All rights reserved. Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 7 of 17 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 191 - 200 Statements Last Updated: Sep 23, 2013 Goal: Operations and Algebraic Thinking Skills and Concepts to Enhance (73% Probability*) 181 - 190 Skills and Concepts to Develop (50% Probability*) 191 - 200 Skills and Concepts to Introduce (27% Probability*) 201 - 210 Represent and Solve Problems Represent and Solve Problems Represent and Solve Problems • Uses rounding to estimate answers to real-world problems involving addition of numbers less than 100 (whole numbers only) • Instantly recalls basic addition facts with sums to 18 in a table • Solves real-world whole number addition problems with sums to 20 (result unknown) - with extraneous information given • Solves real-world whole number addition problems with sums to 100 (result unknown) • Instantly recalls basic subtraction facts with minuend less than 10 • Solves real-world whole number problems involving subtraction with numbers under 20 • Solves real-world whole number problems involving subtraction with numbers 100 and under • Solves real-world whole number problems involving subtraction with numbers under 1000 • Solves problems using the inverse relationship between addition and subtraction • Uses counting by multiples for multiplication • Instantly recalls basic multiplication facts where one factor is 6-12 and the other factor is 0-12 • Multiplies basic facts to 10 x 10 vertically • Solves word problems involving basic whole number multiplication facts to 10 x 10 • Uses manipulatives to divide a small set of objects into groups of equal size • Uses sharing for division • Models whole number multiplication and division algorithms (e.g., shows multiplication as repeated addition and division as repeated subtraction) • Models multiplication and division algorithms using arrays (whole numbers) • Instantly recalls division facts with dividend and divisors less than 10 • Solves real-world whole number problems involving addition and subtraction • Recognizes addition and subtraction fact families through 18 • Demonstrates an understanding of the zero property of multiplication • Demonstrates an understanding of the inverse relationship between multiplication and division • Solves basic facts addition and subtraction open sentences using diagrams and models (e.g., using balances) • Solves 1-step open sentences with missing addends (numbers 100 and under) • Uses rounding to estimate answers to real-world problems involving numbers less than 1000 with addition and subtraction (whole numbers only) • Solves real-world whole number addition problems with sums to 20 (result unknown) - with extraneous information given • Solves real-world whole number addition problems with sums to 20 (change unknown) • Solves real-world whole number problems involving subtraction with numbers 100 and under • Solves real-world whole number problems involving subtraction with numbers under 1000 • Solves whole number subtraction word problems with numbers over 1000 • Solves problems using the inverse relationship between addition and subtraction • Instantly recalls basic multiplication facts where one factor is 6-12 and the other factor is 0-12 • Solves word problems involving basic whole number multiplication facts to 10 x 10 • Solves word problems involving whole number multiplication with numbers greater than 10 x 10 • Uses manipulatives to divide a small set of objects into groups of equal size • Models whole number multiplication and division algorithms (e.g., shows multiplication as repeated addition and division as repeated subtraction) • Instantly recalls division facts with dividend and divisors less than 10 • Instantly recalls division facts with dividend and divisors less than 13 • Solves word problems with whole number division facts with dividend and divisors less than 11 • Solves simple word problems involving whole number division with remainder (e.g., 1-step, 1-digit divisor) • Evaluates numerical expressions using grouping symbols (whole numbers only) • Demonstrates an understanding of the commutative property of multiplication with simple problems • Demonstrates an understanding of the zero property of multiplication • Uses algebraic reasoning to solve problems involving equality relationships • Solves 1-step open sentences with missing addends (numbers 100 and under) • Uses rounding to estimate answers to real-world problems involving numbers 1000 or greater with addition and subtraction (whole numbers only) • Solves real-world whole number problems involving subtraction with numbers 100 and under (analysis) • Solves whole number subtraction word problems with numbers over 1000 • Solves problems using the inverse relationship between addition and subtraction • Solves word problems involving whole number multiplication with numbers greater than 10 x 10 • Models whole number multiplication and division algorithms (e.g., uses physical materials to show 4 groups of 3 objects) • Instantly recalls division facts with dividend and divisors less than 13 • Performs mental computation with division • Solves word problems with whole number division facts with dividend and divisors less than 11 • Solves simple word problems involving whole number division with remainder (e.g., 1-step, 1-digit divisor) • Solves whole number word problems with division over 10 x 10 • Determines the remainder in a real-world problem (whole numbers) • Uses division for multiple-step real-world problems (whole numbers) • Evaluates numerical expressions using grouping symbols (whole numbers only) • Solves real-world problems involving 2-step multiple operations, whole numbers only • Demonstrates an understanding of the commutative property of multiplication with simple problems • Understands equivalence and extends the concept to number sentences involving variables (e.g., 8 + 2 = [] + 2) • Uses algebraic reasoning to solve problems involving equality relationships • Uses simple linear equations to represent problem situations • Describes a realistic situation using information given in a linear equation • Solves simple open sentences with missing factors (numbers 100 and under) • Solves 2-step open sentences with missing addends • Solves open sentences with basic-facts calculations on both sides of the sentence • Translates a 1-step problem to a symbolic expression or equation

Explanatory Notes * At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version. Generated 10/2/13, 9:34:57 AM © 2006-2013 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.

