4
Mathematics 2-5
Contents
Goal: Operations and Algebraic Thinking......................................................
1
RIT Score Range: Below 161..............................................................
1
RIT Score Range: 161-170..................................................................
2
RIT Score Range: 171-180..................................................................
3
RIT Score Range: 181-190..................................................................
5
RIT Score Range: 191-200..................................................................
7
RIT Score Range: 201-210..................................................................
9
RIT Score Range: 211-220..................................................................
11
RIT Score Range: 221-230..................................................................
13
RIT Score Range: 231-240..................................................................
15
RIT Score Range: 241-250..................................................................
16
RIT Score Range: Above 250..............................................................
17
Goal: Number and Operations........................................................................
18
RIT Score Range: Below 161..............................................................
18
RIT Score Range: 161-170..................................................................
19
RIT Score Range: 171-180..................................................................
20
RIT Score Range: 181-190..................................................................
22
RIT Score Range: 191-200..................................................................
24
RIT Score Range: 201-210..................................................................
27
RIT Score Range: 211-220..................................................................
30
RIT Score Range: 221-230..................................................................
33
RIT Score Range: 231-240..................................................................
36
RIT Score Range: Above 240..............................................................
38
Goal: Measurement and Data..........................................................................
39
RIT Score Range: Below 161..............................................................
39
RIT Score Range: 161-170..................................................................
40
RIT Score Range: 171-180..................................................................
41
RIT Score Range: 181-190..................................................................
43
RIT Score Range: 191-200..................................................................
45
RIT Score Range: 201-210..................................................................
47
RIT Score Range: 211-220..................................................................
49
RIT Score Range: 221-230..................................................................
51
RIT Score Range: 231-240..................................................................
53
RIT Score Range: 241-250..................................................................
55
RIT Score Range: 251-260..................................................................
56
RIT Score Range: Above 260..............................................................
57
Goal: Geometry................................................................................................
58
RIT Score Range: Below 161..............................................................
58
RIT Score Range: 161-170..................................................................
59
RIT Score Range: 171-180..................................................................
60
RIT Score Range: 181-190..................................................................
61
RIT Score Range: 191-200..................................................................
62
RIT Score Range: 201-210..................................................................
63
RIT Score Range: 211-220..................................................................
64
RIT Score Range: 221-230..................................................................
65
RIT Score Range: 231-240..................................................................
66
RIT Score Range: Above 240..............................................................
67
ii
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
< 161
Goal: Operations and Algebraic Thinking
Skills and Concepts to Develop (50% Probability*)
< 161
Represent and Solve Problems
Skills and Concepts to Introduce (27% Probability*)
161 - 170
Represent and Solve Problems
• Adds two 1-digit numbers with sums to 10 in horizontal format
• Instantly recalls basic multiplication facts where one factor is 0-5 and
the other factor is 0-12
• Uses models to construct whole number addition facts with addends
through 10
• Subtracts a 1-digit number from a 2-digit number that is less than 20
(whole numbers only)
• Subtracts two 1-digit numbers vertically
• Solves basic-facts open sentences - addition and subtraction
• Uses a number line to construct addition facts with sums through 20
(whole numbers)
• Adds two 1-digit numbers with sums to 10 in horizontal format
• Adds two 1-digit numbers with sums between 10 and 19 in horizontal
format
• Adds two 1-digit numbers with sums between 10 and 19 in vertical
format
• Solves real-world whole number addition problems with sums to 20
(result unknown)
Analyze Patterns and Relationships
Analyze Patterns and Relationships
New Vocabulary: None
New Vocabulary: None
New Signs and Symbols: None
New Signs and Symbols: + addition, = is equal to, × multiplication, 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.
Page 4-1
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
161 - 170
Goal: Operations and Algebraic Thinking
Skills and concepts to Enhance (73% Probability*)
< 161
Represent and Solve Problems
Skills and Concepts to Develop (50% Probability*)
161 - 170
Represent and Solve Problems
Skills and Concepts to Introduce (27% Probability*)
171 - 180
Represent and Solve Problems
• Adds two 1-digit numbers with sums to 10 in horizontal format
• Instantly recalls basic multiplication facts where one factor is 0-5 and
the other factor is 0-12
• Counts by 2's to 100
• Subtracts a 1-digit number from a 2-digit number that is less than 20
(whole numbers only)
• Determines the operation needed from a simple problem
• Uses models to construct whole number addition facts with addends
through 10
• Subtracts two 1-digit numbers vertically
• Solves basic facts open sentences - multiplication and division
• Writes a number sentence for a simple problem solving situation
• Solves basic-facts open sentences - addition and subtraction
• Writes equivalent forms of whole number expressions (e.g., 15 + 5 =
10 + 10)
• Uses a number line to construct addition facts with sums through 20
(whole numbers)
• Uses a number line to construct addition facts with sums through 20
(whole numbers)
• Adds two 1-digit numbers with sums to 10 in horizontal format
• Solves real-world whole number addition problems with sums to 20
