Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 4 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 181 - 190 Statements Last Updated: Aug 4, 2014 Goal: Operations and Algebraic Thinking Skills and Concepts to Enhance (73% Probability*) 171 - 180 Skills and Concepts to Develop (50% Probability*) 181 - 190 Skills and Concepts to Introduce (27% Probability*) 191 - 200 Expressions and Equations Expressions and Equations Expressions and Equations • Represents a basic facts addition problem with a number sentence • Solves basic-facts open sentences - addition and subtraction • Solves linear equations with basic facts - 1-step addition using a letter for the variable • Solves basic facts open sentences - multiplication and division • Writes a number sentence for a simple problem solving situation • Writes equivalent forms of whole number expressions (e.g., 15 + 5 = 10 + 10) • Solves real-world whole number problems involving subtraction with numbers under 1000 • Demonstrates an understanding of the zero property of multiplication • Solves basic facts addition and subtraction open sentences using diagrams and models (e.g., using balances) • Solves linear equations with basic facts - 1-step addition using a letter for the variable • Solves 1-step open sentences with missing addends (numbers 100 and under) • Writes a number sentence for a simple problem solving situation • Writes equivalent forms of whole numbers 11 to 20 using addition (e.g., 14 = 7 + 7) • Solves real-world whole number problems involving subtraction with numbers under 1000 • Solves whole number subtraction word problems with numbers over 1000 • Evaluates numerical expressions using grouping symbols (whole numbers only) • Demonstrates an understanding of the zero property of multiplication • Computes half price (multiplication/division) • Uses algebraic reasoning to solve problems involving equality relationships • Solves 1-step open sentences with missing addends (numbers 100 and under) • Solves 1-step open sentences with missing addends (numbers over 100) • Solves simple open sentences with missing factors (numbers 100 and under) • Solves 2-step open sentences with missing addends • Writes equivalent forms of whole numbers 11 to 20 using addition (e.g., 14 = 7 + 7) Use Functions to Model Relationships Use Functions to Model Relationships Use Functions to Model 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 • Identifies transformations of plane figures (translations/slides) • Reads data in a line graph - no calculations • 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) • Reads data in a line graph - no calculations New Vocabulary: None New Signs and Symbols: None New Vocabulary: None New Signs and Symbols: × multiplication New Vocabulary: longer New Signs and Symbols: ( ) order of operations, ÷ division, $ dollar sign 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 8/7/14, 9:50:06 PM © 2006-2014 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 5 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 191 - 200 Statements Last Updated: Aug 4, 2014 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 Expressions and Equations Expressions and Equations Expressions and Equations • Solves real-world whole number problems involving subtraction with numbers under 1000 • Demonstrates an understanding of the zero property of multiplication • Solves basic facts addition and subtraction open sentences using diagrams and models (e.g., using balances) • Solves linear equations with basic facts - 1-step addition using a letter for the variable • Solves 1-step open sentences with missing addends (numbers 100 and under) • Writes a number sentence for a simple problem solving situation • Writes equivalent forms of whole numbers 11 to 20 using addition (e.g., 14 = 7 + 7) • Solves real-world whole number problems involving subtraction with numbers under 1000 • Solves whole number subtraction word problems with numbers over 1000 • Evaluates numerical expressions using grouping symbols (whole numbers only) • Demonstrates an understanding of the zero property of multiplication • Computes half price (multiplication/division) • Uses algebraic reasoning to solve problems involving equality relationships • Solves 1-step open sentences with missing addends (numbers 100 and under) • Solves 1-step open sentences with missing addends (numbers over 100) • Solves simple open sentences with missing factors (numbers 100 and under) • Solves 2-step open sentences with missing addends • Writes equivalent forms of whole numbers 11 to 20 using addition (e.g., 14 = 7 + 7) • Uses rounding to estimate answers to 2-step problems involving money (using decimals) • Solves whole number subtraction word problems with numbers over 1000 • Evaluates numerical expressions using grouping symbols (whole numbers only) • Demonstrates an understanding of the commutative property of addition • 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 1-step open sentences with missing addends (numbers over 100) • 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 2-step problem to a symbolic expression or equation • Solves real-world problems using reasoning strategies Use Functions to Model Relationships Use Functions to Model Relationships Use Functions to Model Relationships • Extends a growing arithmetic pattern, defined by numbers • Analyzes a growing, arithmetic pattern with numbers to determine the rule • Identifies transformations of plane figures (translations/slides) • Reads data in a line graph - no calculations • 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) • Reads data in a line graph - no calculations • 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) • Predicts from simple charts and tables New Vocabulary: None New Signs and Symbols: × multiplication New Vocabulary: longer New Signs and Symbols: ( ) order of operations, ÷ division, $ dollar sign New Vocabulary: minimum, plus New Signs and Symbols: °C degrees Celsius, = is equal to, min minute, - negative number, p.m., + positive number

Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 5 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 191 - 200 Statements Last Updated: Aug 4, 2014 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 Expressions and Equations Expressions and Equations Expressions and Equations • Solves real-world whole number problems involving subtraction with numbers under 1000 • Demonstrates an understanding of the zero property of multiplication • Solves basic facts addition and subtraction open sentences using diagrams and models (e.g., using balances) • Solves linear equations with basic facts - 1-step addition using a letter for the variable • Solves 1-step open sentences with missing addends (numbers 100 and under) • Writes a number sentence for a simple problem solving situation • Writes equivalent forms of whole numbers 11 to 20 using addition (e.g., 14 = 7 + 7) • Solves real-world whole number problems involving subtraction with numbers under 1000 • Solves whole number subtraction word problems with numbers over 1000 • Evaluates numerical expressions using grouping symbols (whole numbers only) • Demonstrates an understanding of the zero property of multiplication • Computes half price (multiplication/division) • Uses algebraic reasoning to solve problems involving equality relationships • Solves 1-step open sentences with missing addends (numbers 100 and under) • Solves 1-step open sentences with missing addends (numbers over 100) • Solves simple open sentences with missing factors (numbers 100 and under) • Solves 2-step open sentences with missing addends • Writes equivalent forms of whole numbers 11 to 20 using addition (e.g., 14 = 7 + 7) • Uses rounding to estimate answers to 2-step problems involving money (using decimals) • Solves whole number subtraction word problems with numbers over 1000 • Evaluates numerical expressions using grouping symbols (whole numbers only) • Demonstrates an understanding of the commutative property of addition • 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 1-step open sentences with missing addends (numbers over 100) • 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 2-step problem to a symbolic expression or equation • Solves real-world problems using reasoning strategies Use Functions to Model Relationships Use Functions to Model Relationships Use Functions to Model Relationships • Extends a growing arithmetic pattern, defined by numbers • Analyzes a growing, arithmetic pattern with numbers to determine the rule • Identifies transformations of plane figures (translations/slides) • Reads data in a line graph - no calculations • 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) • Reads data in a line graph - no calculations • 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) • Predicts from simple charts and tables New Vocabulary: None New Signs and Symbols: × multiplication New Vocabulary: longer New Signs and Symbols: ( ) order of operations, ÷ division, $ dollar sign New Vocabulary: minimum, plus New Signs and Symbols: °C degrees Celsius, = is equal to, min minute, - negative number, p.m., + 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 8/7/14, 9:50:06 PM © 2006-2014 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 6 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 201 - 210 Statements Last Updated: Aug 4, 2014 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 Expressions and Equations Expressions and Equations Expressions and Equations • Solves real-world whole number problems involving subtraction with numbers under 1000 • Solves whole number subtraction word problems with numbers over 1000 • Evaluates numerical expressions using grouping symbols (whole numbers only) • Demonstrates an understanding of the zero property of multiplication • Computes half price (multiplication/division) • Uses algebraic reasoning to solve problems involving equality relationships • Solves 1-step open sentences with missing addends (numbers 100 and under) • Solves 1-step open sentences with missing addends (numbers over 100) • Solves simple open sentences with missing factors (numbers 100 and under) • Solves 2-step open sentences with missing addends • Writes equivalent forms of whole numbers 11 to 20 using addition (e.g., 14 = 7 + 7) • Uses rounding to estimate answers to 2-step problems involving money (using decimals) • Solves whole number subtraction word problems with numbers over 1000 • Evaluates numerical expressions using grouping symbols (whole numbers only) • Demonstrates an understanding of the commutative property of addition • 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 1-step open sentences