All rights reserved. Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 8 of 17 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 191 - 200 Statements Last Updated: Sep 23, 2013 Goal: Operations and Algebraic Thinking Skills and Concepts to Enhance (73% Probability*) 181 - 190 Skills and Concepts to Develop (50% Probability*) 191 - 200 Skills and Concepts to Introduce (27% Probability*) 201 - 210 Represent and Solve Problems Represent and Solve Problems Represent and Solve Problems • Determines the operation needed from a simple problem • Writes a number sentence for a simple problem solving situation • Interprets a chart or table - calculation required • Writes equivalent forms of whole numbers 11 to 20 using addition (e.g., 14 = 7 + 7) • Distinguishes between odd and even numbers • Solves simple open sentences with missing factors (numbers 100 and under) • Solves 2-step open sentences with missing addends • Determines the operation needed from a simple problem • Translates a 1-step problem to a symbolic expression or equation • Interprets a chart or table - calculation required • Solves problems using tables • Writes equivalent forms of whole numbers 11 to 20 using addition (e.g., 14 = 7 + 7) • Distinguishes between odd and even numbers • Translates a 2-step problem to a symbolic expression or equation • Solves problems using tables • Uses number sense strategies to solve problems (addition/subtraction only) Analyze Patterns and Relationships Analyze Patterns and Relationships Analyze Patterns and Relationships • Extends a growing arithmetic pattern, defined by numbers • Analyzes a growing, arithmetic pattern with numbers to determine the rule • Extends a growing arithmetic pattern, defined by objects or diagrams • Analyzes a growing, arithmetic pattern with numbers to determine the rule • Completes a simple function table based on real-life situations (e.g., the number of tricycles related to the number of wheels) • Identifies numbers as composite • Extends a growing arithmetic pattern, defined by objects or diagrams • Completes a simple function table based on real-life situations (e.g., the number of tricycles related to the number of wheels) • Completes a function table given a simple rule (e.g., x + 2) • Determines the rule and completes a simple function machine output • Predicts from simple charts and tables New Vocabulary: gave, left, row, unifix cubes New Signs and Symbols: ÷ division, long division symbol New Vocabulary: composite number, each, prime number New Signs and Symbols: °F degrees Fahrenheit, $ dollar sign, lb pound New Vocabulary: minimum, plus New Signs and Symbols: ¢ cent sign, = is equal to, + positive number

Explanatory Notes * At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version. Generated 10/2/13, 9:34:57 AM © 2006-2013 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.

