żÄ pwJ06 SS’żĄ ww;MDTżĄ (żĄ @ @ MD;LBTżĄ (żĄ @ @ 3;üTżĄ (żĄ @ @ ^CC.3.MD.3 Represent and interpret data. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep how many more and how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.J06TTłĄ @ @ ;LBTżĄ (żĄ @ @ 3;ŌR
TżĄ (żĄ @ @ SD.3.S.1.1 (Application) Students are able to ask and answer questions from data represented in bar graphs, pictographs and tally charts.;LBTżĄ (żĄ @ @ S;NFTżĄ (żĄ @ @ 1.1;LBTżĄ (żĄ @ @ 0;øT żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@T
żÄ (żÄ pwJ06 TT’żĄ ww;MDUżĄ (żĄ @ @ MD;LBUżĄ (żĄ @ @ 3;üUżĄ (żĄ @ @ ^CC.3.MD.3 Represent and interpret data. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep how many more and how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.J06UUłĄ @ @ ;LBUżĄ (żĄ @ @ 3;Ä2UżĄ (żĄ @ @ ySD.3.S.1.2 (Application) Students are able to gather data and use the information to complete a scaled and labeled graph.;LBUżĄ (żĄ @ @ S;NFUżĄ (żĄ @ @ 1.2;LBUżĄ (żĄ @ @ 0J06UU żĄ @ @ ;K@U
żÄ (żÄ pwJ06 UU’żĄ ww;MDVżĄ (żĄ @ @ MD;LBVżĄ (żĄ @ @ 4;ujVżĄ (żĄ @ @ CC.3.MD.4 Represent and interpret data. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters.J06VVłĄ @ @ ;LBVżĄ (żĄ @ @ 3;āVżĄ (żĄ @ @ QSD.3.M.1.5 (Knowledge) Students are able to measure length to the nearest ½ inch.;LBVżĄ (żĄ @ @ M;NFVżĄ (żĄ @ @ 1.5;LBVżĄ (żĄ @ @ 0;®V żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@V
żÄ (żÄ pwJ06 VV’żĄ ww;MDWżĄ (żĄ @ @ MD;LBWżĄ (żĄ @ @ 4;uj WżĄ (żĄ @ @ CC.3.MD.4 Represent and interpret data. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters.J06WWłĄ @ @ ;LB”WżĄ (żĄ @ @ 4;¦ö¢WżĄ (żĄ @ @ [SD.4.M.1.4 (Comprehension) Students are able to measure length to the nearest quarter inch.;LB£WżĄ (żĄ @ @ M;NF¤WżĄ (żĄ @ @ 1.4;MD„WżĄ (żĄ @ @ 1J06WW żĄ @ @ ;K@¦W
żÄ (żÄ pwJ06 WW’żĄ ww;MD§XżĄ (żĄ @ @ MD;LBØXżĄ (żĄ @ @ 7;ų©XżĄ (żĄ @ @ CC.3.MD.7 Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Relate area to the operations of multiplication and addition.J06XXłĄ @ @ ;LBŖXżĄ (żĄ @ @ 6;ĶD«XżĄ (żĄ @ @ SD.6.M.1.2 (Comprehension) Students are able to find the perimeter and area of squares and rectangles (whole number measurements).;LB¬XżĄ (żĄ @ @ M;NFXżĄ (żĄ @ @ 1.2;MD®XżĄ (żĄ @ @ 3;®ÆX żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@°X
żÄ (żÄ pwJ06 XX’żĄ ww;MD±YżĄ (żĄ @ @ MD;LB²YżĄ (żĄ @ @ 8;ė³YżĄ (żĄ @ @ CC.3.MD.8 Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different area or with the same area and different perimeter.J06YYłĄ @ @ ;LB“YżĄ (żĄ @ @ 6;ĶDµYżĄ (żĄ @ @ SD.6.M.1.2 (Comprehension) Students are able to find the perimeter and area of squares and rectangles (whole number measurements).;LB¶YżĄ (żĄ @ @ M;NF·YżĄ (żĄ @ @ 1.2;MDøYżĄ (żĄ @ @ 3;®¹Y żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@ŗY
żÄ (żÄ pwJ06 YY’żĄ ww;LB»ZżĄ (żĄ @ @ G;LB¼ZżĄ (żĄ @ @ 1;ū ½ZżĄ (żĄ @ @ °CC.3.G.1 Reason with shapes and their attributes. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.J06ZZłĄ @ @ ;LB¾ZżĄ (żĄ @ @ 3;śæZżĄ (żĄ @ @ ÆSD.3.G.1.1 (Comprehension) Students are able to recognize and compare the following plane and solid geometric figures: square, rectangle, triangle, cube, sphere, and cylinder.;LBĄZżĄ (żĄ @ @ G;NFĮZżĄ (żĄ @ @ 1.1;LBĀZżĄ (żĄ @ @ 0;®ĆZ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@ÄZ
żÄ (żÄ pwJ06 ZZ’żĄ ww;LBÅ[żĄ (żĄ @ @ G;LBĘ[żĄ (żĄ @ @ 1;ū Ē[żĄ (żĄ @ @ °CC.3.G.1 Reason with shapes and their attributes. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.J06[[łĄ @ @ ;LBČ[żĄ (żĄ @ @ 3;Å4É[żĄ (żĄ @ @ zSD.3.G.2.1 (Comprehension) Students are able to demonstrate relationships between figures using similarity and congruence.;LBŹ[żĄ (żĄ @ @ G;NFĖ[żĄ (żĄ @ @ 2.1;LBĢ[żĄ (żĄ @ @ 0J06[[ żĄ @ @ ;K@Ķ[
żÄ (żÄ pwJ06 [[’żĄ ww;LBĪ\żĄ (żĄ @ @ G;LBĻ\żĄ (żĄ @ @ 1;ū Š\żĄ (żĄ @ @ °CC.3.G.1 Reason with shapes and their attributes. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.J06\\łĄ @ @ ;LBŃ\żĄ (żĄ @ @ 4;ź~Ņ\żĄ (żĄ @ @ SD.4.G.1.1 (Knowledge) Students are able to identify the following plane and solid figures: pentagon, hexagon, octagon, pyramid, rectangular prism, and cone. ;LBÓ\żĄ (żĄ @ @ G;NFŌ\żĄ (żĄ @ @ 1.1;MDÕ\żĄ (żĄ @ @ 1J06\\ żĄ @ @ ;K@Ö\
żÄ (żÄ pwJ06 \\’żĄ ww;LB×]żĄ (żĄ @ @ G;LBŲ]żĄ (żĄ @ @ 1;ū Ł]żĄ (żĄ @ @ °CC.3.G.1 Reason with shapes and their attributes. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.J06]]łĄ @ @ ;LBŚ]żĄ (żĄ @ @ 4;ŠJŪ]żĄ (żĄ @ @
SD.4.G.2.1 (Comprehension) Students are able to compare geometric figures using size, shape, orientation, congruence, and similarity.;LBÜ]żĄ (żĄ @ @ G;NFŻ]żĄ (żĄ @ @ 2.1;MDŽ]żĄ (żĄ @ @ 1J06]] żĄ @ @ ;K@ß]
żÄ (żÄ pwJ06 ]]’żĄ ww;LBą^żĄ (żĄ @ @ G;LBį^żĄ (żĄ @ @ 2;j~ā^żĄ (żĄ @ @ CC.3.G.2 Reason with shapes and their attributes. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part is 1/4 of the area of the shape.J06^^łĄ @ @ ;LBć^żĄ (żĄ @ @ 3;¬ä^żĄ (żĄ @ @ aSD.3.N.1.3 (Knowledge) Students are able to name and write fractions from visual representations.;LBå^żĄ (żĄ @ @ N;NFę^żĄ (żĄ @ @ 1.3;LBē^żĄ (żĄ @ @ 0;øč^ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@é^
żÄ (żÄ pwJ06 ^^’żĄ ww;MDź_żĄ (żĄ @ @ OA;LBė_żĄ (żĄ @ @ 3;¶ģ_żĄ (żĄ @ @ »CC.4.OA.3 Use the four operations with whole numbers to solve problems. Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.J06__łĄ @ @ ;LBķ_żĄ (żĄ @ @ 4;ŌRī_żĄ (żĄ @ @ SD.4.A.3.1 (Application) Students are able to write and solve number sentences that represent onestep word problems using whole numbers.;LBļ_żĄ (żĄ @ @ A;NFš_żĄ (żĄ @ @ 3.1;LBń_żĄ (żĄ @ @ 0;øņ_ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@ó_
żÄ (żÄ pwJ06 __’żĄ ww;MDō`żĄ (żĄ @ @ OA;LBõ`żĄ (żĄ @ @ 3;¶ö`żĄ (żĄ @ @ »CC.4.OA.3 Use the four operations with whole numbers to solve problems. Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.J06``łĄ @ @ ;LB÷`żĄ (żĄ @ @ 4;ßhų`żĄ (żĄ @ @ SD.4.N.3.1 (Application) Students are able to estimate sums and differences in whole numbers and money to determine if a given answer is reasonable.;LBł`żĄ (żĄ @ @ N;NFś`żĄ (żĄ @ @ 3.1;LBū`żĄ (żĄ @ @ 0J06`` żĄ @ @ ;K@ü`
żÄ (żÄ pwJ06 ``’żĄ ww;MDżażĄ (żĄ @ @ OA;LBžażĄ (żĄ @ @ 3;¶’ażĄ (żĄ @ @ »CC.4.OA.3 Use the four operations with whole numbers to solve problems. Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.J06aałĄ @ @ ;LBażĄ (żĄ @ @ 3;¼"ażĄ (żĄ @ @ qSD.3.A.2.2 (Application) Students are able to solve problems involving addition and subtraction of whole numbers.;LBażĄ (żĄ @ @ A;NFażĄ (żĄ @ @ 2.2;LBażĄ (żĄ @ @ 1J06aa żĄ @ @ ;K@a
żÄ (żÄ pwJ06 aa’żĄ ww;MDbżĄ (żĄ @ @ OA;LBbżĄ (żĄ @ @ 3;¶bżĄ (żĄ @ @ »CC.4.OA.3 Use the four operations with whole numbers to solve problems. Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.J06bbłĄ @ @ ;LB bżĄ (żĄ @ @ 5;Øś
bżĄ (żĄ @ @ ]SD.5.A.1.1 (Application) Students are able to use a variable to write an addition expression.;LBbżĄ (żĄ @ @ A;NFbżĄ (żĄ @ @ 1.1;MD
bżĄ (żĄ @ @ 1J06bb żĄ @ @ ;K@b
żÄ (żÄ pwJ06 bb’żĄ ww;MDcżĄ (żĄ @ @ OA;LBcżĄ (żĄ @ @ 3;¶cżĄ (żĄ @ @ »CC.4.OA.3 Use the four operations with whole numbers to solve problems. Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.J06ccłĄ @ @ ;LBcżĄ (żĄ @ @ 5;ŅNcżĄ (żĄ @ @ SD.5.A.2.1 (Application) Students are able to write onestep first degree equations using the set of whole numbers and find a solution.;LBcżĄ (żĄ @ @ A;NFcżĄ (żĄ @ @ 2.1;MDcżĄ (żĄ @ @ 1J06cc żĄ @ @ ;K@c
żÄ (żÄ pwJ06 cc’żĄ ww;MDdżĄ (żĄ @ @ OA;LBdżĄ (żĄ @ @ 3;¶dżĄ (żĄ @ @ »CC.4.OA.3 Use the four operations with whole numbers to solve problems. Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.J06ddłĄ @ @ ;LBdżĄ (żĄ @ @ 5;ü¢dżĄ (żĄ @ @ ±SD.5.N.3.1 (Application) Students are able to use different estimation strategies to solve problems involving whole numbers, decimals, and fractions to the nearest whole number.;LBdżĄ (żĄ @ @ N;NFdżĄ (żĄ @ @ 3.1;MDdżĄ (żĄ @ @ 1J06dd żĄ @ @ ;K@ d
żÄ (żÄ pwJ06 dd’żĄ ww;MD!eżĄ (żĄ @ @ OA;LB"eżĄ (żĄ @ @ 3;¶#eżĄ (żĄ @ @ »CC.4.OA.3 Use the four operations with whole numbers to solve problems. Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.J06eełĄ @ @ ;LB$eżĄ (żĄ @ @ 5;ÖV%eżĄ (żĄ @ @ SD.5.A.3.1 (Application) Students are able to, using whole numbers, write and solve number sentences that represent twostep word problems.;LB&eżĄ (żĄ @ @ A;NF'eżĄ (żĄ @ @ 3.1;MD(eżĄ (żĄ @ @ 1J06ee żĄ @ @ ;K@)e
żÄ (żÄ pwJ06 ee’żĄ ww;MD*fżĄ (żĄ @ @ OA;LB+fżĄ (żĄ @ @ 4;ø,fżĄ (żĄ @ @ mCC.4.OA.4 Gain familiarity with factors and multiples. Find all factor pairs for a whole number in the range 1100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1100 is a multiple of a given onedigit number. Determine whether a given whole number in the range 1100 is prime or composite.J06ffłĄ @ @ ;LBfżĄ (żĄ @ @ 4;¦ö.fżĄ (żĄ @ @ [SD.4.N.1.2 (Comprehension) Students are able to find multiples of whole numbers through 12.;LB/fżĄ (żĄ @ @ N;NF0fżĄ (żĄ @ @ 1.2;LB1fżĄ (żĄ @ @ 0;®2f żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@3f
żÄ (żÄ pwJ06 ff’żĄ ww;MD4gżĄ (żĄ @ @ OA;LB5gżĄ (żĄ @ @ 4;ø6gżĄ (żĄ @ @ mCC.4.OA.4 Gain familiarity with factors and multiples. Find all factor pairs for a whole number in the range 1100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1100 is a multiple of a given onedigit number. Determine whether a given whole number in the range 1100 is prime or composite.J06ggłĄ @ @ ;LB7gżĄ (żĄ @ @ 5;¼"8gżĄ (żĄ @ @ qSD.5.N.1.2 (Comprehension) Students are able to find prime, composite, and factors of whole numbers from 1 to 50.;LB9gżĄ (żĄ @ @ N;NF:gżĄ (żĄ @ @ 1.2;MD;gżĄ (żĄ @ @ 1J06gg żĄ @ @ ;K@<g
żÄ (żÄ pwJ06 gg’żĄ ww;MD=hżĄ (żĄ @ @ OA;LB>hżĄ (żĄ @ @ 5;Ćø?hżĄ (żĄ @ @ ¼CC.4.OA.5 Generate and analyze patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule Add 3 and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. J06hhłĄ @ @ ;LB@hżĄ (żĄ @ @ 4;Ä2AhżĄ (żĄ @ @ ySD.4.A.4.1 (Application) Students are able to solve problems involving pattern identification and completion of patterns.;LBBhżĄ (żĄ @ @ A;NFChżĄ (żĄ @ @ 4.1;LBDhżĄ (żĄ @ @ 0;®Eh żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@Fh
żÄ (żÄ pwJ06 hh’żĄ ww;NFGiżĄ (żĄ @ @ NBT;LBHiżĄ (żĄ @ @ 2;ńIiżĄ (żĄ @ @ ¦CC.4.NBT.2 Generalize place value understanding for multidigit whole numbers. Read and write multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)J06iiłĄ @ @ ;LBJiżĄ (żĄ @ @ 4;É<KiżĄ (żĄ @ @ ~SD.4.A.2.1 (Comprehension) Students are able to select appropriate relational symbols (<, >, =) to make number sentences true.;LBLiżĄ (żĄ @ @ A;NFMiżĄ (żĄ @ @ 2.1;LBNiżĄ (żĄ @ @ 0;øOi żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@Pi
żÄ (żÄ pwJ06 ii’żĄ ww;NFQjżĄ (żĄ @ @ NBT;LBRjżĄ (żĄ @ @ 2;ńSjżĄ (żĄ @ @ ¦CC.4.NBT.2 Generalize place value understanding for multidigit whole numbers. Read and write multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)J06jjłĄ @ @ ;LBTjżĄ (żĄ @ @ 4;¹UjżĄ (żĄ @ @ nSD.4.N.1.1 (Comprehension) Students are able to read, write, order, and compare numbers from .01 to 1,000,000.;LBVjżĄ (żĄ @ @ N;NFWjżĄ (żĄ @ @ 1.1;LBXjżĄ (żĄ @ @ 0J06jj żĄ @ @ ;K@Yj
żÄ (żÄ pwJ06 jj’żĄ ww;NFZkżĄ (żĄ @ @ NBT;LB[kżĄ (żĄ @ @ 3;NF\kżĄ (żĄ @ @ CC.4.NBT.3 Generalize place value understanding for multidigit whole numbers. Use place value understanding to round multidigit whole numbers to any place. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)J06kkłĄ @ @ ;LB]kżĄ (żĄ @ @ 3;ān^kżĄ (żĄ @ @ SD.3.N.3.1 (Application) Students are able to round twodigit whole numbers to the nearest tens, and threedigit whole numbers to the nearest hundreds.;LB_kżĄ (żĄ @ @ N;NF`kżĄ (żĄ @ @ 3.1;LBakżĄ (żĄ @ @ 1;øbk żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@ck
żÄ (żÄ pwJ06 kk’żĄ ww;NFdlżĄ (żĄ @ @ NBT;LBelżĄ (żĄ @ @ 4;ÄflżĄ (żĄ @ @ BCC.4.NBT.4 Use place value understanding and properties of operations to perform multidigit arithmetic. Fluently add and subtract multidigit whole numbers using the standard algorithm. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.)J06llłĄ @ @ ;LBglżĄ (żĄ @ @ 3;ŠJhlżĄ (żĄ @ @
SD.3.N.2.1 (Application) Students are able to add and subtract whole numbers up to three digits and multiply two digits by one digit.;LBilżĄ (żĄ @ @ N;NFjlżĄ (żĄ @ @ 2.1;LBklżĄ (żĄ @ @ 1;øll żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@ml
żÄ (żÄ pwJ06 ll’żĄ ww;NFnmżĄ (żĄ @ @ NBT;LBomżĄ (żĄ @ @ 5;UTpmżĄ (żĄ @ @
CC.4.NBT.5 Use place value understanding and properties of operations to perform multidigit arithmetic. Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.)J06mmłĄ @ @ ;LBqmżĄ (żĄ @ @ 5;Ć0rmżĄ (żĄ @ @ xSD.5.A.1.2 (Application) Students are able to recognize and use the associative property of addition and multiplication.;LBsmżĄ (żĄ @ @ A;NFtmżĄ (żĄ @ @ 1.2;MDumżĄ (żĄ @ @ 1;®vm żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@wm
żÄ (żÄ pwJ06 mm’żĄ ww;NFxnżĄ (żĄ @ @ NBT;LBynżĄ (żĄ @ @ 5;UTznżĄ (żĄ @ @
CC.4.NBT.5 Use place value understanding and properties of operations to perform multidigit arithmetic. Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.)J06nnłĄ @ @ ;LB{nżĄ (żĄ @ @ 4;ŽfnżĄ (żĄ @ @ SD.4.N.2.1 (Application) Students are able to find the products of twodigit factors and quotient of two natural numbers using a onedigit divisor.;LB}nżĄ (żĄ @ @ N;NF~nżĄ (żĄ @ @ 2.1;LBnżĄ (żĄ @ @ 0J06nn żĄ @ @ ;K@n
żÄ (żÄ pwJ06 nn’żĄ ww;NFożĄ (żĄ @ @ NBT;LBożĄ (żĄ @ @ 6;
“ożĄ (żĄ @ @ :CC.4.NBT.6 Use place value understanding and properties of operations to perform multidigit arithmetic. Find wholenumber quotients and remainders with up to fourdigit dividends and onedigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.)J06oołĄ @ @ ;LBożĄ (żĄ @ @ 4;Žf
ożĄ (żĄ @ @ SD.4.N.2.1 (Application) Students are able to find the products of twodigit factors and quotient of two natural numbers using a onedigit divisor.;LBożĄ (żĄ @ @ N;NFożĄ (żĄ @ @ 2.1;LBożĄ (żĄ @ @ 0;®o żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@o
