Download Math 6+: Algebra

DesCartes: A Continuum of Learning®
< 171
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Develop (50% Probability*)
< 171
Functions: Representations, Linear & Non Linear
Skills and Concepts to Introduce (27% Probability*)
171 - 180
Functions: Representations, Linear & Non Linear
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
• Identifies the missing operation symbol - 1-step number sentence
• Represents a basic facts addition problem with a number sentence
• Solves basic-facts open sentences - addition and subtraction
• Identifies the missing operation symbol - 1-step number sentence
• Solves basic-facts open sentences - addition and subtraction
• Solves basic facts open sentences - multiplication and division
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
• Completes a growing arithmetic pattern by naming missing members
• Extends a growing arithmetic pattern, defined by numbers
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
• Extends repeating patterns - geometric shapes
• Extends repeating patterns - geometric shapes
• Completes a growing arithmetic pattern by naming missing members
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Solves linear equations with basic facts - 1-step addition using a letter
for the variable
New Vocabulary: None
New Vocabulary: None
New Signs and Symbols: + addition, ÷ division, = is equal to, ×
multiplication, - subtraction, variable
New Signs and Symbols: None
Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
1
of
19
DesCartes: A Continuum of Learning®
171 - 180
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Enhance (73% Probability*)
< 171
Functions: Representations, Linear & Non Linear
Skills and Concepts to Develop (50% Probability*)
171 - 180
Functions: Representations, Linear & Non Linear
Skills and Concepts to Introduce (27% Probability*)
181 - 190
Functions: Representations, Linear & Non Linear
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
• Identifies the missing operation symbol - 1-step number sentence
• Represents a basic facts addition problem with a number sentence
• Identifies the missing operation symbol - 2-step number sentence
• Solves basic-facts open sentences - addition and subtraction
• Identifies the missing operation symbol - 1-step number sentence
• Demonstrates an understanding of the associative property of addition
• Solves basic-facts open sentences - addition and subtraction
• Solves basic facts addition and subtraction open sentences using
diagrams and models (e.g., using balances)
• Solves basic facts open sentences - multiplication and division
• Solves 1-step open sentences with missing addends (numbers 100
and under)
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
• Completes a growing arithmetic pattern by naming missing members
• Extends a growing arithmetic pattern, defined by numbers
• Extends a growing arithmetic pattern, defined by numbers
• Completes a growing arithmetic pattern by naming missing members
• Completes a growing arithmetic pattern using models by identifying the
missing members
• Completes arithmetic growth patterns in number tables by identifying
the missing elements
• Extends a decreasing arithmetic patterns
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
• Extends repeating patterns - geometric shapes
• Extends repeating patterns - geometric shapes
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Solves linear equations with basic facts - 1-step addition using a letter
for the variable
• Solves linear equations with basic facts - 1-step addition using a letter
for the variable
New Vocabulary: None
New Vocabulary: None
New Vocabulary: None
New Signs and Symbols: + addition, ÷ division, = is equal to, ×
multiplication, - subtraction, variable
New Signs and Symbols: None
New Signs and Symbols: ( ) order of operations, < less than
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
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
2
of
19
DesCartes: A Continuum of Learning®
181 - 190
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Enhance (73% Probability*)
171 - 180
Functions: Representations, Linear & Non Linear
Skills and Concepts to Develop (50% Probability*)
181 - 190
Functions: Representations, Linear & Non Linear
Skills and Concepts to Introduce (27% Probability*)
191 - 200
Functions: Representations, Linear & Non Linear
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
• Represents a basic facts addition problem with a number sentence
• Identifies the missing operation symbol - 2-step number sentence
• Identifies the missing operation symbol - 2-step number sentence
• Identifies the missing operation symbol - 1-step number sentence
• Demonstrates an understanding of the associative property of addition
• Solves basic-facts open sentences - addition and subtraction
• Solves basic facts addition and subtraction open sentences using
diagrams and models (e.g., using balances)
• Demonstrates an understanding of the commutative property of
multiplication with simple problems
• Solves basic facts open sentences - multiplication and division
• Solves 1-step open sentences with missing addends (numbers 100
and under)
• 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)
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
• Extends a growing arithmetic pattern, defined by numbers
• Extends a growing arithmetic pattern, defined by numbers
• Extends a growing arithmetic pattern, defined by objects or diagrams
• Completes a growing arithmetic pattern by naming missing members
• Completes a growing arithmetic pattern using models by identifying the
missing members
• Completes a growing arithmetic pattern using models by identifying the
missing members
• Completes arithmetic growth patterns in number tables by identifying
the missing elements
• Extends a decreasing arithmetic patterns
• Extends a decreasing arithmetic patterns
• Completes a simple function table based on real-life situations (e.g.,
the number of tricycles related to the number of wheels)
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
• Extends repeating patterns - geometric shapes
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Solves linear equations with basic facts - 1-step addition using a letter
for the variable
• Solves linear equations with basic facts - 1-step addition using a letter
for the variable
New Vocabulary: None
New Vocabulary: None
New Vocabulary: None
New Signs and Symbols: None
New Signs and Symbols: ( ) order of operations, < less than
New Signs and Symbols: None
Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
3
of
19
DesCartes: A Continuum of Learning®
