curriculum Operations and Algebraic Thinking 6 12
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
1
of
21
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
< 161
Statements Last Updated: Aug 4, 2014
Goal: Operations and Algebraic Thinking
Skills and Concepts to Develop (50% Probability*)
< 161
Skills and Concepts to Introduce (27% Probability*)
161 - 170
Use Functions to Model Relationships
Use Functions to Model Relationships
New Vocabulary: None
New Signs and Symbols: None
New Vocabulary: None
New Signs and Symbols: + addition, = is equal to, - subtraction, variable
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
2
of
21
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
161 - 170
Statements Last Updated: Aug 4, 2014
Goal: Operations and Algebraic Thinking
Skills and Concepts to Enhance (73% Probability*)
< 161
Skills and Concepts to Develop (50% Probability*)
161 - 170
Skills and Concepts to Introduce (27% Probability*)
171 - 180
Expressions and Equations
Expressions and Equations
Expressions and Equations
• Solves basic-facts open sentences - addition and subtraction
• Represents a basic facts addition problem with a number sentence
• Solves basic-facts open sentences - addition and subtraction
• Solves linear equations with basic facts - 1-step addition using a letter
for the variable
• Solves basic facts open sentences - multiplication and division
• Writes a number sentence for a simple problem solving situation
• Writes equivalent forms of whole number expressions (e.g., 15 + 5 =
10 + 10)
Use Functions to Model Relationships
Use Functions to Model Relationships
Use Functions to Model Relationships
• Extends a growing arithmetic pattern, defined by numbers
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
New Vocabulary: None
New Signs and Symbols: None
New Vocabulary: None
New Signs and Symbols: + addition, = is equal to, - subtraction, variable
New Vocabulary: None
New Signs and Symbols: None
Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
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
3
of
21
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
171 - 180
Statements Last Updated: Aug 4, 2014
Goal: Operations and Algebraic Thinking
Skills and Concepts to Enhance (73% Probability*)
161 - 170
Skills and Concepts to Develop (50% Probability*)
171 - 180
Skills and Concepts to Introduce (27% Probability*)
181 - 190
Expressions and Equations
Expressions and Equations
Expressions and Equations
• Solves basic-facts open sentences - addition and subtraction
• Represents a basic facts addition problem with a number sentence
• Solves basic-facts open sentences - addition and subtraction
• Solves linear equations with basic facts - 1-step addition using a letter
for the variable
• Solves basic facts open sentences - multiplication and division
• Writes a number sentence for a simple problem solving situation
• Writes equivalent forms of whole number expressions (e.g., 15 + 5 =
10 + 10)
• Solves real-world whole number problems involving subtraction with
numbers under 1000
• Demonstrates an understanding of the zero property of multiplication
• Solves basic facts addition and subtraction open sentences using
diagrams and models (e.g., using balances)
• Solves linear equations with basic facts - 1-step addition using a letter
for the variable
• Solves 1-step open sentences with missing addends (numbers 100
and under)
• Writes a number sentence for a simple problem solving situation
• Writes equivalent forms of whole numbers 11 to 20 using addition
(e.g., 14 = 7 + 7)
Use Functions to Model Relationships
Use Functions to Model Relationships
Use Functions to Model Relationships
• Extends a growing arithmetic pattern, defined by numbers
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Extends a growing arithmetic pattern, defined by numbers
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Identifies transformations of plane figures (translations/slides)
• Reads data in a line graph - no calculations
New Vocabulary: None
New Signs and Symbols: + addition, = is equal to, - subtraction, variable
New Vocabulary: None
New Signs and Symbols: None
New Vocabulary: None
New Signs and Symbols: × multiplication
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
4
of
21
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
181 - 190
Statements Last Updated: Aug 4, 2014
Goal: Operations and Algebraic Thinking
Skills and Concepts to Enhance (73% Probability*)
171 - 180
Skills and Concepts to Develop (50% Probability*)
181 - 190
Skills and Concepts to Introduce (27% Probability*)
191 - 200
Expressions and Equations
Expressions and Equations
Expressions and Equations
• Represents a basic facts addition problem with a number sentence
• Solves basic-facts open sentences - addition and subtraction
• Solves linear equations with basic facts - 1-step addition using a letter
for the variable
• Solves basic facts open sentences - multiplication and division
• Writes a number sentence for a simple problem solving situation
• Writes equivalent forms of whole number expressions (e.g., 15 + 5 =
10 + 10)
• Solves real-world whole number problems involving subtraction with
