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 13 of 17 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 221 - 230 Statements Last Updated: Sep 23, 2013 Goal: Operations and Algebraic Thinking Skills and Concepts to Enhance (73% Probability*) 211 - 220 Skills and Concepts to Develop (50% Probability*) 221 - 230 Skills and Concepts to Introduce (27% Probability*) 231 - 240 Represent and Solve Problems Represent and Solve Problems Represent and Solve Problems • 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 • 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 algorithms using place value concepts (multiplication and division with whole numbers) • Solves complex word problems involving whole number division with remainder (e.g., 2-step, 2-digit divisor) • Solves real-world multiple-step problems involving whole numbers • Demonstrates an understanding of multiple properties • Represents relationships of quantities in the form of an expression • Solves open sentences with calculations on both sides of the sentence • Applies algebraic methods to solve theoretical problems • Applies algebraic methods to solve real-world problems • Uses pictures to represent problems • Uses multiple number theory concepts to solve problems (e.g., factors, digits, odd/even, divisibility) • Models algorithms using place value concepts (multiplication and division with whole numbers) • Evaluates numerical expressions using the order of operations (whole numbers only) • Solves multiple-step problems involving proportions • Represents relationships of quantities in the form of an expression • Applies algebraic methods to solve real-world problems • Solves problems comparing unit prices • Uses pictures to represent problems Analyze Patterns and Relationships Analyze Patterns and Relationships Analyze Patterns and Relationships • Completes a function table given a simple rule (e.g., x + 2) • Determines the rule given a simple real-world function table (e.g., # Dogs compared to # Legs) • Determines the rule and completes a simple function machine output • Extends a growing pattern of triangular numbers, defined by objects or diagrams • Looks for a growing pattern to solve a problem • Determines factors of whole numbers

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. Educational Standard: Common Core Mathematics K-12: 2010 Page 14 of 17 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 221 - 230 Statements Last Updated: Sep 23, 2013 Goal: Operations and Algebraic Thinking Skills and Concepts to Enhance (73% Probability*) 211 - 220 Skills and Concepts to Develop (50% Probability*) 221 - 230 Skills and Concepts to Introduce (27% Probability*) 231 - 240 Analyze Patterns and Relationships Analyze Patterns and Relationships Analyze Patterns and Relationships • Looks for a growing pattern to solve a problem • Determines factors of whole numbers • Identifies numbers as prime • Uses factor and multiple concepts to solve simple problems New Vocabulary: None New Signs and Symbols: ( ) parenthesis around an integer, { } set notation New Vocabulary: None New Signs and Symbols: None New Vocabulary: None New Signs and Symbols: None

Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 14 of 17 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 221 - 230 Statements Last Updated: Sep 23, 2013 Goal: Operations and Algebraic Thinking Skills and Concepts to Enhance (73% Probability*) 211 - 220 Skills and Concepts to Develop (50% Probability*) 221 - 230 Skills and Concepts to Introduce (27% Probability*) 231 - 240 Analyze Patterns and Relationships Analyze Patterns and Relationships Analyze Patterns and Relationships • Looks for a growing pattern to solve a problem • Determines factors of whole numbers • Identifies numbers as prime • Uses factor and multiple concepts to solve simple problems New Vocabulary: None New Signs and Symbols: ( ) parenthesis around an integer, { } set notation New Vocabulary: None New Signs and Symbols: None New Vocabulary: None New Signs and Symbols: None 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. Educational Standard: Common Core Mathematics K-12: 2010 Page 15 of 17 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 231 - 240 Statements Last Updated: Sep 23, 2013 Goal: Operations and Algebraic Thinking Skills and Concepts to Enhance (73% Probability*) 221 - 230 Skills and Concepts to Develop (50% Probability*) 231 - 240 Skills and Concepts to Introduce (27% Probability*) 241 - 250 Represent and Solve Problems Represent and Solve Problems Represent and Solve Problems • 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 algorithms using place value concepts (multiplication and division with whole numbers) • Solves complex word problems involving whole number division with remainder (e.g., 2-step, 2-digit divisor) • Solves real-world multiple-step problems involving whole numbers • Demonstrates an understanding of multiple properties • Represents relationships of quantities in the form of an expression • Solves open sentences with calculations on both sides of the sentence • Applies algebraic methods to solve theoretical problems • Applies algebraic methods to solve real-world problems • Uses pictures to represent problems • Uses multiple number theory concepts to solve problems (e.g., factors, digits, odd/even, divisibility) • Models algorithms using place value concepts (multiplication and division with whole numbers) • Evaluates numerical expressions using the order of operations (whole numbers only) • Solves multiple-step problems involving proportions • Represents relationships of quantities in the form of an expression • Applies algebraic methods to solve real-world problems • Solves problems comparing unit prices • Uses pictures to represent problems • Solves multiple-step problems involving proportions • Applies algebraic methods to solve real-world problems • Uses reasoning strategies to solve problems Analyze Patterns and Relationships Analyze Patterns and Relationships Analyze Patterns and Relationships • Extends a growing pattern of triangular numbers, defined by objects or diagrams • Looks for a growing pattern to solve a problem • Determines factors of whole numbers • Uses factor and multiple concepts to solve simple problems New Vocabulary: None New Signs and Symbols: None New Vocabulary: None New Signs and Symbols: None New Vocabulary: None New Signs and Symbols: None

Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 15 of 17 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 231 - 240 Statements Last Updated: Sep 23, 2013 Goal: Operations and Algebraic Thinking Skills and Concepts to Enhance (73% Probability*) 221 - 230 Skills and Concepts to Develop (50% Probability*) 231 - 240 Skills and Concepts to Introduce (27% Probability*) 241 - 250 Represent and Solve Problems Represent and Solve Problems Represent and Solve Problems • 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 algorithms using place value concepts (multiplication and division with whole numbers) • Solves complex word problems involving whole number division with remainder (e.g., 2-step, 2-digit divisor) • Solves real-world multiple-step problems involving whole numbers • Demonstrates an understanding of multiple properties • Represents relationships of quantities in the form of an expression • Solves open sentences with calculations on both sides of the sentence • Applies algebraic methods to solve theoretical problems • Applies algebraic methods to solve real-world problems • Uses pictures to represent problems • Uses multiple number theory concepts to solve problems (e.g., factors, digits, odd/even, divisibility) • Models algorithms using place value concepts (multiplication and division with whole numbers) • Evaluates numerical expressions using the order of operations (whole numbers only) • Solves multiple-step problems involving proportions • Represents relationships of quantities in the form of an expression • Applies algebraic methods to solve real-world problems • Solves problems comparing unit prices • Uses pictures to represent problems • Solves multiple-step problems involving proportions • Applies algebraic methods to solve real-world problems • Uses reasoning strategies to solve problems Analyze Patterns and Relationships Analyze Patterns and Relationships Analyze Patterns and Relationships • Extends a growing pattern of triangular numbers, defined by objects or diagrams • Looks for a growing pattern to solve a problem • Determines factors of whole numbers • Uses factor and multiple concepts to solve simple problems New Vocabulary: None New Signs and Symbols: None New Vocabulary: None New Signs and Symbols: None New Vocabulary: None New Signs and Symbols: None 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. Educational Standard: Common Core Mathematics K-12: 2010 Page 16 of 17 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 241 - 250 Statements Last Updated: Sep 23, 2013 Goal: Operations and Algebraic Thinking Skills and Concepts to Enhance (73% Probability*) 231 - 240 Skills and Concepts to Develop (50% Probability*) 241 - 250 Skills and Concepts to Introduce (27% Probability*) > 250 Represent and Solve Problems Represent and Solve Problems Represent and Solve Problems • Models algorithms using place value concepts (multiplication and division with whole numbers) • Evaluates numerical expressions using the order of operations (whole numbers only) • Solves multiple-step problems involving proportions • Represents relationships of quantities in the form of an expression • Applies algebraic methods to solve real-world problems • Solves problems comparing unit prices • Uses pictures to represent problems • Solves multiple-step problems involving proportions • Applies algebraic methods to solve real-world problems • Uses reasoning strategies to solve problems • Uses reasoning strategies to solve problems Analyze Patterns and Relationships Analyze Patterns and Relationships Analyze Patterns and Relationships New Vocabulary: None New Signs and Symbols: None New Vocabulary: None New Signs and Symbols: None New Vocabulary: None New Signs and Symbols: None