żÄ (żÄ pwJ06 oo’żĄ ww;MDpżĄ (żĄ @ @ NF;LBpżĄ (żĄ @ @ 1;(śpżĄ (żĄ @ @ ŻCC.4.NF.1 Extend understanding of fraction equivalence and ordering. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)J06ppłĄ @ @ ;LBpżĄ (żĄ @ @ 5;ĶDpżĄ (żĄ @ @ SD.5.N.2.2 (Application) Students are able to determine equivalent fractions including simplification (lowest terms of fractions).;LBpżĄ (żĄ @ @ N;NFpżĄ (żĄ @ @ 2.2;MDpżĄ (żĄ @ @ 1;øp żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@p
żÄ (żÄ pwJ06 pp’żĄ ww;MDqżĄ (żĄ @ @ NF;LBqżĄ (żĄ @ @ 2;ŠqżĄ (żĄ @ @ HCC.4.NF.2 Extend understanding of fraction equivalence and ordering. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)J06qqłĄ @ @ ;LBqżĄ (żĄ @ @ 4;ärqżĄ (żĄ @ @ SD.4.N.1.3 (Comprehension) Students are able to use a number line to compare numerical value of fractions or mixed numbers (fourths, halves, and thirds).;LBqżĄ (żĄ @ @ N;NFqżĄ (żĄ @ @ 1.3;LBqżĄ (żĄ @ @ 0;®q żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@q
żÄ (żÄ pwJ06 qq’żĄ ww;MDrżĄ (żĄ @ @ NF;LB rżĄ (żĄ @ @ 5;é”rżĄ (żĄ @ @ CC.4.NF.5 Understand decimal notation for fractions, and compare decimal fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100 and add 3/10 + 4/100 = 34/100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)J06rrłĄ @ @ ;LB¢rżĄ (żĄ @ @ 5;čz£rżĄ (żĄ @ @ SD.5.N.1.3 (Knowledge) Students are able to identify alternative representations of fractions and decimals involving tenths, fourths, halves, and hundredths.;LB¤rżĄ (żĄ @ @ N;NF„rżĄ (żĄ @ @ 1.3;MD¦rżĄ (żĄ @ @ 1;®§r żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@Ør
żÄ (żÄ pwJ06 rr’żĄ ww;MD©sżĄ (żĄ @ @ NF;LBŖsżĄ (żĄ @ @ 5;é«sżĄ (żĄ @ @ CC.4.NF.5 Understand decimal notation for fractions, and compare decimal fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100 and add 3/10 + 4/100 = 34/100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)J06ssłĄ @ @ ;LB¬sżĄ (żĄ @ @ 5;ĶDsżĄ (żĄ @ @ SD.5.N.2.2 (Application) Students are able to determine equivalent fractions including simplification (lowest terms of fractions).;LB®sżĄ (żĄ @ @ N;NFÆsżĄ (żĄ @ @ 2.2;MD°sżĄ (żĄ @ @ 1J06ss żĄ @ @ ;K@±s
żÄ (żÄ pwJ06 ss’żĄ ww;MD²tżĄ (żĄ @ @ NF;LB³tżĄ (żĄ @ @ 6;Ą*“tżĄ (żĄ @ @ uCC.4.NF.6 Understand decimal notation for fractions, and compare decimal fractions. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)J06ttłĄ @ @ ;LBµtżĄ (żĄ @ @ 5;čz¶tżĄ (żĄ @ @ SD.5.N.1.3 (Knowledge) Students are able to identify alternative representations of fractions and decimals involving tenths, fourths, halves, and hundredths.;LB·tżĄ (żĄ @ @ N;NFøtżĄ (żĄ @ @ 1.3;MD¹tżĄ (żĄ @ @ 1;øŗt żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@»t
żÄ (żÄ pwJ06 tt’żĄ ww;MD¼użĄ (żĄ @ @ NF;LB½użĄ (żĄ @ @ 7;0
¾użĄ (żĄ @ @ åCC.4.NF.7 Understand decimal notation for fractions, and compare decimal fractions. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons comparisons are valid only when two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)J06uułĄ @ @ ;LBæużĄ (żĄ @ @ 4;É<ĄużĄ (żĄ @ @ ~SD.4.A.2.1 (Comprehension) Students are able to select appropriate relational symbols (<, >, =) to make number sentences true.;LBĮużĄ (żĄ @ @ A;NFĀużĄ (żĄ @ @ 2.1;LBĆużĄ (żĄ @ @ 0;®Äu żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@Åu
żÄ (żÄ pwJ06 uu’żĄ ww;MDĘvżĄ (żĄ @ @ NF;LBĒvżĄ (żĄ @ @ 7;0
ČvżĄ (żĄ @ @ åCC.4.NF.7 Understand decimal notation for fractions, and compare decimal fractions. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons comparisons are valid only when two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)J06vvłĄ @ @ ;LBÉvżĄ (żĄ @ @ 4;¹ŹvżĄ (żĄ @ @ nSD.4.N.1.1 (Comprehension) Students are able to read, write, order, and compare numbers from .01 to 1,000,000.;LBĖvżĄ (żĄ @ @ N;NFĢvżĄ (żĄ @ @ 1.1;LBĶvżĄ (żĄ @ @ 0J06vv żĄ @ @ ;K@Īv
żÄ (żÄ pwJ06 vv’żĄ ww;MDĻwżĄ (żĄ @ @ MD;LBŠwżĄ (żĄ @ @ 1;üŃwżĄ (żĄ @ @ ^CC.4.MD.1 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. For example: Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), & . J06wwłĄ @ @ ;LBŅwżĄ (żĄ @ @ 3; ¼ÓwżĄ (żĄ @ @ ¾SD.3.M.1.4 (Application) Students are able to select appropriate units to measure length (inch, foot, mile, yard); weight (ounces, pounds, tons); and capacity (cups, pints, quarts, gallons).;LBŌwżĄ (żĄ @ @ M;NFÕwżĄ (żĄ @ @ 1.4;LBÖwżĄ (żĄ @ @ 1;®×w żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@Ųw
żÄ (żÄ pwJ06 ww’żĄ ww;MDŁxżĄ (żĄ @ @ MD;LBŚxżĄ (żĄ @ @ 1;üŪxżĄ (żĄ @ @ ^CC.4.MD.1 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. For example: Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), & . J06xxłĄ @ @ ;LBÜxżĄ (żĄ @ @ 4;±ŻxżĄ (żĄ @ @ fSD.4.M.1.3 (Application) Students are able to use scales of length, temperature, capacity, and weight.;LBŽxżĄ (żĄ @ @ M;NFßxżĄ (żĄ @ @ 1.3;LBąxżĄ (żĄ @ @ 0J06xx żĄ @ @ ;K@įx
żÄ (żÄ pwJ06 xx’żĄ ww;MDāyżĄ (żĄ @ @ MD;LBćyżĄ (żĄ @ @ 1;üäyżĄ (żĄ @ @ ^CC.4.MD.1 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. For example: Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), & . J06yyłĄ @ @ ;LBåyżĄ (żĄ @ @ 5;Ś^ęyżĄ (żĄ @ @ SD.5.M.1.3 (Application) Students are able to use and convert U.S. Customary units of length (inches, feet, yard), and weight (ounces, pounds).;LBēyżĄ (żĄ @ @ M;NFčyżĄ (żĄ @ @ 1.3;MDéyżĄ (żĄ @ @ 1J06yy żĄ @ @ ;K@źy
żÄ (żÄ pwJ06 yy’żĄ ww;MDėzżĄ (żĄ @ @ MD;LBģzżĄ (żĄ @ @ 2;RNķzżĄ (żĄ @ @ CC.4.MD.2 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.J06zzłĄ @ @ ;LBīzżĄ (żĄ @ @ 4;®ļzżĄ (żĄ @ @ cSD.4.M.1.1 (Knowledge) Students are able to identify equivalent periods of time and solve problems.;LBšzżĄ (żĄ @ @ M;NFńzżĄ (żĄ @ @ 1.1;LBņzżĄ (żĄ @ @ 0;®óz żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@ōz
żÄ (żÄ pwJ06 zz’żĄ ww;MDõ{żĄ (żĄ @ @ MD;LBö{żĄ (żĄ @ @ 2;RN÷{żĄ (żĄ @ @ CC.4.MD.2 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.J06{{łĄ @ @ ;LBų{żĄ (żĄ @ @ 4;²ł{żĄ (żĄ @ @ gSD.4.M.1.2 (Application) Students are able to solve problems involving money including unit conversion.;LBś{żĄ (żĄ @ @ M;NFū{żĄ (żĄ @ @ 1.2;LBü{żĄ (żĄ @ @ 0J06{{ żĄ @ @ ;K@ż{
żÄ (żÄ pwJ06 {{’żĄ ww;MDžżĄ (żĄ @ @ MD;LB’żĄ (żĄ @ @ 2;RNżĄ (żĄ @ @ ’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ż’’’ż’’’
!"#$%&'()*+,./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{}~CC.4.MD.2 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.J06łĄ @ @ ;LBżĄ (żĄ @ @ 5;Ä2żĄ (żĄ @ @ ySD.5.M.1.1 (Comprehension) Students are able to determine elapsed time within an a.m. or p.m. period on the quarterhour.;LBżĄ (żĄ @ @ M;NFżĄ (żĄ @ @ 1.1;MDżĄ (żĄ @ @ 1J06 żĄ @ @ ;K@
żÄ (żÄ pwJ06 ’żĄ ww;MD}żĄ (żĄ @ @ MD;LB}żĄ (żĄ @ @ 2;RN }żĄ (żĄ @ @ CC.4.MD.2 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.J06}}łĄ @ @ ;LB
}żĄ (żĄ @ @ 5;°
}żĄ (żĄ @ @ eSD.5.M.1.2 (Application) Students are able to solve problems involving money including making change.;LB}żĄ (żĄ @ @ M;NF
}żĄ (żĄ @ @ 1.2;MD}żĄ (żĄ @ @ 1J06}} żĄ @ @ ;K@}
żÄ (żÄ pwJ06 }}’żĄ ww;MD~żĄ (żĄ @ @ MD;LB~żĄ (żĄ @ @ 2;RN~żĄ (żĄ @ @ CC.4.MD.2 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.J06~~łĄ @ @ ;LB~żĄ (żĄ @ @ 5;ü¢~żĄ (żĄ @ @ ±SD.5.N.3.1 (Application) Students are able to use different estimation strategies to solve problems involving whole numbers, decimals, and fractions to the nearest whole number.;LB~żĄ (żĄ @ @ N;NF~żĄ (żĄ @ @ 3.1;MD~żĄ (żĄ @ @ 1J06~~ żĄ @ @ ;K@~
żÄ (żÄ pwJ06 ~~’żĄ ww;MDżĄ (żĄ @ @ MD;LBżĄ (żĄ @ @ 3;ĪFżĄ (żĄ @ @ CC.4.MD.3 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.J06łĄ @ @ ;LBżĄ (żĄ @ @ 5;ÓPżĄ (żĄ @ @ SD.5.M.1.4 (Application) Students are able to use appropriate tools to measure length, weight, temperature, and area in problem solving.;LBżĄ (żĄ @ @ M;NFżĄ (żĄ @ @ 1.4;MD żĄ (żĄ @ @ 1;®! żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;TR"
żÄ (żÄ pw very weakJ06 ’żĄ ww;MD#żĄ (żĄ @ @ MD;LB$żĄ (żĄ @ @ 4;ĢB%żĄ (żĄ @ @ CC.4.MD.4 Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.J06łĄ @ @ ;LB&żĄ (żĄ @ @ 4;¼"'żĄ (żĄ @ @ qSD.4.S.1.1 (Application) Students are able to interpret data from graphical representations and draw conclusions.;LB(żĄ (żĄ @ @ S;NF)żĄ (żĄ @ @ 1.1;LB*żĄ (żĄ @ @ 0;®+ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@,
żÄ (żÄ pwJ06 ’żĄ ww;MDżĄ (żĄ @ @ MD;LB.żĄ (żĄ @ @ 5;mb/żĄ (żĄ @ @ CC.4.MD.5 Geometric measurement: understand concepts of angle and measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
 a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a onedegree angle, and can be used to measure angles.
 b. An angle that turns through n onedegree angles is said to have an angle measure of n degrees.J06łĄ @ @ ;LB0żĄ (żĄ @ @ 5; ź1żĄ (żĄ @ @ USD.5.G.1.2 (Knowledge) Students are able to identify acute, obtuse, and right angles.;LB2żĄ (żĄ @ @ G;NF3żĄ (żĄ @ @ 1.2;MD4żĄ (żĄ @ @ 1;®5 żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;m6
żÄ (żÄ pw"very weak,practically non existentJ06 ’żĄ ww;LB7żĄ (żĄ @ @ G;LB8żĄ (żĄ @ @ 1;MD9żĄ (żĄ @ @ CC.4.G.1 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.J06łĄ @ @ ;LB:żĄ (żĄ @ @ 3;ą;żĄ (żĄ @ @ PSD.3.G.1.2 Students are able to identify points, lines, line segments, and rays.;LB<żĄ (żĄ @ @ G;NF=żĄ (żĄ @ @ 1.2;LB>żĄ (żĄ @ @ 1;®? żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@@
żÄ (żÄ pwJ06 ’żĄ ww;LBAżĄ (żĄ @ @ G;LBBżĄ (żĄ @ @ 1;MDCżĄ (żĄ @ @ CC.4.G.1 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.J06łĄ @ @ ;LBDżĄ (żĄ @ @ 5; źEżĄ (żĄ @ @ USD.5.G.1.2 (Knowledge) Students are able to identify acute, obtuse, and right angles.;LBFżĄ (żĄ @ @ G;NFGżĄ (żĄ @ @ 1.2;MDHżĄ (żĄ @ @ 1J06 żĄ @ @ ;K@I
żÄ (żÄ pwJ06 ’żĄ ww;LBJżĄ (żĄ @ @ G;LBKżĄ (żĄ @ @ 1;MDLżĄ (żĄ @ @ CC.4.G.1 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.J06łĄ @ @ ;LBMżĄ (żĄ @ @ 4;°
NżĄ (żĄ @ @ eSD.4.G.1.2 (Knowledge) Students are able to identify parallel, perpendicular, and intersecting lines.;LBOżĄ (żĄ @ @ G;NFPżĄ (żĄ @ @ 1.2;LBQżĄ (żĄ @ @ 0J06 żĄ @ @ ;K@R
żÄ (żÄ pwJ06 ’żĄ ww;LBS
żĄ (żĄ @ @ G;LBT
żĄ (żĄ @ @ 2;ąU
żĄ (żĄ @ @ PCC.4.G.2 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.J06
łĄ @ @ ;LBV
żĄ (żĄ @ @ 4;°
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żĄ (żĄ @ @ eSD.4.G.1.2 (Knowledge) Students are able to identify parallel, perpendicular, and intersecting lines.;LBX
żĄ (żĄ @ @ G;NFY
żĄ (żĄ @ @ 1.2;LBZ
żĄ (żĄ @ @ 0;®[
żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@\
żÄ (żÄ pwJ06
’żĄ ww;LB]żĄ (żĄ @ @ G;LB^żĄ (żĄ @ @ 2;ą_żĄ (żĄ @ @ PCC.4.G.2 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.J06łĄ @ @ ;LB`żĄ (żĄ @ @ 4;ź~ażĄ (żĄ @ @ SD.4.G.1.1 (Knowledge) Students are able to identify the following plane and solid figures: pentagon, hexagon, octagon, pyramid, rectangular prism, and cone. ;LBbżĄ (żĄ @ @ G;NFcżĄ (żĄ @ @ 1.1;LBdżĄ (żĄ @ @ 0J06 żĄ @ @ ;K@e
żÄ (żÄ pwJ06 ’żĄ ww;LBfżĄ (żĄ @ @ G;LBgżĄ (żĄ @ @ 2;ąhżĄ (żĄ @ @ PCC.4.G.2 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.J06łĄ @ @ ;LBiżĄ (żĄ @ @ 4;ŠJjżĄ (żĄ @ @
SD.4.G.2.1 (Comprehension) Students are able to compare geometric figures using size, shape, orientation, congruence, and similarity.;LBkżĄ (żĄ @ @ G;NFlżĄ (żĄ @ @ 2.1;LBmżĄ (żĄ @ @ 0J06 żĄ @ @ ;K@n
żÄ (żÄ pwJ06 ’żĄ ww;LBożĄ (żĄ @ @ G;LBpżĄ (żĄ @ @ 2;ąqżĄ (żĄ @ @ PCC.4.G.2 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.J06łĄ @ @ ;LBrżĄ (żĄ @ @ 5;Ś^sżĄ (żĄ @ @ SD.5.G.1.1 (Knowledge) Students are able to describe and identify isosceles and equilateral triangles, pyramids, rectangular prisms, and cones.;LBtżĄ (żĄ @ @ G;NFużĄ (żĄ @ @ 1.1;MDvżĄ (żĄ @ @ 1J06 żĄ @ @ ;K@w
żÄ (żÄ pwJ06 ’żĄ ww;LBxżĄ (żĄ @ @ G;LByżĄ (żĄ @ @ 3;ÄzżĄ (żĄ @ @ BCC.4.G.3 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry.J06łĄ @ @ ;LB{żĄ (żĄ @ @ 5;½$żĄ (żĄ @ @ rSD.5.G.2.1 (Comprehension) Students are able to determine lines of symmetry in rectangles, squares, and triangles.;LB}żĄ (żĄ @ @ G;NF~żĄ (żĄ @ @ 2.1;MDżĄ (żĄ @ @ 1;ø żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@
żÄ (żÄ pwJ06 ’żĄ ww;MDżĄ (żĄ @ @ OA;LBżĄ (żĄ @ @ 1;ėżĄ (żĄ @ @ CC.5.OA.1 Write and interpret numerical expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.J06łĄ @ @ ;LB
żĄ (żĄ @ @ 5;ŅNżĄ (żĄ @ @ SD.5.A.2.1 (Application) Students are able to write onestep first degree equations using the set of whole numbers and find a solution.;LBżĄ (żĄ @ @ A;NFżĄ (żĄ @ @ 2.1;LBżĄ (żĄ @ @ 0;x żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@
żÄ (żÄ pwJ06 ’żĄ ww;MDżĄ (żĄ @ @ OA;LBżĄ (żĄ @ @ 1;ėżĄ (żĄ @ @ CC.5.OA.1 Write and interpret numerical expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.J06łĄ @ @ ;LBżĄ (żĄ @ @ 5;ÖVżĄ (żĄ @ @ SD.5.A.3.1 (Application) Students are able to, using whole numbers, write and solve number sentences that represent twostep word problems.;LBżĄ (żĄ @ @ A;NFżĄ (żĄ @ @ 3.1;LBżĄ (żĄ @ @ 0J06 żĄ @ @ ;K@
żÄ (żÄ pwJ06 ’żĄ ww;MDżĄ (żĄ @ @ OA;LBżĄ (żĄ @ @ 1;ėżĄ (żĄ @ @ CC.5.OA.1 Write and interpret numerical expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.J06łĄ @ @ ;LBżĄ (żĄ @ @ 6;ćpżĄ (żĄ @ @ SD.6.A.1.1 (Application) Students are able to use order of operations, excluding nested parentheses and exponents, to simplify whole number expressions.;LBżĄ (żĄ @ @ A;NFżĄ (żĄ @ @ 1.1;MDżĄ (żĄ @ @ 1J06 żĄ @ @ ;K@
żÄ (żÄ pwJ06 ’żĄ ww;MDżĄ (żĄ @ @ OA;LBżĄ (żĄ @ @ 2;aV żĄ (żĄ @ @ CC.5.OA.2 Write and interpret numerical expressions. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation add 8 and 7, then multiply by 2 as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.J06łĄ @ @ ;LB”żĄ (żĄ @ @ 5;Øś¢żĄ (żĄ @ @ ]SD.5.A.1.1 (Application) Students are able to use a variable to write an addition expression.;LB£żĄ (żĄ @ @ A;NF¤żĄ (żĄ @ @ 1.1;LB„żĄ (żĄ @ @ 0;®¦ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@§
żÄ (żÄ pwJ06 ’żĄ ww;MDØżĄ (żĄ @ @ OA;LB©żĄ (żĄ @ @ 2;aVŖżĄ (żĄ @ @ CC.5.OA.2 Write and interpret numerical expressions. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation add 8 and 7, then multiply by 2 as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.J06łĄ @ @ ;LB«żĄ (żĄ @ @ 5;Ć0¬żĄ (żĄ @ @ xSD.5.A.1.2 (Application) Students are able to recognize and use the associative property of addition and multiplication.;LBżĄ (żĄ @ @ A;NF®żĄ (żĄ @ @ 1.2;LBÆżĄ (żĄ @ @ 0J06 żĄ @ @ ;K@°