All rights reserved. Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 9 of 17 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 201 - 210 Statements Last Updated: Sep 23, 2013 Goal: Operations and Algebraic Thinking Skills and Concepts to Enhance (73% Probability*) 191 - 200 Skills and Concepts to Develop (50% Probability*) 201 - 210 Skills and Concepts to Introduce (27% Probability*) 211 - 220 Represent and Solve Problems Represent and Solve Problems Represent and Solve Problems • Uses rounding to estimate answers to real-world problems involving numbers less than 1000 with addition and subtraction (whole numbers only) • Solves real-world whole number addition problems with sums to 20 (result unknown) - with extraneous information given • Solves real-world whole number addition problems with sums to 20 (change unknown) • Solves real-world whole number problems involving subtraction with numbers 100 and under • Solves real-world whole number problems involving subtraction with numbers under 1000 • Solves whole number subtraction word problems with numbers over 1000 • Solves problems using the inverse relationship between addition and subtraction • Instantly recalls basic multiplication facts where one factor is 6-12 and the other factor is 0-12 • Solves word problems involving basic whole number multiplication facts to 10 x 10 • Solves word problems involving whole number multiplication with numbers greater than 10 x 10 • Uses manipulatives to divide a small set of objects into groups of equal size • Models whole number multiplication and division algorithms (e.g., shows multiplication as repeated addition and division as repeated subtraction) • Instantly recalls division facts with dividend and divisors less than 10 • Instantly recalls division facts with dividend and divisors less than 13 • Solves word problems with whole number division facts with dividend and divisors less than 11 • Solves simple word problems involving whole number division with remainder (e.g., 1-step, 1-digit divisor) • Evaluates numerical expressions using grouping symbols (whole numbers only) • Demonstrates an understanding of the commutative property of multiplication with simple problems • Demonstrates an understanding of the zero property of multiplication • Uses algebraic reasoning to solve problems involving equality relationships • Solves 1-step open sentences with missing addends (numbers 100 and under) • Uses rounding to estimate answers to real-world problems involving numbers 1000 or greater with addition and subtraction (whole numbers only) • Solves real-world whole number problems involving subtraction with numbers 100 and under (analysis) • Solves whole number subtraction word problems with numbers over 1000 • Solves problems using the inverse relationship between addition and subtraction • Solves word problems involving whole number multiplication with numbers greater than 10 x 10 • Models whole number multiplication and division algorithms (e.g., uses physical materials to show 4 groups of 3 objects) • Instantly recalls division facts with dividend and divisors less than 13 • Performs mental computation with division • Solves word problems with whole number division facts with dividend and divisors less than 11 • Solves simple word problems involving whole number division with remainder (e.g., 1-step, 1-digit divisor) • Solves whole number word problems with division over 10 x 10 • Determines the remainder in a real-world problem (whole numbers) • Uses division for multiple-step real-world problems (whole numbers) • Evaluates numerical expressions using grouping symbols (whole numbers only) • Solves real-world problems involving 2-step multiple operations, whole numbers only • Demonstrates an understanding of the commutative property of multiplication with simple problems • Understands equivalence and extends the concept to number sentences involving variables (e.g., 8 + 2 = [] + 2) • Uses algebraic reasoning to solve problems involving equality relationships • Uses simple linear equations to represent problem situations • Describes a realistic situation using information given in a linear equation • Solves simple open sentences with missing factors (numbers 100 and under) • Solves 2-step open sentences with missing addends • Solves open sentences with basic-facts calculations on both sides of the sentence • Translates a 1-step problem to a symbolic expression or equation • Uses rounding to estimate answers to real-world problems involving multiplication and division of numbers less than 100 (whole numbers only) • Uses rounding to estimate answers to real-world problems involving numbers less than 1000 with multiplication and division (whole numbers only) • Models whole number multiplication and division algorithms (e.g., uses physical materials to show 4 groups of 3 objects) • Performs mental computation with division • Solves whole number word problems with division over 10 x 10 • Solves complex word problems involving whole number division with remainder (e.g., 2-step, 2-digit divisor) • Solves real-world problems involving 2-step multiple operations, whole numbers only • Solves real-world multiple-step problems involving whole numbers • Predicts the relative size of the answer when multiplying whole numbers • Demonstrates an understanding of the inverse relationship between addition and subtraction • Demonstrates an understanding of the commutative property of multiplication with simple problems • Demonstrates an understanding of the associative property of multiplication • Demonstrates an understanding of the distributive property of multiplication by decomposing a term • Understands equivalence and extends the concept to number sentences involving variables (e.g., 8 + 2 = [] + 2) • Uses algebraic reasoning to solve problems involving equality relationships • Uses simple linear equations to represent problem situations • Solves simple open sentences with missing factors (numbers over 100) • Solves open sentences using the distributive property • Solves open sentences with calculations on both sides of the sentence • Applies algebraic methods to solve theoretical problems • Uses pictures to represent problems • Translates a 2-step problem to a symbolic expression or equation