191 - 200
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Enhance (73% Probability*)
181 - 190
Functions: Representations, Linear & Non Linear
Skills and Concepts to Develop (50% Probability*)
191 - 200
Functions: Representations, Linear & Non Linear
Skills and Concepts to Introduce (27% Probability*)
201 - 210
Functions: Representations, Linear & Non Linear
• Determines the rule and completes a simple function machine output
• Graphs ordered pairs in the first quadrant
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
• Identifies the missing operation symbol - 2-step number sentence
• Identifies the missing operation symbol - 2-step number sentence
• Identifies the missing operation symbol - 2-step number sentence
• Demonstrates an understanding of the associative property of addition
• Demonstrates an understanding of the commutative property of
multiplication with simple problems
• Demonstrates an understanding of the commutative property of
addition
• Solves 1-step open sentences with missing addends (numbers 100
and under)
• Demonstrates an understanding of the commutative property of
multiplication with simple problems
• Solves 1-step open sentences with missing addends (numbers over
100)
• Uses the commutative property of addition with rational numbers
• Solves basic facts addition and subtraction open sentences using
diagrams and models (e.g., using balances)
• Solves 1-step open sentences with missing addends (numbers 100
and under)
• Solves simple open sentences with missing factors (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)
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
• Extends a growing arithmetic pattern, defined by numbers
• Extends a growing arithmetic pattern, defined by objects or diagrams
• Extends a growing arithmetic pattern, defined by objects or diagrams
• Completes a growing arithmetic pattern using models by identifying the
missing members
• Completes a growing arithmetic pattern using models by identifying the
missing members
• Uses simple linear equations to represent problem situations
• Completes arithmetic growth patterns in number tables by identifying
the missing elements
• Extends a decreasing arithmetic patterns
• Describes a realistic situation using information given in a linear
equation
• Extends a decreasing arithmetic patterns
• Completes a simple function table based on real-life situations (e.g.,
the number of tricycles related to the number of wheels)
• Completes a simple function table based on real-life situations (e.g.,
the number of tricycles related to the number of wheels)
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Extends a pattern formed by rotating a geometric figure
• Completes a function table given a simple rule (e.g., x + 2)
• Solves linear equations with basic facts - 1-step addition using a letter
for the variable
New Vocabulary: None
New Vocabulary: None
New Vocabulary: coordinate point, minimum
New Signs and Symbols: ( ) order of operations, < less than
New Signs and Symbols: None
New Signs and Symbols: ( ) ordered pair, ∙ point
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
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
4
of
19
DesCartes: A Continuum of Learning®
201 - 210
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Enhance (73% Probability*)
191 - 200
Functions: Representations, Linear & Non Linear
Skills and Concepts to Develop (50% Probability*)
201 - 210
Functions: Representations, Linear & Non Linear
Skills and Concepts to Introduce (27% Probability*)
211 - 220
Functions: Representations, Linear & Non Linear
• Determines the rule and completes a simple function machine output
• Determines the rule and completes a simple function machine output
• Graphs ordered pairs in the first quadrant
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
• Identifies the missing operation symbol - 2-step number sentence
• Identifies the missing operation symbol - 2-step number sentence
• Demonstrates an understanding of the commutative property of
multiplication with simple problems
• Demonstrates an understanding of the commutative property of
addition
• Demonstrates an understanding of the commutative property of
multiplication with simple problems
• Solves 1-step open sentences with missing addends (numbers 100
and under)
• Demonstrates an understanding of the commutative property of
multiplication with simple problems
• Solves 1-step open sentences with missing addends (numbers over
100)
• Uses the commutative property of addition with rational numbers
• Solves simple open sentences with missing factors (numbers 100 and
under)
• Solves 1-step open sentences with missing addends (numbers over
100)
• Demonstrates an understanding of the associative property of
multiplication
• Demonstrates an understanding of the distributive property of
multiplication by decomposing a term
• Uses the commutative property of addition with rational numbers
• Solves open sentences using the distributive property
• Solves simple open sentences with missing factors (numbers 100 and
under)
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
• Extends a growing arithmetic pattern, defined by objects or diagrams
• Extends a growing arithmetic pattern, defined by objects or diagrams
• Completes a function table given a simple rule (e.g., x + 2)
• Completes a growing arithmetic pattern using models by identifying the
missing members
• Uses simple linear equations to represent problem situations
• Determines the rule given a simple real-world function table (e.g., #
Dogs compared to # Legs)
• Extends a decreasing arithmetic patterns
• Describes a realistic situation using information given in a linear
equation
• Completes a simple function table based on real-life situations (e.g.,
the number of tricycles related to the number of wheels)
• Completes a simple function table based on real-life situations (e.g.,
the number of tricycles related to the number of wheels)
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Extends a pattern formed by rotating a geometric figure
• Solves 1-step linear equations
• Solves problems involving simple functions
• Uses simple linear equations to represent problem situations
• Completes a function table given a simple rule (e.g., x + 2)
• Extends, or completes, growing patterns defined by equations or
number facts
New Vocabulary: None
New Vocabulary: coordinate point, minimum
New Vocabulary: triple
New Signs and Symbols: None
New Signs and Symbols: ( ) ordered pair, ∙ point
New Signs and Symbols: ( ) parenthesis around an integer, a.m., ¢ cent
sign, °F degrees Fahrenheit, $ dollar sign, $ dollar sign, = is equal to, ?