żÄ (żÄ pwJ06 ’żĄ ww;MD±żĄ (żĄ @ @ OA;LB²żĄ (żĄ @ @ 3;ŪŠ³żĄ (żĄ @ @ HCC.5.OA.3 Analyze patterns and relationships. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. J06łĄ @ @ ;LB“żĄ (żĄ @ @ 5;¹µżĄ (żĄ @ @ nSD.5.A.4.1 (Application) Students are able to solve problems using patterns involving more than one operation.;LB¶żĄ (żĄ @ @ A;NF·żĄ (żĄ @ @ 4.1;LBøżĄ (żĄ @ @ 0;®¹ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@ŗ
żÄ (żÄ pwJ06 ’żĄ ww;NF»żĄ (żĄ @ @ NBT;LB¼żĄ (żĄ @ @ 3;Ŗž½żĄ (żĄ @ @ _CC.5.NBT.3 Understand the place value system. Read, write, and compare decimals to thousandths.J06łĄ @ @ ;LB¾żĄ (żĄ @ @ 5;¾&æżĄ (żĄ @ @ sSD.5.N.1.1 (Comprehension) Students are able to read, write, order, and compare numbers from .001 to 1,000,000,000.;LBĄżĄ (żĄ @ @ N;NFĮżĄ (żĄ @ @ 1.1;LBĀżĄ (żĄ @ @ 0;øĆ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@Ä
żÄ (żÄ pwJ06 ’żĄ ww;NFÅżĄ (żĄ @ @ NBT;MDĘżĄ (żĄ @ @ 3a;ĀĒżĄ (żĄ @ @ ĮCC.5.NBT.3a Read and write decimals to thousandths using baseten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). J06łĄ @ @ ;LBČżĄ (żĄ @ @ 5;¾&ÉżĄ (żĄ @ @ sSD.5.N.1.1 (Comprehension) Students are able to read, write, order, and compare numbers from .001 to 1,000,000,000.;LBŹżĄ (żĄ @ @ N;NFĖżĄ (żĄ @ @ 1.1;LBĢżĄ (żĄ @ @ 0;øĶ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@Ī
żÄ (żÄ pwJ06 ’żĄ ww;NFĻżĄ (żĄ @ @ NBT;MDŠżĄ (żĄ @ @ 3b;éŃżĄ (żĄ @ @ CC.5.NBT.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.J06łĄ @ @ ;LBŅżĄ (żĄ @ @ 4;É<ÓżĄ (żĄ @ @ ~SD.4.A.2.1 (Comprehension) Students are able to select appropriate relational symbols (<, >, =) to make number sentences true.;LBŌżĄ (żĄ @ @ A;NFÕżĄ (żĄ @ @ 2.1;LBÖżĄ (żĄ @ @ 1;ø× żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@Ų
żÄ (żÄ pwJ06 ’żĄ ww;NFŁżĄ (żĄ @ @ NBT;MDŚżĄ (żĄ @ @ 3b;éŪżĄ (żĄ @ @ CC.5.NBT.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.J06łĄ @ @ ;LBÜżĄ (żĄ @ @ 5;¾&ŻżĄ (żĄ @ @ sSD.5.N.1.1 (Comprehension) Students are able to read, write, order, and compare numbers from .001 to 1,000,000,000.;LBŽżĄ (żĄ @ @ N;NFßżĄ (żĄ @ @ 1.1;LBążĄ (żĄ @ @ 0J06 żĄ @ @ ;K@į
żÄ (żÄ pwJ06 ’żĄ ww;NFāżĄ (żĄ @ @ NBT;LBćżĄ (żĄ @ @ 5;óäżĄ (żĄ @ @ ØCC.5.NBT.5 Perform operations with multidigit whole numbers and with decimals to hundredths. Fluently multiply multidigit whole numbers using the standard algorithm. J06łĄ @ @ ;LBåżĄ (żĄ @ @ 4;ŽfężĄ (żĄ @ @ SD.4.N.2.1 (Application) Students are able to find the products of twodigit factors and quotient of two natural numbers using a onedigit divisor.;LBēżĄ (żĄ @ @ N;NFčżĄ (żĄ @ @ 2.1;LBéżĄ (żĄ @ @ 1;®ź żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@ė
żÄ (żÄ pwJ06 ’żĄ ww;NFģżĄ (żĄ @ @ NBT;LBķżĄ (żĄ @ @ 6;ōīżĄ (żĄ @ @ ©CC.5.NBT.6 Perform operations with multidigit whole numbers and with decimals to hundredths. Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. J06łĄ @ @ ;LBļżĄ (żĄ @ @ 5;µšżĄ (żĄ @ @ jSD.5.N.2.1 (Application) Students are able to find the quotient of whole numbers using twodigit divisors.;LBńżĄ (żĄ @ @ N;NFņżĄ (żĄ @ @ 2.1;LBóżĄ (żĄ @ @ 0;®ō żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@õ
żÄ (żÄ pwJ06 ’żĄ ww;NFöżĄ (żĄ @ @ NBT;LB÷żĄ (żĄ @ @ 7;Č:ųżĄ (żĄ @ @ }CC.5.NBT.7 Perform operations with multidigit whole numbers and with decimals to hundredths. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.J06łĄ @ @ ;LBłżĄ (żĄ @ @ 4;ŗśżĄ (żĄ @ @ oSD.4.N.2.2 (Application) Students are able to add and subtract decimals with the same number of decimal places.;LBūżĄ (żĄ @ @ N;NFüżĄ (żĄ @ @ 2.2;LBżżĄ (żĄ @ @ 1;®ž żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@’
żÄ (żÄ pwJ06 ’żĄ ww;NFżĄ (żĄ @ @ NBT;LBżĄ (żĄ @ @ 7;Č:żĄ (żĄ @ @ }CC.5.NBT.7 Perform operations with multidigit whole numbers and with decimals to hundredths. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.J06łĄ @ @ ;LBżĄ (żĄ @ @ 5;±żĄ (żĄ @ @ fSD.5.N.2.3 (Application) Students are able to multiply and divide decimals by natural numbers (1  9).;LBżĄ (żĄ @ @ N;NFżĄ (żĄ @ @ 2.3;LBżĄ (żĄ @ @ 0J06 żĄ @ @ ;K@
żÄ (żÄ pwJ06 ’żĄ ww;MD żĄ (żĄ @ @ MD;LB
żĄ (żĄ @ @ 1;VVżĄ (żĄ @ @ CC.5.MD.1 Convert like measurement units within a given measurement system. Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep real world problems.J06łĄ @ @ ;LBżĄ (żĄ @ @ 5;Ś^
żĄ (żĄ @ @ SD.5.M.1.3 (Application) Students are able to use and convert U.S. Customary units of length (inches, feet, yard), and weight (ounces, pounds).;LBżĄ (żĄ @ @ M;NFżĄ (żĄ @ @ 1.3;LBżĄ (żĄ @ @ 0;K@ żĄ (żĄ @ @ ;et
żÄ (żÄ pwSD does not include metricJ06 ’żĄ ww;MDżĄ (żĄ @ @ MD;LBżĄ (żĄ @ @ 1;VVżĄ (żĄ @ @ CC.5.MD.1 Convert like measurement units within a given measurement system. Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep real world problems.J06łĄ @ @ ;LBżĄ (żĄ @ @ 5;ÓPżĄ (żĄ @ @ SD.5.M.1.4 (Application) Students are able to use appropriate tools to measure length, weight, temperature, and area in problem solving.;LBżĄ (żĄ @ @ M;NFżĄ (żĄ @ @ 1.4;LBżĄ (żĄ @ @ 0J06 żĄ @ @ ;et
żÄ (żÄ pwSD does not include metricJ06 ’żĄ ww;MDżĄ (żĄ @ @ MD;LBżĄ (żĄ @ @ 2;ž¦żĄ (żĄ @ @ ³CC.5.MD.2 Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.J06łĄ @ @ ;LBżĄ (żĄ @ @ 5;Ä żĄ (żĄ @ @ BSD.5.S.1.1 Students are able to gather, graph, and interpret data.;LB!żĄ (żĄ @ @ S;NF"żĄ (żĄ @ @ 1.1;LB#żĄ (żĄ @ @ 0;®$ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;TR%
żÄ (żÄ pw very weakJ06 ’żĄ ww;MD&żĄ (żĄ @ @ MD;LB'żĄ (żĄ @ @ 2;ž¦(żĄ (żĄ @ @ ³CC.5.MD.2 Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.J06łĄ @ @ ;LB)żĄ (żĄ @ @ 5;°
*żĄ (żĄ @ @ eSD.5.S.1.2 (Application) Students are able to calculate and explain mean for a whole number data set.;LB+żĄ (żĄ @ @ S;NF,żĄ (żĄ @ @ 1.2;LBżĄ (żĄ @ @ 0J06 żĄ @ @ ;TR.
żÄ (żÄ pw very weakJ06 ’żĄ ww;MD/żĄ (żĄ @ @ MD;MD0żĄ (żĄ @ @ 5a;ĪF1żĄ (żĄ @ @ CC.5.MD.5a Find the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication.J06łĄ @ @ ;LB2żĄ (żĄ @ @ 8;¾&3żĄ (żĄ @ @ sSD.8.M.1.2 (Comprehension) Students are able to find area, volume, and surface area with whole number measurements.;LB4żĄ (żĄ @ @ M;NF5żĄ (żĄ @ @ 1.2;MD6żĄ (żĄ @ @ 3;®7 żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@8
żÄ (żÄ pwJ06 ’żĄ ww;MD9żĄ (żĄ @ @ MD;MD:żĄ (żĄ @ @ 5b;'ų;żĄ (żĄ @ @ ÜCC.5.MD.5b Apply the formulas V =(l)(w)(h) and V = (b)(h) for rectangular prisms to find volumes of right rectangular prisms with wholenumber edge lengths in the context of solving real world and mathematical problems. J06łĄ @ @ ;LB<żĄ (żĄ @ @ 5;®=żĄ (żĄ @ @ cSD.5.A.3.2 (Application) Students are able to identify information and apply it to a given formula.;LB>żĄ (żĄ @ @ A;NF?żĄ (żĄ @ @ 3.2;LB@żĄ (żĄ @ @ 0;øA żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@B
żÄ (żÄ pwJ06 ’żĄ ww;LBCżĄ (żĄ @ @ G;LBDżĄ (żĄ @ @ 1;
ÄEżĄ (żĄ @ @ ĀCC.5.G.1 Graph points on the coordinate plane to solve realworld and mathematical problems. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate).
J06łĄ @ @ ;LBFżĄ (żĄ @ @ 5;ŲZGżĄ (żĄ @ @ SD.5.G.2.3 (Application) Students are able to use twodimensional coordinate grids to find locations and represent points and simple figures.;LBHżĄ (żĄ @ @ G;NFIżĄ (żĄ @ @ 2.3;LBJżĄ (żĄ @ @ 0;®K żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@L
żÄ (żÄ pwJ06 ’żĄ ww;LBMżĄ (żĄ @ @ G;LBNżĄ (żĄ @ @ 3;ÖOżĄ (żĄ @ @ KCC.5.G.3 Classify twodimensional figures into categories based on their properties. Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.J06łĄ @ @ ;LBPżĄ (żĄ @ @ 5;Ś^QżĄ (żĄ @ @ SD.5.G.1.1 (Knowledge) Students are able to describe and identify isosceles and equilateral triangles, pyramids, rectangular prisms, and cones.;LBRżĄ (żĄ @ @ G;NFSżĄ (żĄ @ @ 1.1;LBTżĄ (żĄ @ @ 0;®U żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@V
żÄ (żÄ pwJ06 ’żĄ ww;LBW żĄ (żĄ @ @ G;LBX żĄ (żĄ @ @ 3;ÖY żĄ (żĄ @ @ KCC.5.G.3 Classify twodimensional figures into categories based on their properties. Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.J06 łĄ @ @ ;LBZ żĄ (żĄ @ @ 4;ŠJ[ żĄ (żĄ @ @
SD.4.G.2.1 (Comprehension) Students are able to compare geometric figures using size, shape, orientation, congruence, and similarity.;LB\ żĄ (żĄ @ @ G;NF] żĄ (żĄ @ @ 2.1;LB^ żĄ (żĄ @ @ 1J06 żĄ @ @ ;K@_
żÄ (żÄ pwJ06 ’żĄ ww;LB`”żĄ (żĄ @ @ G;LBa”żĄ (żĄ @ @ 4;ärb”żĄ (żĄ @ @ CC.5.G.4 Classify twodimensional figures into categories based on their properties. Classify twodimensional figures in a hierarchy based on properties.J06””łĄ @ @ ;LBc”żĄ (żĄ @ @ 5;Ś^d”żĄ (żĄ @ @ SD.5.G.1.1 (Knowledge) Students are able to describe and identify isosceles and equilateral triangles, pyramids, rectangular prisms, and cones.;LBe”żĄ (żĄ @ @ G;NFf”żĄ (żĄ @ @ 1.1;LBg”żĄ (żĄ @ @ 0;®h” żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@i”
żÄ (żÄ pwJ06 ””’żĄ ww;LBj¢żĄ (żĄ @ @ G;LBk¢żĄ (żĄ @ @ 4;ärl¢żĄ (żĄ @ @ CC.5.G.4 Classify twodimensional figures into categories based on their properties. Classify twodimensional figures in a hierarchy based on properties.J06¢¢łĄ @ @ ;LBm¢żĄ (żĄ @ @ 4;ŠJn¢żĄ (żĄ @ @
SD.4.G.2.1 (Comprehension) Students are able to compare geometric figures using size, shape, orientation, congruence, and similarity.;LBo¢żĄ (żĄ @ @ G;NFp¢żĄ (żĄ @ @ 2.1;LBq¢żĄ (żĄ @ @ 1J06¢¢ żĄ @ @ ;K@r¢
żÄ (żÄ pwJ06 ¢¢’żĄ ww;MDs£żĄ (żĄ @ @ RP;LBt£żĄ (żĄ @ @ 1;g\u£żĄ (żĄ @ @ CC.6.RP.1 Understand ratio concepts and use ratio reasoning to solve problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. For every vote candidate A received, candidate C received nearly three votes. J06££łĄ @ @ ;LBv£żĄ (żĄ @ @ 6;¬w£żĄ (żĄ @ @ aSD.6.A.3.2 (Application) Students are able to solve onestep problems involving ratios and rates.;LBx£żĄ (żĄ @ @ A;NFy£żĄ (żĄ @ @ 3.2;LBz£żĄ (żĄ @ @ 0;®{£ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;°£
żÄ (żÄ pw8SD standard does not state understand SD states one stepJ06 ££’żĄ ww;MD}¤żĄ (żĄ @ @ RP;LB~¤żĄ (żĄ @ @ 2;i^¤żĄ (żĄ @ @ CC.6.RP.2 Understand ratio concepts and use ratio reasoning to solve problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b `" 0 (b not equal to zero), and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." (Expectations for unit rates in this grade are limited to noncomplex fractions.)J06¤¤łĄ @ @ ;LB¤żĄ (żĄ @ @ 6;¬¤żĄ (żĄ @ @ aSD.6.A.3.2 (Application) Students are able to solve onestep problems involving ratios and rates.;LB¤żĄ (żĄ @ @ A;NF¤żĄ (żĄ @ @ 3.2;LB¤żĄ (żĄ @ @ 0;K@
¤ żĄ (żĄ @ @ ;¬¤
żÄ (żÄ pwaSD standards do not state understand and limits to one step rate is not addressed in SD standardsJ06 ¤¤’żĄ ww;MD„żĄ (żĄ @ @ RP;LB„żĄ (żĄ @ @ 3;UT„żĄ (żĄ @ @
CC.6.RP.3 Understand ratio concepts and use ratio reasoning to solve problems. Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.J06„„łĄ @ @ ;LB„żĄ (żĄ @ @ 6;¬„żĄ (żĄ @ @ aSD.6.A.3.2 (Application) Students are able to solve onestep problems involving ratios and rates.;LB„żĄ (żĄ @ @ A;NF„żĄ (żĄ @ @ 3.2;LB„żĄ (żĄ @ @ 0;x„ żĄ (żĄ @ @ 3 = Excellent match between the two documents;i„
żÄ (żÄ pwSD standards limit to one stepJ06 „„’żĄ ww;MD¦żĄ (żĄ @ @ RP;MD¦żĄ (żĄ @ @ 3a;!ģ¦żĄ (żĄ @ @ ÖCC.6.RP.3a Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.J06¦¦łĄ @ @ ;LB¦żĄ (żĄ @ @ 7;ł¦żĄ (żĄ @ @ ®SD.7.A.4.1 (Application) Students are able to recognize onestep patterns using tables, graphs, and models and create onestep algebraic expressions representing the pattern.;LB¦żĄ (żĄ @ @ A;NF¦żĄ (żĄ @ @ 4.1;MD¦żĄ (żĄ @ @ 1;x¦ żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@¦
żÄ (żÄ pwJ06 ¦¦’żĄ ww;MD§żĄ (żĄ @ @ RP;MD§żĄ (żĄ @ @ 3c;ŗ§żĄ (żĄ @ @ ½CC.6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole given a part and the percent.J06§§łĄ @ @ ;LB§żĄ (żĄ @ @ 6;°§żĄ (żĄ @ @ øSD.6.N.1.1 (Comprehension) Students are able to represent fractions in equivalent forms and convert between fractions, decimals, and percents using halves, fourths, tenths, hundredths.;LB §żĄ (żĄ @ @ N;NF”§żĄ (żĄ @ @ 1.1;LB¢§żĄ (żĄ @ @ 0;K@£§ żĄ (żĄ @ @ ;®¤§
żÄ (żÄ pw7SD restricts to halves, fourthes, tenths and hundredthsJ06 §§’żĄ ww;MD„ØżĄ (żĄ @ @ RP;MD¦ØżĄ (żĄ @ @ 3d;Żd§ØżĄ (żĄ @ @ CC.6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.J06ØØłĄ @ @ ;LBØØżĄ (żĄ @ @ 6;Ä2©ØżĄ (żĄ @ @ ySD.6.M.1.1 (Comprehension) Students are able to select, use, and convert appropriate unit of measurement for a situation.;LBŖØżĄ (żĄ @ @ M;NF«ØżĄ (żĄ @ @ 1.1;LB¬ØżĄ (żĄ @ @ 0;K@Ø ’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ż’’’ż’’’
”¢£¤„¦§Ø©Ŗ«¬®Æ°±²³“µ¶·ø¹ŗ»¼½¾æĄĮĀĆÄÅĘĒČÉŹĖĢĶĪĻŠŃŅÓŌÕÖ×ŲŁŚŪÜŻŽßąįāćäåęēčéźėģķīļšńņóōõö÷ųłśūüżž’żĄ (żĄ @ @ ;j~®Ø
żÄ (żÄ pwSD does not use ratio reasoningJ06 ØØ’żĄ ww;MDÆ©żĄ (żĄ @ @ NS;LB°©żĄ (żĄ @ @ 1;l±©żĄ (żĄ @ @ !CC.6.NS.1 Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?J06©©łĄ @ @ ;LB²©żĄ (żĄ @ @ 8;ø³©żĄ (żĄ @ @ mSD.8.N.2.1 (Application) Students are able to read, write, and compute within any subset of rational numbers.;LB“©żĄ (żĄ @ @ N;NFµ©żĄ (żĄ @ @ 2.1;MD¶©żĄ (żĄ @ @ 2;K@·© żĄ (żĄ @ @ ;`jø©
żÄ (żÄ pwSD doesn't generalizeJ06 ©©’żĄ ww;MD¹ŖżĄ (żĄ @ @ NS;LBŗŖżĄ (żĄ @ @ 1;l»ŖżĄ (żĄ @ @ !CC.6.NS.1 Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?J06ŖŖłĄ @ @ ;LB¼ŖżĄ (żĄ @ @ 7;Žf½ŖżĄ (żĄ @ @ SD.7.N.3.1 (Application) Students are able to use various strategies to solve one and twostep problems involving positive fractions and integers.;LB¾ŖżĄ (żĄ @ @ N;NFæŖżĄ (żĄ @ @ 3.1;MDĄŖżĄ (żĄ @ @ 1J06ŖŖ żĄ @ @ ;`jĮŖ
żÄ (żÄ pwSD doesn't generalizeJ06 ŖŖ’żĄ ww;MDĀ«żĄ (żĄ @ @ NS;LBĆ«żĄ (żĄ @ @ 2;čzÄ«żĄ (żĄ @ @ CC.6.NS.2 Compute fluently with multidigit numbers and find common factors and multiples. Fluently divide multidigit numbers using the standard algorithm. J06««łĄ @ @ ;LBÅ«żĄ (żĄ @ @ 6;£šĘ«żĄ (żĄ @ @ XSD.6.N.1.2 (Knowledge) Students are able to find factors and multiples of whole numbers.;LBĒ«żĄ (żĄ @ @ N;NFČ«żĄ (żĄ @ @ 1.2;LBÉ«żĄ (żĄ @ @ 0;K@Ź« żĄ (żĄ @ @ ;etĖ«
żÄ (żÄ pwSD doesn't require fluencyJ06 ««’żĄ ww;MDĢ¬żĄ (żĄ @ @ NS;LBĶ¬żĄ (żĄ @ @ 3;ŚĪ¬żĄ (żĄ @ @ ĶCC.6.NS.3 Compute fluently with multidigit numbers and find common factors and multiples. Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation.J06¬¬łĄ @ @ ;LBĻ¬żĄ (żĄ @ @ 6;ØśŠ¬żĄ (żĄ @ @ ]SD.6.N.2.1 (Comprehension) Students are able to add, subtract, multiply, and divide decimals.;LBŃ¬żĄ (żĄ @ @ N;NFŅ¬żĄ (żĄ @ @ 2.1;LBÓ¬żĄ (żĄ @ @ 0;øŌ¬ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;`jÕ¬