with missing addends (numbers over 100) • 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 2-step problem to a symbolic expression or equation • Solves real-world problems using reasoning strategies • Uses rounding to estimate answers to 2-step problems involving money (using decimals) • Demonstrates an understanding of the associative property of multiplication • Demonstrates an understanding of the distributive property of multiplication by decomposing a term • Calculates the value of a power (e.g., 2^3 = 8) • Uses a table of input/output values to represent patterns • 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 • Solves 2-step open sentences with missing factors • Solves 1-step linear equations • Applies algebraic methods to solve theoretical problems • Translates a 2-step problem to a symbolic expression or equation • Solves real-world problems using reasoning strategies • Uses powers to represent 10, 100, 1000, 10,000, and 100,000 Use Functions to Model Relationships Use Functions to Model Relationships Use Functions to Model Relationships • 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) • Reads data in a line graph - no calculations • 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) • Predicts from simple charts and tables • Completes a function table given a simple rule (e.g., x + 2) • Solves problems involving simple functions • Looks for a growing pattern to solve a problem • Interprets data in line graphs (e.g., change over time) New Vocabulary: longer New Signs and Symbols: ( ) order of operations, ÷ division, $ dollar sign New Vocabulary: minimum, plus New Signs and Symbols: °C degrees Celsius, = is equal to, min minute, - negative number, p.m., + positive number New Vocabulary: None New Signs and Symbols: ( ) parenthesis around an integer, a.m., ¢ cent sign, °F degrees Fahrenheit, $ dollar sign, lb pound, mph miles per hour

Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 6 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 201 - 210 Statements Last Updated: Aug 4, 2014 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 Expressions and Equations Expressions and Equations Expressions and Equations • Solves real-world whole number problems involving subtraction with numbers under 1000 • Solves whole number subtraction word problems with numbers over 1000 • Evaluates numerical expressions using grouping symbols (whole numbers only) • Demonstrates an understanding of the zero property of multiplication • Computes half price (multiplication/division) • Uses algebraic reasoning to solve problems involving equality relationships • Solves 1-step open sentences with missing addends (numbers 100 and under) • Solves 1-step open sentences with missing addends (numbers over 100) • Solves simple open sentences with missing factors (numbers 100 and under) • Solves 2-step open sentences with missing addends • Writes equivalent forms of whole numbers 11 to 20 using addition (e.g., 14 = 7 + 7) • Uses rounding to estimate answers to 2-step problems involving money (using decimals) • Solves whole number subtraction word problems with numbers over 1000 • Evaluates numerical expressions using grouping symbols (whole numbers only) • Demonstrates an understanding of the commutative property of addition • 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 1-step open sentences with missing addends (numbers over 100) • 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 2-step problem to a symbolic expression or equation • Solves real-world problems using reasoning strategies • Uses rounding to estimate answers to 2-step problems involving money (using decimals) • Demonstrates an understanding of the associative property of multiplication • Demonstrates an understanding of the distributive property of multiplication by decomposing a term • Calculates the value of a power (e.g., 2^3 = 8) • Uses a table of input/output values to represent patterns • 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 • Solves 2-step open sentences with missing factors • Solves 1-step linear equations • Applies algebraic methods to solve theoretical problems • Translates a 2-step problem to a symbolic expression or equation • Solves real-world problems using reasoning strategies • Uses powers to represent 10, 100, 1000, 10,000, and 100,000 Use Functions to Model Relationships Use Functions to Model Relationships Use Functions to Model Relationships • 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) • Reads data in a line graph - no calculations • 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) • Predicts from simple charts and tables • Completes a function table given a simple rule (e.g., x + 2) • Solves problems involving simple functions • Looks for a growing pattern to solve a problem • Interprets data in line graphs (e.g., change over time) New Vocabulary: longer New Signs and Symbols: ( ) order of operations, ÷ division, $ dollar sign New Vocabulary: minimum, plus New Signs and Symbols: °C degrees Celsius, = is equal to, min minute, - negative number, p.m., + positive number New Vocabulary: None New Signs and Symbols: ( ) parenthesis around an integer, a.m., ¢ cent sign, °F degrees Fahrenheit, $ dollar sign, lb pound, mph miles per hour 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 8/7/14, 9:50:06 PM © 2006-2014 