next in sequence, + 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
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
5
of
19
DesCartes: A Continuum of Learning®
211 - 220
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Enhance (73% Probability*)
201 - 210
Functions: Representations, Linear & Non Linear
Skills and Concepts to Develop (50% Probability*)
211 - 220
Functions: Representations, Linear & Non Linear
• Determines the rule and completes a simple function machine output
• Determines the rule and completes a simple function machine output
Skills and Concepts to Introduce (27% Probability*)
221 - 230
Functions: Representations, Linear & Non Linear
• Graphs ordered pairs in the first quadrant
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
• Identifies the missing operation symbol - 2-step number sentence
• Demonstrates an understanding of the commutative property of
multiplication with simple problems
• Writes equivalent forms of algebraic expressions (e.g., (x + 3)/2 = x/2 +
3/2)
• Demonstrates an understanding of the associative property of
multiplication
• Demonstrates an understanding of multiple properties
• Demonstrates an understanding of the distributive property of
multiplication by decomposing a term
• Uses basic operations on algebraic expressions (substituting for
unknowns)
• Uses the commutative property of addition with rational numbers
• Recognizes commutative, associative, distributive, symmetric,
transitive, and reflexive properties
• Demonstrates an understanding of the commutative property of
addition
• Demonstrates an understanding of the commutative property of
multiplication with simple problems
• Uses the commutative property of addition with rational numbers
• Solves 1-step open sentences with missing addends (numbers over
100)
• Solves open sentences using the distributive property
• Solves simple open sentences with missing factors (numbers 100 and
under)
• Uses the distributive property
• Uses basic operations on algebraic expressions (expanding monomial by a binomial)
• Demonstrates an understanding of properties (e.g., commutative,
associative, distributive, properties of 0)
• Uses basic operations on algebraic expressions (uses correct order of
operations)
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
• Extends a growing arithmetic pattern, defined by objects or diagrams
• Completes a function table given a simple rule (e.g., x + 2)
• Solves complex problems involving miles/kilometers per hour
• Uses simple linear equations to represent problem situations
• Determines the rule given a simple real-world function table (e.g., #
Dogs compared to # Legs)
• Represents geometric sequences using written descriptions in
recursive terms (present term, next term)
• Solves problems involving simple functions
• Solves problems involving simple functions
• Uses simple linear equations to represent problem situations
• Determines an appropriate scale for representing an object in a scale
drawing
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
• Extends a pattern formed by rotating a geometric figure
• Solves 1-step linear equations
• Solves linear equations in a real-world context using a given formula
• Extends, or completes, growing patterns defined by equations or
number facts
• Expresses a simple linear equation from a contextual situation
• Describes a realistic situation using information given in a linear
equation
• 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)
• Solves 1-step linear equations
• Solves 2-step linear equations
• Solves linear equations with decimals
• Solves linear equations with integers
• Solves linear equations using substitution
• 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)
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
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
6
of
19
DesCartes: A Continuum of Learning®
211 - 220
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Enhance (73% Probability*)
201 - 210
New Vocabulary: coordinate point, minimum
Skills and Concepts to Develop (50% Probability*)
211 - 220
New Vocabulary: triple
Skills and Concepts to Introduce (27% Probability*)
221 - 230
New Vocabulary: algebra, reflexive, scale factor, transitive
New Signs and Symbols: ( ) ordered pair, ∙ point
New Signs and Symbols: ( ) parenthesis around an integer, a.m., ¢ cent
sign, °F degrees Fahrenheit, $ dollar sign, $ dollar sign, = is equal to, ?
next in sequence, + positive number
New Signs and Symbols: ft feet, in. inch, - negative number, 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
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
7
of
19
DesCartes: A Continuum of Learning®
221 - 230
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Enhance (73% Probability*)
211 - 220
Functions: Representations, Linear & Non Linear
Skills and Concepts to Develop (50% Probability*)
221 - 230
Functions: Representations, Linear & Non Linear
• Determines the rule and completes a simple function machine output
Skills and Concepts to Introduce (27% Probability*)
231 - 240
Functions: Representations, Linear & Non Linear
• Describes and uses a variable with whole numbers, multiplication, and
division in a contextual situation
• Identifies the graph type, given equations of linear and nonlinear
functions
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
• Demonstrates an understanding of the commutative property of
multiplication with simple problems
• Writes equivalent forms of algebraic expressions (e.g., (x + 3)/2 = x/2 +
3/2)
• Evaluates expressions containing powers (e.g., 3^2 x 2^3)
• Demonstrates an understanding of the associative property of
multiplication
• Demonstrates an understanding of multiple properties
• Demonstrates an understanding of the distributive property of
multiplication by decomposing a term
• Uses basic operations on algebraic expressions (substituting for
unknowns)
• Uses the commutative property of addition with rational numbers
• Recognizes commutative, associative, distributive, symmetric,
transitive, and reflexive properties
• Solves open sentences using the distributive property
• Uses the distributive property
• 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)
• Uses basic operations on algebraic expressions (expanding monomial by a binomial)
• Demonstrates an understanding of properties (e.g., commutative,
associative, distributive, properties of 0)
• Uses basic operations on algebraic expressions (uses correct order of
operations)
• Uses basic operations on algebraic expressions (uses correct order of
operations)
• Writes equivalent forms of algebraic expressions (e.g., (x + 3)/2 = x/2 +
3/2)
• Evaluates numerical expressions using the order of operations (whole
numbers only)
• Evaluates expressions using the order of operations, including
exponents (whole numbers only)
• Uses the distributive property
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
• Completes a function table given a simple rule (e.g., x + 2)
• Solves complex problems involving miles/kilometers per hour
• Converts from Celsius to Fahrenheit, given conversion ratios
