Grade 6 Mathematics Crosswalk CCSS to CT Standards

Mathematics Crosswalk Common Core State Standards to Connecticut State Standards to District Curriculum

Grade 6 Grade 6 Mathematics Crosswalk – CCSS to CT Standards

RATIOS AND PROPORTIONAL RELATIONSHIPS Understand ratio concepts and use ratio reasoning to solve problems. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.RP.1 Understand the CT.3.2.1.9 Describe CMT 6.12 Ratios and Understanding the concept of concept of a ratio and use quantitative relationships Proportions a ratio is included in the ratio language to describe a using ratios and identify A. Solve problems Grades 3, 4, 5 and 6 CT ratio relationship between patterns with equivalent involving simple ratios. standards and is assessed on two quantities. For ratios such as 3 out of 6 the Grades 6 CMT. example, "The ratio of crayons are red or 4 out of wings to beaks in the bird 8 crayons are red and are house at the zoo was 2:1, the same as 1 out of 2 because for every 2 wings crayons is red. there was 1 beak." "For every vote candidate A CT.4.2.1.12 Express a ratio received, candidate C or division problem as a received nearly three fraction and describe the votes." relationship between the divisor and the remainder written as a fraction. For example: When determining the number of groups of three in fourteen we say 14 ÷ 3 = 4 with a remainder of 2 or 4 ⅔. CT.5.2.1.9 Use models and pictures to identify and compare ratios and to represent ratios in equivalent fraction and decimal forms. CT.6.2.1.7. Use ratios and rates (involving different 2 Connecticut State Department of Education September 2010 Grade 6 Mathematics Crosswalk – CCSS to CT Standards

RATIOS AND PROPORTIONAL RELATIONSHIPS Understand ratio concepts and use ratio reasoning to solve problems. CCSS CT Standard Match District Correlation CT Assessment Notes units) to compare quantities. CC.6.RP.2 Understand the CT.6.2.1.7 Use ratios and CMT 6.12 Ratios and "Unit rates" are not specified concept of a unit rate a/b rates (involving different Proportions in the CT standards. Ratios associated with a ratio a:b units) to compare A. Solve problems as rates are included in the with b ≠ 0 (b not equal to quantities. involving simple ratios. Grades 6 and 7 CT zero), and use rate language standards. in the context of a ratio CT.6.2.2.11 Solve practical CMT 7.12 Ratios and relationship. For example, problems involving rates, Proportions Solving problems with ratios “This recipe has a ratio of 3 ratios, percentages and A. Solve problems (including rates) is assessed cups of flour to 4 cups of proportionality. involving ratios. on the Grades 6, 7 and 8 sugar, so there is 3/4 cup of CMT. flour for each cup of CT.7.2.2.10 Write ratios CMT 8.12 Ratios and sugar.” “We paid $75 for and proportions to solve Proportions 15 hamburgers, which is a problems in context A. Solve problems rate of $5 per hamburger.” involving rates, scale involving ratios. (Expectations for unit rates factors and percentages. in this grade are limited to CT.8.2.2.8 Estimate non-complex fractions.) reasonable answers and solve problems in context involving rational and common irrational numbers, ratios and percentages, including percentage of increase and decrease, and justify solutions in writing.

3 Connecticut State Department of Education September 2010 Grade 6 Mathematics Crosswalk – CCSS to CT Standards

RATIOS AND PROPORTIONAL RELATIONSHIPS Understand ratio concepts and use ratio reasoning to solve problems. CC.6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations: CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.RP.3a Make tables of CT.4.2.1.12 Solve practical CMT 6.12 Ratios and The CT standards about equivalent ratios relating problems involving simple Proportions modeling ratios span Grades quantities with whole- ratios and proportions, e.g., A. Solve problems 4, 5 and 6 and include number measurements, find determining distance on involving simple ratios. models, pictures and number missing values in the tables, maps, by using models, patterns. and plot the pairs of values pictures and number CMT 7.12 Ratios and on the coordinate plane. patterns. Proportions The CMT does not include Use tables to compare A. Solve problems plotting pairs of values on ratios. CT.5.2.1.9 Use models and involving ratios. the coordinate plane to pictures to identify and model equivalent ratios. compare ratios and to CMT 8.12 Ratios and represent ratios in Proportions equivalent fraction and A. Solve problems decimal forms. involving ratios. CT.6.1.2.2 Create tables of values and scatter plots from mathematical relationships and equations and vice versa to solve problems. CC.6.RP.3b Solve unit rate CT.6.2.2.11 Solve practical CMT 6.12 Ratios and "Unit rates" are not specified problems including those problems involving rates, Proportions in the CT standards. Solving involving unit pricing and ratios, percentages and A. Solve problems rate problems are included in constant speed. For proportionality. involving simple ratios. the Grades 6 and 7 CT example, If it took 7 hours standards. to mow 4 lawns, then at CT.7.2.2.10 Write ratios CMT 7.12 Ratios and that rate, how many lawns and proportions to solve Proportions Solving problems with ratios problems in context (including rates) is assessed 4 Connecticut State Department of Education September 2010 Grade 6 Mathematics Crosswalk – CCSS to CT Standards