(result unknown)
• Adds two 1-digit numbers with sums between 10 and 19 in horizontal
format
• Adds two 1-digit numbers with sums between 10 and 19 in vertical
format
• Solves real-world whole number addition problems with sums to 20
(result unknown)
• Solves real-world whole number addition problems with sums to 20
(start unknown)
• Solves real-world whole number addition problems with sums to 100
(result unknown)
• Represents a basic facts addition problem with a number sentence
• Subtracts a 1-digit number from a 2-digit number that is less than 20
(whole numbers only)
• Solves real-world whole number problems involving subtraction with
numbers under 20
• Instantly recalls basic multiplication facts where one factor is 0-5 and
the other factor is 0-12
• Multiplies basic facts to 10 x 10 vertically
• Adds 1-digit numbers with sums to 18 (with parentheses)
• Recognizes addition and subtraction fact families through 18
• Solves basic-facts open sentences - addition and subtraction
Analyze Patterns and Relationships
Analyze Patterns and Relationships
Analyze Patterns and Relationships
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Extends a growing arithmetic pattern, defined by numbers
New Vocabulary: None
New Vocabulary: None
New Vocabulary: fact family
New Signs and Symbols: None
New Signs and Symbols: + addition, = is equal to, × multiplication, subtraction, variable
New Signs and Symbols: ( ) order of operations, | tally mark
Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Page 4-2
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
171 - 180
Goal: Operations and Algebraic Thinking
Skills and concepts to Enhance (73% Probability*)
161 - 170
Represent and Solve Problems
Skills and Concepts to Develop (50% Probability*)
171 - 180
Represent and Solve Problems
Skills and Concepts to Introduce (27% Probability*)
181 - 190
Represent and Solve Problems
• Instantly recalls basic multiplication facts where one factor is 0-5 and
the other factor is 0-12
• Counts by 2's to 100
• Solves basic facts open sentences - multiplication and division
• Writes equivalent forms of whole numbers 11 to 20 using addition
(e.g., 14 = 7 + 7)
• Subtracts a 1-digit number from a 2-digit number that is less than 20
(whole numbers only)
• Determines the operation needed from a simple problem
• Determines the operation needed from a simple problem
• Writes a number sentence for a simple problem solving situation
• Writes a number sentence for a simple problem solving situation
• Interprets a chart or table - calculation required
• Solves basic-facts open sentences - addition and subtraction
• Writes equivalent forms of whole number expressions (e.g., 15 + 5 =
10 + 10)
• Uses a number line to construct addition facts with sums through 20
(whole numbers)
• Uses a number line to construct addition facts with sums through 20
(whole numbers)
• Uses rounding to estimate answers to real-world problems involving
addition of numbers less than 100 (whole numbers only)
• Adds two 1-digit numbers with sums to 10 in horizontal format
• Solves real-world whole number addition problems with sums to 20
(result unknown)
• Instantly recalls basic addition facts with sums to 18 in a table
• Subtracts two 1-digit numbers vertically
• Adds two 1-digit numbers with sums between 10 and 19 in horizontal
format
• Adds two 1-digit numbers with sums between 10 and 19 in vertical
format
• Solves real-world whole number addition problems with sums to 20
(result unknown)
• Solves real-world whole number addition problems with sums to 20
(start unknown)
• Solves real-world whole number addition problems with sums to 100
(result unknown)
• Represents a basic facts addition problem with a number sentence
• Subtracts a 1-digit number from a 2-digit number that is less than 20
(whole numbers only)
• Solves real-world whole number problems involving subtraction with
numbers under 20
• Instantly recalls basic multiplication facts where one factor is 0-5 and
the other factor is 0-12
• Distinguishes between odd and even numbers
• Solves real-world whole number addition problems with sums to 20
(result unknown) - with extraneous information given
• Solves real-world whole number addition problems with sums to 100
(result unknown)
• Instantly recalls basic subtraction facts with minuend less than 10
• Solves real-world whole number problems involving subtraction with
numbers under 20
• Solves real-world whole number problems involving subtraction with
numbers 100 and under
• Solves real-world whole number problems involving subtraction with
numbers under 1000
• Multiplies basic facts to 10 x 10 vertically
• Solves problems using the inverse relationship between addition and
subtraction
• Adds 1-digit numbers with sums to 18 (with parentheses)
• Uses counting by multiples for multiplication
• Recognizes addition and subtraction fact families through 18
• Instantly recalls basic multiplication facts where one factor is 6-12 and
the other factor is 0-12
• Solves basic-facts open sentences - addition and subtraction
• Multiplies basic facts to 10 x 10 vertically
• Solves word problems involving basic whole number multiplication
facts to 10 x 10
• Uses manipulatives to divide a small set of objects into groups of equal
size
• Uses sharing for division
• Models whole number multiplication and division algorithms (e.g.,
shows multiplication as repeated addition and division as repeated
subtraction)
• Models multiplication and division algorithms using arrays (whole
numbers)
• Instantly recalls division facts with dividend and divisors less than 10
• Solves real-world whole number problems involving addition and
subtraction
• Recognizes addition and subtraction fact families through 18
• Demonstrates an understanding of the zero property of multiplication
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.
Page 4-3
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
171 - 180
Goal: Operations and Algebraic Thinking
Skills and concepts to Enhance (73% Probability*)
161 - 170
Represent and Solve Problems
Skills and Concepts to Develop (50% Probability*)
171 - 180
Represent and Solve Problems
Skills and Concepts to Introduce (27% Probability*)
181 - 190
Represent and Solve Problems
• Demonstrates an understanding of the inverse relationship between
multiplication and division
• Solves basic facts addition and subtraction open sentences using
diagrams and models (e.g., using balances)
• Solves 1-step open sentences with missing addends (numbers 100
and under)
Analyze Patterns and Relationships
Analyze Patterns and Relationships
Analyze Patterns and Relationships
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Extends a growing arithmetic pattern, defined by numbers
• Extends a growing arithmetic pattern, defined by numbers
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
New Vocabulary: None
New Vocabulary: fact family
New Vocabulary: gave, left, row, unifix cubes
New Signs and Symbols: + addition, = is equal to, × multiplication, subtraction, variable
New Signs and Symbols: ( ) order of operations, | tally mark
New Signs and Symbols: ÷ division, long division symbol
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.
