Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 10 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 • Writes a number expressed in scientific notation in standard form • Applies algebraic methods to solve real-world problems • Determines slope from a linear equation • Uses polynomial equations to solve complex real-world problems (e.g., using distributive property, variables on both sides) • Uses graphs to solve simple systems of linear equations • Solves simple one-step inequality open sentences • Expresses a simple linear inequality from a contextual situation • Describes the relationship or a real-world situation represented by a simple linear inequality (e.g., 1- or 2-step) • Solves simple linear inequalities using graphs • Solves problems involving capacity in the metric system and converts to larger or smaller units • Converts from Celsius to Fahrenheit, given conversion ratios • Determines the prime factorization of a number • Writes a whole number in scientific notation Use Functions to Model Relationships Use Functions to Model Relationships Use Functions to Model Relationships • 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 • Recognizes and extends arithmetic sequences (predicts nth term) • Represents geometric sequences using written descriptions in recursive terms (present term, next term) • Recognizes and extends the Fibonacci sequence • Writes linear equations when given ordered pairs • Writes the equation of a horizontal or vertical line when given the graph of the line • Represents real-world functions using an equation • Uses mapping diagrams to represent functions • Uses tables to determine function equations • Identifies the graph type, given equations of linear and nonlinear functions • Solves problems involving simple functions • Solves problems involving complex functions • Interprets data given in line graphs to solve problems 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 New Vocabulary: algebraic sentence, depreciate, equation of a line, is less than, regression equation, time-and-a-half New Signs and Symbols: ≤, ≥, ( ) ordered pair, f(x) the value of the function f at x, > greater than, > greater than, ≥ greater than or equal to, km kilometer/kilometre, ≤ less than or equal to, ∙ multiplication symbol (dot), - subtraction 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 11 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 231 - 240 Statements Last Updated: Aug 4, 2014 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 Expressions and Equations Expressions and Equations Expressions and Equations • 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 • Evaluates expressions using the order of operations, including exponents (whole numbers only) • Solves real-world problems involving rate of pay with time and a half • Evaluates numerical expressions using the order of operations (using integers) • Evaluates expressions using the order of operations, including exponents (using integers) • Solves problems involving simple interest rates without the formula • Simplifies rational expressions with scientific notation • 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 • Evaluates expressions by substituting with rational numbers • Simplifies polynomial expressions • Multiplies binomials • Factors trinomials in the form x^2 + bx + c • Factors polynomials using difference of squares • Uses basic operations on algebraic expressions (uses correct order of operations) • Uses linear equations to represent situations involving variable quantities • Solves 2-step open sentences with missing factors (variables on both sides of the sentence) • Solves linear equations with fractions • Solves linear equations using rational numbers • Solves open sentences with fractions • Applies algebraic methods to solve real-world problems • Applies algebraic methods to solve a variety of real-world and theoretical problems • Solves problems involving consecutive numbers • Uses polynomial equations to solve complex real-world problems (e.g., using distributive property, variables on both sides) • Uses algebraic methods to solve systems of linear equations • Solves simple one-step inequality open sentences • Solves single variable linear inequalities with the variable in only one member using number lines • Describes the relationship or a real-world situation represented by a simple linear inequality (e.g., 1- or 2-step) • Solves linear inequalities using graphs

Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 11 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 231 - 240 Statements Last Updated: Aug 4, 2014 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 Expressions and Equations Expressions and Equations Expressions and Equations • 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 • Evaluates expressions using the order of operations, including exponents (whole numbers only) • Solves real-world problems involving rate of pay with time and a half • Evaluates numerical expressions using the order of operations (using integers) • Evaluates expressions using the order of operations, including exponents (using integers) • Solves problems involving simple interest rates without the formula • Simplifies rational expressions with scientific notation • 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 • Evaluates expressions by substituting with rational numbers • Simplifies polynomial expressions • Multiplies binomials • Factors trinomials in the form x^2 + bx + c • Factors polynomials using difference of squares • Uses basic operations on algebraic expressions (uses correct order of operations) • Uses linear equations to represent situations involving variable quantities • Solves 2-step open sentences with missing factors (variables on both sides of the sentence) • Solves linear equations with fractions • Solves linear equations using rational numbers • Solves open sentences with fractions • Applies algebraic methods to solve real-world problems • Applies algebraic methods to solve a variety of real-world and theoretical problems • Solves problems involving consecutive numbers • Uses polynomial equations to solve complex real-world problems (e.g., using distributive property, variables on both sides) • Uses algebraic methods to solve systems of linear equations • Solves simple one-step inequality open sentences • Solves single variable linear inequalities with the variable in only one member using number lines • Describes the relationship or a real-world situation represented by a simple linear inequality (e.g., 1- or 2-step) • Solves linear inequalities using graphs 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 12 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 231 - 240 Statements Last Updated: Aug 4, 2014 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 Expressions and Equations Expressions and Equations Expressions and Equations • Writes a number expressed in scientific notation in standard form • Applies algebraic methods to solve real-world problems • Determines slope from a linear equation • Uses polynomial equations to solve complex real-world problems (e.g., using distributive property, variables on both sides) • Uses graphs to solve simple systems of linear equations • Solves simple one-step inequality open sentences • Expresses a simple linear inequality from a contextual situation • Describes the relationship or a real-world situation represented by a simple linear inequality (e.g., 1- or 2-step) • Solves simple linear inequalities using graphs • Solves problems involving capacity in the metric system and converts to larger or smaller units • Converts from Celsius to Fahrenheit, given conversion ratios • Determines the prime factorization of a number • Writes a whole number in scientific notation • Solves complex real-world problems involving capacity • Solves problems involving capacity in the metric system and converts to larger or smaller units • Converts from Celsius to Fahrenheit, given conversion ratios • Uses reasoning strategies to solve problems • Determines the prime factorization of a number using powers • Writes a whole number in scientific notation • Writes a decimal in scientific notation Use Functions to Model Relationships Use Functions to Model Relationships Use Functions to Model Relationships • 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 • Recognizes and extends arithmetic sequences (predicts nth term) • Represents geometric sequences using written descriptions in recursive terms (present term, next term) • Recognizes and extends the Fibonacci sequence • Writes linear equations when given ordered pairs • Writes the equation of a horizontal or vertical line when given the graph of the line • Represents real-world functions using an equation • Uses mapping diagrams to represent functions • Uses tables to determine function equations • Identifies the graph type, given equations of linear and nonlinear functions • Solves problems involving simple functions • Solves problems involving complex functions • Interprets data given in line graphs to solve problems • Represents growing arithmetic patterns using algebraic expressions or equations • Writes linear equations when given ordered pairs • Writes the equation of a horizontal or vertical line when given the graph of the line • Determines x- or y-intercept of a given linear equation • Identifies and describes situations with varying rates of change • Solves quadratic equations using concrete models and tables • Uses tables to determine function equations • Represents a real-world function using a complex equation (e.g., variables on both sides, distributive, rational) • Models real life functions using function notation • Determines the minimum and maximum of a quadratic function • Analyzes the properties and characteristics of exponential functions • Determines the x- and/or y-intercept of an equation of a function • Performs operations on functions • Solves problems involving complex functions • Determines the domain and range of a function New Vocabulary: algebra, net, reflexive, short, transitive New Signs and Symbols: < less than, m meter/metre, repeating decimal overbar, △ triangle New Vocabulary: algebraic sentence, depreciate, equation of a line, is less than, regression equation, time-and-a-half New Signs and Symbols: ≤, ≥, ( ) ordered pair, f(x) the value of the function f at x, > greater than, > greater than, ≥ greater than or equal to, km kilometer/kilometre, ≤ less than or equal to, ∙ multiplication symbol (dot), - subtraction New Vocabulary: polynomial, solution set, y-intercept New Signs and Symbols: % percent

Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 12 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 231 - 240 Statements Last Updated: Aug 4, 2014 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 Expressions and Equations Expressions and Equations Expressions and Equations • Writes a number expressed in scientific notation in standard form • Applies algebraic methods to solve real-world problems • Determines slope from a linear equation • Uses polynomial equations to solve complex real-world problems (e.g., using distributive property, variables on both sides) • Uses graphs to solve simple systems of linear equations • Solves simple one-step inequality open sentences • Expresses a simple linear inequality from a contextual situation • Describes the relationship or a real-world situation represented by a simple linear inequality (e.g., 1- or 2-step) • Solves simple linear inequalities using graphs • Solves problems involving capacity in the metric system and converts to larger or smaller units • Converts from Celsius to Fahrenheit, given conversion ratios • Determines the prime factorization of a number • Writes a whole number in scientific notation • Solves complex real-world problems involving capacity • Solves problems involving capacity in the metric system and converts to larger or smaller units • Converts from Celsius to Fahrenheit, given conversion ratios • Uses reasoning strategies to solve problems • Determines the prime factorization of a number using powers • Writes a whole number in scientific notation • Writes a decimal in scientific notation Use Functions to Model Relationships Use Functions to Model Relationships Use Functions to Model Relationships • 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 • Recognizes and extends arithmetic sequences (predicts nth term) • Represents geometric sequences using written descriptions in recursive terms (present term, next term) • Recognizes and extends the Fibonacci sequence • Writes linear equations when given ordered pairs • Writes the equation of a horizontal or vertical line when given the graph of the line • Represents real-world functions using an equation • Uses mapping diagrams to represent functions • Uses tables to determine function equations • Identifies the graph type, given equations of linear and nonlinear functions • Solves problems involving simple functions • Solves problems involving complex functions • Interprets data given in line graphs to solve problems • Represents growing arithmetic patterns using algebraic expressions or equations • Writes linear equations when given ordered pairs • Writes the equation of a horizontal or vertical line when given the graph of the line • Determines x- or y-intercept of a given linear equation • Identifies and describes situations with varying rates of change • Solves quadratic equations using concrete models and tables • Uses tables to determine function equations • Represents a real-world function using a complex equation (e.g., variables on both sides, distributive, rational) • Models real life functions using function notation • Determines the minimum and maximum of a quadratic function • Analyzes the properties and characteristics of exponential functions • Determines the x- and/or y-intercept of an equation of a function • Performs operations on functions • Solves problems involving complex functions • Determines the domain and range of a function New Vocabulary: algebra, net, reflexive, short, transitive New Signs and Symbols: < less than, m meter/metre, repeating decimal overbar, △ triangle New Vocabulary: algebraic sentence, depreciate, equation of a line, is less than, regression equation, time-and-a-half New Signs and Symbols: ≤, ≥, ( ) ordered pair, f(x) the value of the function f at x, > greater than, > greater than, ≥ greater than or equal to, km kilometer/kilometre, ≤ less than or equal to, ∙ multiplication symbol (dot), - subtraction New Vocabulary: polynomial, solution set, y-intercept New Signs and Symbols: % percent 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 13 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 241 - 250 Statements Last Updated: Aug 4, 2014 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*) 251 - 260 Expressions and Equations Expressions and Equations Expressions and Equations • 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 • Evaluates expressions using the order of operations, including exponents (whole numbers only) • Solves real-world problems involving rate of pay with time and a half • Evaluates numerical expressions using the order of operations (using integers) • Evaluates expressions using the order of operations, including exponents (using integers) • Solves problems involving simple interest rates without the formula • Simplifies rational expressions with scientific notation • 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 • Evaluates expressions by substituting with rational numbers • Simplifies polynomial expressions • Multiplies binomials • Factors trinomials in the form x^2 + bx + c • Factors polynomials using difference of squares • Uses basic operations on algebraic expressions (uses correct order of operations) • Uses linear equations to represent situations involving variable quantities • Solves 2-step open sentences with missing factors (variables on both sides of the sentence) • Solves linear equations with fractions • Solves linear equations using rational numbers • Solves open sentences with fractions • Applies algebraic methods to solve real-world problems • Applies algebraic methods to solve a variety of real-world and theoretical problems • Solves problems involving consecutive numbers • Uses polynomial equations to solve complex real-world problems (e.g., using distributive property, variables on both