• Determines the rule given a simple real-world function table (e.g., #
Dogs compared to # Legs)
• Represents geometric sequences using written descriptions in
recursive terms (present term, next term)
• Solves multiple-step problems involving proportions
• Solves problems involving simple functions
• Solves problems involving simple functions
• Recognizes and extends arithmetic sequences (predicts nth term)
• Uses simple linear equations to represent problem situations
• Determines an appropriate scale for representing an object in a scale
drawing
• Represents geometric sequences using written descriptions in
recursive terms (present term, next term)
• Solves problems involving percent increase and decrease
• Determines the graph of a horizontal or vertical line when given the
equation
• Represents real-world functions using an equation
• Uses tables to determine function equations
• Determines an appropriate scale for representing an object in a scale
drawing
• Solves problems involving simple functions
• Solves problems comparing unit prices
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
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
8
of
19
DesCartes: A Continuum of Learning®
221 - 230
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Enhance (73% Probability*)
211 - 220
Linear, Quadratic, Root: Equations & Inequalities
Skills and Concepts to Develop (50% Probability*)
221 - 230
Linear, Quadratic, Root: Equations & Inequalities
Skills and Concepts to Introduce (27% Probability*)
231 - 240
Linear, Quadratic, Root: Equations & Inequalities
• Solves 1-step linear equations
• Solves linear equations in a real-world context using a given formula
• Solves linear equations with fractions
• Extends, or completes, growing patterns defined by equations or
number facts
• Expresses a simple linear equation from a contextual situation
• Expresses a simple linear equation from a contextual situation
• Solves 1-step linear equations
• Solves 2-step linear equations
• Solves 2-step linear equations
• Solves linear equations with integers
• Solves linear equations with decimals
• Solves linear equations using rational numbers
• Solves linear equations with integers
• Writes linear equations when given ordered pairs
• Solves linear equations using substitution
• Writes the equation of a horizontal or vertical line when given the
graph of the line
• Uses graphs to solve simple systems of linear equations
• Applies systems-of-linear-equations methods to solve theoretical
problems
• Uses graphs to solve simple systems of linear equations
• Describes the relationship or a real-world situation represented by a
simple linear inequality (e.g., 1- or 2-step)
• Describes the relationship or a real-world situation represented by a
simple linear inequality (e.g., 1- or 2-step)
New Vocabulary: triple
New Vocabulary: algebra, reflexive, scale factor, transitive
New Signs and Symbols: ( ) parenthesis around an integer, a.m., ¢ cent
sign, °F degrees Fahrenheit, $ dollar sign, $ dollar sign, = is equal to, ?
next in sequence, + positive number
New Signs and Symbols: ft feet, in. inch, - negative number, repeating
decimal overbar, △ triangle
• Expresses a simple linear inequality from a contextual situation
New Vocabulary: algebraic sentence, arithmetic progression, equation of
a line, is less than, representative sample
New Signs and Symbols: °C degrees Celsius, f(x) the value of the
function f at x, > greater than, ≥ greater than or equal to, ≤ less than or
equal to, ∙ multiplication symbol (dot), % 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
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
9
of
19
DesCartes: A Continuum of Learning®
231 - 240
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Enhance (73% Probability*)
221 - 230
Functions: Representations, Linear & Non Linear
Skills and Concepts to Develop (50% Probability*)
231 - 240
Functions: Representations, Linear & Non Linear
Skills and Concepts to Introduce (27% Probability*)
241 - 250
Functions: Representations, Linear & Non Linear
• Describes and uses a variable with whole numbers, multiplication, and
division in a contextual situation
• Describes and uses a variable with whole numbers, multiplication, and
division in a contextual situation
• Identifies the graph type, given equations of linear and nonlinear
functions
• Identifies and describes situations with varying rates of change
• Completes a function table according to a rule (rational numbers)
• Determines the minimum and maximum of a quadratic function
• Determines the x- and/or y-intercept of an equation of a function
• Determines the domain and range of a function
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
• Writes equivalent forms of algebraic expressions (e.g., (x + 3)/2 = x/2 +
3/2)
• Evaluates expressions containing powers (e.g., 3^2 x 2^3)
• Evaluates expressions using the order of operations, including
exponents (whole numbers only)
• Demonstrates an understanding of multiple properties
• Uses the distributive property
• Uses basic operations on algebraic expressions (substituting for
unknowns)
• Uses basic operations on algebraic expressions (substituting for
unknowns)
• Uses basic operations on algebraic expressions (substituting for
unknown exponents)
• Evaluates expressions using the order of operations, including
exponents (using integers)
• Identifies the associative property of addition
• Recognizes commutative, associative, distributive, symmetric,
transitive, and reflexive properties
• Evaluates expressions by substituting with rational numbers
• Uses basic operations on algebraic expressions (combining like terms)
• Multiplies binomials
• Uses basic operations on algebraic expressions (expanding monomial by a binomial)
• Uses basic operations on algebraic expressions (expanding monomial by a binomial)
• Factors trinomials in the form x^2 + bx + c
• Demonstrates an understanding of properties (e.g., commutative,
associative, distributive, properties of 0)
• Uses basic operations on algebraic expressions (uses correct order of
operations)
• Uses basic operations on algebraic expressions (uses correct order of
operations)
• Writes equivalent forms of algebraic expressions (e.g., (x + 3)/2 = x/2 +
3/2)
• Recognizes commutative, associative, distributive, symmetric,
transitive, and reflexive properties
• Simplifies polynomial expressions
• Factors polynomials using difference of squares
• Uses basic operations on algebraic expressions (uses correct order of
operations)
• Evaluates numerical expressions using the order of operations (whole
numbers only)
• Evaluates expressions using the order of operations, including
exponents (whole numbers only)
• Uses the distributive property
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
• Solves complex problems involving miles/kilometers per hour
• Converts from Celsius to Fahrenheit, given conversion ratios
• Solves multiple-step problems involving proportions
• Represents geometric sequences using written descriptions in
recursive terms (present term, next term)