RATIOS AND PROPORTIONAL RELATIONSHIPS Understand ratio concepts and use ratio reasoning to solve problems. CC.6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations: CCSS CT Standard Match District Correlation CT Assessment Notes could be mowed in 35 involving rates, scale A. Solve problems on the Grades 6, 7 and 8 hours? At what rate were factors and percentages. involving ratios. CMT. lawns being mowed? CT.8.2.2.8 Estimate CMT 8.12 Ratios and reasonable answers and Proportions solve problems in context A. Solve problems involving rational and involving ratios. common irrational numbers, ratios and percentages, including percentage of increase and decrease, and justify solutions in writing. CC.6.RP.3c Find a CT.6.2.2.10 Estimate and CMT 7.13 Computation Solving percent problems is percentage of a quantity as find percentages of a with Percents included in the Grades 6, 7, a rate per 100 (e.g., 30% of number in context using and 8 CT standards. a quantity means 30/100 benchmarks and number A. Find percents of whole times the quantity); solve patterns and ratios to 100. numbers or the percent a Solving problems with problems involving finding given number is of another percents is not assessed on the whole given a part and CT.7.2.2.12 Solve percent number. the Grade 6 CMT but is the percentage. problems in context using a assessed on the Grades 7 and variety of strategies i.e., B. Solve 1-step problems 8 CMT. proportions or equations, involving percents in including what percentage context. one number is of another and finding percentage CMT 8.13 Computation increase and/or decrease. with Percents A. Find percents of whole CT.8.2.2.10 Solve a variety numbers or the percent a of problems in context given number is of another 5 Connecticut State Department of Education September 2010 Grade 6 Mathematics Crosswalk – CCSS to CT Standards

RATIOS AND PROPORTIONAL RELATIONSHIPS Understand ratio concepts and use ratio reasoning to solve problems. CC.6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations: CCSS CT Standard Match District Correlation CT Assessment Notes involving percents, number. including the following: • Percentage of a number B. Solve problems • The percentage one involving percents in number is of another context. number • The percentage of a missing amount • Percentage increase/ decrease

RATIOS AND PROPORTIONAL RELATIONSHIPS Understand ratio concepts and use ratio reasoning to solve problems. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.RP.3d Use ratio CT.5.3.3.10 Solve length CMT 5.16 Customary and Measurement conversions reasoning to convert problems involving Metric Measures are included in the Grades 5 measurement units; conversions of measure D. Solve problems through 8 CT standards and manipulate and transform within the customary involving conversions of are assessed on the Grades 5, units appropriately when (inches, feet, yards and measures of length. 6, 7 and 8 CMT. Specific multiplying or dividing miles) or metric systems reference to using ratios to quantities. (millimeters, centimeters, CMT 6.16 Customary and convert is included in the meters and kilometers). Metric Measures Grade 6 CT standard. C. Identify the correct CT.6.3.3.9 Use ratios to solution to problems convert between customary involving the conversions units of length, mass, of measures of length, capacity and time. mass, capacity and time. CT.6.3.3.10 Use ratios and powers of 10 to convert D. Solve problems between metric units. involving conversions of measures of length, mass, CT.7.3.3.11 Write and capacity and time. solve problems in context involving conversions of CMT 7.16 Customary and customary or metric units Metric Measures and units of time. D. Solve problems involving conversions of CT.8.3.3.10 Solve customary or metric units customary or metric of measure. measurement problems in context using Dimensional E Solve problems involving Analysis (the Unit Factor conversions of time units. Method) and justify the results in writing. CMT 8.16 Customary and 7 Connecticut State Department of Education September 2010 Grade 6 Mathematics Crosswalk – CCSS to CT Standards

RATIOS AND PROPORTIONAL RELATIONSHIPS Understand ratio concepts and use ratio reasoning to solve problems. CCSS CT Standard Match District Correlation CT Assessment Notes Metric Measures C. Solve problems involving conversions and/or operations within customary or metric units of measure.

THE NUMBER SYSTEM Apply and extend previous understandings of multiplication and division to divide fractions by fractions. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.NS.1 Interpret and CT.6.2.2.15 Use the NA The CT standards do not compute quotients of inverse relationship specify the use of "visual fractions, and solve word between multiplication and fraction models and problems involving division division to make sense of equations to represent the of fractions by fractions, procedures for multiplying problems." e.g., by using visual and dividing fractions. fraction models and Division of fractions is not CT.6.2.2.19 Write and assessed on the CMT. equations to represent the solve multistep problems in problem. For example, context involving addition, create a story context for subtraction, multiplication (2/3) ÷ (3/4) and use a and division with whole visual fraction model to numbers, fractions, show the quotient; use the decimals, money and relationship between simple percentages. multiplication and division to explain that (2/3) ÷ (3/4) CT.6.2.2.14 Examine the = 8/9 because 3/4 of 8/9 is relationships between 2/3. (In general, (a/b) ÷ multiplication by a unit (c/d) = ad/bc.). How much fraction and dividing by the chocolate will each person fraction's denominator, e.g., get if 3 people share 1/2 lb 1/2 of $6 is the same as $6 of chocolate equally? How ÷ 2, and use this to solve many 3/4-cup servings are problems. in 2/3 of a cup of yogurt? CT.6.2.2.16 Understand How wide is a rectangular and defend in writing the strip of land with length 3/4 magnitude of the result of mi and area 1/2 square mi? multiplication or division problems involving fractions or decimals.