żÄ (żÄ pwSD allows calculatorsJ06 ¬¬’żĄ ww;MDÖżĄ (żĄ @ @ NS;LB×żĄ (żĄ @ @ 4;ĻÄŲżĄ (żĄ @ @ ĀCC.6.NS.4 Compute fluently with multidigit numbers and find common factors and multiples. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1 100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).J06łĄ @ @ ;LBŁżĄ (żĄ @ @ 6;£šŚżĄ (żĄ @ @ XSD.6.N.1.2 (Knowledge) Students are able to find factors and multiples of whole numbers.;LBŪżĄ (żĄ @ @ N;NFÜżĄ (żĄ @ @ 1.2;LBŻżĄ (żĄ @ @ 0;®Ž żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;uß
żÄ (żÄ pw*SD does not require fluency or GCF and LCMJ06 ’żĄ ww;MDą®żĄ (żĄ @ @ NS;LBį®żĄ (żĄ @ @ 5;"īā®żĄ (żĄ @ @ ×CC.6.NS.5 Apply and extend previous understandings of numbers to the system of rational numbers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in realworld contexts, explaining the meaning of 0 in each situation.J06®®łĄ @ @ ;LBć®żĄ (żĄ @ @ 7;öä®żĄ (żĄ @ @ «SD.7.N.1.1 (Comprehension) Students are able to represent numbers in a variety of forms by describing, ordering, and comparing integers, decimals, percents, and fractions.;LBå®żĄ (żĄ @ @ N;NFę®żĄ (żĄ @ @ 1.1;MDē®żĄ (żĄ @ @ 1;®č® żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;vé®
żÄ (żÄ pw+SD does not require an explaination of zeroJ06 ®®’żĄ ww;MDźÆżĄ (żĄ @ @ NS;LBėÆżĄ (żĄ @ @ 5;"īģÆżĄ (żĄ @ @ ×CC.6.NS.5 Apply and extend previous understandings of numbers to the system of rational numbers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in realworld contexts, explaining the meaning of 0 in each situation.J06ÆÆłĄ @ @ ;LBķÆżĄ (żĄ @ @ 8;ŠJīÆżĄ (żĄ @ @
SD.8.N.1.1 (Comprehension) Students are able to represent numbers in a variety of forms and identify the subsets of rational numbers.;LBļÆżĄ (żĄ @ @ N;NFšÆżĄ (żĄ @ @ 1.1;MDńÆżĄ (żĄ @ @ 2J06ÆÆ żĄ @ @ ;vņÆ
żÄ (żÄ pw+SD does not require an explaination of zeroJ06 ÆÆ’żĄ ww;MDó°żĄ (żĄ @ @ NS;MDō°żĄ (żĄ @ @ 6a;+ õ°żĄ (żĄ @ @ šCC.6.NS.6a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., ( 3) = 3, and that 0 is its own opposite.J06°°łĄ @ @ ;LBö°żĄ (żĄ @ @ 8;ŠJ÷°żĄ (żĄ @ @
SD.8.N.1.1 (Comprehension) Students are able to represent numbers in a variety of forms and identify the subsets of rational numbers.;LBų°żĄ (żĄ @ @ N;NFł°żĄ (żĄ @ @ 1.1;MDś°żĄ (żĄ @ @ 2;®ū° żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;uü°
żÄ (żÄ pw*SD does not require in depth understandingJ06 °°’żĄ ww;MDż±żĄ (żĄ @ @ NS;MDž±żĄ (żĄ @ @ 6b;MD’±żĄ (żĄ @ @ CC.6.NS.6b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. J06±±łĄ @ @ ;LB±żĄ (żĄ @ @ 6;¼"±żĄ (żĄ @ @ qSD.6.A.3.1 (Knowledge) Students are able to identify and graph ordered pairs in Quadrant I on a coordinate plane.;LB±żĄ (żĄ @ @ A;NF±żĄ (żĄ @ @ 3.1;LB±żĄ (żĄ @ @ 0;®± żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;Ś±
żÄ (żÄ pwMSD limits to one guadrant SD doesn't include location or reflections of pointJ06 ±±’żĄ ww;MD²żĄ (żĄ @ @ NS;MD²żĄ (żĄ @ @ 6b;MD ²żĄ (żĄ @ @ CC.6.NS.6b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. J06²²łĄ @ @ ;LB
²żĄ (żĄ @ @ 7;ŅN²żĄ (żĄ @ @ SD.7.A.3.1 (Application) Students are able to identify and graph ordered pairs on a coordinate plane and inequalities on a number line.;LB²żĄ (żĄ @ @ A;NF
²żĄ (żĄ @ @ 3.1;MD²żĄ (żĄ @ @ 1J06²² żĄ @ @ ;Ś²
żÄ (żÄ pwMSD limits to one guadrant SD doesn't include location or reflections of pointJ06 ²²’żĄ ww;MD³żĄ (żĄ @ @ NS;MD³żĄ (żĄ @ @ 6c;Ī³żĄ (żĄ @ @ ĒCC.6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.J06³³łĄ @ @ ;LB³żĄ (żĄ @ @ 7;ŅN³żĄ (żĄ @ @ SD.7.A.3.1 (Application) Students are able to identify and graph ordered pairs on a coordinate plane and inequalities on a number line.;LB³żĄ (żĄ @ @ A;NF³żĄ (żĄ @ @ 3.1;MD³żĄ (żĄ @ @ 1;®³ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;
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żÄ (żÄ pw:SD doesn't require finding or positioning on a number lineJ06 ³³’żĄ ww;MD“żĄ (żĄ @ @ NS;LB“żĄ (żĄ @ @ 7;čz“żĄ (żĄ @ @ CC.6.NS.7 Apply and extend previous understandings of numbers to the system of rational numbers. Understand ordering and absolute value of rational numbers. J06““łĄ @ @ ;LB“żĄ (żĄ @ @ 7;ö“żĄ (żĄ @ @ «SD.7.N.1.1 (Comprehension) Students are able to represent numbers in a variety of forms by describing, ordering, and comparing integers, decimals, percents, and fractions.;LB“żĄ (żĄ @ @ N;NF “żĄ (żĄ @ @ 1.1;MD!“żĄ (żĄ @ @ 1;ø"“ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@#“
żÄ (żÄ pwJ06 ““’żĄ ww;MD$µżĄ (żĄ @ @ NS;LB%µżĄ (żĄ @ @ 7;čz&µżĄ (żĄ @ @ CC.6.NS.7 Apply and extend previous understandings of numbers to the system of rational numbers. Understand ordering and absolute value of rational numbers. J06µµłĄ @ @ ;LB'µżĄ (żĄ @ @ 8;ŠJ(µżĄ (żĄ @ @
SD.8.N.1.1 (Comprehension) Students are able to represent numbers in a variety of forms and identify the subsets of rational numbers.;LB)µżĄ (żĄ @ @ N;NF*µżĄ (żĄ @ @ 1.1;MD+µżĄ (żĄ @ @ 2J06µµ żĄ @ @ ;K@,µ
żÄ (żÄ pwJ06 µµ’żĄ ww;MD¶żĄ (żĄ @ @ NS;MD.¶żĄ (żĄ @ @ 7a;OD/¶żĄ (żĄ @ @ CC.6.NS.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret 3 > 7 as a statement that 3 is located to the right of 7 on a number line oriented from left to right.J06¶¶łĄ @ @ ;LB0¶żĄ (żĄ @ @ 7;ŅN1¶żĄ (żĄ @ @ SD.7.A.3.1 (Application) Students are able to identify and graph ordered pairs on a coordinate plane and inequalities on a number line.;LB2¶żĄ (żĄ @ @ A;NF3¶żĄ (żĄ @ @ 3.1;MD4¶żĄ (żĄ @ @ 1;®5¶ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;[`6¶
żÄ (żÄ pwSD has identify J06 ¶¶’żĄ ww;MD7·żĄ (żĄ @ @ NS;MD8·żĄ (żĄ @ @ 7c;É¾9·żĄ (żĄ @ @ ?CC.6.NS.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a realworld situation. For example, for an account balance of 30 dollars, write  30 = 30 to describe the size of the debt in dollars.J06··łĄ @ @ ;LB:·żĄ (żĄ @ @ 7;ö;·żĄ (żĄ @ @ «SD.7.N.1.1 (Comprehension) Students are able to represent numbers in a variety of forms by describing, ordering, and comparing integers, decimals, percents, and fractions.;LB<·żĄ (żĄ @ @ N;NF=·żĄ (żĄ @ @ 1.1;MD>·żĄ (żĄ @ @ 1;®?· żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;s@·
żÄ (żÄ pw(Not in SD standards, shown as an exampleJ06 ··’żĄ ww;MDAøżĄ (żĄ @ @ NS;LBBøżĄ (żĄ @ @ 8;„ōCøżĄ (żĄ @ @ ZCC.6.NS.8 Apply and extend previous understandings of numbers to the system of rational numbers. Solve realworld and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.J06øøłĄ @ @ ;LBDøżĄ (żĄ @ @ 7;ŅNEøżĄ (żĄ @ @ SD.7.A.3.1 (Application) Students are able to identify and graph ordered pairs on a coordinate plane and inequalities on a number line.;LBFøżĄ (żĄ @ @ A;NFGøżĄ (żĄ @ @ 3.1;MDHøżĄ (żĄ @ @ 1;®Iø żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;¢Jø
żÄ (żÄ pw1SD only addresses second sentence in CC standardsJ06 øø’żĄ ww;MDK¹żĄ (żĄ @ @ EE;LBL¹żĄ (żĄ @ @ 1;ńM¹żĄ (żĄ @ @ ¦CC.6.EE.1 Apply and extend previous understandings of arithmetic to algebraic expressions. Write and evaluate numerical expressions involving wholenumber exponents.J06¹¹łĄ @ @ ;LBN¹żĄ (żĄ @ @ 6;ĪFO¹żĄ (żĄ @ @ SD.6.A.1.2 (Application) Students are able to write algebraic expressions involving addition or multiplication using whole numbers.;LBP¹żĄ (żĄ @ @ A;NFQ¹żĄ (żĄ @ @ 1.2;LBR¹żĄ (żĄ @ @ 0;®S¹ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;ŠT¹
żÄ (żÄ pwHSD does not require exponents in 6th 7th shows exponents in the examplesJ06 ¹¹’żĄ ww;MDUŗżĄ (żĄ @ @ EE;LBVŗżĄ (żĄ @ @ 1;ńWŗżĄ (żĄ @ @ ¦CC.6.EE.1 Apply and extend previous understandings of arithmetic to algebraic expressions. Write and evaluate numerical expressions involving wholenumber exponents.J06ŗŗłĄ @ @ ;LBXŗżĄ (żĄ @ @ 7;Į,YŗżĄ (żĄ @ @ vSD.7.A.1.1 (Application) Students are able to write and evaluate algebraic expressions using the set of whole numbers.;LBZŗżĄ (żĄ @ @ A;NF[ŗżĄ (żĄ @ @ 1.1;MD\ŗżĄ (żĄ @ @ 1J06ŗŗ żĄ @ @ ;Š]ŗ
żÄ (żÄ pwHSD does not require exponents in 6th 7th shows exponents in the examplesJ06 ŗŗ’żĄ ww;MD^»żĄ (żĄ @ @ EE;LB_»żĄ (żĄ @ @ 2;š`»żĄ (żĄ @ @ „CC.6.EE.2 Apply and extend previous understandings of arithmetic to algebraic expressions. Write, read, and evaluate expressions in which letters stand for numbers.J06»»łĄ @ @ ;LBa»żĄ (żĄ @ @ 7;Į,b»żĄ (żĄ @ @ vSD.7.A.1.1 (Application) Students are able to write and evaluate algebraic expressions using the set of whole numbers.;LBc»żĄ (żĄ @ @ A;NFd»żĄ (żĄ @ @ 1.1;MDe»żĄ (żĄ @ @ 1;®f» żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;čg»
żÄ (żÄ pwTSD does not use language of letters standing for numbers, we show it in the examplesJ06 »»’żĄ ww;MDh¼żĄ (żĄ @ @ EE;MDi¼żĄ (żĄ @ @ 2a;”j¼żĄ (żĄ @ @ «CC.6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5 y. J06¼¼łĄ @ @ ;LBk¼żĄ (żĄ @ @ 6;ĪFl¼żĄ (żĄ @ @ SD.6.A.1.2 (Application) Students are able to write algebraic expressions involving addition or multiplication using whole numbers.;LBm¼żĄ (żĄ @ @ A;NFn¼żĄ (żĄ @ @ 1.2;LBo¼żĄ (żĄ @ @ 0;®p¼ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;xq¼
żÄ (żÄ pwSD only allows for addition or multiplicationJ06 ¼¼’żĄ ww;MDr½żĄ (żĄ @ @ EE;MDs½żĄ (żĄ @ @ 2c;Öt½żĄ (żĄ @ @ ĖCC.6.EE.2c Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in realworld problems. Perform arithmetic operations, including those involving wholenumber exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = 1/2. J06½½łĄ @ @ ;LBu½żĄ (żĄ @ @ 6;ćpv½żĄ (żĄ @ @ SD.6.A.1.1 (Application) Students are able to use order of operations, excluding nested parentheses and exponents, to simplify whole number expressions.;LBw½żĄ (żĄ @ @ A;NFx½żĄ (żĄ @ @ 1.1;LBy½żĄ (żĄ @ @ 0;øz½ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;Ŗ{½
żÄ (żÄ pw5SD does not require real world except in the examplesJ06 ½½’żĄ ww;MD¾żĄ (żĄ @ @ EE;LB}¾żĄ (żĄ @ @ 3;%ō~¾żĄ (żĄ @ @ ŚCC.6.EE.3 Apply and extend previous understandings of arithmetic to algebraic expressions. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.J06¾¾łĄ @ @ ;LB¾żĄ (żĄ @ @ 7;ąj¾żĄ (żĄ @ @ SD.7.A.1.2 (Knowledge) Students are able to identify associative, commutative, distributive, and identity properties involving algebraic expressions.;LB¾żĄ (żĄ @ @ A;NF¾żĄ (żĄ @ @ 1.2;MD¾żĄ (żĄ @ @ 1;®¾ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;et
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żÄ (żÄ pwSD not require applicationJ06 ¾¾’żĄ ww;MDæżĄ (żĄ @ @ EE;LBæżĄ (żĄ @ @ 6;¬æżĄ (żĄ @ @ 6CC.6.EE.6 Reason about and solve onevariable equations and inequalities. Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.J06ææłĄ @ @ ;LBæżĄ (żĄ @ @ 8;°æżĄ (żĄ @ @ øSD.8.A.2.1 (Application) Students are able to write and solve twostep 1st degree equations, with one variable, and onestep inequalities, with one variable, using the set of integers.;LBæżĄ (żĄ @ @ A;NFæżĄ (żĄ @ @ 2.1;MDæżĄ (żĄ @ @ 2;®æ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;læ
żÄ (żÄ pw!SD does not require understandingJ06 ææ’żĄ ww;MDĄżĄ (żĄ @ @ EE;LBĄżĄ (żĄ @ @ 9;ŗĄżĄ (żĄ @ @ ½CC.6.EE.9 Represent and analyze quantitative relationships between dependent and independent variables. Use variables to represent two quantities in a realworld problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.J06ĄĄłĄ @ @ ;LBĄżĄ (żĄ @ @ 8;ärĄżĄ (żĄ @ @ SD.8.A.4.1 Students are able to create rules to explain the relationship between numbers when a change in the first variable affects the second variable.;LBĄżĄ (żĄ @ @ A;NFĄżĄ (żĄ @ @ 4.1;MDĄżĄ (żĄ @ @ 2;øĄ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;j~Ą
żÄ (żÄ pwSD requires the synthesis levelJ06 ĄĄ’żĄ ww;LBĮżĄ (żĄ @ @ G;LBĮżĄ (żĄ @ @ 4;ŹĮżĄ (żĄ @ @ ECC.6.G.4 Solve realworld and mathematical problems involving area, surface area, and volume. Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems.J06ĮĮłĄ @ @ ;LBĮżĄ (żĄ @ @ 8;µĮżĄ (żĄ @ @ jSD.8.G.1.1 (Application) Students are able to describe and classify prisms, pyramids, cylinders, and cone.;LBĮżĄ (żĄ @ @ G;NF ĮżĄ (żĄ @ @ 1.1;MD”ĮżĄ (żĄ @ @ 2;®¢Į żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;s£Į
żÄ (żÄ pw(SD adds nets as an enabling skill for HSJ06 ĮĮ’żĄ ww;MD¤ĀżĄ (żĄ @ @ SP;LB„ĀżĄ (żĄ @ @ 2;$ņ¦ĀżĄ (żĄ @ @ ŁCC.6.SP.2 Develop understanding of statistical variability. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.J06ĀĀłĄ @ @ ;LB§ĀżĄ (żĄ @ @ 8;ÕTØĀżĄ (żĄ @ @ SD.8.S.1.2 (Application) Students are able to use a variety of visual representations to display data to make comparisons and predictions.;LB©ĀżĄ (żĄ @ @ S;NFŖĀżĄ (żĄ @ @ 1.2;MD«ĀżĄ (żĄ @ @ 2;®¬Ā żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;lĀ
żÄ (żÄ pw!SD does not require understandingJ06 ĀĀ’żĄ ww;MD®ĆżĄ (żĄ @ @ SP;LBÆĆżĄ (żĄ @ @ 4;Żd°ĆżĄ (żĄ @ @ CC.6.SP.4 Summarize and describe distributions. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. J06ĆĆłĄ @ @ ;LB±ĆżĄ (żĄ @ @ 7;ō²ĆżĄ (żĄ @ @ ©SD.7.S.1.2 (Application) Students are able to display data, using frequency tables, line plots, stemandleaf plots, and make predictions from data displayed in a graph.;LB³ĆżĄ (żĄ @ @ S;NF“ĆżĄ (żĄ @ @ 1.2;MDµĆżĄ (żĄ @ @ 1;®¶Ć żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;¢·Ć
żÄ (żÄ pw1not all representaions are listed in SD standardsJ06 ĆĆ’żĄ ww;MDøÄżĄ (żĄ @ @ SP;LB¹ÄżĄ (żĄ @ @ 4;ŻdŗÄżĄ (żĄ @ @ CC.6.SP.4 Summarize and describe distributions. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. J06ÄÄłĄ @ @ ;LB»ÄżĄ (żĄ @ @ 8;ÕT¼ÄżĄ (żĄ @ @ SD.8.S.1.2 (Application) Students are able to use a variety of visual representations to display data to make comparisons and predictions.;LB½ÄżĄ (żĄ @ @ S;NF¾ÄżĄ (żĄ @ @ 1.2;MDæÄżĄ (żĄ @ @ 2J06ÄÄ żĄ @ @ ;¢ĄÄ
żÄ (żÄ pw1not all representaions are listed in SD standardsJ06 ÄÄ’żĄ ww;MDĮÅżĄ (żĄ @ @ SP;LBĀÅżĄ (żĄ @ @ 5;8ĆÅżĄ (żĄ @ @ ķCC.6.SP.5 Summarize and describe distributions. Summarize numerical data sets in relation to their context, such as by:
 a. Reporting the number of observations.