• Solves multiple-step problems involving proportions
• Solves problems involving percent increase and decrease
• Represents growing arithmetic patterns using algebraic expressions or
equations
• Solves problems involving simple functions
• Recognizes and extends arithmetic sequences (predicts nth term)
• Solves problems involving successive discounts
• Determines an appropriate scale for representing an object in a scale
drawing
• Represents geometric sequences using written descriptions in
recursive terms (present term, next term)
• Determines x- or y-intercept of a given linear equation
• Determines the graph of a horizontal or vertical line when given the
equation
• Uses tables to determine function equations
• Recognizes the slope of horizontal and vertical lines
• Represents real-world functions using an equation
• Represents a real-world function using a complex equation (e.g.,
variables on both sides, distributive, rational)
• Uses tables to determine function equations
• Models real life functions using function notation
• Determines an appropriate scale for representing an object in a scale
drawing
• Uses ordered pairs to graph a parabola
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
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
10
of
19
DesCartes: A Continuum of Learning®
231 - 240
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Enhance (73% Probability*)
221 - 230
Functions: Linear, Quadratic, Exponential
Skills and Concepts to Develop (50% Probability*)
231 - 240
Functions: Linear, Quadratic, Exponential
Skills and Concepts to Introduce (27% Probability*)
241 - 250
Functions: Linear, Quadratic, Exponential
• Solves problems involving simple functions
• Uses dimensional analysis for unit conversions (time)
• Solves problems comparing unit prices
• Converts from Celsius to Fahrenheit, given conversion ratios
• Solves problems involving rate conversions (e.g., mi/hr to ft/sec)
• Uses dimensional analysis for unit conversions (area)
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
• Solves linear equations in a real-world context using a given formula
• Solves linear equations with fractions
• Expresses a simple linear equation from a contextual situation
• Expresses a simple linear equation from a contextual situation
• Uses linear equations to represent situations involving variable
quantities
• Solves 1-step linear equations
• Solves 2-step linear equations
• Solves linear equations with fractions
• Solves 2-step linear equations
• Solves linear equations with integers
• Solves linear equations using rational numbers
• Solves linear equations with decimals
• Solves linear equations using rational numbers
• Solves linear equations with integers
• Writes linear equations when given ordered pairs
• Applies algebraic methods to solve a variety of real-world and
theoretical problems
• Solves linear equations using substitution
• Writes the equation of a horizontal or vertical line when given the
graph of the line
• Uses graphs to solve simple systems of linear equations
• Applies systems-of-linear-equations methods to solve theoretical
problems
• Uses graphs to solve simple systems of linear equations
• Describes the relationship or a real-world situation represented by a
simple linear inequality (e.g., 1- or 2-step)
• Describes the relationship or a real-world situation represented by a
simple linear inequality (e.g., 1- or 2-step)
• Expresses a simple linear inequality from a contextual situation
• Solves problems involving consecutive numbers
• Writes linear equations when given ordered pairs
• Writes the equation of a horizontal or vertical line when given the
graph of the line
• Solves quadratic equations using concrete models and tables
• Uses algebraic methods to solve systems of linear equations
• Uses graphs to solve systems of linear equations in real-world
situations
• Describes the relationship or a real-world situation represented by a
simple linear inequality (e.g., 1- or 2-step)
New Vocabulary: algebra, reflexive, scale factor, transitive
New Signs and Symbols: ft feet, in. inch, - negative number, repeating
decimal overbar, △ triangle
New Vocabulary: algebraic sentence, arithmetic progression, equation of
a line, is less than, representative sample
New Vocabulary: feet per second, polynomial, solution set, x-axis, yintercept
New Signs and Symbols: °C degrees Celsius, f(x) the value of the
function f at x, > greater than, ≥ greater than or equal to, ≤ less than or
equal to, ∙ multiplication symbol (dot), % percent
New Signs and Symbols: mph miles per hour, sec second
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
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
11
of
19
DesCartes: A Continuum of Learning®
241 - 250
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Enhance (73% Probability*)
231 - 240
Functions: Representations, Linear & Non Linear
Skills and Concepts to Develop (50% Probability*)
241 - 250
Functions: Representations, Linear & Non Linear
Skills and Concepts to Introduce (27% Probability*)
251 - 260
Functions: Representations, Linear & Non Linear
• Describes and uses a variable with whole numbers, multiplication, and
division in a contextual situation
• Describes and uses a variable with whole numbers, multiplication, and
division in a contextual situation
• Describes and uses a variable with whole numbers, multiplication, and
division in a contextual situation
• Identifies the graph type, given equations of linear and nonlinear
functions
• Identifies and describes situations with varying rates of change
• Identifies and describes situations with varying rates of change
• Completes a function table according to a rule (rational numbers)
• Determines the vertex of a parabola
• Determines the minimum and maximum of a quadratic function
• Determines the minimum and maximum of a quadratic function
• Determines the x- and/or y-intercept of an equation of a function
• Determines the effects of parameter changes on functions
• Determines the domain and range of a function
• Determines the domain and range of a function
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
• Evaluates expressions containing powers (e.g., 3^2 x 2^3)
• Evaluates expressions using the order of operations, including
exponents (whole numbers only)
• Identifies the commutative property of multiplication
• Evaluates expressions using the order of operations, including
exponents (using integers)
• Evaluates expressions by substituting with rational numbers
• Uses basic operations on algebraic expressions (substituting for
unknowns)
• Uses basic operations on algebraic expressions (substituting for
unknown exponents)
• Identifies the associative property of addition
• Recognizes commutative, associative, distributive, symmetric,
transitive, and reflexive properties
• Evaluates expressions by substituting with rational numbers
• Uses basic operations on algebraic expressions (combining like terms)
• Multiplies binomials
• Uses basic operations on algebraic expressions (expanding monomial by a binomial)