THE NUMBER SYSTEM Compute fluently with multi-digit numbers and find common factors and multiples. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.NS.2 Fluently divide CT.5.2.2.12 Develop and CMT 5.7 Computation The CCSS standards move multi-digit numbers using use strategies involving with Whole Numbers and from concrete models for the standard algorithm. place value relationships, Decimals division of multi-digit inverse operations and C. Multiply and divide 2- numbers in Grade 5 to the algebraic properties and 3-digit whole numbers abstract ("the standard (commutative, associative and money amounts less algorithm") in Grade 6. and distributive) to simplify than $10 by 1-digit addition, subtraction and numbers. Division of multi-digit multiplication problems numbers is included in the with 3-, 4- and 5-digit CMT 6.7 Computation Grades 5, 6, 7 and 8 CT numbers and money with Whole Numbers and standards. The CT standards include "various strategies" amounts and division by Decimals and are not limited to use of one-digit factors. C. Multiply and divide 2- the "standard algorithm." and 3-digit whole numbers CT.6.2.2.9 Develop, and money amounts by 1- describe and use strategies Division of multi-digit digit numbers and 1-digit numbers is assessed on the for solving, simplifying and decimals. estimating multiplication Grades 5, 6, 7 and 8 CMT. and division problems CMT 7.7 Computation involving large numbers, with Whole Numbers and decimals and powers of 10, Decimals e.g., 4.25 × 100 = 425 and B. Multiply and divide 2- 365,000 ÷ 6,000 = 365 ÷ 6; and 3-digit whole numbers, 365 ÷ 6 ≈ 360 ÷ 6 ≈ 60. money amounts and CT.6.2.2.19 Write and decimals by 1-digit solve multistep problems in numbers and decimals context involving addition, (multiply only). subtraction, multiplication and division with whole CMT 8.7 Computation with Whole Numbers and 10 Connecticut State Department of Education September 2010 Grade 6 Mathematics Crosswalk – CCSS to CT Standards

THE NUMBER SYSTEM Compute fluently with multi-digit numbers and find common factors and multiples. CCSS CT Standard Match District Correlation CT Assessment Notes numbers, fractions, Decimals decimals, money and B. Multiply 2- and 3-digit simple percentages. whole numbers, money amounts and decimals by 1- CT.7.2.2.9 Apply a variety or 2-digit numbers and of strategies to write and decimals. Divide 2- and 3- solve problems involving digit whole numbers, addition, subtraction, money amounts and multiplication and division decimals by 1-digit whole of positive rational numbers and decimals. numbers, including whole numbers, fractions and decimals.

THE NUMBER SYSTEM Compute fluently with multi-digit numbers and find common factors and multiples. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.NS.3 Fluently add, CT.5.2.2.16 Add and CMT 5.7 Computation The CCSS standards move subtract, multiply, and subtract fractions, decimals with Whole Numbers and from concrete models for divide multi-digit decimals and mixed numbers using a Decimals computing with multi-digit using the standard variety of strategies, e.g., A. Add and subtract 2-, 3- decimals in Grade 5 to the algorithm for each models, mental math, and 4-digit whole numbers abstract ("the standard operation. equivalence and and money amounts less algorithm") in Grade 6. substitution: 1/2 + 3/4 can than $100. also be solved using 0.5 + Computation with multi-digit 0.75. CMT 5.7 Computation decimals is included in the with Whole Numbers and Grades 5, 6, 7 and 8 CT CT.5.2.2.13 Multiply and Decimals standards. The CT standards include "various strategies" divide decimals and money C. Multiply and divide 2- and are not limited to use of amounts by whole numbers. and 3-digit whole numbers the "standard algorithm." and money amounts less CT.6.2.2.9 Develop, than $10 by 1-digit Computations with multi- describe and use strategies numbers. digit decimals is assessed on for solving, simplifying and the Grades 5 (money estimating multiplication CMT 6.7 Computation amounts), 6, 7 and 8 CMT. and division problems with Whole Numbers and involving large numbers, Decimals decimals and powers of 10. A. Add and subtract 2-, 3- For example: 4.25 × 100 = and 4-digit whole numbers, 425; and 365,000 ÷ 6,000 = money amounts and 365 ÷ 6, 365 ÷ 6 ≈ 360 ÷ 6 decimals. ≈ 60. B. Multiply and divide CT.6.2.2.12 Add, subtract, whole numbers and multiply and divide by decimals by 10, 100 and fractions and decimals in 1,000. context. C. Multiply and divide 2- and 3-digit whole numbers 12 Connecticut State Department of Education September 2010 Grade 6 Mathematics Crosswalk – CCSS to CT Standards

THE NUMBER SYSTEM Compute fluently with multi-digit numbers and find common factors and multiples. CCSS CT Standard Match District Correlation CT Assessment Notes and money amounts by 1- digit numbers and 1-digit decimals.

CMT 7.7 Computation with Whole Numbers and Decimals A. Add and subtract 2-, 3- and 4-digit whole numbers, money amounts and decimals. B. Multiply and divide 2- and 3-digit whole numbers, money amounts and decimals by 1-digit numbers and decimals (multiply only). C. Multiply and divide whole numbers and decimals by 10, 100 and 1,000. CMT 8.7 Computation with Whole Numbers and Decimals A. Add and subtract 3-, 4- and 5-digit whole numbers, money amounts and decimals. B. Multiply 2- and 3-digit 13 Connecticut State Department of Education September 2010 Grade 6 Mathematics Crosswalk – CCSS to CT Standards

THE NUMBER SYSTEM Compute fluently with multi-digit numbers and find common factors and multiples. CCSS CT Standard Match District Correlation CT Assessment Notes whole numbers, money amounts and decimals by 1- or 2-digit numbers and decimals. Divide 2- and 3- digit whole numbers, money amounts and decimals by 1-digit whole numbers and decimals. C .Multiply and divide whole numbers and decimals by 10, 100, 1,000, 0.1 and 0.01.