Page 4-4
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
181 - 190
Goal: Operations and Algebraic Thinking
Skills and concepts to Enhance (73% Probability*)
171 - 180
Represent and Solve Problems
Skills and Concepts to Develop (50% Probability*)
181 - 190
Represent and Solve Problems
Skills and Concepts to Introduce (27% Probability*)
191 - 200
Represent and Solve Problems
• Counts by 2's to 100
• Solves basic facts open sentences - multiplication and division
• Writes equivalent forms of whole numbers 11 to 20 using addition
(e.g., 14 = 7 + 7)
• Solves real-world whole number addition problems with sums to 20
(result unknown) - with extraneous information given
• Determines the operation needed from a simple problem
• Determines the operation needed from a simple problem
• Writes a number sentence for a simple problem solving situation
• Writes a number sentence for a simple problem solving situation
• Writes equivalent forms of whole number expressions (e.g., 15 + 5 =
10 + 10)
• Interprets a chart or table - calculation required
• Uses rounding to estimate answers to real-world problems involving
numbers less than 1000 with addition and subtraction (whole numbers
only)
• Distinguishes between odd and even numbers
• Solves real-world whole number addition problems with sums to 20
(change unknown)
• Uses a number line to construct addition facts with sums through 20
(whole numbers)
• Uses rounding to estimate answers to real-world problems involving
addition of numbers less than 100 (whole numbers only)
• Solves real-world whole number problems involving subtraction with
numbers 100 and under
• Solves real-world whole number addition problems with sums to 20
(result unknown)
• Instantly recalls basic addition facts with sums to 18 in a table
• Solves real-world whole number problems involving subtraction with
numbers under 1000
• Solves real-world whole number addition problems with sums to 20
(start unknown)
• Solves real-world whole number addition problems with sums to 100
(result unknown)
• Solves real-world whole number addition problems with sums to 20
(result unknown) - with extraneous information given
• Solves real-world whole number addition problems with sums to 100
(result unknown)
• Solves whole number subtraction word problems with numbers over
1000
• Instantly recalls basic subtraction facts with minuend less than 10
• Solves problems using the inverse relationship between addition and
subtraction
• Solves real-world whole number problems involving subtraction with
numbers under 20
• Instantly recalls basic multiplication facts where one factor is 6-12 and
the other factor is 0-12
• Solves real-world whole number problems involving subtraction with
numbers 100 and under
• Solves word problems involving basic whole number multiplication
facts to 10 x 10
• Solves real-world whole number problems involving subtraction with
numbers under 1000
• Solves word problems involving whole number multiplication with
numbers greater than 10 x 10
• Multiplies basic facts to 10 x 10 vertically
• Solves problems using the inverse relationship between addition and
subtraction
• Uses manipulatives to divide a small set of objects into groups of equal
size
• Adds 1-digit numbers with sums to 18 (with parentheses)
• Uses counting by multiples for multiplication
• Recognizes addition and subtraction fact families through 18
• Instantly recalls basic multiplication facts where one factor is 6-12 and
the other factor is 0-12
• Models whole number multiplication and division algorithms (e.g.,
shows multiplication as repeated addition and division as repeated
subtraction)
• Multiplies basic facts to 10 x 10 vertically
• Instantly recalls division facts with dividend and divisors less than 10
• Solves word problems involving basic whole number multiplication
facts to 10 x 10
• Instantly recalls division facts with dividend and divisors less than 13
• Represents a basic facts addition problem with a number sentence
• Subtracts a 1-digit number from a 2-digit number that is less than 20
(whole numbers only)
• Solves real-world whole number problems involving subtraction with
numbers under 20
• Instantly recalls basic multiplication facts where one factor is 0-5 and
the other factor is 0-12
• Solves basic-facts open sentences - addition and subtraction
• Uses manipulatives to divide a small set of objects into groups of equal
size
• Uses sharing for division
• Models whole number multiplication and division algorithms (e.g.,
shows multiplication as repeated addition and division as repeated
subtraction)
• Models multiplication and division algorithms using arrays (whole
numbers)
• Instantly recalls division facts with dividend and divisors less than 10
• Solves real-world whole number problems involving addition and
subtraction
• Recognizes addition and subtraction fact families through 18
• Demonstrates an understanding of the zero property of multiplication
• Solves word problems with whole number division facts with dividend
and divisors less than 11
• Solves simple word problems involving whole number division with
remainder (e.g., 1-step, 1-digit divisor)
• Evaluates numerical expressions using grouping symbols (whole
numbers only)
• Demonstrates an understanding of the commutative property of
multiplication with simple problems
• Demonstrates an understanding of the zero property of multiplication
• Uses algebraic reasoning to solve problems involving equality
relationships
• Solves 1-step open sentences with missing addends (numbers 100
and under)
• Solves simple open sentences with missing factors (numbers 100 and
under)
Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Page 4-5
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
181 - 190
Goal: Operations and Algebraic Thinking
Skills and concepts to Enhance (73% Probability*)
171 - 180
Represent and Solve Problems
Skills and Concepts to Develop (50% Probability*)
181 - 190
Represent and Solve Problems
Skills and Concepts to Introduce (27% Probability*)
191 - 200
Represent and Solve Problems
• Demonstrates an understanding of the inverse relationship between
multiplication and division
• Solves 2-step open sentences with missing addends
• Solves basic facts addition and subtraction open sentences using
diagrams and models (e.g., using balances)
• Translates a 1-step problem to a symbolic expression or equation
• Solves 1-step open sentences with missing addends (numbers 100
and under)
• Solves problems using tables
• Determines the operation needed from a simple problem
• Interprets a chart or table - calculation required
• Writes equivalent forms of whole numbers 11 to 20 using addition
(e.g., 14 = 7 + 7)
• Distinguishes between odd and even numbers
Analyze Patterns and Relationships
Analyze Patterns and Relationships
Analyze Patterns and Relationships
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Extends a growing arithmetic pattern, defined by numbers
• Identifies numbers as composite
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Extends a growing arithmetic pattern, defined by objects or diagrams
• Extends a growing arithmetic pattern, defined by numbers
• 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)
New Vocabulary: fact family
New Vocabulary: gave, left, row, unifix cubes
New Vocabulary: composite number, each, prime number
New Signs and Symbols: ( ) order of operations, | tally mark
New Signs and Symbols: ÷ division, long division symbol
New Signs and Symbols: °F degrees Fahrenheit, $ dollar sign, lb pound
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.