• Factors trinomials in the form x^2 + bx + c
• Uses basic operations on algebraic expressions (uses correct order of
operations)
• Writes equivalent forms of algebraic expressions (e.g., (x + 3)/2 = x/2 +
3/2)
• Simplifies polynomial expressions
• Factors polynomials using difference of squares
• Uses basic operations on algebraic expressions (uses correct order of
operations)
• Simplifies rational expressions with exponents
• 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
• Evaluates numerical expressions using the order of operations (whole
numbers only)
• Evaluates expressions using the order of operations, including
exponents (whole numbers only)
• Uses the distributive property
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
• Converts from Celsius to Fahrenheit, given conversion ratios
• Solves multiple-step problems involving proportions
• Solves problems involving successive discounts
• Solves multiple-step problems involving proportions
• Determines x- or y-intercept of a given linear equation
• Solves problems involving percent increase and decrease
• Represents growing arithmetic patterns using algebraic expressions or
equations
• Recognizes and extends arithmetic sequences (predicts nth term)
• Solves problems involving successive discounts
• Determines slope from graphs
• Represents geometric sequences using written descriptions in
recursive terms (present term, next term)
• Determines x- or y-intercept of a given linear equation
• Recognizes the slope of horizontal and vertical lines
• Interprets the meaning of slope and intercepts in problem solving
situations
• Determines the graph of a horizontal or vertical line when given the
equation
• Uses tables to determine function equations
• Determines the slope of perpendicular lines
• Represents real-world functions using an equation
• Represents a real-world function using a complex equation (e.g.,
variables on both sides, distributive, rational)
• Represents a real-world function using a complex equation (e.g.,
variables on both sides, distributive, rational)
• Uses tables to determine function equations
• Models real life functions using function notation
• Models real life functions using function notation
• Determines an appropriate scale for representing an object in a scale
drawing
• Uses ordered pairs to graph a parabola
• Uses graphs to represent functions and interpret slope
• Determines the graph of a line when given the equation
Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
12
of
19
DesCartes: A Continuum of Learning®
241 - 250
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Enhance (73% Probability*)
231 - 240
Functions: Linear, Quadratic, Exponential
Skills and Concepts to Develop (50% Probability*)
241 - 250
Functions: Linear, Quadratic, Exponential
Skills and Concepts to Introduce (27% Probability*)
251 - 260
Functions: Linear, Quadratic, Exponential
• Solves problems involving simple functions
• Uses dimensional analysis for unit conversions (time)
• Identifies the equation of a parabola
• Solves problems comparing unit prices
• Converts from Celsius to Fahrenheit, given conversion ratios
• Uses dimensional analysis for unit conversions (time)
• Solves problems involving rate conversions (e.g., mi/hr to ft/sec)
• Solves problems involving rate conversions (e.g., mi/hr to ft/sec)
• Uses dimensional analysis for unit conversions (area)
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
• Solves linear equations with fractions
• Rewrites a complex formula to solve for a specific variable
• Expresses a simple linear equation from a contextual situation
• Uses linear equations to represent situations involving variable
quantities
• Solves 2-step linear equations
• Solves linear equations with fractions
• Solves linear equations using rational numbers
• Solves linear equations with integers
• Solves linear equations using rational numbers
• Writes linear equations, given two points on a line
• Solves linear equations using rational numbers
• Applies algebraic methods to solve a variety of real-world and
theoretical problems
• Identifies discriminants and roots
• Writes linear equations when given ordered pairs
• Writes the equation of a horizontal or vertical line when given the graph
of the line
• Uses graphs to solve simple systems of linear equations
• 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 problems involving consecutive numbers
• Writes linear equations when given ordered pairs
• Writes the equation of a horizontal or vertical line when given the
graph of the line
• Solves quadratic equations using concrete models and tables
• Uses algebraic methods to solve systems of linear equations
• Uses graphs to solve systems of linear equations in real-world
situations
• Describes the relationship or a real-world situation represented by a
simple linear inequality (e.g., 1- or 2-step)
• Writes the equation of the line when given the graph of the line
• Solves quadratic equations by factoring
• Solves quadratic equations by completing the square
• 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
• Uses graphs to solve systems of linear equations in real-world
situations
• Solves real-world systems of linear equations
• Solves absolute value inequalities
• Uses graphs to solve systems of linear inequalities
New Vocabulary: algebraic sentence, arithmetic progression, equation of
a line, is less than, representative sample
New Vocabulary: feet per second, polynomial, solution set, x-axis, yintercept
New Vocabulary: coordinate plane, quadratic equation, x-coordinate, ycoordinate
New Signs and Symbols: °C degrees Celsius, f(x) the value of the
function f at x, > greater than, ≥ greater than or equal to, ≤ less than or
equal to, ∙ multiplication symbol (dot), % percent
New Signs and Symbols: mph miles per hour, sec second
New Signs and Symbols: [ ] square brackets, { } set notation, || absolute
value, P perimeter
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
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
13
of
19
DesCartes: A Continuum of Learning®
251 - 260
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Enhance (73% Probability*)
241 - 250
Functions: Representations, Linear & Non Linear
Skills and Concepts to Develop (50% Probability*)
251 - 260
Functions: Representations, Linear & Non Linear
Skills and Concepts to Introduce (27% Probability*)
261 - 270
Functions: Representations, Linear & Non Linear
• Describes and uses a variable with whole numbers, multiplication, and
division in a contextual situation
• Describes and uses a variable with whole numbers, multiplication, and
division in a contextual situation
• Determines the minimum and maximum of a quadratic function
• Identifies and describes situations with varying rates of change
• Identifies and describes situations with varying rates of change
• Completes a function table according to a rule (rational numbers)
• Determines the vertex of a parabola
• Determines the minimum and maximum of a quadratic function
• Determines the minimum and maximum of a quadratic function