CC.6.NS.4 Find the CT.7.2.2.8 Apply the order NA Greatest common factor and greatest common factor of of operations and algebraic least common multiple are two whole numbers less properties (commutative, not included in the CT than or equal to 100 and the associative, distributive, standards and are not least common multiple of inverse operations, and the assessed on the CMT. The 14 Connecticut State Department of Education September 2010 Grade 6 Mathematics Crosswalk – CCSS to CT Standards

THE NUMBER SYSTEM Compute fluently with multi-digit numbers and find common factors and multiples. CCSS CT Standard Match District Correlation CT Assessment Notes two whole numbers less additive and multiplicative distributive property is not than or equal to 12. Use the identities) to write, simplify directly assessed on the distributive property to and solve problems, CMT; however, students express a sum of two whole including those with may use it as a numbers 1–100 with a parentheses and exponents. computational strategy. common factor as a For example: 4 (3½) = 4 (3) multiple of a sum of two + 4 (½) = 12 + 2 = 14. whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

THE NUMBER SYSTEM Apply and extend previous understandings of numbers to the system of rational numbers. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.NS.5 Understand that CT.5.2.1.4 Investigate CMT 6.4 Order, Using positive and negative positive and negative negative integers (values Magnitude and Rounding integers to represent numbers are used together less than zero) using place of Numbers quantities in real-world to describe quantities value models, diagrams and G. Locate points on number contexts is limited to having opposite directions number lines and represent lines and scales, including locating integers on number or values (e.g., temperature negative integers in fractions, decimals and lines and scales on the CMT. above/below zero, elevation practical applications, e.g. integers. above/below sea level, temperatures, money and debits/credits, locations below sea level. CMT.8.4 Order, positive/negative electric Magnitude charge); use positive and and Rounding of negative numbers to Numbers represent quantities in real- D. Locate points on number world contexts, explaining lines and scales, including the meaning of 0 in each fractions, mixed numbers, situation. decimals and integers.

THE NUMBER SYSTEM Apply and extend previous understandings of numbers to the system of rational numbers. CC.6.NS.6 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. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.NS.6a Recognize CT.5.2.1.4 Investigate NA The Grade 6 CT standard opposite signs of numbers negative integers (values does not specify "opposite of as indicating locations on less than zero) using place the opposite of a number." opposite sides of 0 on the value models, diagrams and number line; recognize that number lines; represent Recognizing opposite signs the opposite of the opposite negative integers in of numbers as indicating of a number is the number practical applications such locations on opposite sides itself, e.g., –(–3) = 3, and as temperatures, money and of 0 on the number line and that 0 is its own opposite. locations below sea level. recognizing that the opposite of the opposite of a number is the number itself are not assessed on the CMT CC.6.NS.6b Understand CT.6.2.1.1 Locate and label NA Understanding the meaning signs of numbers in ordered whole numbers, fractions, of signs of numbers in pairs as indicating locations decimals and positive and ordered pairs and in quadrants of the negative integers on recognizing that when two coordinate plane; recognize number lines, scales, ordered pairs differ only by that when two ordered pairs coordinate grids (all four signs, the locations of the differ only by signs, the quadrants) and points are related by locations of the points are measurement tools. reflections across one or both related by reflections across axes are not specified in the one or both axes. CT standards and are not assessed on the CMT.

THE NUMBER SYSTEM Apply and extend previous understandings of numbers to the system of rational numbers. CC.6.NS.6 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. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.NS.6c Find and CT.6.2.1.1 Locate and label CMT 6.4 Order, Finding and positioning position integers and other whole numbers, fractions, Magnitude and Rounding points on a first-quadrant rational numbers on a decimals and positive and of Numbers grid is assessed on the horizontal or vertical negative integers on G. Locate points on number Grades 5 and 6 CMT. number line diagram; find number lines, scales, lines and scales, including Finding and positioning and position pairs of coordinate grids (all four fractions, decimals and points on a four-quadrant integers and other rational quadrants) and integers. grid is assessed on the numbers on a coordinate measurement tools. Grades 7 and 8 CMT. plane. CMT 6.18 Spatial CT.7.2.1.1 Compare and Relationships order rational numbers such E. Locate and draw points as -2, ⅜, -3.15 or 0.8 in on grids. context and locate them on number lines, scales and CMT 7.4 Order, coordinate grids. Magnitude and Rounding of Numbers CT.8.2.1.1 Compare and F. Locate points on number order rational and common lines and scales, including irrational numbers such as fractions, mixed numbers, -5, 1⁄16, -4½, √2, and π; decimals and integers. and locate them on number lines, scales and coordinate CMT 7.18 Spatial grids. Relationships E. Locate and draw points on grids.

CMT 8.4 Order, Magnitude and Rounding of Numbers

THE NUMBER SYSTEM Apply and extend previous understandings of numbers to the system of rational numbers. CC.6.NS.6 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. CCSS CT Standard Match District Correlation CT Assessment Notes D. Locate points on number lines and scales, including fractions, mixed numbers, decimals and integers.

CMT 8.18 Spatial Relationships C. Locate and draw points on four-quadrant coordinate grids.

THE NUMBER SYSTEM Apply and extend previous understandings of numbers to the system of rational numbers. CC.6.NS.7 Understand the ordering and the absolute value of rational numbers. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.NS.7a Interpret CT.6.2.1.2 Compare and NA Comparing and ordering statements of inequality as order whole numbers, integers and other rational statements about the fractions, decimals and numbers is not assessed on relative position of two positive and negative the CMT. numbers on a number line integers in context using diagram. For example, number lines and scales. interpret –3 > –7 as a statement that –3 is located CT.7.2.1.1 Compare and to the right of –7 on a order rational numbers such number line oriented from as -2, ⅜, -3.15 or 0.8 in left to right. context and locate them on number lines, scales and coordinate grids. CC.6.NS.7b Write, CT.6.2.1.2 Compare and NA Comparing and ordering interpret, and explain order whole numbers, integers and other rational statements of order for fractions, decimals and numbers is not assessed on rational numbers in real- positive and negative the CMT. world contexts. For integers in context using example, write –3 degrees number lines and scales. C > –7 degrees C to express the fact that –3 degrees C is CT.7.2.1.1 Compare and warmer than –7 degrees C. order rational numbers such as -2, ⅜, -3.15 or 0.8 in context and locate them on number lines, scales and coordinate grids.