Page 4-6
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
191 - 200
Goal: Operations and Algebraic Thinking
Skills and concepts to Enhance (73% Probability*)
181 - 190
Represent and Solve Problems
Skills and Concepts to Develop (50% Probability*)
191 - 200
Represent and Solve Problems
Skills and Concepts to Introduce (27% Probability*)
201 - 210
Represent and Solve Problems
• Writes equivalent forms of whole numbers 11 to 20 using addition
(e.g., 14 = 7 + 7)
• Solves real-world whole number addition problems with sums to 20
(result unknown) - with extraneous information given
• Determines the operation needed from a simple problem
• Uses rounding to estimate answers to real-world problems involving
numbers less than 1000 with addition and subtraction (whole numbers
only)
• Uses rounding to estimate answers to real-world problems involving
numbers 1000 or greater with addition and subtraction (whole numbers
only)
• Writes a number sentence for a simple problem solving situation
• Interprets a chart or table - calculation required
• Solves real-world whole number problems involving subtraction with
numbers 100 and under (analysis)
• Distinguishes between odd and even numbers
• Solves real-world whole number addition problems with sums to 20
(change unknown)
• Solves whole number subtraction word problems with numbers over
1000
• Uses rounding to estimate answers to real-world problems involving
addition of numbers less than 100 (whole numbers only)
• Solves real-world whole number problems involving subtraction with
numbers 100 and under
• Solves problems using the inverse relationship between addition and
subtraction
• Instantly recalls basic addition facts with sums to 18 in a table
• Solves real-world whole number problems involving subtraction with
numbers under 1000
• Solves word problems involving whole number multiplication with
numbers greater than 10 x 10
• Solves whole number subtraction word problems with numbers over
1000
• Models whole number multiplication and division algorithms (e.g., uses
physical materials to show 4 groups of 3 objects)
• Solves problems using the inverse relationship between addition and
subtraction
• Instantly recalls division facts with dividend and divisors less than 13
• Instantly recalls basic subtraction facts with minuend less than 10
• Solves real-world whole number problems involving subtraction with
numbers under 20
• Instantly recalls basic multiplication facts where one factor is 6-12 and
the other factor is 0-12
• Solves word problems with whole number division facts with dividend
and divisors less than 11
• Solves real-world whole number problems involving subtraction with
numbers 100 and under
• Solves word problems involving basic whole number multiplication
facts to 10 x 10
• Solves simple word problems involving whole number division with
remainder (e.g., 1-step, 1-digit divisor)
• Solves real-world whole number problems involving subtraction with
numbers under 1000
• Solves word problems involving whole number multiplication with
numbers greater than 10 x 10
• Solves whole number word problems with division over 10 x 10
• Solves problems using the inverse relationship between addition and
subtraction
• Uses manipulatives to divide a small set of objects into groups of equal
size
• Uses division for multiple-step real-world problems (whole numbers)
• Uses counting by multiples for multiplication
• Instantly recalls basic multiplication facts where one factor is 6-12 and
the other factor is 0-12
• Models whole number multiplication and division algorithms (e.g.,
shows multiplication as repeated addition and division as repeated
subtraction)
• Multiplies basic facts to 10 x 10 vertically
• Instantly recalls division facts with dividend and divisors less than 10
• Solves word problems involving basic whole number multiplication
facts to 10 x 10
• Instantly recalls division facts with dividend and divisors less than 13
• Solves real-world whole number addition problems with sums to 20
(result unknown) - with extraneous information given
• Solves real-world whole number addition problems with sums to 100
(result unknown)
• Uses manipulatives to divide a small set of objects into groups of equal
size
• Uses sharing for division
• Models whole number multiplication and division algorithms (e.g.,
shows multiplication as repeated addition and division as repeated
subtraction)
• Models multiplication and division algorithms using arrays (whole
numbers)
• Instantly recalls division facts with dividend and divisors less than 10
• Solves real-world whole number problems involving addition and
subtraction
• Recognizes addition and subtraction fact families through 18
• Demonstrates an understanding of the zero property of multiplication
• Solves word problems with whole number division facts with dividend
and divisors less than 11
• Solves simple word problems involving whole number division with
remainder (e.g., 1-step, 1-digit divisor)
• Evaluates numerical expressions using grouping symbols (whole
numbers only)
• Performs mental computation with division
• Determines the remainder in a real-world problem (whole numbers)
• Evaluates numerical expressions using grouping symbols (whole
numbers only)
• Solves real-world problems involving 2-step multiple operations, whole
numbers only
• Demonstrates an understanding of the commutative property of
multiplication with simple problems
• 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
• Demonstrates an understanding of the commutative property of
multiplication with simple problems
• Describes a realistic situation using information given in a linear
equation
• Demonstrates an understanding of the zero property of multiplication
• Solves 2-step open sentences with missing addends
• Uses algebraic reasoning to solve problems involving equality
relationships
• Solves simple open sentences with missing factors (numbers 100 and
under)
• Solves 1-step open sentences with missing addends (numbers 100
and under)
• Solves open sentences with basic-facts calculations on both sides of
the sentence
• Solves simple open sentences with missing factors (numbers 100 and
under)
• Translates a 1-step problem to a symbolic expression or equation
• Translates a 2-step problem to a symbolic expression or 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.
Page 4-7
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
191 - 200
Goal: Operations and Algebraic Thinking
Skills and concepts to Enhance (73% Probability*)
181 - 190
Represent and Solve Problems
Skills and Concepts to Develop (50% Probability*)
191 - 200
Represent and Solve Problems
Skills and Concepts to Introduce (27% Probability*)
201 - 210
Represent and Solve Problems
• Demonstrates an understanding of the inverse relationship between
multiplication and division
• Solves 2-step open sentences with missing addends
• Solves problems using tables
• Determines the operation needed from a simple problem
• Solves basic facts addition and subtraction open sentences using
diagrams and models (e.g., using balances)
• Translates a 1-step problem to a symbolic expression or equation
• Uses number sense strategies to solve problems (addition/subtraction
only)
• Solves 1-step open sentences with missing addends (numbers 100
and under)
• Solves problems using tables
• Interprets a chart or table - calculation required
• Writes equivalent forms of whole numbers 11 to 20 using addition
(e.g., 14 = 7 + 7)
• Distinguishes between odd and even numbers
Analyze Patterns and Relationships
Analyze Patterns and Relationships
Analyze Patterns and Relationships
• Extends a growing arithmetic pattern, defined by numbers
• Identifies numbers as composite
• Extends a growing arithmetic pattern, defined by objects or diagrams
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Extends a growing arithmetic pattern, defined by objects or diagrams
• Predicts from simple charts and tables
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Determines the rule and completes a simple function machine output
• 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)
• Completes a function table given a simple rule (e.g., x + 2)
New Vocabulary: gave, left, row, unifix cubes
New Vocabulary: composite number, each, prime number
New Vocabulary: minimum, plus
New Signs and Symbols: ÷ division, long division symbol
New Signs and Symbols: °F degrees Fahrenheit, $ dollar sign, lb pound
New Signs and Symbols: ¢ cent sign, = is equal to, + 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.