numbers under 1000
• Demonstrates an understanding of the zero property of multiplication
• Solves basic facts addition and subtraction open sentences using
diagrams and models (e.g., using balances)
• Solves linear equations with basic facts - 1-step addition using a letter
for the variable
• Solves 1-step open sentences with missing addends (numbers 100
and under)
• Writes a number sentence for a simple problem solving situation
• Writes equivalent forms of whole numbers 11 to 20 using addition
(e.g., 14 = 7 + 7)
• Solves real-world whole number problems involving subtraction with
numbers under 1000
• Solves whole number subtraction word problems with numbers over
1000
• Evaluates numerical expressions using grouping symbols (whole
numbers only)
• Demonstrates an understanding of the zero property of multiplication
• Computes half price (multiplication/division)
• Uses algebraic reasoning to solve problems involving equality
relationships
• Solves 1-step open sentences with missing addends (numbers 100
and under)
• Solves 1-step open sentences with missing addends (numbers over
100)
• Solves simple open sentences with missing factors (numbers 100 and
under)
• Solves 2-step open sentences with missing addends
• Writes equivalent forms of whole numbers 11 to 20 using addition
(e.g., 14 = 7 + 7)
Use Functions to Model Relationships
Use Functions to Model Relationships
Use Functions to Model Relationships
• Extends a growing arithmetic pattern, defined by numbers
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Extends a growing arithmetic pattern, defined by numbers
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Identifies transformations of plane figures (translations/slides)
• Reads data in a line graph - no calculations
• Extends a growing arithmetic pattern, defined by objects or diagrams
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Completes a simple function table based on real-life situations (e.g.,
the number of tricycles related to the number of wheels)
• Reads data in a line graph - no calculations
New Vocabulary: None
New Signs and Symbols: None
New Vocabulary: None
New Signs and Symbols: × multiplication
New Vocabulary: longer
New Signs and Symbols: ( ) order of operations, ÷ division, $ dollar sign
Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:50:06 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
5
of
21
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
191 - 200
Statements Last Updated: Aug 4, 2014
Goal: Operations and Algebraic Thinking
Skills and Concepts to Enhance (73% Probability*)
181 - 190
Skills and Concepts to Develop (50% Probability*)
191 - 200
Skills and Concepts to Introduce (27% Probability*)
201 - 210
Expressions and Equations
Expressions and Equations
Expressions and Equations
• Solves real-world whole number problems involving subtraction with
numbers under 1000
• Demonstrates an understanding of the zero property of multiplication
• Solves basic facts addition and subtraction open sentences using
diagrams and models (e.g., using balances)
• Solves linear equations with basic facts - 1-step addition using a letter
for the variable
• Solves 1-step open sentences with missing addends (numbers 100
and under)
• Writes a number sentence for a simple problem solving situation
• Writes equivalent forms of whole numbers 11 to 20 using addition
(e.g., 14 = 7 + 7)
• Solves real-world whole number problems involving subtraction with
numbers under 1000
• Solves whole number subtraction word problems with numbers over
1000
• Evaluates numerical expressions using grouping symbols (whole
numbers only)
• Demonstrates an understanding of the zero property of multiplication
• Computes half price (multiplication/division)
• Uses algebraic reasoning to solve problems involving equality
relationships
• Solves 1-step open sentences with missing addends (numbers 100
and under)
• Solves 1-step open sentences with missing addends (numbers over
100)
• Solves simple open sentences with missing factors (numbers 100 and
under)
• Solves 2-step open sentences with missing addends
• Writes equivalent forms of whole numbers 11 to 20 using addition
(e.g., 14 = 7 + 7)
• Uses rounding to estimate answers to 2-step problems involving
money (using decimals)
• Solves whole number subtraction word problems with numbers over
1000
• Evaluates numerical expressions using grouping symbols (whole
numbers only)
• Demonstrates an understanding of the commutative property of
addition
• Understands equivalence and extends the concept to number
sentences involving variables (e.g., 8 + 2 = [] + 2)
• Uses algebraic reasoning to solve problems involving equality
relationships
• Uses simple linear equations to represent problem situations
• Describes a realistic situation using information given in a linear
equation
• Solves 1-step open sentences with missing addends (numbers over
100)
• Solves simple open sentences with missing factors (numbers 100 and
under)
• Solves 2-step open sentences with missing addends
• Solves open sentences with basic-facts calculations on both sides of
the sentence