CC.6.NS.7c Understand the CT.7.2.2.17 Develop an NA CT standards do not specify absolute value of a rational understanding of absolute any context for absolute 20 Connecticut State Department of Education September 2010 Grade 6 Mathematics Crosswalk – CCSS to CT Standards

THE NUMBER SYSTEM Apply and extend previous understandings of numbers to the system of rational numbers. CC.6.NS.7 Understand the ordering and the absolute value of rational numbers. CCSS CT Standard Match District Correlation CT Assessment Notes number as its distance from value using a number line value beyond distance. 0 on the number line; while solving problems interpret absolute value as involving distance. Absolute value is not magnitude for a positive or assessed on the CMT. negative quantity in a real- world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.

CC.6.NS.7d Distinguish NA CT standards do not specify comparisons of absolute comparisons of absolute value from statements value statements and about order. For example, statements of order. recognize that an account balance less than –30 Absolute value is not dollars represents a debt assessed on the CMT. greater than 30 dollars.

THE NUMBER SYSTEM Apply and extend previous understandings of numbers to the system of rational numbers. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.NS.8 Solve real- NA Solving problems by world and mathematical graphing points in a problems by graphing coordinate plane or finding points in all four quadrants distance between points is of the coordinate plane. not included in the CT Include use of coordinates standards and is not and absolute value to find assessed on the CMT. distances between points with the same first coordinate or the same second coordinate.

EXPRESSIONS AND EQUATIONS Apply and extend previous understandings of arithmetic to algebraic expressions. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.EE.1 Write and CT.6.2.1.4 Represent chain NA Writing and evaluating evaluate numerical multiplication, including numerical expressions expressions involving powers of 10 in exponential involving whole-number whole-number exponents. and standard form, e.g., 5 × exponents is not assessed 5 × 5 = 53 = 125. on the CMT.

EXPRESSIONS AND EQUATIONS Apply and extend previous understandings of arithmetic to algebraic expressions. CC.6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.EE.2a Write CT.5.1.2.3 Represent and CMT 7.23 Algebraic Writing expressions is expressions that record describe mathematical Concepts included in the Grades 5 operations with numbers relationships using D. Represent situations and 6 CT standards and is and with letters standing for variables or symbols in with algebraic expressions. assessed on the Grades 7 numbers. For example, expressions, equations and and 8 CMT. express the calculation inequalities CMT 8.23 Algebraic "Subtract y from 5" as 5 - y. Concepts CT.6.1.2.4 Write D. Represent situations expressions, formulas, with algebraic expressions equations or inequalities or equations. using symbols or variables to denote a pattern or CMT 8.23 Algebraic represent a contextual Concepts situation. E. Write an expression or equation to represent a situation.

EXPRESSIONS AND EQUATIONS Apply and extend previous understandings of arithmetic to algebraic expressions. CC.6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.EE.2b Identify parts CT.5.1.2.3 Represent and NA Identifying parts of an of an expression using describe mathematical expression using mathematical terms (sum, relationships using mathematical terms (sum, term, product, factor, variables or symbols in term, product, factor, quotient, coefficient); view expressions, equations and quotient, coefficient) is not one or more parts of an inequalities. included in the CT expression as a single standards and is not entity. For example, assessed on the CMT. 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. CC.6.EE.2c Evaluate CT.5.1.3.5 Replace CMT 7.23 Algebraic Evaluating expressions is expressions by substituting variables or symbols in Concepts included in the Grades 5, 6, values for their variables. algebraic expressions with C. Evaluate expressions or 7 and 8 CT standards and is Include expressions that given values and evaluate solve equations and use assessed on the Grades 7 arise from formulas in real- or simplify the expression, formulas. and 8 CMT. world problems. Perform e.g., If = 5, find the value arithmetic operations, of 4 x +7. CMT 8.23 Algebraic including those involving Concepts whole-number exponents, CT.6.1.3.5 Evaluate C. Evaluate expressions or in the conventional order algebraic expressions and solve equations and use when there are no formulas using substitution. formulas. parentheses to specify a particular order (Order of CT.7.1.3.7 Evaluate and Operations). For example, simplify algebraic use the formulas V = s^3 expressions, equations and and A = 6 s^2 to find the formulas using algebraic volume and surface area of properties (i.e.,

EXPRESSIONS AND EQUATIONS Apply and extend previous understandings of arithmetic to algebraic expressions. CC.6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. CCSS CT Standard Match District Correlation CT Assessment Notes a cube with sides of length commutative, associative, s = 1/2. distributive, inverse operations, and the additive and multiplicative identities) and the order of operations. CT.8.1.3.10 Evaluate and simplify algebraic expressions, equations and formulas, including those with powers, using algebraic properties and the order of operations.

EXPRESSIONS AND EQUATIONS Apply and extend previous understandings of arithmetic to algebraic expressions. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.EE.3 Apply the CT.7.1.3.7 Evaluate and NA Writing equivalent properties of operations as simplify algebraic expressions using strategies to generate expressions, equations and properties of operations is equivalent expressions. For formulas using algebraic included in the Grades 7 example, apply the properties (i.e., and 8 CT standard but is distributive property to the commutative, associative, not assessed on the CMT. expression 3(2 + x) to distributive, inverse produce the equivalent operations, and the additive expression 6 + 3x; apply and multiplicative properties of operations to y identities) and the order of + y + y to produce the operations. equivalent expression 3y. CT.8.1.3.10 Evaluate and simplify algebraic expressions, equations and formulas, including those with powers, using algebraic properties and the order of operations.