• Determines the x- and/or y-intercept of an equation of a function
• Determines the effects of parameter changes on functions
• Determines the domain and range of a function
• Determines the domain and range of a function
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
• Evaluates expressions using the order of operations, including
exponents (whole numbers only)
• Identifies the commutative property of multiplication
• Simplifies rational expressions with exponents
• Simplifies rational expressions with exponents
• Simplifies monomials
• Evaluates expressions using the order of operations, including
exponents (using integers)
• Evaluates expressions by substituting with rational numbers
• Simplifies polynomial expressions using power laws
• Simplifies monomials
• Factors polynomials by identifying a common monomial and then
factoring the trinomial
• Identifies the associative property of addition
• Evaluates expressions by substituting with rational numbers
• Simplifies polynomial expressions
• Simplifies polynomial expressions
• Simplifies algebraic expressions with integer exponents
• Multiplies binomials
• Multiplies binomials
• Multiplies a polynomial by a polynomial
• Factors trinomials in the form x^2 + bx + c
• Divides a polynomial by a monomial
• Factors polynomials using difference of squares
• Uses basic operations on algebraic expressions (uses correct order of
operations)
• Factors polynomials by identifying common factors
• Factors trinomials in the form x^2 + bx + c
• Factors polynomials using difference of squares
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
• Solves multiple-step problems involving proportions
• Solves problems involving successive discounts
• Determines the slope of perpendicular lines
• Represents growing arithmetic patterns using algebraic expressions or
equations
• Determines x- or y-intercept of a given linear equation
• Uses the compound interest equation to solve problems
• Determines the graph of a line when given the equation
• Solves problems involving successive discounts
• Solves problems involving successive discounts
• Determines slope from graphs
• Models real life functions using function notation
• Determines x- or y-intercept of a given linear equation
• Solves problems involving rate conversions (e.g., mi/hr to ft/sec)
• Recognizes the slope of horizontal and vertical lines
• Interprets the meaning of slope and intercepts in problem solving
situations
• Uses tables to determine function equations
• Determines the slope of perpendicular lines
• Represents a real-world function using a complex equation (e.g.,
variables on both sides, distributive, rational)
• Represents a real-world function using a complex equation (e.g.,
variables on both sides, distributive, rational)
• Models real life functions using function notation
• Models real life functions using function notation
• Uses ordered pairs to graph a parabola
• Uses graphs to represent functions and interpret slope
• Uses dimensional analysis for unit conversions (time)
• Identifies the equation of a parabola
• Converts from Celsius to Fahrenheit, given conversion ratios
• Uses dimensional analysis for unit conversions (time)
• Solves problems involving rate conversions (e.g., mi/hr to ft/sec)
• Solves problems involving rate conversions (e.g., mi/hr to ft/sec)
• Uses dimensional analysis for unit conversions (area)
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
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
14
of
19
DesCartes: A Continuum of Learning®
251 - 260
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Enhance (73% Probability*)
241 - 250
Linear, Quadratic, Root: Equations & Inequalities
Skills and Concepts to Develop (50% Probability*)
251 - 260
Linear, Quadratic, Root: Equations & Inequalities
Skills and Concepts to Introduce (27% Probability*)
261 - 270
Linear, Quadratic, Root: Equations & Inequalities
• Uses linear equations to represent situations involving variable
quantities
• Rewrites a complex formula to solve for a specific variable
• Rewrites a complex formula to solve for a specific variable
• Writes the equation of the line when given the graph of the line
• Writes the equation of the line when given the graph of the line
• Solves linear equations with fractions
• Solves linear equations using rational numbers
• Writes linear equations, given slope and point on a line
• Solves linear equations using rational numbers
• Writes linear equations, given two points on a line
• Solves quadratic equations using the quadratic formula
• Applies algebraic methods to solve a variety of real-world and
theoretical problems
• Identifies discriminants and roots
• Solves quadratic equations by completing the square
• Solves quadratic equations by factoring
• Solves real-world systems of linear equations
• Solves quadratic equations by completing the square
• Solves absolute value inequalities
• Uses the Multiplication Property of Equality as a first step in solving
systems of linear equations
• Uses graphs to solve systems of linear inequalities
• Solves problems involving consecutive numbers
• Writes linear equations when given ordered pairs
• Writes the equation of a horizontal or vertical line when given the graph
of the line
• Solves quadratic equations using concrete models and tables
• Uses algebraic methods to solve systems of linear equations
• Uses graphs to solve systems of linear equations in real-world
situations
• Describes the relationship or a real-world situation represented by a
simple linear inequality (e.g., 1- or 2-step)
• 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
• Uses graphs to solve systems of linear equations in real-world
situations
• Solves real-world systems of linear equations
• Solves absolute value inequalities
• Uses graphs to solve systems of linear inequalities
New Vocabulary: feet per second, polynomial, solution set, x-axis, yintercept
New Vocabulary: coordinate plane, quadratic equation, x-coordinate, ycoordinate
New Signs and Symbols: mph miles per hour, sec second
New Signs and Symbols: [ ] square brackets, { } set notation, || absolute
value, P perimeter
New Vocabulary: semi-annual
New Signs and Symbols: P principal, r rate, t time
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
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
15
of
19
DesCartes: A Continuum of Learning®
261 - 270
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Enhance (73% Probability*)
251 - 260
Functions: Representations, Linear & Non Linear
Skills and Concepts to Develop (50% Probability*)
261 - 270
Functions: Representations, Linear & Non Linear
• Describes and uses a variable with whole numbers, multiplication, and
division in a contextual situation
• Determines the minimum and maximum of a quadratic function
Skills and Concepts to Introduce (27% Probability*)
271 - 280
Functions: Representations, Linear & Non Linear
• Identifies and describes situations with varying rates of change
• Determines the vertex of a parabola
• Determines the minimum and maximum of a quadratic function