Page 4-8
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
201 - 210
Goal: Operations and Algebraic Thinking
Skills and concepts to Enhance (73% Probability*)
191 - 200
Represent and Solve Problems
Skills and Concepts to Develop (50% Probability*)
201 - 210
Represent and Solve Problems
Skills and Concepts to Introduce (27% Probability*)
211 - 220
Represent and Solve Problems
• Solves real-world whole number addition problems with sums to 20
(result unknown) - with extraneous information given
• Uses rounding to estimate answers to real-world problems involving
numbers 1000 or greater with addition and subtraction (whole numbers
only)
• Translates a 2-step problem to a symbolic expression or equation
• Uses rounding to estimate answers to real-world problems involving
numbers less than 1000 with addition and subtraction (whole numbers
only)
• Solves real-world whole number problems involving subtraction with
numbers 100 and under (analysis)
• Uses rounding to estimate answers to real-world problems involving
multiplication and division of numbers less than 100 (whole numbers
only)
• Solves real-world whole number addition problems with sums to 20
(change unknown)
• Solves whole number subtraction word problems with numbers over
1000
• Uses rounding to estimate answers to real-world problems involving
numbers less than 1000 with multiplication and division (whole numbers
only)
• Solves real-world whole number problems involving subtraction with
numbers 100 and under
• Solves problems using the inverse relationship between addition and
subtraction
• Models whole number multiplication and division algorithms (e.g., uses
physical materials to show 4 groups of 3 objects)
• Solves real-world whole number problems involving subtraction with
numbers under 1000
• Solves word problems involving whole number multiplication with
numbers greater than 10 x 10
• Performs mental computation with division
• Solves whole number subtraction word problems with numbers over
1000
• Models whole number multiplication and division algorithms (e.g., uses
physical materials to show 4 groups of 3 objects)
• Solves complex word problems involving whole number division with
remainder (e.g., 2-step, 2-digit divisor)
• Solves problems using the inverse relationship between addition and
subtraction
• Instantly recalls division facts with dividend and divisors less than 13
• Solves real-world problems involving 2-step multiple operations, whole
numbers only
• Instantly recalls basic multiplication facts where one factor is 6-12 and
the other factor is 0-12
• Solves word problems with whole number division facts with dividend
and divisors less than 11
• Solves word problems involving basic whole number multiplication
facts to 10 x 10
• Solves simple word problems involving whole number division with
remainder (e.g., 1-step, 1-digit divisor)
• Solves word problems involving whole number multiplication with
numbers greater than 10 x 10
• Solves whole number word problems with division over 10 x 10
• Uses manipulatives to divide a small set of objects into groups of equal
size
• Uses division for multiple-step real-world problems (whole numbers)
• Demonstrates an understanding of the commutative property of
multiplication with simple problems
• Evaluates numerical expressions using grouping symbols (whole
numbers only)
• Demonstrates an understanding of the associative property of
multiplication
• Solves real-world problems involving 2-step multiple operations, whole
numbers only
• Demonstrates an understanding of the distributive property of
multiplication by decomposing a term
• Demonstrates an understanding of the commutative property of
multiplication with simple problems
• Understands equivalence and extends the concept to number
sentences involving variables (e.g., 8 + 2 = [] + 2)
• 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 algebraic reasoning to solve problems involving equality
relationships
• Uses simple linear equations to represent problem situations
• Uses simple linear equations to represent problem situations
• Solves open sentences using the distributive property
• Demonstrates an understanding of the commutative property of
multiplication with simple problems
• Describes a realistic situation using information given in a linear
equation
• Solves open sentences with calculations on both sides of the sentence
• Demonstrates an understanding of the zero property of multiplication
• Solves 2-step open sentences with missing addends
• Uses pictures to represent problems
• Uses algebraic reasoning to solve problems involving equality
relationships
• Solves simple open sentences with missing factors (numbers 100 and
under)
• Solves 1-step open sentences with missing addends (numbers 100
and under)
• Solves open sentences with basic-facts calculations on both sides of
the sentence
• Solves simple open sentences with missing factors (numbers 100 and
under)
• Translates a 1-step problem to a symbolic expression or equation
• Models whole number multiplication and division algorithms (e.g.,
shows multiplication as repeated addition and division as repeated
subtraction)
• Instantly recalls division facts with dividend and divisors less than 10
• Instantly recalls division facts with dividend and divisors less than 13
• Solves word problems with whole number division facts with dividend
and divisors less than 11
• Solves simple word problems involving whole number division with
remainder (e.g., 1-step, 1-digit divisor)
• Evaluates numerical expressions using grouping symbols (whole
numbers only)
• Performs mental computation with division
• Determines the remainder in a real-world problem (whole numbers)
• Solves whole number word problems with division over 10 x 10
• Solves real-world multiple-step problems involving whole numbers
• Predicts the relative size of the answer when multiplying whole
numbers
• Demonstrates an understanding of the inverse relationship between
addition and subtraction
• Solves simple open sentences with missing factors (numbers over 100)
• Applies algebraic methods to solve theoretical problems
• Translates a 2-step problem to a symbolic expression or 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.
Page 4-9
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
201 - 210
Goal: Operations and Algebraic Thinking
Skills and concepts to Enhance (73% Probability*)
191 - 200
Represent and Solve Problems
Skills and Concepts to Develop (50% Probability*)
201 - 210
Represent and Solve Problems
• Solves 2-step open sentences with missing addends
• Solves problems using tables
• Determines the operation needed from a simple problem
• Uses number sense strategies to solve problems (addition/subtraction
only)
• Translates a 1-step problem to a symbolic expression or equation
Skills and Concepts to Introduce (27% Probability*)
211 - 220
Represent and Solve Problems
• Interprets a chart or table - calculation required
• Solves problems using tables
• Writes equivalent forms of whole numbers 11 to 20 using addition
(e.g., 14 = 7 + 7)
• Distinguishes between odd and even numbers
Analyze Patterns and Relationships
Analyze Patterns and Relationships
Analyze Patterns and Relationships
• Identifies numbers as composite
• Extends a growing arithmetic pattern, defined by objects or diagrams
• Extends a growing arithmetic pattern, defined by objects or diagrams
• Predicts from simple charts and tables
• Determines the rule given a simple real-world function table (e.g., #
Dogs compared to # Legs)
• Analyzes a growing, arithmetic pattern with numbers to determine the
rule
• Determines the rule and completes a simple function machine output
• Identifies numbers as prime
• Completes a function table given a simple rule (e.g., x + 2)
• Completes a function table given a simple rule (e.g., x + 2)
• 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)
• Determines the rule and completes a simple function machine output
• Determines factors of whole numbers
• Looks for a growing pattern to solve a problem
New Vocabulary: composite number, each, prime number
New Vocabulary: minimum, plus
New Vocabulary: None
New Signs and Symbols: °F degrees Fahrenheit, $ dollar sign, lb pound
New Signs and Symbols: ¢ cent sign, = is equal to, + positive number
New Signs and Symbols: ( ) parenthesis around an integer, { } set notation
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.