CT.8.3.12 Write and solve multistep equations using various algebraic methods, including the distributive property such as 3 (x + 2) =10), combining like terms such as 3x + 2x = 15, and properties of equality and justify the solutions.

EXPRESSIONS AND EQUATIONS Apply and extend previous understandings of arithmetic to algebraic expressions. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.EE.4 Identify when CT.7.1.3.7 Evaluate and NA Identifying when two two expressions are simplify algebraic expressions are equivalent equivalent (i.e., when the expressions, equations and is included in the Grades 7 two expressions name the formulas using algebraic and 8 CT standards (This same number regardless of properties (i.e., skill is implied in the CT which value is substituted commutative, associative, standard 8.1.3.12.) but is into them). For example, distributive, inverse not assessed on the CMT. the expressions y + y + y operations, and the additive and 3y are equivalent and multiplicative because they name the identities) and the order of same number regardless of operations. which number y stands for. CT.8.1.3.10 Evaluate and simplify algebraic expressions, equations and formulas, including those with powers, using algebraic properties and the order of operations.

CT.8.1.3.12 Write and solve multistep equations using various algebraic methods, including the distributive property such as 3 (x + 2) =10), combining like terms such as 3x + 2x = 15, and properties of equality and justify the solutions.

EXPRESSIONS AND EQUATIONS Reason about and solve one-variable equations and inequalities. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.EE.5 Understand CT.5.1.3.5 Replace CMT 5.23 Algebraic solving an equation or variables or symbols in Concepts inequality as a process of algebraic expressions with A. Solve simple one-step answering a question: given values, and evaluate algebraic equations which values from a or simplify the expressions. involving addition, specified set, if any, make For example: If □ =5, find subtraction, multiplication the equation or inequality the value of 4 x □ +7. and fact families. true? Use substitution to determine whether a given CT.5.1.3.6 Model, write CMT 6.23 Algebraic number in a specified set and solve one-step Concepts makes an equation or equations by using A. Solve simple 1-step inequality true. appropriate concrete algebraic equations. materials that model equivalence. For example: CMT 6.23 Algebraic If 4 x  = 36, then  equals Concepts 9. B. Evaluate equations, identify fact-family CT.6.1.3.6 Write, model relationships and use and solve one-step formulas equations using mental provided. math, tables, substitution and concrete models that demonstrate equivalence and justify the solution. CC.6.EE.6 Use variables CT.5.1.2.3 Represent and CMT 8.23 Algebraic Solving problems by to represent numbers and describe mathematical Concepts writing equations is write expressions when relationships using D. Represent situations included in the Grades 5, 6, solving a real-world or variables or symbols in with algebraic expressions and 7 CT standards. mathematical problem; expressions, equations and or equations. understand that a variable inequalities. Writing equations is 28 Connecticut State Department of Education September 2010 Grade 6 Mathematics Crosswalk – CCSS to CT Standards

EXPRESSIONS AND EQUATIONS Reason about and solve one-variable equations and inequalities. CCSS CT Standard Match District Correlation CT Assessment Notes can represent an unknown CMT 8.23 Algebraic assessed on the Grade 8 number, or, depending on CT.5.1.3.6 Model, write Concepts CMT. the purpose at hand, any and solve one-step E. Write an expression or number in a specified set. equations by using equation to represent a appropriate concrete situation. materials that model equivalence. For example: If 4 x  = 36, then  equals 9.

CT.6.1.2.4 Write expressions, formulas, equations or inequalities using symbols or variables to denote a pattern or represent a contextual situation.

CT.7.1.2.4 Write expressions, formulas, equations or inequalities using variables to represent mathematical relationships and solve problems.

CT.7.1.3.8 Solve real world problems using a variety of algebraic methods including tables, graphs, equations and inequalities.

EXPRESSIONS AND EQUATIONS Reason about and solve one-variable equations and inequalities. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.EE.7 Solve real- CT.5.1.2.3 Represent and CMT 8.23 Algebraic Solving problems by world and mathematical describe mathematical Concepts writing equations is problems by writing and relationships using D. Represent situations included in the Grades 5, 6 solving equations of the variables or symbols in with algebraic expressions and 7 CT standards, form x + p = q and px = q expressions, equations and or equations. however, there is no for cases in which p, q and inequalities. specific reference to x are all nonnegative CMT 8.23 Algebraic equations of the form x + p rational numbers. CT.5.1.3.6 Model, write Concepts = q and px = q for cases in and solve one-step E. Write an expression or which p, q and x are all equations by using equation to represent a nonnegative rational appropriate concrete situation. numbers. materials that model equivalence. For example: Writing equations is If 4 x  = 36, then  equals assessed on the Grade 8 9. CMT.

CT.6.1.2.4 Write expressions, formulas, equations or inequalities using symbols or variables to denote a pattern or represent a contextual situation.

CT.7.1.2.4 Write expressions, formulas, equations or inequalities using variables to represent mathematical relationships and solve problems.