sides) • Uses algebraic methods to solve systems of linear equations • Solves simple one-step inequality open sentences • Solves single variable linear inequalities with the variable in only one member using number lines • Describes the relationship or a real-world situation represented by a simple linear inequality (e.g., 1- or 2-step) • Solves linear inequalities using graphs • Simplifies rational expressions with exponents • 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 • Evaluates expressions by substituting with rational numbers • Simplifies monomials • Simplifies polynomial expressions • Simplifies algebraic expressions with integer exponents • Multiplies binomials • Multiplies a polynomial by a polynomial • Divides a polynomial by a monomial • Factors polynomials by identifying common factors • Factors trinomials in the form x^2 + bx + c • Factors polynomials using difference of squares • Writes equivalent forms of algebraic equations using multiplication and division • Solves linear equations using rational numbers • Applies algebraic methods to solve complex real-world and theoretical problems • Rewrites a complex formula to solve for a specific variable • Identifies discriminants and roots • Solves quadratic equations by factoring • Solves quadratic equations by completing the square • Solves polynomial equations (e.g., ax = b + cx, a(x + b) = c, ax + b = cx + d, a(bx + c) = d(ex + f), a/x = b) • Uses polynomial equations to solve area and perimeter problems • Solves polynomial equations with integers as exponents • Uses the Multiplication Property of Equality as a first step in solving systems of linear equations • Uses substitution as a first step in solving systems of linear equations • Uses algebraic methods to solve systems of linear equations • Uses graphs to solve systems of linear equations • Solves real-world systems of linear equations • Solves single variable linear inequalities with the variable in only one member using number lines • Solves single variable linear inequalities with variable in both members using number lines

Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 13 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 241 - 250 Statements Last Updated: Aug 4, 2014 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*) 251 - 260 Expressions and Equations Expressions and Equations Expressions and Equations • 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 • Evaluates expressions using the order of operations, including exponents (whole numbers only) • Solves real-world problems involving rate of pay with time and a half • Evaluates numerical expressions using the order of operations (using integers) • Evaluates expressions using the order of operations, including exponents (using integers) • Solves problems involving simple interest rates without the formula • Simplifies rational expressions with scientific notation • 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 • Evaluates expressions by substituting with rational numbers • Simplifies polynomial expressions • Multiplies binomials • Factors trinomials in the form x^2 + bx + c • Factors polynomials using difference of squares • Uses basic operations on algebraic expressions (uses correct order of operations) • Uses linear equations to represent situations involving variable quantities • Solves 2-step open sentences with missing factors (variables on both sides of the sentence) • Solves linear equations with fractions • Solves linear equations using rational numbers • Solves open sentences with fractions • Applies algebraic methods to solve real-world problems • Applies algebraic methods to solve a variety of real-world and theoretical problems • Solves problems involving consecutive numbers • Uses polynomial equations to solve complex real-world problems (e.g., using distributive property, variables on both sides) • Uses algebraic methods to solve systems of linear equations • Solves simple one-step inequality open sentences • Solves single variable linear inequalities with the variable in only one member using number lines • Describes the relationship or a real-world situation represented by a simple linear inequality (e.g., 1- or 2-step) • Solves linear inequalities using graphs • Simplifies rational expressions with exponents • 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 • Evaluates expressions by substituting with rational numbers • Simplifies monomials • Simplifies polynomial expressions • Simplifies algebraic expressions with integer exponents • Multiplies binomials • Multiplies a polynomial by a polynomial • Divides a polynomial by a monomial • Factors polynomials by identifying common factors • Factors trinomials in the form x^2 + bx + c • Factors polynomials using difference of squares • Writes equivalent forms of algebraic equations using multiplication and division • Solves linear equations using rational numbers • Applies algebraic methods to solve complex real-world and theoretical problems • Rewrites a complex formula to solve for a specific variable • Identifies discriminants and roots • Solves quadratic equations by factoring • Solves quadratic equations by completing the square • Solves polynomial equations (e.g., ax = b + cx, a(x + b) = c, ax + b = cx + d, a(bx + c) = d(ex + f), a/x = b) • Uses polynomial equations to solve area and perimeter problems • Solves polynomial equations with integers as exponents • Uses the Multiplication Property of Equality as a first step in