 b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
 c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data was gathered.
 d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered.J06ÅÅłĄ @ @ ;LBÄÅżĄ (żĄ @ @ 6;½$ÅÅżĄ (żĄ @ @ rSD.6.S.1.1 (Comprehension) Students are able to find the mean, mode, and range of an ordered set of positive data.;LBĘÅżĄ (żĄ @ @ S;NFĒÅżĄ (żĄ @ @ 1.1;LBČÅżĄ (żĄ @ @ 0;®ÉÅ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@ŹÅ
żÄ (żÄ pwJ06 ÅÅ’żĄ ww;MDĖĘżĄ (żĄ @ @ SP;LBĢĘżĄ (żĄ @ @ 5;8ĶĘżĄ (żĄ @ @ ķCC.6.SP.5 Summarize and describe distributions. Summarize numerical data sets in relation to their context, such as by:
 a. Reporting the number of observations.
 b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
 c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data was gathered.
 d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered.J06ĘĘłĄ @ @ ;LBĪĘżĄ (żĄ @ @ 7;³ĻĘżĄ (żĄ @ @ hSD.7.S.1.1 (Comprehension) Students are able to find the mean, median, mode, and range of a set of data.;LBŠĘżĄ (żĄ @ @ S;NFŃĘżĄ (żĄ @ @ 1.1;MDŅĘżĄ (żĄ @ @ 1J06ĘĘ żĄ @ @ ;K@ÓĘ
żÄ (żÄ pwJ06 ĘĘ’żĄ ww;MDŌĒżĄ (żĄ @ @ SP;LBÕĒżĄ (żĄ @ @ 5;8ÖĒżĄ (żĄ @ @ ķCC.6.SP.5 Summarize and describe distributions. Summarize numerical data sets in relation to their context, such as by:
 a. Reporting the number of observations.
 b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
 c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data was gathered.
 d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered.J06ĒĒłĄ @ @ ;LB×ĒżĄ (żĄ @ @ 8;Ś^ŲĒżĄ (żĄ @ @ SD.8.S.1.1 (Comprehension) Students are able to find the mean, median, mode, and range of a data set from a stemandleaf plot and a line plot.;LBŁĒżĄ (żĄ @ @ S;NFŚĒżĄ (żĄ @ @ 1.1;MDŪĒżĄ (żĄ @ @ 2J06ĒĒ żĄ @ @ ;K@ÜĒ
żÄ (żÄ pwJ06 ĒĒ’żĄ ww;MDŻČżĄ (żĄ @ @ RP;LBŽČżĄ (żĄ @ @ 2;śßČżĄ (żĄ @ @ ÆCC.7.RP.2 Analyze proportional relationships and use them to solve realworld and mathematical problems. Recognize and represent proportional relationships between quantities.J06ČČłĄ @ @ ;LBąČżĄ (żĄ @ @ 8;ÖVįČżĄ (żĄ @ @ SD.8.M.1.1 (Application) Students are able to apply proportional reasoning to solve measurement problems with rational number measurements.;LBāČżĄ (żĄ @ @ M;NFćČżĄ (żĄ @ @ 1.1;MDäČżĄ (żĄ @ @ 1;®åČ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;etęČ
żÄ (żÄ pwSD applies doesn't analyzeJ06 ČČ’żĄ ww;MDēÉżĄ (żĄ @ @ RP;MDčÉżĄ (żĄ @ @ 2a;2éÉżĄ (żĄ @ @ ēCC.7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.J06ÉÉłĄ @ @ ;LBźÉżĄ (żĄ @ @ 8;§ųėÉżĄ (żĄ @ @ \SD.8.A.3.1 (Comprehension) Students are able to describe and determine linear relationships.;LBģÉżĄ (żĄ @ @ A;NFķÉżĄ (żĄ @ @ 3.1;MDīÉżĄ (żĄ @ @ 1;®ļÉ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;®šÉ
żÄ (żÄ pw7SD does not mention tables or graphing as straight lineJ06 ÉÉ’żĄ ww;MDńŹżĄ (żĄ @ @ RP;MDņŹżĄ (żĄ @ @ 2b;éóŹżĄ (żĄ @ @ CC.7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.J06ŹŹłĄ @ @ ;LBōŹżĄ (żĄ @ @ 7;łõŹżĄ (żĄ @ @ ®SD.7.A.4.1 (Application) Students are able to recognize onestep patterns using tables, graphs, and models and create onestep algebraic expressions representing the pattern.;LBöŹżĄ (żĄ @ @ A;NF÷ŹżĄ (żĄ @ @ 4.1;LBųŹżĄ (żĄ @ @ 0;®łŹ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;²śŹ
żÄ (żÄ pw9SD does not require proprtionality or verbal descriptionsJ06 ŹŹ’żĄ ww;MDūĖżĄ (żĄ @ @ RP;LBüĖżĄ (żĄ @ @ 3;ŗżĖżĄ (żĄ @ @ =CC.7.RP.3 Analyze proportional relationships and use them to solve realworld and mathematical problems. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.J06ĖĖłĄ @ @ ;LBžĖżĄ (żĄ @ @ 7;č’ĖżĄ (żĄ @ @ TSD.7.A.3.2 Students are able to model and solve multistep problems involving rates.;LBĖżĄ (żĄ @ @ A;NFĖżĄ (żĄ @ @ 3.2;LBĖżĄ (żĄ @ @ 0;®Ė żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;ÄĖ
żÄ (żÄ pwBSD does not require proportional relationships or percent problemsJ06 ĖĖ’żĄ ww;MDĢżĄ (żĄ @ @ NS;LBĢżĄ (żĄ @ @ 1;ŠĢżĄ (żĄ @ @ HCC.7.NS.1 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.J06ĢĢłĄ @ @ ;LBĢżĄ (żĄ @ @ 7;½$ ĢżĄ (żĄ @ @ rSD.7.N.2.1 (Application) Students are able to add, subtract, multiply, and divide integers and positive fractions.;LB
ĢżĄ (żĄ @ @ N;NFĢżĄ (żĄ @ @ 2.1;LBĢżĄ (żĄ @ @ 0;®
Ģ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;ĢĢ
żÄ (żÄ pwFSD only require positive fractions; does not talk about representationJ06 ĢĢ’żĄ ww;MDĶżĄ (żĄ @ @ NS;MDĶżĄ (żĄ @ @ 1d;©üĶżĄ (żĄ @ @ ^CC.7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. J06ĶĶłĄ @ @ ;LBĶżĄ (żĄ @ @ 8;øĶżĄ (żĄ @ @ mSD.8.N.2.1 (Application) Students are able to read, write, and compute within any subset of rational numbers.;LBĶżĄ (żĄ @ @ N;NFĶżĄ (żĄ @ @ 2.1;MDĶżĄ (żĄ @ @ 1;xĶ żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@Ķ
żÄ (żÄ pwJ06 ĶĶ’żĄ ww;MDĪżĄ (żĄ @ @ NS;LBĪżĄ (żĄ @ @ 2;WXĪżĄ (żĄ @ @ CC.7.NS.2 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. J06ĪĪłĄ @ @ ;LBĪżĄ (żĄ @ @ 8;øĪżĄ (żĄ @ @ mSD.8.N.2.1 (Application) Students are able to read, write, and compute within any subset of rational numbers.;LBĪżĄ (żĄ @ @ N;NFĪżĄ (żĄ @ @ 2.1;MD ĪżĄ (żĄ @ @ 1;x!Ī żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@"Ī
żÄ (żÄ pwJ06 ĪĪ’żĄ ww;MD#ĻżĄ (żĄ @ @ NS;MD$ĻżĄ (żĄ @ @ 2c;«%ĻżĄ (żĄ @ @ `CC.7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.J06ĻĻłĄ @ @ ;LB&ĻżĄ (żĄ @ @ 7;Žf'ĻżĄ (żĄ @ @ SD.7.N.3.1 (Application) Students are able to use various strategies to solve one and twostep problems involving positive fractions and integers.;LB(ĻżĄ (żĄ @ @ N;NF)ĻżĄ (żĄ @ @ 3.1;LB*ĻżĄ (żĄ @ @ 0;ø+Ļ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;s,Ļ
żÄ (żÄ pw(SD standards require positive fractions J06 ĻĻ’żĄ ww;MDŠżĄ (żĄ @ @ NS;MD.ŠżĄ (żĄ @ @ 2c;«/ŠżĄ (żĄ @ @ `CC.7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.J06ŠŠłĄ @ @ ;LB0ŠżĄ (żĄ @ @ 7;½$1ŠżĄ (żĄ @ @ rSD.7.N.2.1 (Application) Students are able to add, subtract, multiply, and divide integers and positive fractions.;LB2ŠżĄ (żĄ @ @ N;NF3ŠżĄ (żĄ @ @ 2.1;LB4ŠżĄ (żĄ @ @ 0J06ŠŠ żĄ @ @ ;s5Š
żÄ (żÄ pw(SD standards require positive fractions J06 ŠŠ’żĄ ww;MD6ŃżĄ (żĄ @ @ NS;LB7ŃżĄ (żĄ @ @ 3;ä8ŃżĄ (żĄ @ @ RCC.7.NS.3 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Solve realworld and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
J06ŃŃłĄ @ @ ;LB9ŃżĄ (żĄ @ @ 7;½$:ŃżĄ (żĄ @ @ rSD.7.N.2.1 (Application) Students are able to add, subtract, multiply, and divide integers and positive fractions.;LB;ŃżĄ (żĄ @ @ N;NF<ŃżĄ (żĄ @ @ 2.1;LB=ŃżĄ (żĄ @ @ 0;®>Ń żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;n?Ń
żÄ (żÄ pw#SD only requires positive fractionsJ06 ŃŃ’żĄ ww;MD@ŅżĄ (żĄ @ @ EE;LBAŅżĄ (żĄ @ @ 3;Å4BŅżĄ (żĄ @ @ zCC.7.EE.3 Solve reallife and mathematical problems using numerical and algebraic expressions and equations. Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.J06ŅŅłĄ @ @ ;LBCŅżĄ (żĄ @ @ 8;Č:DŅżĄ (żĄ @ @ }SD.8.N.3.1 (Application) Students are able to use various strategies to solve multistep problems involving rational numbers.;LBEŅżĄ (żĄ @ @ N;NFFŅżĄ (żĄ @ @ 3.1;MDGŅżĄ (żĄ @ @ 1;øHŅ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@IŅ
żÄ (żÄ pwJ06 ŅŅ’żĄ ww;MDJÓżĄ (żĄ @ @ EE;LBKÓżĄ (żĄ @ @ 4;kLÓżĄ (żĄ @ @ CC.7.EE.4 Solve reallife and mathematical problems using numerical and algebraic expressions and equations. Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.J06ÓÓłĄ @ @ ;LBMÓżĄ (żĄ @ @ 8;Č:NÓżĄ (żĄ @ @ }SD.8.N.3.1 (Application) Students are able to use various strategies to solve multistep problems involving rational numbers.;LBOÓżĄ (żĄ @ @ N;NFPÓżĄ (żĄ @ @ 3.1;MDQÓżĄ (żĄ @ @ 1;®RÓ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;hzSÓ
żÄ (żÄ pwlack of depth of inequalitiesJ06 ÓÓ’żĄ ww;MDTŌżĄ (żĄ @ @ EE;LBUŌżĄ (żĄ @ @ 4;kVŌżĄ (żĄ @ @ CC.7.EE.4 Solve reallife and mathematical problems using numerical and algebraic expressions and equations. Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.J06ŌŌłĄ @ @ ;LBWŌżĄ (żĄ @ @ 8;·XŌżĄ (żĄ @ @ lSD.8.A.4.2 (Analysis) Students are able ’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ż’’’ż’’’
!"#$%&'()*+,./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{}~to describe and represent relations using tables, graphs, and rules.;LBYŌżĄ (żĄ @ @ A;NFZŌżĄ (żĄ @ @ 4.2;MD[ŌżĄ (żĄ @ @ 1J06ŌŌ żĄ @ @ ;hz\Ō
żÄ (żÄ pwlack of depth of inequalitiesJ06 ŌŌ’żĄ ww;MD]ÕżĄ (żĄ @ @ EE;MD^ÕżĄ (żĄ @ @ 4a;×X_ÕżĄ (żĄ @ @ CC.7.EE.4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?J06ÕÕłĄ @ @ ;LB`ÕżĄ (żĄ @ @ 8;Č:aÕżĄ (żĄ @ @ }SD.8.N.3.1 (Application) Students are able to use various strategies to solve multistep problems involving rational numbers.;LBbÕżĄ (żĄ @ @ N;NFcÕżĄ (żĄ @ @ 3.1;MDdÕżĄ (żĄ @ @ 1;®eÕ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;wfÕ
żÄ (żÄ pw,SD does not mention context or word problemsJ06 ÕÕ’żĄ ww;LBgÖżĄ (żĄ @ @ G;LBhÖżĄ (żĄ @ @ 1;hziÖżĄ (żĄ @ @ CC.7.G.1 Draw, construct, and describe geometrical figures and describe the relationships between them. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.J06ÖÖłĄ @ @ ;LBjÖżĄ (żĄ @ @ 7;¹kÖżĄ (żĄ @ @ nSD.7.G.1.1 (Application) Students are able to identify, describe, and classify polygons having up to 10 sides.;LBlÖżĄ (żĄ @ @ G;NFmÖżĄ (żĄ @ @ 1.1;LBnÖżĄ (żĄ @ @ 0;®oÖ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed; źpÖ
żÄ (żÄ pwUSD does not construct or solve problems to produce scale drawing at a different scaleJ06 ÖÖ’żĄ ww;LBq×żĄ (żĄ @ @ G;LBr×żĄ (żĄ @ @ 1;hzs×żĄ (żĄ @ @ CC.7.G.1 Draw, construct, and describe geometrical figures and describe the relationships between them. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.J06××łĄ @ @ ;LBt×żĄ (żĄ @ @ 8;ÖVu×żĄ (żĄ @ @ SD.8.M.1.1 (Application) Students are able to apply proportional reasoning to solve measurement problems with rational number measurements.;LBv×żĄ (żĄ @ @ M;NFw×żĄ (żĄ @ @ 1.1;MDx×żĄ (żĄ @ @ 1J06×× żĄ @ @ ; źy×
żÄ (żÄ pwUSD does not construct or solve problems to produce scale drawing at a different scaleJ06 ××’żĄ ww;LBzŲżĄ (żĄ @ @ G;LB{ŲżĄ (żĄ @ @ 2;Å4ŲżĄ (żĄ @ @ zCC.7.G.2 Draw, construct, and describe geometrical figures and describe the relationships between them. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.J06ŲŲłĄ @ @ ;LB}ŲżĄ (żĄ @ @ 7;¹~ŲżĄ (żĄ @ @ nSD.7.G.1.1 (Application) Students are able to identify, describe, and classify polygons having up to 10 sides.;LBŲżĄ (żĄ @ @ G;NFŲżĄ (żĄ @ @ 1.1;LBŲżĄ (żĄ @ @ 0;®Ų żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@Ų
żÄ (żÄ pwJ06 ŲŲ’żĄ ww;LBŁżĄ (żĄ @ @ G;LB
ŁżĄ (żĄ @ @ 4;tŁżĄ (żĄ @ @ )CC.7.G.4 Solve reallife and mathematical problems involving angle measure, area, surface area, and volume. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.J06ŁŁłĄ @ @ ;LBŁżĄ (żĄ @ @ 7;ČŁżĄ (żĄ @ @ ÄSD.7.M.1.2 (Comprehension) Students, when given the formulas, are able to find circumference, perimeter, and area of circles, parallelograms, triangles, and trapezoids (whole number measurements).;LBŁżĄ (żĄ @ @ M;NFŁżĄ (żĄ @ @ 1.2;LBŁżĄ (żĄ @ @ 0J06ŁŁ żĄ @ @ J06ŁŁ
żÄ pwJ06 ŁŁ’żĄ ww;MDŚżĄ (żĄ @ @ SP;LBŚżĄ (żĄ @ @ 4;ĶDŚżĄ (żĄ @ @ CC.7.SP.4 Draw informal comparative inferences about two populations. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventhgrade science book are generally longer than the words in a chapter of a fourthgrade science book.J06ŚŚłĄ @ @ ;LBŚżĄ (żĄ @ @ 8;ÕTŚżĄ (żĄ @ @ SD.8.S.1.2 (Application) Students are able to use a variety of visual representations to display data to make comparisons and predictions.;LBŚżĄ (żĄ @ @ S;NFŚżĄ (żĄ @ @ 1.2;MDŚżĄ (żĄ @ @ 1;®Ś żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;tŚ
żÄ (żÄ pw)SD does not require visual representationJ06 ŚŚ’żĄ ww;MDŪżĄ (żĄ @ @ SP;LBŪżĄ (żĄ @ @ 5;
¾ŪżĄ (żĄ @ @ æCC.7.SP.5 Investigate chance processes and develop, use, and evaluate probability models. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.J06ŪŪłĄ @ @ ;LBŪżĄ (żĄ @ @ 7;½$ŪżĄ (żĄ @ @ rSD.7.S.2.1 (Comprehension) Students are able, given a sample space, to find the probability of a specific outcome.;LBŪżĄ (żĄ @ @ S;NFŪżĄ (żĄ @ @ 2.1;LBŪżĄ (żĄ @ @ 0;®Ū żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;etŪ
żÄ (żÄ pwSD does not mention 0 or 1J06 ŪŪ’żĄ ww;MD ÜżĄ (żĄ @ @ NS;LB”ÜżĄ (żĄ @ @ 1;ĢB¢ÜżĄ (żĄ @ @ CC.8.NS.1. Know that there are numbers that are not rational, and approximate them by rational numbers. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.J06ÜÜłĄ @ @ ;OH£ÜżĄ (żĄ @ @ 912;±¤ÜżĄ (żĄ @ @ fSD.912.N.1.1 (Comprehension) Students are able to identify multiple representations of a real number.;LB„ÜżĄ (żĄ @ @ N;NF¦ÜżĄ (żĄ @ @ 1.1;SP§ÜżĄ (żĄ @ @ 1 to 4;®ØÜ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@©Ü
żÄ (żÄ pwJ06 ÜÜ’żĄ ww;MDŖŻżĄ (żĄ @ @ NS;LB«ŻżĄ (żĄ @ @ 2;%¬ŻżĄ (żĄ @ @ ķCC.8.NS.2 Know that there are numbers that are not rational, and approximate them by rational numbers. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., Ą^2). For example, by truncating the decimal expansion of "2 (square root of 2), show that "2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.J06ŻŻłĄ @ @ ;OHŻżĄ (żĄ @ @ 912;ęv®ŻżĄ (żĄ @ @ SD.912.N.1.2A (Application) Students are able to apply properties and axioms of the real number system to various subsets, e.g., axioms of order, closure.;LBÆŻżĄ (żĄ @ @ N;OH°ŻżĄ (żĄ @ @ 1.2A;SP±ŻżĄ (żĄ @ @ 1 to 4;®²Ż żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;r³Ż
żÄ (żÄ pw'SD only compart rational and irrationalJ06 ŻŻ’żĄ ww;MD“ŽżĄ (żĄ @ @ EE;LBµŽżĄ (żĄ @ @ 1;ŻŅ¶ŽżĄ (żĄ @ @ ÉCC.8.EE.1 Work with radicals and integer exponents. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 × 3^( 5) = 3^( 3) = 1/(3^3) = 1/27.J06ŽŽłĄ @ @ ;OH·ŽżĄ (żĄ @ @ 912;ĢBøŽżĄ (żĄ @ @ SD.912.N.2.1 (Comprehension) Students are able to add, subtract, multiply, and divide real numbers including integral exponents.;LB¹ŽżĄ (żĄ @ @ N;NFŗŽżĄ (żĄ @ @ 2.1;SP»ŽżĄ (żĄ @ @ 1 to 4;®¼Ž żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@½Ž