• Translates a 2-step problem to a symbolic expression or equation
• Solves real-world problems using reasoning strategies
Use Functions to Model Relationships
Use Functions to Model Relationships
Use Functions to Model Relationships
• Extends a growing arithmetic pattern, defined by numbers
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Identifies transformations of plane figures (translations/slides)
• Reads data in a line graph - no calculations
• Extends a growing arithmetic pattern, defined by objects or diagrams
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Completes a simple function table based on real-life situations (e.g.,
the number of tricycles related to the number of wheels)
• Reads data in a line graph - no calculations
• Extends a growing arithmetic pattern, defined by objects or diagrams
• Completes a simple function table based on real-life situations (e.g.,
the number of tricycles related to the number of wheels)
• Completes a function table given a simple rule (e.g., x + 2)
• Predicts from simple charts and tables
New Vocabulary: None
New Signs and Symbols: × multiplication
New Vocabulary: longer
New Signs and Symbols: ( ) order of operations, ÷ division, $ dollar sign
New Vocabulary: minimum, plus
New Signs and Symbols: °C degrees Celsius, = is equal to, min minute, -
negative number, p.m., + positive number
Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:50:06 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
6
of
21
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
201 - 210
Statements Last Updated: Aug 4, 2014
Goal: Operations and Algebraic Thinking
Skills and Concepts to Enhance (73% Probability*)
191 - 200
Skills and Concepts to Develop (50% Probability*)
201 - 210
Skills and Concepts to Introduce (27% Probability*)
211 - 220
Expressions and Equations
Expressions and Equations
Expressions and Equations
• Solves real-world whole number problems involving subtraction with
numbers under 1000
• Solves whole number subtraction word problems with numbers over
1000
• Evaluates numerical expressions using grouping symbols (whole
numbers only)
• Demonstrates an understanding of the zero property of multiplication
• Computes half price (multiplication/division)
• Uses algebraic reasoning to solve problems involving equality
relationships
• Solves 1-step open sentences with missing addends (numbers 100
and under)
• Solves 1-step open sentences with missing addends (numbers over
100)
• Solves simple open sentences with missing factors (numbers 100 and
under)
• Solves 2-step open sentences with missing addends
• Writes equivalent forms of whole numbers 11 to 20 using addition
(e.g., 14 = 7 + 7)
• Uses rounding to estimate answers to 2-step problems involving
money (using decimals)
• Solves whole number subtraction word problems with numbers over
1000
• Evaluates numerical expressions using grouping symbols (whole
numbers only)
• Demonstrates an understanding of the commutative property of
addition
• Understands equivalence and extends the concept to number
sentences involving variables (e.g., 8 + 2 = [] + 2)
• Uses algebraic reasoning to solve problems involving equality
relationships
• Uses simple linear equations to represent problem situations
• Describes a realistic situation using information given in a linear
equation
• Solves 1-step open sentences with missing addends (numbers over
100)
• Solves simple open sentences with missing factors (numbers 100 and
under)
• Solves 2-step open sentences with missing addends
• Solves open sentences with basic-facts calculations on both sides of
the sentence
• Translates a 2-step problem to a symbolic expression or equation
• Solves real-world problems using reasoning strategies
• Uses rounding to estimate answers to 2-step problems involving
money (using decimals)
• Demonstrates an understanding of the associative property of
multiplication
• Demonstrates an understanding of the distributive property of
multiplication by decomposing a term
• Calculates the value of a power (e.g., 2^3 = 8)
• Uses a table of input/output values to represent patterns
• Understands equivalence and extends the concept to number
sentences involving variables (e.g., 8 + 2 = [] + 2)
• Uses algebraic reasoning to solve problems involving equality
relationships
• Uses simple linear equations to represent problem situations
• Solves simple open sentences with missing factors (numbers over 100)
• Solves open sentences using the distributive property
• Solves open sentences with calculations on both sides of the sentence
• Solves 2-step open sentences with missing factors
• Solves 1-step linear equations
• Applies algebraic methods to solve theoretical problems
• Translates a 2-step problem to a symbolic expression or equation
• Solves real-world problems using reasoning strategies
• Uses powers to represent 10, 100, 1000, 10,000, and 100,000
Use Functions to Model Relationships
Use Functions to Model Relationships
Use Functions to Model Relationships
• Extends a growing arithmetic pattern, defined by objects or diagrams
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Completes a simple function table based on real-life situations (e.g.,
