All rights reserved. Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 2 of 17 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 161 - 170 Statements Last Updated: Sep 23, 2013 Goal: Operations and Algebraic Thinking Skills and Concepts to Enhance (73% Probability*) < 161 Skills and Concepts to Develop (50% Probability*) 161 - 170 Skills and Concepts to Introduce (27% Probability*) 171 - 180 Represent and Solve Problems Represent and Solve Problems Represent and Solve Problems • Uses models to construct whole number addition facts with addends through 10 • Adds two 1-digit numbers with sums to 10 in horizontal format • Uses a number line to construct addition facts with sums through 20 (whole numbers) • Adds two 1-digit numbers with sums to 10 in horizontal format • Adds two 1-digit numbers with sums between 10 and 19 in horizontal format • Adds two 1-digit numbers with sums between 10 and 19 in vertical format • Solves real-world whole number addition problems with sums to 20 (result unknown) • Subtracts a 1-digit number from a 2-digit number that is less than 20 (whole numbers only) • Subtracts two 1-digit numbers vertically • Instantly recalls basic multiplication facts where one factor is 0-5 and the other factor is 0-12 • Solves basic-facts open sentences - addition and subtraction • Uses a number line to construct addition facts with sums through 20 (whole numbers) • Solves real-world whole number addition problems with sums to 20 (result unknown) • Solves real-world whole number addition problems with sums to 20 (start unknown) • Solves real-world whole number addition problems with sums to 100 (result unknown) • Represents a basic facts addition problem with a number sentence • Subtracts a 1-digit number from a 2-digit number that is less than 20 (whole numbers only) • Solves real-world whole number problems involving subtraction with numbers under 20 • Instantly recalls basic multiplication facts where one factor is 0-5 and the other factor is 0-12 • Multiplies basic facts to 10 x 10 vertically • Adds 1-digit numbers with sums to 18 (with parentheses) • Recognizes addition and subtraction fact families through 18 • Solves basic-facts open sentences - addition and subtraction • Solves basic facts open sentences - multiplication and division • Determines the operation needed from a simple problem • Writes a number sentence for a simple problem solving situation • Counts by 2's to 100 • Writes equivalent forms of whole number expressions (e.g., 15 + 5 = 10 + 10) 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 New Vocabulary: None New Signs and Symbols: None New Vocabulary: None New Signs and Symbols: + addition, = is equal to, × multiplication, - subtraction, variable New Vocabulary: fact family New Signs and Symbols: ( ) order of operations, | tally mark

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 3 of 17 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 171 - 180 Statements Last Updated: Sep 23, 2013 Goal: Operations and Algebraic Thinking Skills and Concepts to Enhance (73% Probability*) 161 - 170 Skills and Concepts to Develop (50% Probability*) 171 - 180 Skills and Concepts to Introduce (27% Probability*) 181 - 190 Represent and Solve Problems Represent and Solve Problems Represent and Solve Problems • Uses a number line to construct addition facts with sums through 20 (whole numbers) • Adds two 1-digit numbers with sums to 10 in horizontal format • Adds two 1-digit numbers with sums between 10 and 19 in horizontal format • Adds two 1-digit numbers with sums between 10 and 19 in vertical format • Solves real-world whole number addition problems with sums to 20 (result unknown) • Subtracts a 1-digit number from a 2-digit number that is less than 20 (whole numbers only) • Subtracts two 1-digit numbers vertically • Instantly recalls basic multiplication facts where one factor is 0-5 and the other factor is 0-12 • Solves basic-facts open sentences - addition and subtraction • Uses a number line to construct addition facts with sums through 20 (whole numbers) • Solves real-world whole number addition problems with sums to 20 (result unknown) • Solves real-world whole number addition problems with sums to 20 (start unknown) • Solves real-world whole number addition problems with sums to 100 (result unknown) • Represents a basic facts addition problem with a number sentence • Subtracts a 1-digit number from a 2-digit number that is less than 20 (whole numbers only) • Solves real-world whole number problems involving subtraction with numbers under 20 • Instantly recalls basic multiplication facts where one factor is 0-5 and the other factor is 0-12 • Multiplies basic facts to 10 x 10 vertically • Adds 1-digit numbers with sums to 18 (with parentheses) • Recognizes addition and subtraction fact families through 18 • Solves basic-facts open sentences - addition and subtraction • Solves basic facts open sentences - multiplication and division • Determines the operation needed from a simple problem • Writes a number sentence for a simple problem solving situation • Counts by 2's to 100 • Writes equivalent forms of whole number expressions (e.g., 15 + 5 = 10 + 10) • 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)

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 4 of 17 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 171 - 180 Statements Last Updated: Sep 23, 2013 Goal: Operations and Algebraic Thinking Skills and Concepts to Enhance (73% Probability*) 161 - 170 Skills and Concepts to Develop (50% Probability*) 171 - 180 Skills and Concepts to Introduce (27% Probability*) 181 - 190 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 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 numbers • Analyzes a growing, arithmetic pattern with numbers to determine the rule New Vocabulary: None New Signs and Symbols: + addition, = is equal to, × multiplication, - subtraction, variable New Vocabulary: fact family New Signs and Symbols: ( ) order of operations, | tally mark New Vocabulary: gave, left, row, unifix cubes New Signs and Symbols: ÷ division, long division symbol