Page 4-10
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
211 - 220
Goal: Operations and Algebraic Thinking
Skills and concepts to Enhance (73% Probability*)
201 - 210
Represent and Solve Problems
Skills and Concepts to Develop (50% Probability*)
211 - 220
Represent and Solve Problems
Skills and Concepts to Introduce (27% Probability*)
221 - 230
Represent and Solve Problems
• Uses rounding to estimate answers to real-world problems involving
numbers 1000 or greater with addition and subtraction (whole numbers
only)
• Translates a 2-step problem to a symbolic expression or equation
• Applies algebraic methods to solve real-world problems
• Uses rounding to estimate answers to real-world problems involving
multiplication and division of numbers less than 100 (whole numbers
only)
• Demonstrates an understanding of multiple properties
• Solves real-world whole number problems involving subtraction with
numbers 100 and under (analysis)
• Represents relationships of quantities in the form of an expression
• Solves open sentences with calculations on both sides of the sentence
• Solves whole number subtraction word problems with numbers over
1000
• Uses rounding to estimate answers to real-world problems involving
numbers less than 1000 with multiplication and division (whole numbers
only)
• Solves problems using the inverse relationship between addition and
subtraction
• Models whole number multiplication and division algorithms (e.g., uses
physical materials to show 4 groups of 3 objects)
• Uses pictures to represent problems
• Solves word problems involving whole number multiplication with
numbers greater than 10 x 10
• Performs mental computation with division
• Models whole number multiplication and division algorithms (e.g., uses
physical materials to show 4 groups of 3 objects)
• Solves complex word problems involving whole number division with
remainder (e.g., 2-step, 2-digit divisor)
• Uses rounding to estimate answers to real-world problems involving
multiplication and division of numbers less than 100 (whole numbers
only)
• Instantly recalls division facts with dividend and divisors less than 13
• Solves real-world problems involving 2-step multiple operations, whole
numbers only
• Performs mental computation with division
• Solves word problems with whole number division facts with dividend
and divisors less than 11
• Solves simple word problems involving whole number division with
remainder (e.g., 1-step, 1-digit divisor)
• Solves whole number word problems with division over 10 x 10
• Determines the remainder in a real-world problem (whole numbers)
• Solves whole number word problems with division over 10 x 10
• Uses multiple number theory concepts to solve problems (e.g., factors,
digits, odd/even, divisibility)
• Applies algebraic methods to solve theoretical problems
• Uses rounding to estimate answers to real-world problems involving
numbers less than 1000 with multiplication and division (whole numbers
only)
• Solves real-world multiple-step problems involving whole numbers
• Models algorithms using place value concepts (multiplication and
division with whole numbers)
• Predicts the relative size of the answer when multiplying whole
numbers
• Solves complex word problems involving whole number division with
remainder (e.g., 2-step, 2-digit divisor)
• Demonstrates an understanding of the inverse relationship between
addition and subtraction
• Solves real-world multiple-step problems involving whole numbers
• Uses division for multiple-step real-world problems (whole numbers)
• Demonstrates an understanding of the commutative property of
multiplication with simple problems
• Evaluates numerical expressions using grouping symbols (whole
numbers only)
• Demonstrates an understanding of the associative property of
multiplication
• Solves real-world problems involving 2-step multiple operations, whole
numbers only
• Demonstrates an understanding of the distributive property of
multiplication by decomposing a term
• Demonstrates an understanding of the commutative property of
multiplication with simple problems
• Understands equivalence and extends the concept to number
sentences involving variables (e.g., 8 + 2 = [] + 2)
• 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 algebraic reasoning to solve problems involving equality
relationships
• Uses simple linear equations to represent problem situations
• Uses simple linear equations to represent problem situations
• Solves open sentences using the distributive property
• Describes a realistic situation using information given in a linear
equation
• Solves open sentences with calculations on both sides of the sentence
• Solves 2-step open sentences with missing addends
• Uses pictures to represent problems
• Solves simple open sentences with missing factors (numbers over 100)
• Applies algebraic methods to solve theoretical problems
• Solves simple open sentences with missing factors (numbers 100 and
under)
• Solves open sentences with basic-facts calculations on both sides of
the sentence
• Translates a 1-step problem to a symbolic expression or equation
• Translates a 2-step problem to a symbolic expression or 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.
Page 4-11
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
211 - 220
Goal: Operations and Algebraic Thinking
Skills and concepts to Enhance (73% Probability*)
201 - 210
Represent and Solve Problems
Skills and Concepts to Develop (50% Probability*)
211 - 220
Represent and Solve Problems
Skills and Concepts to Introduce (27% Probability*)
221 - 230
Represent and Solve Problems
Analyze Patterns and Relationships
Analyze Patterns and Relationships
Analyze Patterns and Relationships
• Extends a growing arithmetic pattern, defined by objects or diagrams
• Looks for a growing pattern to solve a problem
• Predicts from simple charts and tables
• Determines the rule given a simple real-world function table (e.g., #
Dogs compared to # Legs)
• Determines the rule and completes a simple function machine output
• Identifies numbers as prime
• Completes a function table given a simple rule (e.g., x + 2)
• Completes a function table given a simple rule (e.g., x + 2)
• Extends a growing pattern of triangular numbers, 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)
• Determines the rule and completes a simple function machine output
• Uses factor and multiple concepts to solve simple problems
• Solves problems using tables
• Uses number sense strategies to solve problems (addition/subtraction
only)
• Determines factors of whole numbers
• Determines factors of whole numbers
• Looks for a growing pattern to solve a problem
New Vocabulary: minimum, plus
New Vocabulary: None
New Signs and Symbols: ¢ cent sign, = is equal to, + positive number
New Signs and Symbols: ( ) parenthesis around an integer, { } set notation New Signs and Symbols: None
New Vocabulary: 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.