the number of tricycles related to the number of wheels)
• Reads data in a line graph - no calculations
• Extends a growing arithmetic pattern, defined by objects or diagrams
• Completes a simple function table based on real-life situations (e.g.,
the number of tricycles related to the number of wheels)
• Completes a function table given a simple rule (e.g., x + 2)
• Predicts from simple charts and tables
• Completes a function table given a simple rule (e.g., x + 2)
• Solves problems involving simple functions
• Looks for a growing pattern to solve a problem
• Interprets data in line graphs (e.g., change over time)
New Vocabulary: longer
New Signs and Symbols: ( ) order of operations, ÷ division, $ dollar sign
New Vocabulary: minimum, plus
New Signs and Symbols: °C degrees Celsius, = is equal to, min minute, -
negative number, p.m., + positive number
New Vocabulary: None
New Signs and Symbols: ( ) parenthesis around an integer, a.m., ¢ cent
sign, °F degrees Fahrenheit, $ dollar sign, lb pound, mph miles per hour
Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:50:06 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
7
of
21
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
211 - 220
Statements Last Updated: Aug 4, 2014
Goal: Operations and Algebraic Thinking
Skills and Concepts to Enhance (73% Probability*)
201 - 210
Skills and Concepts to Develop (50% Probability*)
211 - 220
Skills and Concepts to Introduce (27% Probability*)
221 - 230
Expressions and Equations
Expressions and Equations
Expressions and Equations
• Uses rounding to estimate answers to 2-step problems involving
money (using decimals)
• Solves whole number subtraction word problems with numbers over
1000
• Evaluates numerical expressions using grouping symbols (whole
numbers only)
• Demonstrates an understanding of the commutative property of
addition
• Understands equivalence and extends the concept to number
sentences involving variables (e.g., 8 + 2 = [] + 2)
• Uses algebraic reasoning to solve problems involving equality
relationships
• Uses simple linear equations to represent problem situations
• Describes a realistic situation using information given in a linear
equation
• Solves 1-step open sentences with missing addends (numbers over
100)
• Solves simple open sentences with missing factors (numbers 100 and
under)
• Solves 2-step open sentences with missing addends
• Solves open sentences with basic-facts calculations on both sides of
the sentence
• Translates a 2-step problem to a symbolic expression or equation
• Solves real-world problems using reasoning strategies
• Uses rounding to estimate answers to 2-step problems involving
money (using decimals)
• Demonstrates an understanding of the associative property of
multiplication
• Demonstrates an understanding of the distributive property of
multiplication by decomposing a term
• Calculates the value of a power (e.g., 2^3 = 8)
• Uses a table of input/output values to represent patterns
• Understands equivalence and extends the concept to number
sentences involving variables (e.g., 8 + 2 = [] + 2)
• Uses algebraic reasoning to solve problems involving equality
relationships
• Uses simple linear equations to represent problem situations
• Solves simple open sentences with missing factors (numbers over 100)
• Solves open sentences using the distributive property
• Solves open sentences with calculations on both sides of the sentence
• Solves 2-step open sentences with missing factors
• Solves 1-step linear equations
• Applies algebraic methods to solve theoretical problems
• Translates a 2-step problem to a symbolic expression or equation
• Solves real-world problems using reasoning strategies
• Uses powers to represent 10, 100, 1000, 10,000, and 100,000
• Solves real-world problems involving rate of pay
• Solves difficult real-world problems involving decimals (e.g., multiple
multiplications, conversions)
• Uses the distributive property
• Calculates the value of a power (e.g., 2^3 = 8)
• Solves problems involving simple interest rates with the formula
• Uses a table of input/output values to represent patterns
• Uses basic operations on algebraic expressions (substituting for
unknowns)
• Recognizes commutative, associative, distributive, symmetric,
transitive, and reflexive properties
• Uses basic operations on algebraic expressions (expanding -
monomial by a binomial)
• Demonstrates an understanding of properties (e.g., commutative,
associative, distributive, properties of 0)
• Writes equivalent forms of algebraic expressions (e.g., (x + 3)/2 = x/2 +
3/2)
• Represents relationships of quantities in the form of an expression
• Uses basic operations on algebraic expressions (uses correct order of
operations)
• Expresses a simple linear equation from a contextual situation
• Solves open sentences with calculations on both sides of the sentence
• Solves 2-step open sentences with missing factors
• Solves 1-step linear equations
• Solves 2-step linear equations
• Solves linear equations with decimals
• Solves linear equations with integers
• Writes equivalent forms of algebraic equations using addition and