• Determines the effects of parameter changes on functions
• Determines the domain and range of a function
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
• Identifies the commutative property of multiplication
• Simplifies rational expressions with exponents
• Simplifies rational expressions with exponents
• Simplifies monomials
• Evaluates expressions by substituting with rational numbers
• Simplifies polynomial expressions using power laws
• Simplifies monomials
• Factors polynomials by identifying a common monomial and then
factoring the trinomial
• Simplifies polynomial expressions
Algebraic and Numerical Expressions; Polynomials
• 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
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
• Solves problems involving successive discounts
• Determines the slope of perpendicular lines
• Determines x- or y-intercept of a given linear equation
• Uses the compound interest equation to solve problems
• Determines the graph of a line when given the equation
• Solves problems involving successive discounts
• Determines slope from graphs
• Models real life functions using function notation
• Interprets the meaning of slope and intercepts in problem solving
situations
• Solves problems involving rate conversions (e.g., mi/hr to ft/sec)
Functions: Linear, Quadratic, Exponential
• Determines the slope of perpendicular lines
• Represents a real-world function using a complex equation (e.g.,
variables on both sides, distributive, rational)
• Models real life functions using function notation
• Uses graphs to represent functions and interpret slope
• Identifies the equation of a parabola
• Uses dimensional analysis for unit conversions (time)
• Solves problems involving rate conversions (e.g., mi/hr to ft/sec)
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
• Rewrites a complex formula to solve for a specific variable
• Rewrites a complex formula to solve for a specific variable
Linear, Quadratic, Root: Equations & Inequalities
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
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
16
of
19
DesCartes: A Continuum of Learning®
261 - 270
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Enhance (73% Probability*)
251 - 260
Linear, Quadratic, Root: Equations & Inequalities
Skills and Concepts to Develop (50% Probability*)
261 - 270
Linear, Quadratic, Root: Equations & Inequalities
Skills and Concepts to Introduce (27% Probability*)
271 - 280
Linear, Quadratic, Root: Equations & Inequalities
• Writes the equation of the line when given the graph of the line
• Writes the equation of the line when given the graph of the line
• Solves linear equations using rational numbers
• Writes linear equations, given slope and point on a line
• Describes a relationship or a real-world situation represented by a
quadratic equation
• Writes linear equations, given two points on a line
• Solves quadratic equations using the quadratic formula
• Identifies discriminants and roots
• Solves quadratic equations by completing the square
• Solves quadratic equations by factoring
• Solves real-world systems of linear equations
• Solves quadratic equations by completing the square
• Solves absolute value inequalities
• Uses the Multiplication Property of Equality as a first step in solving
systems of linear equations
• Uses graphs to solve systems of linear inequalities
• 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
• Uses graphs to solve systems of linear equations in real-world
situations
• Solves real-world systems of linear equations
• Solves absolute value inequalities
• Uses graphs to solve systems of linear inequalities
New Vocabulary: coordinate plane, quadratic equation, x-coordinate, ycoordinate
New Vocabulary: semi-annual
New Vocabulary: squared
New Signs and Symbols: P principal, r rate, t time
New Signs and Symbols: None
New Signs and Symbols: [ ] square brackets, { } set notation, || absolute
value, P perimeter
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
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
17
of
19
DesCartes: A Continuum of Learning®
271 - 280
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Enhance (73% Probability*)
261 - 270
Functions: Representations, Linear & Non Linear
Skills and Concepts to Develop (50% Probability*)
271 - 280
Functions: Representations, Linear & Non Linear
Skills and Concepts to Introduce (27% Probability*)
> 280
Functions: Representations, Linear & Non Linear
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
• Rewrites a complex formula to solve for a specific variable
• Describes a relationship or a real-world situation represented by a
quadratic equation
• Describes a relationship or a real-world situation represented by a
quadratic equation
• Determines the minimum and maximum of a quadratic function
Algebraic and Numerical Expressions; Polynomials
• Simplifies rational expressions with exponents
• Simplifies monomials
• Simplifies polynomial expressions using power laws
• Factors polynomials by identifying a common monomial and then
factoring the trinomial
Functions: Linear, Quadratic, Exponential
• Determines the slope of perpendicular lines
• Uses the compound interest equation to solve problems
• Solves problems involving successive discounts
• Models real life functions using function notation
• Solves problems involving rate conversions (e.g., mi/hr to ft/sec)
• Writes the equation of the line when given the graph of the line
• Writes linear equations, given slope and point on a line
• Solves quadratic equations using the quadratic formula
• Solves quadratic equations by completing the square
• Solves real-world systems of linear equations
• Solves absolute value inequalities
• Uses graphs to solve systems of linear inequalities
New Vocabulary: semi-annual
New Vocabulary: squared
New Vocabulary: None
New Signs and Symbols: P principal, r rate, t time
New Signs and Symbols: None
New Signs and Symbols: None
Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
18
of
19
DesCartes: A Continuum of Learning®
> 280
RIT Score Range:
Statements Last Updated: Mar 10, 2014
Mathematics
Goal: Algebra
Skills and Concepts to Enhance (73% Probability*)
271 - 280
Functions: Representations, Linear & Non Linear
Skills and Concepts to Develop (50% Probability*)
> 280
Functions: Representations, Linear & Non Linear
Algebraic and Numerical Expressions; Polynomials
Algebraic and Numerical Expressions; Polynomials
Functions: Linear, Quadratic, Exponential
Functions: Linear, Quadratic, Exponential
Linear, Quadratic, Root: Equations & Inequalities
Linear, Quadratic, Root: Equations & Inequalities
• Describes a relationship or a real-world situation represented by a
quadratic equation
• Describes a relationship or a real-world situation represented by a
quadratic equation
New Vocabulary: squared
New Vocabulary: None
New Signs and Symbols: None
New Signs and Symbols: None
Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
4/2/14, 2:18:52 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: MN Mathematics K-12: 2007
Page
19
of
19