Page 4-12
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
221 - 230
Goal: Operations and Algebraic Thinking
Skills and concepts to Enhance (73% Probability*)
211 - 220
Represent and Solve Problems
Skills and Concepts to Develop (50% Probability*)
221 - 230
Represent and Solve Problems
Skills and Concepts to Introduce (27% Probability*)
231 - 240
Represent and Solve Problems
• Translates a 2-step problem to a symbolic expression or equation
• Applies algebraic methods to solve real-world problems
• Uses pictures to represent problems
• Uses rounding to estimate answers to real-world problems involving
multiplication and division of numbers less than 100 (whole numbers
only)
• Demonstrates an understanding of multiple properties
• Models algorithms using place value concepts (multiplication and
division with whole numbers)
• Uses rounding to estimate answers to real-world problems involving
numbers less than 1000 with multiplication and division (whole numbers
only)
• Represents relationships of quantities in the form of an expression
• Solves open sentences with calculations on both sides of the sentence
• Uses multiple number theory concepts to solve problems (e.g., factors,
digits, odd/even, divisibility)
• Evaluates numerical expressions using the order of operations (whole
numbers only)
• Solves multiple-step problems involving proportions
• Models whole number multiplication and division algorithms (e.g., uses
physical materials to show 4 groups of 3 objects)
• Uses pictures to represent problems
• Represents relationships of quantities in the form of an expression
• Applies algebraic methods to solve theoretical problems
• Applies algebraic methods to solve real-world problems
• Performs mental computation with division
• Uses rounding to estimate answers to real-world problems involving
multiplication and division of numbers less than 100 (whole numbers
only)
• Solves problems comparing unit prices
• Solves whole number word problems with division over 10 x 10
• Solves complex word problems involving whole number division with
remainder (e.g., 2-step, 2-digit divisor)
• Solves real-world problems involving 2-step multiple operations, whole
numbers only
• Uses rounding to estimate answers to real-world problems involving
numbers less than 1000 with multiplication and division (whole numbers
only)
• Solves real-world multiple-step problems involving whole numbers
• Models algorithms using place value concepts (multiplication and
division with whole numbers)
• Predicts the relative size of the answer when multiplying whole
numbers
• Solves complex word problems involving whole number division with
remainder (e.g., 2-step, 2-digit divisor)
• Demonstrates an understanding of the inverse relationship between
addition and subtraction
• Solves real-world multiple-step problems involving whole numbers
• Demonstrates an understanding of the commutative property of
multiplication with simple problems
• Demonstrates an understanding of the associative property of
multiplication
• Demonstrates an understanding of the distributive property of
multiplication by decomposing a term
• 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
• Applies algebraic methods to solve theoretical problems
• Uses pictures to represent problems
Analyze Patterns and Relationships
Analyze Patterns and Relationships
• Determines the rule given a simple real-world function table (e.g., #
Dogs compared to # Legs)
• Looks for a growing pattern to solve a problem
• Identifies numbers as prime
• Extends a growing pattern of triangular numbers, defined by objects or
diagrams
• Completes a function table given a simple rule (e.g., x + 2)
Analyze Patterns and Relationships
• Determines factors of whole 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.
Page 4-13
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
221 - 230
Goal: Operations and Algebraic Thinking
Skills and concepts to Enhance (73% Probability*)
211 - 220
Analyze Patterns and Relationships
Skills and Concepts to Develop (50% Probability*)
221 - 230
Analyze Patterns and Relationships
• Determines the rule and completes a simple function machine output
• Uses factor and multiple concepts to solve simple problems
Skills and Concepts to Introduce (27% Probability*)
231 - 240
Analyze Patterns and Relationships
• Determines factors of whole numbers
• Looks for a growing pattern to solve a problem
New Vocabulary: None
New Vocabulary: None
New Signs and Symbols: ( ) parenthesis around an integer, { } set notation 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.
Page 4-14
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
231 - 240
Goal: Operations and Algebraic Thinking
Skills and concepts to Enhance (73% Probability*)
221 - 230
Represent and Solve Problems
Skills and Concepts to Develop (50% Probability*)
231 - 240
Represent and Solve Problems
Skills and Concepts to Introduce (27% Probability*)
241 - 250
Represent and Solve Problems
• Applies algebraic methods to solve real-world problems
• Uses pictures to represent problems
• Uses reasoning strategies to solve problems
• Demonstrates an understanding of multiple properties
• Models algorithms using place value concepts (multiplication and
division with whole numbers)
• Applies algebraic methods to solve real-world problems
• Represents relationships of quantities in the form of an expression
• Solves open sentences with calculations on both sides of the sentence
• Uses multiple number theory concepts to solve problems (e.g., factors,
digits, odd/even, divisibility)
• Solves multiple-step problems involving proportions
• Evaluates numerical expressions using the order of operations (whole
numbers only)
• Solves multiple-step problems involving proportions
• Uses pictures to represent problems
• Represents relationships of quantities in the form of an expression
• Applies algebraic methods to solve theoretical problems
• Applies algebraic methods to solve real-world problems
• Uses rounding to estimate answers to real-world problems involving
multiplication and division of numbers less than 100 (whole numbers
only)
• Solves problems comparing unit prices
• Uses rounding to estimate answers to real-world problems involving
numbers less than 1000 with multiplication and division (whole numbers
only)
• Models algorithms using place value concepts (multiplication and
division with whole numbers)
• Solves complex word problems involving whole number division with
remainder (e.g., 2-step, 2-digit divisor)
• Solves real-world multiple-step problems involving whole numbers
Analyze Patterns and Relationships
Analyze Patterns and Relationships
Analyze Patterns and Relationships
New Vocabulary: None
New Vocabulary: None
New Vocabulary: None
New Signs and Symbols: None
New Signs and Symbols: None
New Signs and Symbols: None
• Looks for a growing pattern to solve a problem
• Determines factors of whole numbers
• Extends a growing pattern of triangular numbers, defined by objects or
diagrams
• Uses factor and multiple concepts to solve simple problems
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.