żÄ (żÄ pwJ06 ŽŽ’żĄ ww;MD¾ßżĄ (żĄ @ @ EE;LBæßżĄ (żĄ @ @ 4;ū ĄßżĄ (żĄ @ @ °CC.8.EE.4 Work with radicals and integer exponents. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.J06ßßłĄ @ @ ;OHĮßżĄ (żĄ @ @ 912;ŅNĀßżĄ (żĄ @ @ SD.912.N.1.2 (Comprehension) Students are able to apply the concept of place value, magnitude, and relative magnitude of real numbers.;LBĆßżĄ (żĄ @ @ N;NFÄßżĄ (żĄ @ @ 1.2;SPÅßżĄ (żĄ @ @ 1 to 4;®Ęß żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@Ēß
żÄ (żÄ pwJ06 ßß’żĄ ww;MDČążĄ (żĄ @ @ EE;LBÉążĄ (żĄ @ @ 5;ÜbŹążĄ (żĄ @ @ CC.8.EE.5 Understand the connections between proportional relationships, lines, and linear equations. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distancetime graph to a distancetime equation to determine which of two moving objects has greater speed.J06ąąłĄ @ @ ;LBĖążĄ (żĄ @ @ 8;§ųĢążĄ (żĄ @ @ \SD.8.A.3.1 (Comprehension) Students are able to describe and determine linear relationships.;LBĶążĄ (żĄ @ @ A;NFĪążĄ (żĄ @ @ 3.1;LBĻążĄ (żĄ @ @ 0;®Šą żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;XZŃą
żÄ (żÄ pw
graphing onlyJ06 ąą’żĄ ww;MDŅįżĄ (żĄ @ @ EE;LBÓįżĄ (żĄ @ @ 5;ÜbŌįżĄ (żĄ @ @ CC.8.EE.5 Understand the connections between proportional relationships, lines, and linear equations. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distancetime graph to a distancetime equation to determine which of two moving objects has greater speed.J06įįłĄ @ @ ;OHÕįżĄ (żĄ @ @ 912;±ÖįżĄ (żĄ @ @ fSD.912.A.3.1 (Application) Students are able to create linear models to represent problem situations.;LB×įżĄ (żĄ @ @ A;NFŲįżĄ (żĄ @ @ 3.1;SPŁįżĄ (żĄ @ @ 1 to 4J06įį żĄ @ @ ;XZŚį
żÄ (żÄ pw
graphing onlyJ06 įį’żĄ ww;MDŪāżĄ (żĄ @ @ EE;LBÜāżĄ (żĄ @ @ 7;ĢBŻāżĄ (żĄ @ @ CC.8.EE.7 Analyze and solve linear equations and pairs of simultaneous linear equations. Solve linear equations in one variable.J06āāłĄ @ @ ;LBŽāżĄ (żĄ @ @ 6;÷ßāżĄ (żĄ @ @ ¬SD.6.A.2.1 (Application) Students are able to write and solve onestep 1st degree equations, with one variable, involving inverse operations using the set of whole numbers.;LBąāżĄ (żĄ @ @ A;NFįāżĄ (żĄ @ @ 2.1;LBāāżĄ (żĄ @ @ 2;xćā żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@äā
żÄ (żÄ pwJ06 āā’żĄ ww;MDåćżĄ (żĄ @ @ EE;LBęćżĄ (żĄ @ @ 7;ĢBēćżĄ (żĄ @ @ CC.8.EE.7 Analyze and solve linear equations and pairs of simultaneous linear equations. Solve linear equations in one variable.J06ććłĄ @ @ ;LBčćżĄ (żĄ @ @ 7;ÜéćżĄ (żĄ @ @ ĪSD.7.A.2.1 (Application) Students are able to write and solve onestep 1st degree equations, with one variable, using the set of integers and inequalities, with one variable, using the set of whole numbers.;LBźćżĄ (żĄ @ @ A;NFėćżĄ (żĄ @ @ 2.1;LBģćżĄ (żĄ @ @ 1J06ćć żĄ @ @ ;K@ķć
żÄ (żÄ pwJ06 ćć’żĄ ww;MDīäżĄ (żĄ @ @ EE;LBļäżĄ (żĄ @ @ 7;ĢBšäżĄ (żĄ @ @ CC.8.EE.7 Analyze and solve linear equations and pairs of simultaneous linear equations. Solve linear equations in one variable.J06ääłĄ @ @ ;LBńäżĄ (żĄ @ @ 8;°ņäżĄ (żĄ @ @ øSD.8.A.2.1 (Application) Students are able to write and solve twostep 1st degree equations, with one variable, and onestep inequalities, with one variable, using the set of integers.;LBóäżĄ (żĄ @ @ A;NFōäżĄ (żĄ @ @ 2.1;LBõäżĄ (żĄ @ @ 0J06ää żĄ @ @ ;K@öä
żÄ (żÄ pwJ06 ää’żĄ ww;MD÷åżĄ (żĄ @ @ EE;MDųåżĄ (żĄ @ @ 7a;§ųłåżĄ (żĄ @ @ \CC.8.EE.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).J06ååłĄ @ @ ;LBśåżĄ (żĄ @ @ 8;·ūåżĄ (żĄ @ @ lSD.8.A.4.2 (Analysis) Students are able to describe and represent relations using tables, graphs, and rules.;LBüåżĄ (żĄ @ @ A;NFżåżĄ (żĄ @ @ 4.2;LBžåżĄ (żĄ @ @ 0;®’å żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@å
żÄ (żÄ pwJ06 åå’żĄ ww;MDężĄ (żĄ @ @ EE;MDężĄ (żĄ @ @ 7b;ĀężĄ (żĄ @ @ ĮCC.8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.J06ęęłĄ @ @ ;LBężĄ (żĄ @ @ 8;ćpężĄ (żĄ @ @ SD.8.A.1.1 (Application) Students are able to use properties to expand, combine, and simplify 1st degree algebraic expressions with the set of integers.;LBężĄ (żĄ @ @ A;NFężĄ (żĄ @ @ 1.1;LBężĄ (żĄ @ @ 0;® ę żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@
ę
żÄ (żÄ pwJ06 ęę’żĄ ww;MDēżĄ (żĄ @ @ EE;MDēżĄ (żĄ @ @ 7b;Ā
ēżĄ (żĄ @ @ ĮCC.8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.J06ēēłĄ @ @ ;OHēżĄ (żĄ @ @ 912;×XēżĄ (żĄ @ @ SD.912.A.1.1A (Application) Students are able to write equivalent forms of rational algebraic expressions using properties of real numbers.;LBēżĄ (żĄ @ @ A;OHēżĄ (żĄ @ @ 1.1A;SPēżĄ (żĄ @ @ 1 to 4J06ēē żĄ @ @ ;K@ē
żÄ (żÄ pwJ06 ēē’żĄ ww;MDčżĄ (żĄ @ @ EE;LBčżĄ (żĄ @ @ 8;ŻdčżĄ (żĄ @ @ CC.8.EE.8 Analyze and solve linear equations and pairs of simultaneous linear equations. Analyze and solve pairs of simultaneous linear equations.J06ččłĄ @ @ ;OHčżĄ (żĄ @ @ 912;„ōčżĄ (żĄ @ @ ZSD.912.A.2.1A (Analysis) Students are able to determine solutions of quadratic equations.;LBčżĄ (żĄ @ @ A;OHčżĄ (żĄ @ @ 2.1A;SPčżĄ (żĄ @ @ 1 to 4;®č żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;WXč
żÄ (żÄ pwno analyze
J06 čč’żĄ ww;MDéżĄ (żĄ @ @ EE;MDéżĄ (żĄ @ @ 8b;[` éżĄ (żĄ @ @ CC.8.EE.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.J06ééłĄ @ @ ;OH!éżĄ (żĄ @ @ 912;Č:"éżĄ (żĄ @ @ }SD.912.A.2.2A (Application) Students are able to determine the solution of systems of equations and systems of inequalities.;LB#éżĄ (żĄ @ @ A;OH$éżĄ (żĄ @ @ 2.2A;SP%éżĄ (żĄ @ @ 1 to 4;®&é żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@'é
żÄ (żÄ pwJ06 éé’żĄ ww;LB(źżĄ (żĄ @ @ G;LB)źżĄ (żĄ @ @ 5;<"*źżĄ (żĄ @ @ ńCC.8.G.5 Understand congruence and similarity using physical models, transparencies, or geometry software. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angleangle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the three angles appear to form a line, and give an argument in terms of transversals why this is so.J06źźłĄ @ @ ;OH+źżĄ (żĄ @ @ 912;,źżĄ (żĄ @ @ bSD.912.G.1.2 (Application) Students are able to identify and apply relationships among triangles.;LBźżĄ (żĄ @ @ G;NF.źżĄ (żĄ @ @ 1.2;SP/źżĄ (żĄ @ @ 1 to 4;®0ź żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@1ź
żÄ (żÄ pwJ06 źź’żĄ ww;LB2ėżĄ (żĄ @ @ G;LB3ėżĄ (żĄ @ @ 5;<"4ėżĄ (żĄ @ @ ńCC.8.G.5 Understand congruence and similarity using physical models, transparencies, or geometry software. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angleangle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the three angles appear to form a line, and give an argument in terms of transversals why this is so.J06ėėłĄ @ @ ;OH5ėżĄ (żĄ @ @ 912;¤ņ6ėżĄ (żĄ @ @ YSD.912.G.1.1A (Evaluation) Students are able to justify properties of geometric figures.;LB7ėżĄ (żĄ @ @ G;OH8ėżĄ (żĄ @ @ 1.1A;SP9ėżĄ (żĄ @ @ 1 to 4J06ėė żĄ @ @ ;K@:ė
żÄ (żÄ pwJ06 ėė’żĄ ww;LB;ģżĄ (żĄ @ @ G;LB<ģżĄ (żĄ @ @ 7;Ž=ģżĄ (żĄ @ @ ĻCC.8.G.7 Understand and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions.J06ģģłĄ @ @ ;LB>ģżĄ (żĄ @ @ 8;čz?ģżĄ (żĄ @ @ SD.8.G.1.2 (Application) Students, when given any two sides of an illustrated right triangle, are able to use the Pythagorean Theorem to find the third side.;LB@ģżĄ (żĄ @ @ G;NFAģżĄ (żĄ @ @ 1.2;LBBģżĄ (żĄ @ @ 0;®Cģ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@Dģ
żÄ (żÄ pwJ06 ģģ’żĄ ww;LBEķżĄ (żĄ @ @ G;LBFķżĄ (żĄ @ @ 8;ßhGķżĄ (żĄ @ @ CC.8.G.8 Understand and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.J06ķķłĄ @ @ ;OHHķżĄ (żĄ @ @ 912;ŽfIķżĄ (żĄ @ @ SD.912.G.2.1 (Analysis) Students are able to recognize the relationship between a threedimensional figure and its twodimensional representation.;LBJķżĄ (żĄ @ @ G;NFKķżĄ (żĄ @ @ 2.1;SPLķżĄ (żĄ @ @ 1 to 4;®Mķ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@Nķ
żÄ (żÄ pwJ06 ķķ’żĄ ww;LBOīżĄ (żĄ @ @ G;LBPīżĄ (żĄ @ @ 9;.QīżĄ (żĄ @ @ ćCC.8.G.9 Solve realworld and mathematical problems involving volume of cylinders, cones and spheres. Know the formulas for the volume of cones, cylinders, and spheres and use them to solve realworld and mathematical problems.J06īīłĄ @ @ ;OHRīżĄ (żĄ @ @ 912;Ł\SīżĄ (żĄ @ @ SD.912.G.1.4A (Analysis) Students are able to use formulas for surface area and volume to solve problems involving threedimensional figures.;LBTīżĄ (żĄ @ @ G;OHUīżĄ (żĄ @ @ 1.4A;SPVīżĄ (żĄ @ @ 1 to 4;®Wī żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@Xī
żÄ (żÄ pwJ06 īī’żĄ ww;MDYļżĄ (żĄ @ @ SP;LBZļżĄ (żĄ @ @ 1;Ź[ļżĄ (żĄ @ @ ECC.8.SP.1 Investigate patterns of association in bivariate data. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.J06ļļłĄ @ @ ;LB\ļżĄ (żĄ @ @ 8;ÕT]ļżĄ (żĄ @ @ SD.8.S.1.2 (Application) Students are able to use a variety of visual representations to display data to make comparisons and predictions.;LB^ļżĄ (żĄ @ @ S;NF_ļżĄ (żĄ @ @ 1.2;LB`ļżĄ (żĄ @ @ 0;øaļ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@bļ
żÄ (żÄ pwJ06 ļļ’żĄ ww;MDcšżĄ (żĄ @ @ SP;LBdšżĄ (żĄ @ @ 1;ŹešżĄ (żĄ @ @ ECC.8.SP.1 Investigate patterns of association in bivariate data. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.J06ššłĄ @ @ ;OHfšżĄ (żĄ @ @ 912;¬gšżĄ (żĄ @ @ aSD.912.S.1.2A (Evaluation) Students are able to analyze and evaluate graphical displays of data.;LBhšżĄ (żĄ @ @ S;OHišżĄ (żĄ @ @ 1.2A;SPjšżĄ (żĄ @ @ 1 to 4J06šš żĄ @ @ ;K@kš
żÄ (żÄ pwJ06 šš’żĄ ww;MDlńżĄ (żĄ @ @ SP;LBmńżĄ (żĄ @ @ 1;ŹnńżĄ (żĄ @ @ ECC.8.SP.1 Investigate patterns of association in bivariate data. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.J06ńńłĄ @ @ ;OHońżĄ (żĄ @ @ 912;ānpńżĄ (żĄ @ @ SD.912.S.1.5A (Application) Students are able to use scatterplots, bestfit lines, and correlation coefficients to model data and support conclusions.;LBqńżĄ (żĄ @ @ S;OHrńżĄ (żĄ @ @ 1.5A;SPsńżĄ (żĄ @ @ 1 to 4J06ńń żĄ @ @ ;K@tń
żÄ (żÄ pwJ06 ńń’żĄ ww;MDuņżĄ (żĄ @ @ SP;LBvņżĄ (żĄ @ @ 2;”ģwņżĄ (żĄ @ @ VCC.8.SP.2 Investigate patterns of association in bivariate data. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.J06ņņłĄ @ @ ;OHxņżĄ (żĄ @ @ 912;±yņżĄ (żĄ @ @ fSD.912.S.1.3 (Analysis) Represent a set of data in a variety of graphical forms and draw conclusions.;LBzņżĄ (żĄ @ @ S;NF{ņżĄ (żĄ @ @ 1.3;SPņżĄ (żĄ @ @ 1 to 4;ø}ņ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@~ņ
żÄ (żÄ pwJ06 ņņ’żĄ ww;MDóżĄ (żĄ @ @ SP;LBóżĄ (żĄ @ @ 2;”ģóżĄ (żĄ @ @ VCC.8.SP.2 Investigate patterns of association in bivariate data. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.J06óółĄ @ @ ;OHóżĄ (żĄ @ @ 912;ānóżĄ (żĄ @ @ SD.912.S.1.5A (Application) Students are able to use scatterplots, bestfit lines, and correlation coefficients to model data and support conclusions.;LBóżĄ (żĄ @ @ S;OH
óżĄ (żĄ @ @ 1.5A;SPóżĄ (żĄ @ @ 1 to 4J06óó żĄ @ @ ;K@ó
żÄ (żÄ pwJ06 óó’żĄ ww;LBōżĄ (żĄ @ @ N;OHōżĄ (żĄ @ @ RN.1;īōżĄ (żĄ @ @ £CC.912.N.RN.1 Extend the properties of exponents to rational exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want [5^(1/3)]^3 = 5^[(1/3) x 3] to hold, so [5^(1/3)]^3 must equal 5.J06ōōłĄ @ @ ;OHōżĄ (żĄ @ @ 912;Ė@ōżĄ (żĄ @ @ SD.912.N.2.1A (Application) Students are able to add, subtract, multiply, and divide real numbers including rational exponents.;LBōżĄ (żĄ @ @ N;OHōżĄ (żĄ @ @ 2.1A;LBōżĄ (żĄ @ @ 0;®ō żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;øō
żÄ (żÄ pw<SD standards only require add, subtract, multiply and divideJ06 ōō’żĄ ww;LBõżĄ (żĄ @ @ N;OHõżĄ (żĄ @ @ RN.3;põżĄ (żĄ @ @ %CC.912.N.RN.3 Use properties of rational and irrational numbers. Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.J06õõłĄ @ @ ;OHõżĄ (żĄ @ @ 912;ęvõżĄ (żĄ @ @ SD.912.N.1.2A (Application) Students are able to apply properties and axioms of the real number system to various subsets, e.g., axioms of order, closure.;LBõżĄ (żĄ @ @ N;OHõżĄ (żĄ @ @ 1.2A;LBõżĄ (żĄ @ @ 0;øõ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;nõ
żÄ (żÄ pw#SD does not require an explainationJ06 õõ’żĄ ww;LBöżĄ (żĄ @ @ N;NFöżĄ (żĄ @ @ Q.1;möżĄ (żĄ @ @ "CC.912.N.Q.1 Reason quantitatively and use units to solve problems. Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.*J06ööłĄ @ @ ;OHöżĄ (żĄ @ @ 912;² öżĄ (żĄ @ @ gSD.912.M.1.1 (Comprehension) Students are able to choose appropriate unit label, scale, and precision.;LB”öżĄ (żĄ @ @ M;NF¢öżĄ (żĄ @ @ 1.1;LB£öżĄ (żĄ @ @ 0;ø¤ö żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;Ä„ö
żÄ (żÄ pwBSD does not address choose and interpret scale or origin in graphsJ06 öö’żĄ ww;LB¦÷żĄ (żĄ @ @ N;NF§÷żĄ (żĄ @ @ Q.1;mØ÷żĄ (żĄ @ @ "CC.912.N.Q.1 Reason quantitatively and use units to solve problems. Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.*J06÷÷łĄ @ @ ;OH©÷żĄ (żĄ @ @ 912;°
Ŗ÷żĄ (żĄ @ @ eSD.912.M.1.2 (Comprehension) Students are able to use suitable units when describing rate of change.;LB«÷żĄ (żĄ @ @ M;NF¬÷żĄ (żĄ @ @ 1.2;LB÷żĄ (żĄ @ @ 0J06÷÷ żĄ @ @ ;Ä®÷
żÄ (żÄ pwBSD does not address choose and interpret scale or origin in graphsJ06 ÷÷’żĄ ww;LBÆųżĄ (żĄ @ @ N;NF°ųżĄ (żĄ @ @ Q.1;m±ųżĄ (żĄ @ @ "CC.912.N.Q.1 Reason quantitatively and use units to solve problems. Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.*J06ųųłĄ @ @ ;OH²ųżĄ (żĄ @ @ 912;ŃL³ųżĄ (żĄ @ @ SD.912.M.1.1A (Application) Students are able to use dimensional analysis to check answers and determine units of a problem solution.;LB“ųżĄ (żĄ @ @ M;OHµųżĄ (żĄ @ @ 1.1A;LB¶ųżĄ (żĄ @ @ 0J06ųų żĄ @ @ ;Ä·ų
żÄ (żÄ pwBSD does not address choose and interpret scale or origin in graphsJ06 ųų’żĄ ww;LBøłżĄ (żĄ @ @ N;NF¹łżĄ (żĄ @ @ Q.2;ŲZŗłżĄ (żĄ @ @ CC.912.N.Q.2 Reason quantitatively and use units to solve problems. Define appropriate quantities for the purpose of descriptive modeling.*J06łłłĄ @ @ ;OH»łżĄ (żĄ @ @ 912;²¼łżĄ (żĄ @ @ gSD.912.M.1.1 (Comprehension) Students are able to choose appropriate unit label, scale, and precision.;LB½łżĄ (żĄ @ @ M;NF¾łżĄ (żĄ @ @ 1.1;LBæłżĄ (żĄ @ @ 0;®Ął żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@Įł