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 7 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 211 - 220 Statements Last Updated: Aug 4, 2014 Goal: Operations and Algebraic Thinking Skills and Concepts to Enhance (73% Probability*) 201 - 210 Skills and Concepts to Develop (50% Probability*) 211 - 220 Skills and Concepts to Introduce (27% Probability*) 221 - 230 Expressions and Equations Expressions and Equations Expressions and Equations • Uses rounding to estimate answers to 2-step problems involving money (using decimals) • Solves whole number subtraction word problems with numbers over 1000 • Evaluates numerical expressions using grouping symbols (whole numbers only) • Demonstrates an understanding of the commutative property of addition • 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 1-step open sentences with missing addends (numbers over 100) • 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 2-step problem to a symbolic expression or equation • Solves real-world problems using reasoning strategies • Uses rounding to estimate answers to 2-step problems involving money (using decimals) • Demonstrates an understanding of the associative property of multiplication • Demonstrates an understanding of the distributive property of multiplication by decomposing a term • Calculates the value of a power (e.g., 2^3 = 8) • Uses a table of input/output values to represent patterns • 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 • Solves 2-step open sentences with missing factors • Solves 1-step linear equations • Applies algebraic methods to solve theoretical problems • Translates a 2-step problem to a symbolic expression or equation • Solves real-world problems using reasoning strategies • Uses powers to represent 10, 100, 1000, 10,000, and 100,000 • Solves real-world problems involving rate of pay • Solves difficult real-world problems involving decimals (e.g., multiple multiplications, conversions) • Uses the distributive property • Calculates the value of a power (e.g., 2^3 = 8) • Solves problems involving simple interest rates with the formula • Uses a table of input/output values to represent patterns • Uses basic operations on algebraic expressions (substituting for unknowns) • Recognizes commutative, associative, distributive, symmetric, transitive, and reflexive properties • Uses basic operations on algebraic expressions (expanding - monomial by a binomial) • Demonstrates an understanding of properties (e.g., commutative, associative, distributive, properties of 0) • Writes equivalent forms of algebraic expressions (e.g., (x + 3)/2 = x/2 + 3/2) • Represents relationships of quantities in the form of an expression • Uses basic operations on algebraic expressions (uses correct order of operations) • Expresses a simple linear equation from a contextual situation • Solves open sentences with calculations on both sides of the sentence • Solves 2-step open sentences with missing factors • Solves 1-step linear equations • Solves 2-step linear equations • Solves linear equations with decimals • Solves linear equations with integers • Writes equivalent forms of algebraic equations using addition and subtraction • Solves open sentences with decimals • Solves linear equations in a real-world context using a given formula • Applies algebraic methods to solve theoretical problems • Applies algebraic methods to solve real-world problems • Uses graphs to solve simple systems of linear equations • Applies systems-of-linear-equations methods to solve theoretical problems • Describes the relationship or a real-world situation represented by a simple linear inequality (e.g., 1- or 2-step) • Solves real-world problems using reasoning strategies • Uses powers to represent 10, 100, 1000, 10,000, and 100,000

Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 7 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 211 - 220 Statements Last Updated: Aug 4, 2014 Goal: Operations and Algebraic Thinking Skills and Concepts to Enhance (73% Probability*) 201 - 210 Skills and Concepts to Develop (50% Probability*) 211 - 220 Skills and Concepts to Introduce (27% Probability*) 221 - 230 Expressions and Equations Expressions and Equations Expressions and Equations • Uses rounding to estimate answers to 2-step problems involving money (using decimals) • Solves whole number subtraction word problems with numbers over 1000 • Evaluates numerical expressions using grouping symbols (whole numbers only) • Demonstrates an understanding of the commutative property of addition • 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 1-step open sentences with missing addends (numbers over 100) • 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 2-step problem to a symbolic expression or equation • Solves real-world problems using reasoning strategies • Uses rounding to estimate answers to 2-step problems involving money (using decimals) • Demonstrates an understanding of the associative property of multiplication • Demonstrates an understanding of the distributive property of multiplication by decomposing a term • Calculates the value of a power (e.g., 2^3 = 8) • Uses a table of input/output values to represent patterns • 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 • Solves 2-step open sentences with missing factors • Solves 1-step linear equations • Applies algebraic