subtraction
• Solves open sentences with decimals
• Solves linear equations in a real-world context using a given formula
• Applies algebraic methods to solve theoretical problems
• Applies algebraic methods to solve real-world problems
• Uses graphs to solve simple systems of linear equations
• Applies systems-of-linear-equations methods to solve theoretical
problems
• Describes the relationship or a real-world situation represented by a
simple linear inequality (e.g., 1- or 2-step)
• Solves real-world problems using reasoning strategies
• Uses powers to represent 10, 100, 1000, 10,000, and 100,000
Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:50:06 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
8
of
21
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
211 - 220
Statements Last Updated: Aug 4, 2014
Goal: Operations and Algebraic Thinking
Skills and Concepts to Enhance (73% Probability*)
201 - 210
Skills and Concepts to Develop (50% Probability*)
211 - 220
Skills and Concepts to Introduce (27% Probability*)
221 - 230
Expressions and Equations
Expressions and Equations
Expressions and Equations
• Writes a number expressed in scientific notation in standard form
Use Functions to Model Relationships
Use Functions to Model Relationships
Use Functions to Model Relationships
• Extends a growing arithmetic pattern, defined by objects or diagrams
• Completes a simple function table based on real-life situations (e.g.,
the number of tricycles related to the number of wheels)
• Completes a function table given a simple rule (e.g., x + 2)
• Predicts from simple charts and tables
• Completes a function table given a simple rule (e.g., x + 2)
• Solves problems involving simple functions
• Looks for a growing pattern to solve a problem
• Interprets data in line graphs (e.g., change over time)
• Extends a growing pattern of triangular numbers, defined by objects or
diagrams
• Represents geometric sequences using written descriptions in
recursive terms (present term, next term)
• Solves problems involving simple functions
• Looks for a growing pattern to solve a problem
New Vocabulary: minimum, plus
New Signs and Symbols: °C degrees Celsius, = is equal to, min minute, -
negative number, p.m., + positive number
New Vocabulary: None
New Signs and Symbols: ( ) parenthesis around an integer, a.m., ¢ cent
sign, °F degrees Fahrenheit, $ dollar sign, lb pound, mph miles per hour
New Vocabulary: algebra, net, reflexive, short, transitive
New Signs and Symbols: < less than, m meter/metre, repeating decimal
overbar, △ triangle
Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:50:06 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
9
of
21
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
221 - 230
Statements Last Updated: Aug 4, 2014
Goal: Operations and Algebraic Thinking
Skills and Concepts to Enhance (73% Probability*)
211 - 220
Skills and Concepts to Develop (50% Probability*)
221 - 230
Skills and Concepts to Introduce (27% Probability*)
231 - 240
Expressions and Equations
Expressions and Equations
Expressions and Equations
• Uses rounding to estimate answers to 2-step problems involving
money (using decimals)
• Demonstrates an understanding of the associative property of
multiplication
• Demonstrates an understanding of the distributive property of
multiplication by decomposing a term
• Calculates the value of a power (e.g., 2^3 = 8)
• Uses a table of input/output values to represent patterns
• Understands equivalence and extends the concept to number
sentences involving variables (e.g., 8 + 2 = [] + 2)
• Uses algebraic reasoning to solve problems involving equality
relationships
• Uses simple linear equations to represent problem situations
• Solves simple open sentences with missing factors (numbers over 100)
• Solves open sentences using the distributive property
• Solves open sentences with calculations on both sides of the sentence
• Solves 2-step open sentences with missing factors
• Solves 1-step linear equations
• Applies algebraic methods to solve theoretical problems
• Translates a 2-step problem to a symbolic expression or equation
• Solves real-world problems using reasoning strategies
• Uses powers to represent 10, 100, 1000, 10,000, and 100,000
• Solves real-world problems involving rate of pay
• Solves difficult real-world problems involving decimals (e.g., multiple
multiplications, conversions)
• Uses the distributive property
• Calculates the value of a power (e.g., 2^3 = 8)
• Solves problems involving simple interest rates with the formula
• Uses a table of input/output values to represent patterns
• Uses basic operations on algebraic expressions (substituting for
unknowns)
• Recognizes commutative, associative, distributive, symmetric,
transitive, and reflexive properties
• Uses basic operations on algebraic expressions (expanding -
monomial by a binomial)
• Demonstrates an understanding of properties (e.g., commutative,
associative, distributive, properties of 0)
• Writes equivalent forms of algebraic expressions (e.g., (x + 3)/2 = x/2 +
3/2)
• Represents relationships of quantities in the form of an expression