żÄ (żÄ pwJ06 łł’żĄ ww;LBĀśżĄ (żĄ @ @ N;NFĆśżĄ (żĄ @ @ Q.3;šÄśżĄ (żĄ @ @ „CC.912.N.Q.3 Reason quantitatively and use units to solve problems. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.*J06śśłĄ @ @ ;OHÅśżĄ (żĄ @ @ 912;²ĘśżĄ (żĄ @ @ gSD.912.M.1.1 (Comprehension) Students are able to choose appropriate unit label, scale, and precision.;LBĒśżĄ (żĄ @ @ M;NFČśżĄ (żĄ @ @ 1.1;LBÉśżĄ (żĄ @ @ 0;øŹś żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@Ėś
żÄ (żÄ pwJ06 śś’żĄ ww;LBĢūżĄ (żĄ @ @ N;OHĶūżĄ (żĄ @ @ CN.1;½²ĪūżĄ (żĄ @ @ ¹CC.912.N.CN.1 Perform arithmetic operations with complex numbers. Know there is a complex number i such that i^2 = "1, and every complex number has the form a + bi with a and b real. J06ūūłĄ @ @ ;OHĻūżĄ (żĄ @ @ 912;ŠJŠūżĄ (żĄ @ @
SD.912.N.1.1A (Comprehension) Students are able to describe the relationship of the real number system to the complex number system.;LBŃūżĄ (żĄ @ @ N;OHŅūżĄ (żĄ @ @ 1.1A;LBÓūżĄ (żĄ @ @ 0;øŌū żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@Õū
żÄ (żÄ pwJ06 ūū’żĄ ww;LBÖüżĄ (żĄ @ @ N;OH×üżĄ (żĄ @ @ CN.2;ßŌŲüżĄ (żĄ @ @ ŹCC.912.N.CN.2 Perform arithmetic operations with complex numbers. Use the relation i^2 = 1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.J06üüłĄ @ @ ;OHŁüżĄ (żĄ @ @ 912;ĻHŚüżĄ (żĄ @ @ SD.912.A.1.2A (Application) Students are able to extend the use of real number properties to expressions involving complex numbers.;LBŪüżĄ (żĄ @ @ A;OHÜüżĄ (żĄ @ @ 1.2A;LBŻüżĄ (żĄ @ @ 0;xŽü żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@ßü
żÄ (żÄ pwJ06 üü’żĄ ww;LBążżĄ (żĄ @ @ N;OHįżżĄ (żĄ @ @ CN.3;łāżżĄ (żĄ @ @ ®CC.912.N.CN.3 (+) Perform arithmetic operations with complex numbers. Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.J06żżłĄ @ @ ;OHćżżĄ (żĄ @ @ 912;ĻHäżżĄ (żĄ @ @ SD.912.A.1.2A (Application) Students are able to extend the use of real number properties to expressions involving complex numbers.;LBåżżĄ (żĄ @ @ A;OHężżĄ (żĄ @ @ 1.2A;LBēżżĄ (żĄ @ @ 0;®čż żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;uéż
żÄ (żÄ pw*SD does not identify the conjugate by nameJ06 żż’żĄ ww;LBźžżĄ (żĄ @ @ N;OHėžżĄ (żĄ @ @ CN.7;ćpģžżĄ (żĄ @ @ CC.912.N.CN.7 Use complex numbers in polynomial identities and equations. Solve quadratic equations with real coefficients that have complex solutions.J06žžłĄ @ @ ;OHķžżĄ (żĄ @ @ 912;„ōīžżĄ (żĄ @ @ ZSD.912.A.2.1A (Analysis) Students are able to determine solutions of quadratic equations.;LBļžżĄ (żĄ @ @ A;OHšžżĄ (żĄ @ @ 2.1A;LBńžżĄ (żĄ @ @ 0;xņž żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@óž
żÄ (żÄ pwJ06 žž’żĄ ww;LBō’żĄ (żĄ @ @ A;PJõ’żĄ (żĄ @ @ SSE.2;_Tö’żĄ (żĄ @ @
CC.912.A.SSE.2 Interpret the structure of expressions. Use the structure of an expression to identify ways to rewrite it. For example, see x^4 y^4 as (x^2)^2 (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 y^2)(x^2 + y^2).J06’’łĄ @ @ ;OH÷’żĄ (żĄ @ @ 912;Ś^ų’żĄ (żĄ @ @ SD.912.A.1.1 (Comprehension) Students are able to write equivalent forms of algebraic expressions using properties of the set of real numbers.;LBł’żĄ (żĄ @ @ A;NFś’żĄ (żĄ @ @ 1.1;LBū’żĄ (żĄ @ @ 0;®ü’ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;nż’
żÄ (żÄ pw#SD has students simplify and factorJ06 ’’’żĄ ww;LBžżĄ (żĄ @ @ A;PJ’żĄ (żĄ @ @ SSE.3;āżĄ (żĄ @ @ ŃCC.912.A.SSE.3 Write expressions in equivalent forms to solve problems. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*J06łĄ @ @ ;OHżĄ (żĄ @ @ 912;Ś^żĄ (żĄ @ @ SD.912.A.1.1 (Comprehension) Students are able to write equivalent forms of algebraic expressions using properties of the set of real numbers.;LBżĄ (żĄ @ @ A;NFżĄ (żĄ @ @ 1.1;LBżĄ (żĄ @ @ 0;® żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;s
żÄ (żÄ pw(SD does not address exponential functionJ06 ’żĄ ww;LBżĄ (żĄ @ @ A;PJ żĄ (żĄ @ @ SSE.3;ā
żĄ (żĄ @ @ ŃCC.912.A.SSE.3 Write expressions in equivalent forms to solve problems. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*J06łĄ @ @ ;OHżĄ (żĄ @ @ 912;„ōżĄ (żĄ @ @ ZSD.912.A.2.1A (Analysis) Students are able to determine solutions of quadratic equations.;LB
żĄ (żĄ @ @ A;OHżĄ (żĄ @ @ 2.1A;LBżĄ (żĄ @ @ 0J06 żĄ @ @ ;s
żÄ (żÄ pw(SD does not address exponential functionJ06 ’żĄ ww;LBżĄ (żĄ @ @ A;QLżĄ (żĄ @ @ SSE.3a;ŖžżĄ (żĄ @ @ _CC.912.A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.*J06łĄ @ @ ;OHżĄ (żĄ @ @ 912;Ś^żĄ (żĄ @ @ SD.912.A.1.1 (Comprehension) Students are able to write equivalent forms of algebraic expressions using properties of the set of real numbers.;LBżĄ (żĄ @ @ A;NFżĄ (żĄ @ @ 1.1;LBżĄ (żĄ @ @ 0;’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ż’’’ż’’’
”¢£¤„¦§Ø©Ŗ«¬®Æ°±²³“µ¶·ø¹ŗ»¼½¾æĄĮĀĆÄÅĘĒČÉŹĖĢĶĪĻŠŃŅÓŌÕÖ×ŲŁŚŪÜŻŽßąįāćäåęēčéźėģķīļšńņóōõö÷ųłśūüżž’ø żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@
żÄ (żÄ pwJ06 ’żĄ ww;LBżĄ (żĄ @ @ A;QLżĄ (żĄ @ @ SSE.3a;ŖžżĄ (żĄ @ @ _CC.912.A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.*J06łĄ @ @ ;OHżĄ (żĄ @ @ 912;„ōżĄ (żĄ @ @ ZSD.912.A.2.1A (Analysis) Students are able to determine solutions of quadratic equations.;LB żĄ (żĄ @ @ A;OH!żĄ (żĄ @ @ 2.1A;LB"żĄ (żĄ @ @ 0J06 żĄ @ @ ;K@#
żÄ (żÄ pwJ06 ’żĄ ww;LB$żĄ (żĄ @ @ A;QL%żĄ (żĄ @ @ SSE.3b;ĶD&żĄ (żĄ @ @ CC.912.A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.*J06łĄ @ @ ;OH'żĄ (żĄ @ @ 912;Ś^(żĄ (żĄ @ @ SD.912.A.1.1 (Comprehension) Students are able to write equivalent forms of algebraic expressions using properties of the set of real numbers.;LB)żĄ (żĄ @ @ A;NF*żĄ (żĄ @ @ 1.1;LB+żĄ (żĄ @ @ 0;ø, żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;¼
żÄ (żÄ pw>SD does not ask for completing the square or factoring by nameJ06 ’żĄ ww;LB.żĄ (żĄ @ @ A;QL/żĄ (żĄ @ @ SSE.3b;ĶD0żĄ (żĄ @ @ CC.912.A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.*J06łĄ @ @ ;OH1żĄ (żĄ @ @ 912;ĻH2żĄ (żĄ @ @ SD.912.A.1.2A (Application) Students are able to extend the use of real number properties to expressions involving complex numbers.;LB3żĄ (żĄ @ @ A;OH4żĄ (żĄ @ @ 1.2A;LB5żĄ (żĄ @ @ 0J06 żĄ @ @ ;¼6
żÄ (żÄ pw>SD does not ask for completing the square or factoring by nameJ06 ’żĄ ww;LB7żĄ (żĄ @ @ A;PJ8żĄ (żĄ @ @ SSE.4;C09żĄ (żĄ @ @ ųCC.912.A.SSE.4 Write expressions in equivalent forms to solve problems. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.*J06łĄ @ @ ;OH:żĄ (żĄ @ @ 912;Ė@;żĄ (żĄ @ @ SD.912.A.3.1A (Analysis) Students are able to distinguish between linear, quadratic, inverse variation, and exponential models.;LB<żĄ (żĄ @ @ A;OH=żĄ (żĄ @ @ 3.1A;LB>żĄ (żĄ @ @ 0;K@? żĄ (żĄ @ @ ;u@
żÄ (żÄ pw*SD does not ask them to derive the formulaJ06 ’żĄ ww;LBAżĄ (żĄ @ @ A;PJBżĄ (żĄ @ @ APR.3;B.CżĄ (żĄ @ @ ÷CC.912.A.APR.3 Understand the relationship between zeros and factors of polynomials. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.J06łĄ @ @ ;OHDżĄ (żĄ @ @ 912;ŃLEżĄ (żĄ @ @ SD.912.A.4.2A (Analysis) Students are able to describe the behavior of a polynomial, given the leading coefficient, roots, and degree;LBFżĄ (żĄ @ @ A;OHGżĄ (żĄ @ @ 4.2A;LBHżĄ (żĄ @ @ 0;xI żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@J
żÄ (żÄ pwJ06 ’żĄ ww;LBKżĄ (żĄ @ @ A;PJLżĄ (żĄ @ @ APR.6;ØśMżĄ (żĄ @ @ ]CC.912.A.APR.6 Rewrite rational expressions. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.J06łĄ @ @ ;OHNżĄ (żĄ @ @ 912;×XOżĄ (żĄ @ @ SD.912.A.1.1A (Application) Students are able to write equivalent forms of rational algebraic expressions using properties of real numbers.;LBPżĄ (żĄ @ @ A;OHQżĄ (żĄ @ @ 1.1A;LBRżĄ (żĄ @ @ 0;K@S żĄ (żĄ @ @ ;gxT
żÄ (żÄ pwCC standard is poorly wordedJ06 ’żĄ ww;LBU żĄ (żĄ @ @ A;PJV żĄ (żĄ @ @ CED.1;SPW żĄ (żĄ @ @ CC.912.A.CED.1 Create equations that describe numbers or relationship. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.*J06 łĄ @ @ ;OHX żĄ (żĄ @ @ 912;±Y żĄ (żĄ @ @ fSD.912.A.3.1 (Application) Students are able to create linear models to represent problem situations.;LBZ żĄ (żĄ @ @ A;NF[ żĄ (żĄ @ @ 3.1;LB\ żĄ (żĄ @ @ 0;®] żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;s^
żÄ (żÄ pw(SD address one variable linear equationsJ06 ’żĄ ww;LB_
żĄ (żĄ @ @ A;PJ`
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żĄ (żĄ @ @ ÜCC.912.A.CED.2 Create equations that describe numbers or relationship. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*J06
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żĄ (żĄ @ @ 912;ąjc
żĄ (żĄ @ @ SD.912.A.3.2A (Synthesis) Students are able to create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential.;LBd
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żĄ (żĄ @ @ 3.2A;LBf
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żÄ (żÄ pwJ06
’żĄ ww;LBiżĄ (żĄ @ @ A;PJjżĄ (żĄ @ @ CED.2;'ųkżĄ (żĄ @ @ ÜCC.912.A.CED.2 Create equations that describe numbers or relationship. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*J06łĄ @ @ ;OHlżĄ (żĄ @ @ 912;¼"mżĄ (żĄ @ @ qSD.912.A.4.1 (Application) Students are able to use graphs, tables, and equations to represent linear functions.;LBnżĄ (żĄ @ @ A;NFożĄ (żĄ @ @ 4.1;LBpżĄ (żĄ @ @ 0J06 żĄ @ @ ;K@q
żÄ (żÄ pwJ06 ’żĄ ww;LBrżĄ (żĄ @ @ A;PJsżĄ (żĄ @ @ CED.2;'ųtżĄ (żĄ @ @ ÜCC.912.A.CED.2 Create equations that describe numbers or relationship. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*J06łĄ @ @ ;OHużĄ (żĄ @ @ 912;ŃLvżĄ (żĄ @ @ SD.912.A.4.2A (Analysis) Students are able to describe the behavior of a polynomial, given the leading coefficient, roots, and degree;LBwżĄ (żĄ @ @ A;OHxżĄ (żĄ @ @ 4.2A;LByżĄ (żĄ @ @ 0J06 żĄ @ @ ;K@z
żÄ (żÄ pwJ06 ’żĄ ww;LB{
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żĄ (żĄ @ @ õCC.912.A.CED.4 Create equations that describe numbers or relationship. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm s law V = IR to highlight resistance R.*J06
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żĄ (żĄ @ @ SD.912.A.2.1 (Comprehension) Students are able to use algebraic properties to transform multistep, singlevariable, firstdegree equations.;LB
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żÄ (żÄ pw*SD only asks for single variable equationsJ06
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żĄ (żĄ @ @ A;PJżĄ (żĄ @ @ REI.3;²żĄ (żĄ @ @ ¹CC.912.A.REI.3 Solve equations and inequalities in one variable. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. J06łĄ @ @ ;OHżĄ (żĄ @ @ 912;ŲZżĄ (żĄ @ @ SD.912.A.2.1 (Comprehension) Students are able to use algebraic properties to transform multistep, singlevariable, firstdegree equations.;LBżĄ (żĄ @ @ A;NFżĄ (żĄ @ @ 2.1;LBżĄ (żĄ @ @ 0;ø żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@
żÄ (żÄ pwJ06 ’żĄ ww;LBżĄ (żĄ @ @ A;PJżĄ (żĄ @ @ REI.3;²żĄ (żĄ @ @ ¹CC.912.A.REI.3 Solve equations and inequalities in one variable. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. J06łĄ @ @ ;OHżĄ (żĄ @ @ 912;“żĄ (żĄ @ @ ŗSD.912.A.2.2 (Application) Students are able to use algebraic properties to transform multistep, singlevariable, firstdegree inequalities and represent solutions using a number line.;LBżĄ (żĄ @ @ A;NFżĄ (żĄ @ @ 2.2;LBżĄ (żĄ @ @ 0J06 żĄ @ @ ;K@
żÄ (żÄ pwJ06 ’żĄ ww;LBżĄ (żĄ @ @ A;PJżĄ (żĄ @ @ REI.4;øżĄ (żĄ @ @ mCC.912.A.REI.4 Solve equations and inequalities in one variable. Solve quadratic equations in one variable. J06łĄ @ @ ;OHżĄ (żĄ @ @ 912;„ōżĄ (żĄ @ @ ZSD.912.A.2.1A (Analysis) Students are able to determine solutions of quadratic equations.;LBżĄ (żĄ @ @ A;OHżĄ (żĄ @ @ 2.1A;LBżĄ (żĄ @ @ 0;x żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@”
żÄ (żÄ pwJ06 ’żĄ ww;LB¢żĄ (żĄ @ @ A;QL£żĄ (żĄ @ @ REI.4a;łī¤żĄ (żĄ @ @ ×CC.912.A.REI.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p)^2 = q that has the same solutions. Derive the quadratic formula from this form. J06łĄ @ @ ;OH„żĄ (żĄ @ @ 912;„ō¦żĄ (żĄ @ @ ZSD.912.A.2.1A (Analysis) Students are able to determine solutions of quadratic equations.;LB§żĄ (żĄ @ @ A;OHØżĄ (żĄ @ @ 2.1A;LB©żĄ (żĄ @ @ 0;øŖ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;Ų«
żÄ (żÄ pwLSD does not require completing the square or to derive the quadratic formulaJ06 ’żĄ ww;LB¬żĄ (żĄ @ @ A;QLżĄ (żĄ @ @ REI.4b;Ę®żĄ (żĄ @ @ CCC.912.A.REI.4b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.J06łĄ @ @ ;OHÆżĄ (żĄ @ @ 912;„ō°żĄ (żĄ @ @ ZSD.912.A.2.1A (Analysis) Students are able to determine solutions of quadratic equations.;LB±żĄ (żĄ @ @ A;OH²żĄ (żĄ @ @ 2.1A;LB³żĄ (żĄ @ @ 0;x“ żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@µ
żÄ (żÄ pwJ06 ’żĄ ww;LB¶żĄ (żĄ @ @ A;PJ·żĄ (żĄ @ @ REI.5;.øżĄ (żĄ @ @ ćCC.912.A.REI.5 Solve systems of equations. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.J06łĄ @ @ ;OH¹żĄ (żĄ @ @ 912;Č:ŗżĄ (żĄ @ @ }SD.912.A.2.2A (Application) Students are able to determine the solution of systems of equations and systems of inequalities.;LB»żĄ (żĄ @ @ A;OH¼żĄ (żĄ @ @ 2.2A;LB½żĄ (żĄ @ @ 0;®¾ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;dræ
żÄ (żÄ pwSD does not require proffJ06 ’żĄ ww;LBĄżĄ (żĄ @ @ A;PJĮżĄ (żĄ @ @ REI.6;ŖĀżĄ (żĄ @ @ µCC.912.A.REI.6 Solve systems of equations. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.J06łĄ @ @ ;OHĆżĄ (żĄ @ @ 912;Č:ÄżĄ (żĄ @ @ }SD.912.A.2.2A (Application) Students are able to determine the solution of systems of equations and systems of inequalities.;LBÅżĄ (żĄ @ @ A;OHĘżĄ (żĄ @ @ 2.2A;LBĒżĄ (żĄ @ @ 0;xČ żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@É