methods to solve theoretical problems • Translates a 2-step problem to a symbolic expression or equation • Solves real-world problems using reasoning strategies • Uses powers to represent 10, 100, 1000, 10,000, and 100,000 • Solves real-world problems involving rate of pay • Solves difficult real-world problems involving decimals (e.g., multiple multiplications, conversions) • Uses the distributive property • Calculates the value of a power (e.g., 2^3 = 8) • Solves problems involving simple interest rates with the formula • Uses a table of input/output values to represent patterns • Uses basic operations on algebraic expressions (substituting for unknowns) • Recognizes commutative, associative, distributive, symmetric, transitive, and reflexive properties • Uses basic operations on algebraic expressions (expanding - monomial by a binomial) • Demonstrates an understanding of properties (e.g., commutative, associative, distributive, properties of 0) • Writes equivalent forms of algebraic expressions (e.g., (x + 3)/2 = x/2 + 3/2) • Represents relationships of quantities in the form of an expression • Uses basic operations on algebraic expressions (uses correct order of operations) • Expresses a simple linear equation from a contextual situation • Solves open sentences with calculations on both sides of the sentence • Solves 2-step open sentences with missing factors • Solves 1-step linear equations • Solves 2-step linear equations • Solves linear equations with decimals • Solves linear equations with integers • Writes equivalent forms of algebraic equations using addition and subtraction • Solves open sentences with decimals • Solves linear equations in a real-world context using a given formula • Applies algebraic methods to solve theoretical problems • Applies algebraic methods to solve real-world problems • Uses graphs to solve simple systems of linear equations • Applies systems-of-linear-equations methods to solve theoretical problems • Describes the relationship or a real-world situation represented by a simple linear inequality (e.g., 1- or 2-step) • Solves real-world problems using reasoning strategies • Uses powers to represent 10, 100, 1000, 10,000, and 100,000 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 8/7/14, 9:50:06 PM © 2006-2014 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 8 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 211 - 220 Statements Last Updated: Aug 4, 2014 Goal: Operations and Algebraic Thinking Skills and Concepts to Enhance (73% Probability*) 201 - 210 Skills and Concepts to Develop (50% Probability*) 211 - 220 Skills and Concepts to Introduce (27% Probability*) 221 - 230 Expressions and Equations Expressions and Equations Expressions and Equations • Writes a number expressed in scientific notation in standard form Use Functions to Model Relationships Use Functions to Model Relationships Use Functions to Model Relationships • 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) • Predicts from simple charts and tables • Completes a function table given a simple rule (e.g., x + 2) • Solves problems involving simple functions • Looks for a growing pattern to solve a problem • Interprets data in line graphs (e.g., change over time) • Extends a growing pattern of triangular numbers, defined by objects or diagrams • Represents geometric sequences using written descriptions in recursive terms (present term, next term) • Solves problems involving simple functions • Looks for a growing pattern to solve a problem New Vocabulary: minimum, plus New Signs and Symbols: °C degrees Celsius, = is equal to, min minute, - negative number, p.m., + positive number New Vocabulary: None New Signs and Symbols: ( ) parenthesis around an integer, a.m., ¢ cent sign, °F degrees Fahrenheit, $ dollar sign, lb pound, mph miles per hour New Vocabulary: algebra, net, reflexive, short, transitive New Signs and Symbols: < less than, m meter/metre, repeating decimal overbar, △ triangle

Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 8 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 211 - 220 Statements Last Updated: Aug 4, 2014 Goal: Operations and Algebraic Thinking Skills and Concepts to Enhance (73% Probability*) 201 - 210 Skills and Concepts to Develop (50% Probability*) 211 - 220 Skills and Concepts to Introduce (27% Probability*) 221 - 230 Expressions and Equations Expressions and Equations Expressions and Equations • Writes a number expressed in scientific notation in standard form Use Functions to Model Relationships Use Functions to Model Relationships Use Functions to Model Relationships • 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) • Predicts from simple charts and tables • Completes a function table given a simple rule (e.g., x + 2) • Solves problems involving simple functions • Looks for a growing pattern to solve a problem • Interprets data in line graphs (e.g., change over time) • Extends a growing pattern of triangular numbers, defined by objects or diagrams • Represents geometric sequences using written descriptions in recursive terms (present term, next term) • Solves problems involving simple functions • Looks for a growing pattern to solve a problem New Vocabulary: minimum, plus New Signs and Symbols: °C degrees Celsius, = is equal to, min minute, - negative number, p.m., + positive number New Vocabulary: None New Signs and Symbols: ( ) parenthesis around an integer, a.m., ¢ cent sign, °F degrees Fahrenheit, $ dollar sign, lb pound, mph miles per hour New Vocabulary: algebra, net, reflexive, short, transitive New Signs and Symbols: < less than, m meter/metre, repeating decimal overbar, △ triangle 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 8/7/14, 9:50:06 PM © 2006-2014 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 9 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 221 - 230 Statements Last Updated: Aug 4, 2014 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 Expressions and Equations Expressions and Equations Expressions and Equations • Uses rounding to estimate answers to 2-step problems involving money (using decimals) • Demonstrates an understanding of the associative property of multiplication • Demonstrates an understanding of the distributive property of multiplication by decomposing a term • Calculates the value of a power (e.g., 2^3 = 8) • Uses a table of input/output values to represent patterns • 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 • Solves 2-step open sentences with missing factors • Solves 1-step linear equations • Applies algebraic methods to solve theoretical problems • Translates a 2-step problem to a symbolic expression or equation • Solves real-world problems using reasoning strategies • Uses powers to represent 10, 100, 1000, 10,000, and 100,000 • Solves real-world problems involving rate of pay • Solves difficult real-world problems involving decimals (e.g., multiple multiplications, conversions) • Uses the distributive property • Calculates the value of a power (e.g., 2^3 = 8) • Solves problems involving simple interest rates with the formula • Uses a table of input/output values to represent patterns • Uses basic operations on algebraic expressions (substituting for unknowns) • Recognizes commutative, associative, distributive, symmetric, transitive, and reflexive properties • Uses basic operations on algebraic expressions (expanding - monomial by a binomial) • Demonstrates an understanding of properties (e.g., commutative, associative, distributive, properties of 0) • Writes equivalent forms of algebraic expressions (e.g., (x + 3)/2 = x/2 + 3/2) • Represents relationships of quantities in the form of an expression • Uses basic operations on algebraic expressions (uses correct order of operations) • Expresses a simple linear equation from a contextual situation • Solves open sentences with calculations on both sides of the sentence • Solves 2-step open sentences with missing factors • Solves 1-step linear equations • Solves 2-step linear equations • Solves linear equations with decimals • Solves linear equations with integers • Writes equivalent forms of algebraic equations using addition and subtraction • Solves open sentences with decimals • Solves linear equations in a real-world context using a given formula • Applies algebraic methods to solve theoretical problems • Applies algebraic methods to solve real-world problems • Uses graphs to solve simple systems of linear equations • Applies systems-of-linear-equations methods to solve theoretical problems • Describes the relationship or a real-world situation represented by a simple linear inequality (e.g., 1- or 2-step) • Solves real-world problems using reasoning strategies • Uses powers to represent 10, 100, 1000, 10,000, and 100,000 • Evaluates numerical expressions using the order of operations (whole numbers only) • Evaluates expressions using the order of operations, including exponents (whole numbers only) • Solves real-world problems involving rate of pay • Solves real-world problems involving rate of pay with time and a half • Solves difficult real-world problems involving decimals (e.g., multiple multiplications, conversions) • Evaluates numerical expressions using the order of operations (using integers) • Divides rational expressions in a/b form • Uses the distributive property • Calculates the power of a number (e.g., 8 = 2^3) • Evaluates expressions containing powers (e.g., 3^2 x 2^3) • Applies rules for multiplying and dividing powers • Solves problems with scientific notation • Describes and uses a variable with whole numbers, multiplication, and division in a contextual situation • Uses expressions to represent situations that involve variable quantities with exponents • Uses basic operations on algebraic expressions (substituting for unknowns) • Uses basic operations on algebraic expressions (substituting for unknown exponents) • Recognizes commutative, associative, distributive, symmetric, transitive, and reflexive properties • Uses basic operations on algebraic expressions (combining like terms) • Uses basic operations on algebraic expressions (expanding - monomial by a binomial) • Writes equivalent forms of algebraic expressions (e.g., (x + 3)/2 = x/2 + 3/2) • Represents relationships of quantities in the form of an expression • Uses basic operations on algebraic expressions (uses correct order of operations) • Expresses a simple linear equation from a contextual situation • Solves 2-step open sentences with missing factors (variables on both sides of the sentence) • Solves 2-step linear equations • Solves linear equations with integers • Solves linear equations with fractions • Solves linear equations using rational numbers