solving systems of linear equations • Uses substitution as a first step in solving systems of linear equations • Uses algebraic methods to solve systems of linear equations • Uses graphs to solve systems of linear equations • Solves real-world systems of linear equations • Solves single variable linear inequalities with the variable in only one member using number lines • Solves single variable linear inequalities with variable in both members using number lines 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 14 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 241 - 250 Statements Last Updated: Aug 4, 2014 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*) 251 - 260 Expressions and Equations Expressions and Equations Expressions and Equations • Applies algebraic methods to solve real-world problems • Determines slope from a linear equation • Uses polynomial equations to solve complex real-world problems (e.g., using distributive property, variables on both sides) • Uses graphs to solve simple systems of linear equations • Solves simple one-step inequality open sentences • Expresses a simple linear inequality from a contextual situation • Describes the relationship or a real-world situation represented by a simple linear inequality (e.g., 1- or 2-step) • Solves simple linear inequalities using graphs • Solves problems involving capacity in the metric system and converts to larger or smaller units • Converts from Celsius to Fahrenheit, given conversion ratios • Determines the prime factorization of a number • Writes a whole number in scientific notation • Solves complex real-world problems involving capacity • Solves problems involving capacity in the metric system and converts to larger or smaller units • Converts from Celsius to Fahrenheit, given conversion ratios • Uses reasoning strategies to solve problems • Determines the prime factorization of a number using powers • Writes a whole number in scientific notation • Writes a decimal in scientific notation • Uses graphs to solve systems of linear inequalities • Determines the length of the side of a square, given the area • Uses reasoning strategies to solve problems • Uses fractional and negative exponents as optional ways of representing problem situations (e.g., 27^2/3 = (27^1/3)^2 = 9) Use Functions to Model Relationships Use Functions to Model Relationships Use Functions to Model Relationships • Recognizes and extends arithmetic sequences (predicts nth term) • Represents geometric sequences using written descriptions in recursive terms (present term, next term) • Recognizes and extends the Fibonacci sequence • Writes linear equations when given ordered pairs • Writes the equation of a horizontal or vertical line when given the graph of the line • Represents real-world functions using an equation • Uses mapping diagrams to represent functions • Uses tables to determine function equations • Identifies the graph type, given equations of linear and nonlinear functions • Solves problems involving simple functions • Solves problems involving complex functions • Interprets data given in line graphs to solve problems • Represents growing arithmetic patterns using algebraic expressions or equations • Writes linear equations when given ordered pairs • Writes the equation of a horizontal or vertical line when given the graph of the line • Determines x- or y-intercept of a given linear equation • Identifies and describes situations with varying rates of change • Solves quadratic equations using concrete models and tables • Uses tables to determine function equations • Represents a real-world function using a complex equation (e.g., variables on both sides, distributive, rational) • Models real life functions using function notation • Determines the minimum and maximum of a quadratic function • Analyzes the properties and characteristics of exponential functions • Determines the x- and/or y-intercept of an equation of a function • Performs operations on functions • Solves problems involving complex functions • Determines the domain and range of a function • Uses an algebraic expression to represent a triangular number pattern • Rewrites an equation for a line in standard form • Determines x- or y-intercept of a given linear equation • Writes the equation of the line when given the graph of the line • Determines the graph of a line when given the equation • Writes linear equations, given two points on a line • Determines slope from graphs • Determines slope from ordered pairs and tables • Identifies and describes situations with varying rates of change • Represents a real-world function using a complex equation (e.g., variables on both sides, distributive, rational) • Models real life functions using function notation • Distinguishes between linear and nonlinear functions (analysis) • Uses graphs to represent functions and interpret slope • Identifies the equation of a parabola • Determines the vertex of a parabola • Determines the minimum and maximum of a quadratic function • Analyzes the properties and characteristics of exponential functions • Investigates, describes, and predicts the effects of parameter changes on the graphs of exponential functions • Determines the effects of parameter changes on functions • Determines the domain and range of a function

Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 14 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 241 - 250 Statements Last Updated: Aug 4, 2014 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*) 251 - 260 Expressions and Equations Expressions and Equations Expressions and Equations • Applies algebraic methods to solve real-world problems • Determines slope from a linear equation • Uses polynomial equations to solve complex real-world problems (e.g., using distributive property, variables on both sides) • Uses graphs to solve simple systems of linear equations • Solves simple one-step inequality open sentences • Expresses a simple linear inequality from a contextual situation • Describes the relationship or a real-world situation represented by a simple linear inequality (e.g., 1- or 2-step) • Solves simple linear inequalities using graphs • Solves problems involving capacity in the metric system and converts to larger or smaller units • Converts from Celsius to Fahrenheit, given conversion ratios • Determines the prime factorization of a number • Writes a whole number in scientific notation • Solves complex real-world problems involving capacity • Solves problems involving capacity in the metric system and converts to larger or smaller units • Converts from Celsius to Fahrenheit, given conversion ratios • Uses reasoning strategies to solve problems • Determines the prime factorization of a number using powers • Writes a whole number in scientific notation • Writes a decimal in scientific notation • Uses graphs to solve systems of linear inequalities • Determines the length of the side of a square, given the area • Uses reasoning strategies to solve problems • Uses fractional and negative exponents as optional ways of representing problem situations (e.g., 27^2/3 = (27^1/3)^2 = 9) Use Functions to Model Relationships Use Functions to Model Relationships Use Functions to Model Relationships • Recognizes and extends arithmetic sequences (predicts nth term) • Represents geometric sequences using written descriptions in recursive terms (present term, next term) • Recognizes and extends the Fibonacci sequence • Writes linear equations when given ordered pairs • Writes the equation of a horizontal or vertical line when given the graph of the line • Represents real-world functions using an equation • Uses mapping diagrams to represent functions • Uses tables to determine function equations • Identifies the graph type, given equations of linear and nonlinear functions • Solves problems involving simple functions • Solves problems involving complex functions • Interprets data given in line graphs to solve problems • Represents growing arithmetic patterns using algebraic expressions or equations • Writes linear equations when given ordered pairs • Writes the equation of a horizontal or vertical line when given the graph of the line • Determines x- or y-intercept of a given linear equation • Identifies and describes situations with varying rates of change • Solves quadratic equations using concrete models and tables • Uses tables to determine function equations • Represents a real-world function using a complex equation (e.g., variables on both sides, distributive, rational) • Models real life functions using function notation • Determines the minimum and maximum of a quadratic function • Analyzes the properties and characteristics of exponential functions • Determines the x- and/or y-intercept of an equation of a function • Performs operations on functions • Solves problems involving complex functions • Determines the domain and range of a function • Uses an algebraic expression to represent a triangular number pattern • Rewrites an equation for a line in standard form • Determines x- or y-intercept of a given linear equation • Writes the equation of the line when given the graph of the line • Determines the graph of a line when given the equation • Writes linear equations, given two points on a line • Determines slope from graphs • Determines slope from ordered pairs and tables • Identifies and describes situations with varying rates of change • Represents a real-world function using a complex equation (e.g., variables on both sides, distributive, rational) • Models real life functions using function notation • Distinguishes between linear and nonlinear functions (analysis) • Uses graphs to represent functions and interpret slope • Identifies the equation of a parabola • Determines the vertex of a parabola • Determines the minimum and maximum of a quadratic function • Analyzes the properties and characteristics of exponential functions • Investigates, describes, and predicts the effects of parameter changes on the graphs of exponential functions • Determines the effects of parameter changes on functions • Determines the domain and range of a function 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 15 of 21 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 241 - 250 Statements Last Updated: Aug 4, 2014 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*) 251 - 260 New Vocabulary: algebraic sentence, depreciate, equation of a line, is less than, regression equation, time-and-a-half New Signs and Symbols: ≤, ≥, ( ) ordered pair, f(x) the value of the function f at x, > greater than, > greater than, ≥ greater than or equal to, km kilometer/kilometre, ≤ less than or equal to, ∙ multiplication symbol (dot), - subtraction New Vocabulary: polynomial, solution set, y-intercept New Signs and Symbols: % percent New Vocabulary: coordinate plane, quadratic equation, undefined, wider, x-coordinate, y-coordinate New Signs and Symbols: [ ] square brackets, { } set notation, P perimeter