CT.7.1.3.8 Solve real world 30 Connecticut State Department of Education September 2010 Grade 6 Mathematics Crosswalk – CCSS to CT Standards

EXPRESSIONS AND EQUATIONS Reason about and solve one-variable equations and inequalities. CCSS CT Standard Match District Correlation CT Assessment Notes problems using a variety of algebraic methods including tables, graphs, equations and inequalities. CC.6.EE.8 Write an CT.6.1.2.4 Write NA Representing solutions of inequality of the form x > c expressions, formulas, inequalities on number line or x < c to represent a equations or inequalities diagrams is not specified in constraint or condition in a using symbols or variables the CT standards. real-world or mathematical to denote a pattern or problem. Recognize that represent a contextual Inequalities are not assessed inequalities of the form x > situation. on the CMT. c or x < c have infinitely many solutions; represent CT.7.1.3.8 Solve real- solutions of such world problems using a inequalities on number line variety of algebraic diagrams. methods including tables, graphs, equations and inequalities.

EXPRESSIONS AND EQUATIONS Represent and analyze quantitative relationships between dependent and independent variables. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.EE.9 Use variables CT.5.1.2.4 Describe how a CMT.23 Algebraic Writing equations is to represent two quantities change in one variable Concepts included in the Grades 5, 6, in a real-world problem that relates to a change in a D. Represent situations 7 and 8 CT standards and is change in relationship to second variable in context. with algebraic expressions assessed on the Grade 8 one another; write an For example: If a recipe or equations. CMT. equation to express one requires two cups of flour E. Write an expression or quantity, thought of as the for eight servings, the flour equation to represent a Analyzing the relationship dependent variable, in must be doubled for 16 situation. between the dependent and terms of the other quantity, servings or increased by independent variables using thought of as the one-half for 12 servings. graphs and tables, and independent variable. relating these to the Analyze the relationship CT.6.1.2.2 Create tables of equation is included in the between the dependent and values and scatterplots from Grades 5, 6, 7 and 8 Ct independent variables using mathematical relationships standards but is not graphs and tables, and and equations and vice assessed on the CMT. relate these to the equation. versa to solve problems. For example, in a problem involving motion at CT.7.1.1.2 Identify and constant speed, list and describe in writing the graph ordered pairs of independent and dependent distances and times, and variables in a mathematical write the equation d = 65t situation, e.g., age vs. to represent the relationship height of children. between distance and time. CT.7.1.2.5 Represent and compare the characteristics of linear and nonlinear relationships using verbal descriptions such as linear –“increases $1 per month” 32 Connecticut State Department of Education September 2010 Grade 6 Mathematics Crosswalk – CCSS to CT Standards

EXPRESSIONS AND EQUATIONS Represent and analyze quantitative relationships between dependent and independent variables. CCSS CT Standard Match District Correlation CT Assessment Notes vs. nonlinear – “doubles every month”, tables, graphs, equations or inequalities when possible.

GEOMETRY Solve real-world and mathematical problems involving area, surface area and volume. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.G.1 Find area of right CT.5.3.3.8 Estimate and CMT 5.16 Customary and Finding area is assessed on triangles, other triangles, measure to solve a variety Metric Measures the CMT but is not special quadrilaterals, and of problems that involve B. Measure and determine presented with concrete polygons by composing angles, length, area, weight, perimeters and areas. models, however, students into rectangles or mass, temperature, capacity may use this as a strategy. decomposing into triangles and volume in either metric CMT 6.16 Customary and and other shapes; apply or customary units explain Metric Measures these techniques in the the reasoning used orally A. Measure and determine context of solving real- and in writing. perimeter, area and volume. world and mathematical Explain or show how the problems. CT.6.3.1.4 Use rectangles solution was determined. as basic shapes to model and develop formulas for finding the area of triangles, parallelograms and trapezoids.

CT.6.3.3.8 Select and use appropriate strategies, tools and units to estimate and solve measurement problems involving length, perimeter, area, volume, capacity, mass and weight. CC.6.G.2 Find the volume CT.6.3.2.6 Use and CMT 6.16 Customary and The CT standards and the of a right rectangular prism describe concrete strategies Metric Measures CMT do not make specific with fractional edge lengths for finding the volume of A. Measure and determine reference to "right by packing it with unit rectangular solids and perimeter, area and volume. rectangular prism with cubes of the appropriate cylinders. Explain or show how the fractional edge lengths" and unit fraction edge lengths, solution was determined. "unit cubes of the 34 Connecticut State Department of Education September 2010 Grade 6 Mathematics Crosswalk – CCSS to CT Standards

GEOMETRY Solve real-world and mathematical problems involving area, surface area and volume. CCSS CT Standard Match District Correlation CT Assessment Notes and show that the volume is CT.6.3.3.8 Select and use appropriate unit fraction the same as would be found appropriate strategies, tools edge lengths." by multiplying the edge and units to estimate and CMT 7.16 Customary and lengths of the prism. Apply solve measurement Metric Measures the formulas V = l w h and problems involving length, A. Measure and determine V = b h to find volumes of perimeter, area, volume, perimeters, areas and right rectangular prisms capacity, mass and weight. volumes. Explain or show with fractional edge lengths how the solution was in the context of solving CT.7.3.3.9 Develop and determined. real-world and use formulas to determine mathematical problems. volumes of geometric B. Determine perimeters, solids (rectangular prisms areas and volumes. and cylinders). CMT 8.16 Customary and Metric Measures A. Measure and determine perimeters, areas and volumes. Explain or show how the solution was determined.

B. Determine perimeters, areas and volumes. CC.6.G.3 Draw polygons CT.7.3.1.3 Draw the result CMT.8.18 Spatial The CT standards do not in the coordinate plane of transformations on Relationships specify finding the distance given coordinates for the polygons on coordinate E. Draw geometric between points using vertices; use coordinates to planes including transformations coordinates. find the length of a side translations, rotations, (reflections, rotations and joining points with the reflections and dilations translations). same first coordinate or the (reductions and same second coordinate. enlargements).