• Uses basic operations on algebraic expressions (uses correct order of
operations)
• Expresses a simple linear equation from a contextual situation
• Solves open sentences with calculations on both sides of the sentence
• Solves 2-step open sentences with missing factors
• Solves 1-step linear equations
• Solves 2-step linear equations
• Solves linear equations with decimals
• Solves linear equations with integers
• Writes equivalent forms of algebraic equations using addition and
subtraction
• Solves open sentences with decimals
• Solves linear equations in a real-world context using a given formula
• Applies algebraic methods to solve theoretical problems
• Applies algebraic methods to solve real-world problems
• Uses graphs to solve simple systems of linear equations
• Applies systems-of-linear-equations methods to solve theoretical
problems
• Describes the relationship or a real-world situation represented by a
simple linear inequality (e.g., 1- or 2-step)
• Solves real-world problems using reasoning strategies
• Uses powers to represent 10, 100, 1000, 10,000, and 100,000
• Evaluates numerical expressions using the order of operations (whole
numbers only)
• Evaluates expressions using the order of operations, including
exponents (whole numbers only)
• Solves real-world problems involving rate of pay
• Solves real-world problems involving rate of pay with time and a half
• Solves difficult real-world problems involving decimals (e.g., multiple
multiplications, conversions)
• Evaluates numerical expressions using the order of operations (using
integers)
• Divides rational expressions in a/b form
• Uses the distributive property
• Calculates the power of a number (e.g., 8 = 2^3)
• Evaluates expressions containing powers (e.g., 3^2 x 2^3)
• Applies rules for multiplying and dividing powers
• Solves problems with scientific notation
• Describes and uses a variable with whole numbers, multiplication, and
division in a contextual situation
• Uses expressions to represent situations that involve variable
quantities with exponents
• Uses basic operations on algebraic expressions (substituting for
unknowns)
• Uses basic operations on algebraic expressions (substituting for
unknown exponents)
• Recognizes commutative, associative, distributive, symmetric,
transitive, and reflexive properties
• Uses basic operations on algebraic expressions (combining like terms)
• Uses basic operations on algebraic expressions (expanding -
monomial by a binomial)
• Writes equivalent forms of algebraic expressions (e.g., (x + 3)/2 = x/2 +
3/2)
• Represents relationships of quantities in the form of an expression
• Uses basic operations on algebraic expressions (uses correct order of
operations)
• Expresses a simple linear equation from a contextual situation
• Solves 2-step open sentences with missing factors (variables on both
sides of the sentence)
• Solves 2-step linear equations
• Solves linear equations with integers
• Solves linear equations with fractions
• Solves linear equations using rational numbers
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
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
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
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
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
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
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
16
of
21
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
251 - 260
Statements Last Updated: Aug 4, 2014
Goal: Operations and Algebraic Thinking
Skills and Concepts to Enhance (73% Probability*)
241 - 250
Skills and Concepts to Develop (50% Probability*)
251 - 260
Skills and Concepts to Introduce (27% Probability*)
261 - 270
Expressions and Equations
Expressions and Equations
Expressions and Equations
• 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
• Simplifies rational expressions with exponents
• Simplifies rational expressions with negative exponents
• Estimates the limit of a given infinite sequence (e.g., given the
sequence 1/n, as n gets larger)
• Uses the compound interest equation to solve problems
• Simplifies monomials
• Simplifies polynomial expressions using power laws
• Factors polynomials by identifying a common monomial and then
factoring the trinomial
• Rewrites a complex formula to solve for a specific variable
• Solves quadratic equations using the quadratic formula
• Solves quadratic equations by completing the square
• Solves real-world systems of linear equations
• Solves polynomial inequalities
• Uses graphs to solve systems of linear 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
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
17
of
21
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
251 - 260
Statements Last Updated: Aug 4, 2014
Goal: Operations and Algebraic Thinking
Skills and Concepts to Enhance (73% Probability*)
241 - 250
Skills and Concepts to Develop (50% Probability*)
251 - 260
Skills and Concepts to Introduce (27% Probability*)
261 - 270
Expressions and Equations
Expressions and Equations
Expressions and Equations
• 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