żÄ (żÄ pwJ06 ’żĄ ww;LBŹżĄ (żĄ @ @ A;QLĖżĄ (żĄ @ @ REI.10;A,ĢżĄ (żĄ @ @ öCC.912.A.REI.10 Represent and solve equations and inequalities graphically. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).J06łĄ @ @ ;OHĶżĄ (żĄ @ @ 912;ŃLĪżĄ (żĄ @ @ SD.912.A.4.2A (Analysis) Students are able to describe the behavior of a polynomial, given the leading coefficient, roots, and degree;LBĻżĄ (żĄ @ @ A;OHŠżĄ (żĄ @ @ 4.2A;LBŃżĄ (żĄ @ @ 0;®Ņ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@Ó
żÄ (żÄ pwJ06 ’żĄ ww;LBŌżĄ (żĄ @ @ A;QLÕżĄ (żĄ @ @ REI.11;?(ÖżĄ (żĄ @ @ ōCC.912.A.REI.11 Represent and solve equations and inequalities graphically. Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*J06łĄ @ @ ;OH×żĄ (żĄ @ @ 912;Č:ŲżĄ (żĄ @ @ }SD.912.A.2.2A (Application) Students are able to determine the solution of systems of equations and systems of inequalities.;LBŁżĄ (żĄ @ @ A;OHŚżĄ (żĄ @ @ 2.2A;LBŪżĄ (żĄ @ @ 0;øÜ żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@Ż
żÄ (żÄ pwJ06 ’żĄ ww;LBŽżĄ (żĄ @ @ A;QLßżĄ (żĄ @ @ REI.12;„ōążĄ (żĄ @ @ ZCC.912.A.REI.12 Represent and solve equations and inequalities graphically. Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding halfplanes.J06łĄ @ @ ;OHįżĄ (żĄ @ @ 912;Č:āżĄ (żĄ @ @ }SD.912.A.2.2A (Application) Students are able to determine the solution of systems of equations and systems of inequalities.;LBćżĄ (żĄ @ @ A;OHäżĄ (żĄ @ @ 2.2A;LBåżĄ (żĄ @ @ 0;xę żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@ē
żÄ (żÄ pwJ06 ’żĄ ww;LBčżĄ (żĄ @ @ A;QLéżĄ (żĄ @ @ REI.12;„ōźżĄ (żĄ @ @ ZCC.912.A.REI.12 Represent and solve equations and inequalities graphically. Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding halfplanes.J06łĄ @ @ ;OHėżĄ (żĄ @ @ 912;¤ņģżĄ (żĄ @ @ YSD.912.A.4.6A (Application) Students are able to graph solutions to linear inequalities.;LBķżĄ (żĄ @ @ A;OHīżĄ (żĄ @ @ 4.6A;LBļżĄ (żĄ @ @ 0J06 żĄ @ @ ;K@š
żÄ (żÄ pwJ06 ’żĄ ww;LBńżĄ (żĄ @ @ F;OHņżĄ (żĄ @ @ IF.1;ėóżĄ (żĄ @ @ CC.912.F.IF.1 Understand the concept of a function and use function notation. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).J06łĄ @ @ ;OHōżĄ (żĄ @ @ 912;“õżĄ (żĄ @ @ iSD.912.A.4.1A (Analysis) Students are able to determine the domain, range, and intercepts of a function.;LBöżĄ (żĄ @ @ A;OH÷żĄ (żĄ @ @ 4.1A;LBųżĄ (żĄ @ @ 0;øł żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@ś
żÄ (żÄ pwJ06 ’żĄ ww;LBūżĄ (żĄ @ @ F;OHüżĄ (żĄ @ @ IF.2;+żżĄ (żĄ @ @ ąCC.912.F.IF.2 Understand the concept of a function and use function notation. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.J06łĄ @ @ ;OHžżĄ (żĄ @ @ 912;“’żĄ (żĄ @ @ iSD.912.A.4.1A (Analysis) Students are able to determine the domain, range, and intercepts of a function.;LBżĄ (żĄ @ @ A;OHżĄ (żĄ @ @ 4.1A;LBżĄ (żĄ @ @ 0;® żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@
żÄ (żÄ pwJ06 ’żĄ ww;LBżĄ (żĄ @ @ F;OHżĄ (żĄ @ @ IF.4;?(żĄ (żĄ @ @ ōCC.912.F.IF.4 Interpret functions that arise in applications in terms of the context. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*J06łĄ @ @ ;OHżĄ (żĄ @ @ 912;ŃL żĄ (żĄ @ @ SD.912.A.4.2A (Analysis) Students are able to describe the behavior of a polynomial, given the leading coefficient, roots, and degree;LB
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żÄ (żÄ pwJ06 ’żĄ ww;LBżĄ (żĄ @ @ F;OHżĄ (żĄ @ @ IF.5;ŃLżĄ (żĄ @ @ CC.912.F.IF.5 Interpret functions that arise in applications in terms of the context. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*J06łĄ @ @ ;OHżĄ (żĄ @ @ 912;“żĄ (żĄ @ @ iSD.912.A.4.1A (Analysis) Students are able to determine the domain, range, and intercepts of a function.;LBżĄ (żĄ @ @ A;OHżĄ (żĄ @ @ 4.1A;LBżĄ (żĄ @ @ 0;® żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@
żÄ (żÄ pwJ06 ’żĄ ww;LBżĄ (żĄ @ @ F;OHżĄ (żĄ @ @ IF.7;!ģżĄ (żĄ @ @ ÖCC.912.F.IF.7 Analyze functions using different representations. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*J06łĄ @ @ ;OHżĄ (żĄ @ @ 912;¼"żĄ (żĄ @ @ qSD.912.A.4.1 (Application) Students are able to use graphs, tables, and equations to represent linear functions.;LBżĄ (żĄ @ @ A;NFżĄ (żĄ @ @ 4.1;LB żĄ (żĄ @ @ 0;®! żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@"
żÄ (żÄ pwJ06 ’żĄ ww;LB#żĄ (żĄ @ @ F;OH$żĄ (żĄ @ @ IF.7;!ģ%żĄ (żĄ @ @ ÖCC.912.F.IF.7 Analyze functions using different representations. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*J06łĄ @ @ ;OH&żĄ (żĄ @ @ 912;ŃL'żĄ (żĄ @ @ SD.912.A.4.2A (Analysis) Students are able to describe the behavior of a polynomial, given the leading coefficient, roots, and degree;LB(żĄ (żĄ @ @ A;OH)żĄ (żĄ @ @ 4.2A;LB*żĄ (żĄ @ @ 0J06 żĄ @ @ ;K@+
żÄ (żÄ pwJ06 ’żĄ ww;LB,żĄ (żĄ @ @ F;PJżĄ (żĄ @ @ IF.7a;©ü.żĄ (żĄ @ @ ^CC.912.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.*J06łĄ @ @ ;OH/żĄ (żĄ @ @ 912;¼"0żĄ (żĄ @ @ qSD.912.A.4.1 (Application) Students are able to use graphs, tables, and equations to represent linear functions.;LB1żĄ (żĄ @ @ A;NF2żĄ (żĄ @ @ 4.1;LB3żĄ (żĄ @ @ 0;ø4 żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@5
żÄ (żÄ pwJ06 ’żĄ ww;LB6 żĄ (żĄ @ @ F;PJ7 żĄ (żĄ @ @ IF.7a;©ü8 żĄ (żĄ @ @ ^CC.912.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.*J06 łĄ @ @ ;OH9 żĄ (żĄ @ @ 912;ŃL: żĄ (żĄ @ @ SD.912.A.4.2A (Analysis) Students are able to describe the behavior of a polynomial, given the leading coefficient, roots, and degree;LB; żĄ (żĄ @ @ A;OH< żĄ (żĄ @ @ 4.2A;LB= żĄ (żĄ @ @ 0J06 żĄ @ @ ;K@>
żÄ (żÄ pwJ06 ’żĄ ww;LB?!żĄ (żĄ @ @ F;PJ@!żĄ (żĄ @ @ IF.7c;ŠJA!żĄ (żĄ @ @
CC.912.F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.* J06!!łĄ @ @ ;OHB!żĄ (żĄ @ @ 912;ŃLC!żĄ (żĄ @ @ SD.912.A.4.2A (Analysis) Students are able to describe the behavior of a polynomial, given the leading coefficient, roots, and degree;LBD!żĄ (żĄ @ @ A;OHE!żĄ (żĄ @ @ 4.2A;LBF!żĄ (żĄ @ @ 0;øG! żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@H!
żÄ (żÄ pwJ06 !!’żĄ ww;LBI"żĄ (żĄ @ @ F;PJJ"żĄ (żĄ @ @ IF.7e;ņK"żĄ (żĄ @ @ §CC.912.F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.*J06""łĄ @ @ ;OHL"żĄ (żĄ @ @ 912;øM"żĄ (żĄ @ @ mSD.912.A.4.5A (Analysis) Students are able to describe characteristics of nonlinear functions and relations.;LBN"żĄ (żĄ @ @ A;OHO"żĄ (żĄ @ @ 4.5A;LBP"żĄ (żĄ @ @ 0;øQ" żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@R"
żÄ (żÄ pwJ06 ""’żĄ ww;LBS#żĄ (żĄ @ @ F;PJT#żĄ (żĄ @ @ IF.7e;ņU#żĄ (żĄ @ @ §CC.912.F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.*J06##łĄ @ @ ;OHV#żĄ (żĄ @ @ 912;³W#żĄ (żĄ @ @ hSD.912.A.4.3A (Analysis) Students are able to apply transformations to graphs and describe the results.;LBX#żĄ (żĄ @ @ A;OHY#żĄ (żĄ @ @ 4.3A;LBZ#żĄ (żĄ @ @ 0J06## żĄ @ @ ;K@[#
żÄ (żÄ pwJ06 ##’żĄ ww;LB\$żĄ (żĄ @ @ F;OH]$żĄ (żĄ @ @ IF.8;Ō^$żĄ (żĄ @ @ ŹCC.912.F.IF.8 Analyze functions using different representations. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. J06$$łĄ @ @ ;OH_$żĄ (żĄ @ @ 912;„ō`$żĄ (żĄ @ @ ZSD.912.A.2.1A (Analysis) Students are able to determine solutions of quadratic equations.;LBa$żĄ (żĄ @ @ A;OHb$żĄ (żĄ @ @ 2.1A;LBc$żĄ (żĄ @ @ 0;®d$ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@e$
żÄ (żÄ pwJ06 $$’żĄ ww;LBf%żĄ (żĄ @ @ F;OHg%żĄ (żĄ @ @ IF.8;Ōh%żĄ (żĄ @ @ ŹCC.912.F.IF.8 Analyze functions using different representations. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. J06%%łĄ @ @ ;OHi%żĄ (żĄ @ @ 912;¼"j%żĄ (żĄ @ @ qSD.912.A.4.1 (Application) Students are able to use graphs, tables, and equations to represent linear functions.;LBk%żĄ (żĄ @ @ A;NFl%żĄ (żĄ @ @ 4.1;LBm%żĄ (żĄ @ @ 0J06%% żĄ @ @ ;K@n%
żÄ (żÄ pwJ06 %%’żĄ ww;LBo&żĄ (żĄ @ @ F;PJp&żĄ (żĄ @ @ IF.8a;Čq&żĄ (żĄ @ @ ÄCC.912.F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. J06&&łĄ @ @ ;OHr&żĄ (żĄ @ @ 912;„ōs&żĄ (żĄ @ @ ZSD.912.A.2.1A (Analysis) Students are able to determine solutions of quadratic equations.;LBt&żĄ (żĄ @ @ A;OHu&żĄ (żĄ @ @ 2.1A;LBv&żĄ (żĄ @ @ 0;øw& żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@x&
żÄ (żÄ pwJ06 &&’żĄ ww;LBy'żĄ (żĄ @ @ F;PJz'żĄ (żĄ @ @ IF.8a;Č{'żĄ (żĄ @ @ ÄCC.912.F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. J06''łĄ @ @ ;OH'żĄ (żĄ @ @ 912;ŃL}'żĄ (żĄ @ @ SD.912.A.4.2A (Analysis) Students are able to describe the behavior of a polynomial, given the leading coefficient, roots, and degree;LB~'żĄ (żĄ @ @ A;OH'żĄ (żĄ @ @ 4.2A;LB'żĄ (żĄ @ @ 0J06'' żĄ @ @ ;K@'
żÄ (żÄ pwJ06 ''’żĄ ww;LB(żĄ (żĄ @ @ F;PJ(żĄ (żĄ @ @ IF.8b;p(żĄ (żĄ @ @ %CC.912.F.IF.8b Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as representing exponential growth and decay.J06((łĄ @ @ ;OH
(żĄ (żĄ @ @ 912;Ł\(żĄ (żĄ @ @ SD.912.A.4.4A (Application) Students are able to apply properties and definitions of trigonometric, exponential, and logarithmic expressions.;LB(żĄ (żĄ @ @ A;OH(żĄ (żĄ @ @ 4.4A;LB(żĄ (żĄ @ @ 0;x( żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@(
żÄ (żÄ pwJ06 ((’żĄ ww;LB)żĄ (żĄ @ @ F;OH)żĄ (żĄ @ @ BF.1;ęv)żĄ (żĄ @ @ CC.912.F.BF.1 Build a function that models a relationship between two quantities. Write a function that describes a relationship between two quantities.* J06))łĄ @ @ ;OH)żĄ (żĄ @ @ 912;±)żĄ (żĄ @ @ fSD.912.A.3.1 (Application) Students are able to create linear models to represent problem situations.;LB)żĄ (żĄ @ @ A;NF)żĄ (żĄ @ @ 3.1;LB)żĄ (żĄ @ @ 0;x) żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@)
żÄ (żÄ pwJ06 ))’żĄ ww;LB*żĄ (żĄ @ @ F;OH*żĄ (żĄ @ @ BF.1;ęv*żĄ (żĄ @ @ CC.912.F.BF.1 Build a function that models a relationship between two quantities. Write a function that describes a relationship between two quantities.* J06**łĄ @ @ ;OH*żĄ (żĄ @ @ 912;ąj*żĄ (żĄ @ @ SD.912.A.3.2A (Synthesis) Students are able to create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential.;LB*żĄ (żĄ @ @ A;OH*żĄ (żĄ @ @ 3.2A;LB*żĄ (żĄ @ @ 0J06** żĄ @ @ ;K@*
żÄ (żÄ pwJ06 **’żĄ ww;LB+żĄ (żĄ @ @ F;PJ +żĄ (żĄ @ @ BF.1a;» ”+żĄ (żĄ @ @ pCC.912.F.BF.1a Determine an explicit expression, a recursive process, or steps for calculation from a context. J06++łĄ @ @ ;OH¢+żĄ (żĄ @ @ 912;±£+żĄ (żĄ @ @ fSD.912.A.3.1 (Application) Students are able to create linear models to represent problem situations.;LB¤+żĄ (żĄ @ @ A;NF„+żĄ (żĄ @ @ 3.1;LB¦+żĄ (żĄ @ @ 0;®§+ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@Ø+
żÄ (żÄ pwJ06 ++’żĄ ww;LB©,żĄ (żĄ @ @ F;PJŖ,żĄ (żĄ @ @ BF.1a;» «,żĄ (żĄ @ @ pCC.912.F.BF.1a Determine an explicit expression, a recursive process, or steps for calculation from a context. J06,,łĄ @ @ ;OH¬,żĄ (żĄ @ @ 912;ąj,żĄ (żĄ @ @ SD.912.A.3.2A (Synthesis) Students are able to create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential.;LB®,żĄ (żĄ @ @ A;OHÆ,żĄ (żĄ @ @ 3.2A;LB°,żĄ (żĄ @ @ 0J06,, żĄ @ @ ;K@±,
żÄ (żÄ pwJ06 ,,’żĄ ww;LB²żĄ (żĄ @ @ F;PJ³żĄ (żĄ @ @ BF.1b;F6“żĄ (żĄ @ @ ūCC.912.F.BF.1b Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. J06łĄ @ @ ;OHµżĄ (żĄ @ @ 912;ąj¶żĄ (żĄ @ @ SD.912.A.3.2A (Synthesis) Students are able to create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential.;LB·żĄ (żĄ @ @ A;OHøżĄ (żĄ @ @ 3.2A;LB¹żĄ (żĄ @ @ 0;®ŗ żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@»
żÄ (żÄ pwJ06 ’żĄ ww;LB¼.żĄ (żĄ @ @ F;OH½.żĄ (żĄ @ @ BF.2;9¾.żĄ (żĄ @ @ īCC.912.F.BF.2 Build a function that models a relationship between two quantities. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*J06..łĄ @ @ ;OHæ.żĄ (żĄ @ @ 912;ŖžĄ.żĄ (żĄ @ @ _SD.912.A.3.3A (Analysis) Students are able to use sequences and series to model relationships.;LBĮ.żĄ (żĄ @ @ A;OHĀ.żĄ (żĄ @ @ 3.3A;LBĆ.żĄ (żĄ @ @ 0;®Ä. żĄ (żĄ @ @ 71 = Weak match, major aspects of the CCSS not addressed;K@Å.
żÄ (żÄ pwJ06 ..’żĄ ww;LBĘ/żĄ (żĄ @ @ F;OHĒ/żĄ (żĄ @ @ BF.3;®Č/żĄ (żĄ @ @ ·CC.912.F.BF.3 Build new functions from existing functions. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.J06//łĄ @ @ ;OHÉ/żĄ (żĄ @ @ 912;³Ź/żĄ (żĄ @ @ hSD.912.A.4.3A (Analysis) Students are able to apply transformations to graphs and describe the results.;LBĖ/żĄ (żĄ @ @ A;OHĢ/żĄ (żĄ @ @ 4.3A;LBĶ/żĄ (żĄ @ @ 0;xĪ/ żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@Ļ/
żÄ (żÄ pwJ06 //’żĄ ww;LBŠ0żĄ (żĄ @ @ F;OHŃ0żĄ (żĄ @ @ BF.5;ņŅ0żĄ (żĄ @ @ §CC.912.F.BF.5 (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.J0600łĄ @ @ ;OHÓ0żĄ (żĄ @ @ 912;Ł\Ō0żĄ (żĄ @ @ SD.912.A.4.4A (Application) Students are able to apply properties and definitions of trigonometric, exponential, and logarithmic expressions.;LBÕ0żĄ (żĄ @ @ A;OHÖ0żĄ (żĄ @ @ 4.4A;LB×0żĄ (żĄ @ @ 0;øŲ0 żĄ (żĄ @ @ <2 = Good match, with minor aspects of the CCSS not addressed;K@Ł0
żÄ (żÄ pwJ06 00’żĄ ww;LBŚ1żĄ (żĄ @ @ F;OHŪ1żĄ (żĄ @ @ BF.5;ņÜ1żĄ (żĄ @ @ §CC.912.F.BF.5 (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.J0611łĄ @ @ ;OHŻ1żĄ (żĄ @ @ 912;øŽ1żĄ (żĄ @ @ mSD.912.A.4.5A (Analysis) Students are able to describe characteristics of nonlinear functions and relations.;LBß1żĄ (żĄ @ @ A;OHą1żĄ (żĄ @ @ 4.5A;LBį1żĄ (żĄ @ @ 0J0611 żĄ @ @ ;K@ā1
żÄ (żÄ pwJ06 11’żĄ ww;LBć2żĄ (żĄ @ @ F;OHä2żĄ (żĄ @ @ LE.1;Ųå2żĄ (żĄ @ @ ĢCC.912.F.LE.1 Construct and compare linear, quadratic, and exponential models and solve problems. Distinguish between situations that can be modeled with linear functions and with exponential functions.*J0622łĄ @ @ ;OHę2żĄ (żĄ @ @ 912;®ē2żĄ (żĄ @ @ cSD.912.A.3.2 (Comprehension) Students are able to distinguish between linear and nonlinear models.;LBč2żĄ (żĄ @ @ A;NFé2żĄ (żĄ @ @ 3.2;LBź2żĄ (żĄ @ @ 0;xė2 żĄ (żĄ @ @ 3 = Excellent match between the two documents;K@ģ2
żÄ (żÄ pwJ06 22’żĄ ww;LBķ3żĄ (żĄ @ @ F;OHī3żĄ (żĄ @ @ LE.1;Ųļ3żĄ (żĄ @ @ ĢCC.912.F.LE.1 Construct and compare linear, quadratic, and exponential models and solve problems. Distinguish between situations that can be modeled with linear functions and with exponential functions.*J0633łĄ @ @ ;OHš3żĄ (żĄ @ @ 912;Ė@ń3żĄ (żĄ @ @ SD.912.A.3.1A (Analysis) Students are able to distinguish between linear, quadratic, inverse variation, and exponential models.;LBņ3żĄ (żĄ @ @ A;OHó3żĄ (żĄ @ @ 3.1A;LBō3żĄ (żĄ @ @ 0J0633 żĄ @ @ ;K@õ3
żÄ (żÄ pwJ06 33’żĄ ww;LB