GEOMETRY Solve real-world and mathematical problems involving area, surface area and volume. CCSS CT Standard Match District Correlation CT Assessment Notes Apply these techniques in the context of solving real- world and mathematical problems. CC.6.G.4 Represent three- CT.7.3.2.6 Identify and/or CMT 7.18 Spatial Surface area is not assessed dimensional figures using draw two-dimensional Relationships on the CMT. nets made up of rectangles representations of three H. Relate 2- and 3- and triangles, and use the dimensional geometric dimensional representations nets to find the surface area solids using nets, cross- and vice versa. of these figures. Apply sections, front, side and top these techniques in the views to solve problems. CMT 8.18 Spatial context of solving real- Relationships world and mathematical CT.7.3.2.7 Use two- F. Relate 2- and 3- problems. dimensional representations dimensional representations of rectangular prisms, and vice versa. pyramids and cylinders to determine surface area.

STATISTICS AND PROBABILITY Develop understanding of statistical variability. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.SP.1 Recognize a CT.7.4.1 Formulate NA The CT standards do not statistical question as one questions and design make specific reference to that anticipates variability studies such as surveys, writing good statistical in the data related to the experiments, and research questions; however, it is question and accounts for it using published sources and implied in the Grade 7 in the answers. For the Internet to collect and standards. example, "How old am I?" analyze data. is not a statistical question, Recognizing statistical but "How old are the questions is not assessed on students in my school?" is a the CMT. statistical question because one anticipates variability in students' ages. CC.6.SP.2 Understand that CT.6.4.2.3 Describe the CMT.6.20 Statistics and The CT standards do not a set of data collected to shape of numerical data sets Data specify “overall shape." answer a statistical question using measures of spread Analysis has a distribution which can (range) and central B. Solve problems be described by its center, tendency (mean, median, involving means, medians spread, and overall shape. mode) and outliers. and modes of sets of data.

CMT.7.20 Statistics and Data Analysis C. Solve problems involving means, medians and modes of sets of data.

CMT.8.20 Statistics and Data Analysis 37 Connecticut State Department of Education September 2010 Grade 6 Mathematics Crosswalk – CCSS to CT Standards

STATISTICS AND PROBABILITY Develop understanding of statistical variability. CCSS CT Standard Match District Correlation CT Assessment Notes C. Solve problems involving means, medians, modes and ranges of sets of data

STATISTICS AND PROBABILITY Summarize and describe distributions. CCSS CT Standard Match District Correlation CT Assessment Notes CC.6.SP.3 Recognize that a CT.6.4.2.3 Describe the CMT.6.20 Statistics and Recognizing the difference measure of center for a shape of numerical data sets Data between a measure of numerical data set using measures of spread Analysis center and a measure of summarizes all of its values (range) and central B. Solve problems variation is not assessed on using a single number, tendency (mean, median, involving means, medians the CMT. while a measure of mode) and outliers. and modes of sets of data. variation describes how its values vary using a single CMT.7.20 Statistics and number. Data Analysis C. Solve problems involving means, medians and modes of sets of data. CMT.8.20 Statistics and Data Analysis C. Solve problems involving means, medians, modes and ranges of sets of data. CC.6.SP.4 Display CT.6.4.1.2 Select, create CMT.6.19 Tables, Graphs Dot plots and box plots are numerical data in plots on a and use appropriate and not assessed on the CMT. number line, including dot graphical representations of Charts plots, histograms, and box data including, circle B. Create bar graphs and plots. graphs, scatter plots, pictographs from data in histograms, and stem and tables and charts. leaf plots. CMT.7.19 Tables, Graphs CT.7.4.1.2 Organize and and display data using Charts 39 Connecticut State Department of Education September 2010 Grade 6 Mathematics Crosswalk – CCSS to CT Standards

STATISTICS AND PROBABILITY Summarize and describe distributions. CCSS CT Standard Match District Correlation CT Assessment Notes appropriate graphical B. Create bar graphs, line representation such as graphs and stem-and-leaf tables and charts, line, bar plots from data in tables and circle graphs, Venn and charts. diagrams, stem-and-leaf plots, scatter plots and CMT.8.19 Tables, Graphs histograms. and Charts CT.8.4.1.1 Collect, B. Create graphs from data organize and display data in tables and charts. using an appropriate representation (including box-and-whisker plots, stem and leaf plots, scatter plots, histograms) based on the size and type of data set and purpose for its use. CC.6.SP.5 Summarize and CT.6.4.2.3 Describe the CMT 6.20 Statistics and describe distributions. shape of numerical data sets Data Analysis Summarize numerical data using measures of spread B. Solve problems sets in relation to their (range) and central involving means, medians context, such as by: tendency (mean, median, and modes of sets of data. a. Reporting the number mode) and outliers. of observations. CMT 7.20 Statistics and b. Describing the nature of CT.8.4.2.4 Use descriptive Data Analysis the attribute under statistics, including range, C. Solve problems investigation, including mode, median, mean, involving means, medians, how it was measured and quartiles and outliers to modes and ranges of sets of its units of measurement. describe data and support data. c. Giving quantitative conclusions in writing. measures of center (median CMT 8.20 Statistics and and/or mean) and Data Analysis 40 Connecticut State Department of Education September 2010 Grade 6 Mathematics Crosswalk – CCSS to CT Standards

STATISTICS AND PROBABILITY Summarize and describe distributions. CCSS CT Standard Match District Correlation CT Assessment Notes variability (interquartile C. Solve problems range and/or mean absolute involving means, medians, deviation), as well as modes and ranges of sets of describing any overall data. 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.

41 Connecticut State Department of Education September 2010