• 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
• Writes the equation of the line when given the graph of the line
• Writes linear equations, given slope and point on a line
• Models real life functions using function notation
• Determines the minimum and maximum of a quadratic function
• Analyzes the properties and characteristics of exponential functions
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
New Vocabulary: geometric series, 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
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
18
of
21
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
261 - 270
Statements Last Updated: Aug 4, 2014
Goal: Operations and Algebraic Thinking
Skills and Concepts to Enhance (73% Probability*)
251 - 260
Skills and Concepts to Develop (50% Probability*)
261 - 270
Skills and Concepts to Introduce (27% Probability*)
271 - 280
Expressions and Equations
Expressions and Equations
Expressions and Equations
• 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
• Simplifies rational expressions with exponents
• Simplifies rational expressions with negative exponents
• Estimates the limit of a given infinite sequence (e.g., given the
sequence 1/n, as n gets larger)
• Uses the compound interest equation to solve problems
• Simplifies monomials
• Simplifies polynomial expressions using power laws
• Factors polynomials by identifying a common monomial and then
factoring the trinomial
• Rewrites a complex formula to solve for a specific variable
• Solves quadratic equations using the quadratic formula
• Solves quadratic equations by completing the square
• Solves real-world systems of linear equations
• Solves polynomial inequalities
• Uses graphs to solve systems of linear inequalities
• Describes a relationship or a real-world situation represented by a
quadratic 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
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
19
of
21
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
261 - 270
Statements Last Updated: Aug 4, 2014
Goal: Operations and Algebraic Thinking
Skills and Concepts to Enhance (73% Probability*)
251 - 260
Skills and Concepts to Develop (50% Probability*)
261 - 270
Skills and Concepts to Introduce (27% Probability*)
271 - 280
Expressions and Equations
Expressions and Equations
Expressions and Equations
• 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
• 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
• Writes the equation of the line when given the graph of the line
• Writes linear equations, given slope and point on a line
• Models real life functions using function notation
• Determines the minimum and maximum of a quadratic function
• Analyzes the properties and characteristics of exponential functions
New Vocabulary: coordinate plane, quadratic equation, undefined, wider,
x-coordinate, y-coordinate
New Signs and Symbols: [ ] square brackets, { } set notation, P perimeter
New Vocabulary: geometric series, semi-annual
New Signs and Symbols: P principal, r rate, t time
New Vocabulary: None
New Signs and Symbols: None
Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
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
20
of
21
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
271 - 280
Statements Last Updated: Aug 4, 2014
Goal: Operations and Algebraic Thinking
Skills and Concepts to Enhance (73% Probability*)
261 - 270
Skills and Concepts to Develop (50% Probability*)
271 - 280
Skills and Concepts to Introduce (27% Probability*)
> 280
Expressions and Equations
Expressions and Equations
Expressions and Equations
• Simplifies rational expressions with exponents
• Simplifies rational expressions with negative exponents
• Estimates the limit of a given infinite sequence (e.g., given the
sequence 1/n, as n gets larger)
• Uses the compound interest equation to solve problems
• Simplifies monomials
• Simplifies polynomial expressions using power laws
• Factors polynomials by identifying a common monomial and then
factoring the trinomial
• Rewrites a complex formula to solve for a specific variable
• Solves quadratic equations using the quadratic formula
• Solves quadratic equations by completing the square
• Solves real-world systems of linear equations
• Solves polynomial inequalities
• Uses graphs to solve systems of linear 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: geometric series, semi-annual
New Signs and Symbols: P principal, r rate, t time
New Vocabulary: None
New Signs and Symbols: None
New Vocabulary: None
New Signs and Symbols: None
Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
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
21
of
21
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
> 280
Statements Last Updated: Aug 4, 2014
Goal: Operations and Algebraic Thinking
Skills and Concepts to Enhance (73% Probability*)
271 - 280
Skills and Concepts to Develop (50% Probability*)
> 280
Expressions and Equations
Expressions and Equations
• 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: None
New Signs and Symbols: None
New Vocabulary: None
New Signs and Symbols: None