Page 4-15
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
241 - 250
Goal: Operations and Algebraic Thinking
Skills and concepts to Enhance (73% Probability*)
231 - 240
Represent and Solve Problems
Skills and Concepts to Develop (50% Probability*)
241 - 250
Represent and Solve Problems
Skills and Concepts to Introduce (27% Probability*)
> 250
Represent and Solve Problems
• Uses pictures to represent problems
• Uses reasoning strategies to solve problems
• Uses reasoning strategies to solve problems
• Models algorithms using place value concepts (multiplication and
division with whole numbers)
• Applies algebraic methods to solve real-world problems
• Solves multiple-step problems involving proportions
• Evaluates numerical expressions using the order of operations (whole
numbers only)
• Solves multiple-step problems involving proportions
• Represents relationships of quantities in the form of an expression
• Applies algebraic methods to solve real-world problems
• Solves problems comparing unit prices
Analyze Patterns and Relationships
Analyze Patterns and Relationships
Analyze Patterns and Relationships
New Vocabulary: None
New Vocabulary: None
New Vocabulary: None
New Signs and Symbols: 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.
Page 4-16
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
> 250
Goal: Operations and Algebraic Thinking
Skills and concepts to Enhance (73% Probability*)
241 - 250
Represent and Solve Problems
Skills and Concepts to Develop (50% Probability*)
> 250
Represent and Solve Problems
• Uses reasoning strategies to solve problems
• Uses reasoning strategies to solve problems
• Applies algebraic methods to solve real-world problems
• Solves multiple-step problems involving proportions
Analyze Patterns and Relationships
Analyze Patterns and Relationships
New Vocabulary: None
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
Page 4-17
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
< 161
Goal: Number and Operations
Skills and Concepts to Develop (50% Probability*)
< 161
Understand Place Value, Counting, and Cardinality
Skills and Concepts to Introduce (27% Probability*)
161 - 170
Understand Place Value, Counting, and Cardinality
• Identifies whole numbers under 100 using base-10 blocks
• Identifies whole numbers under 100 using base-10 blocks
• Identifies the numerical and written name for whole numbers 11 to 20
(e.g., 15 is fifteen, and vice versa)
• Identifies the numerical and written name for whole numbers 11 to 20
(e.g., 15 is fifteen, and vice versa)
• Counts 1 to 10 objects
• Identifies missing numbers in a series through 100
• Recognizes and generates equivalent forms for the same number
using physical models for whole numbers 11 to 20
• Orders whole numbers less than 10
• Writes whole numbers in standard and expanded form through the tens
Number and Operations in Base Ten
Number and Operations in Base Ten
• Uses models to calculate whole number sums through 99
• Uses models to calculate whole number sums through 99
• Adds 1-digit to multiple-digit number with no regrouping
• Adds multiple 1-digit numbers
• Adds 1-digit to multiple-digit number with regrouping
• Uses strategies for addition facts (e.g., compatible numbers, counting
on, doubles, neighbors, making tens)
• Adds 1-digit to multiple-digit number with no regrouping
• Adds 1-digit to multiple-digit number with regrouping
• Adds 2-digit numbers with no regrouping
• Subtracts two 1-digit numbers horizontally
• Subtracts a 2-digit number from a 2-digit number, with no regrouping
Number and Operations - Fractions
Number and Operations - Fractions
New Vocabulary: None
New Vocabulary: None
New Signs and Symbols: None
New Signs and Symbols: + addition, = is equal to, × multiplication,
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.
Page 4-18
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
161 - 170
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
< 161
Understand Place Value, Counting, and Cardinality
Skills and Concepts to Develop (50% Probability*)
161 - 170
Understand Place Value, Counting, and Cardinality
Skills and Concepts to Introduce (27% Probability*)
171 - 180
Understand Place Value, Counting, and Cardinality
• Identifies whole numbers under 100 using base-10 blocks
• Identifies whole numbers under 100 using base-10 blocks
• Identifies whole numbers 100 - 999 using base-10 blocks
• Identifies the numerical and written name for whole numbers 11 to 20
(e.g., 15 is fifteen, and vice versa)
• Identifies the numerical and written name for whole numbers 11 to 20
(e.g., 15 is fifteen, and vice versa)
• Identifies the numerical and written name for whole numbers 21 to 100
(e.g., 62 is sixty-two, and vice versa)
• Counts 1 to 10 objects
• Identifies the numeral and written name for whole numbers 101 to 999
(e.g., 342 is three hundred forty-two, and vice versa)
• Identifies missing numbers in a series through 100
• Recognizes and generates equivalent forms for the same number
using physical models for whole numbers 11 to 20
• Orders whole numbers less than 10
• Writes whole numbers in standard and expanded form through the tens
• Identifies missing numbers in a series through 100
• Counts backwards from a given number (given number greater than
10)
• Recognizes and generates equivalent forms for the same number
using physical models for whole numbers 11 to 20
• Compares sets of objects and identifies which is equal to, more than,
or less than the other (1 to 10 objects)
• Compares whole numbers through 999
• Counts objects that are grouped into tens and ones
• Identifies the place value and value of each digit in whole numbers
through the tens place
Number and Operations in Base Ten
Number and Operations in Base Ten
Number and Operations in Base Ten
• Uses models to calculate whole number sums through 99
• Uses models to calculate whole number sums through 99
• Uses models to calculate whole number sums through 999
• Adds 1-digit to multiple-digit number with no regrouping
• Adds multiple 1-digit numbers
• Adds 1-digit to multiple-digit number with regrouping
• Uses strategies for addition facts (e.g., compatible numbers, counting
on, doubles, neighbors, making tens)
• Uses strategies for addition facts (e.g., compatible numbers, counting
on, doubles, neighbors, making tens)
Number and Operations - Fractions
• Adds two or three 2-digit number with regrouping
• Adds 1-digit to multiple-digit number with no regrouping
• Adds 1- and/or 2-digit numbers with sums under 100
• Adds 1-digit to multiple-digit number with regrouping
• Adds 3-digit numbers with no regrouping
• Adds 2-digit numbers with no regrouping
• Adds 3-digit numbers, with regrouping, with sums under 1000
• Subtracts two 1-digit numbers horizontally
• Subtracts a 2-digit number from a 2-digit number, with no regrouping
• Subtracts a 2-digit number from a 2-digit number, with no regrouping
• Subtracts 2- and/or 3-digit numbers with no regrouping
Number and Operations - Fractions
Number and Operations - Fractions
• Represents 1/2 with a diagram or model
• Represents 1/4 with a diagram or model
• Identifies one-half from a region or set
New Vocabulary: None
New Vocabulary: None
New Vocabulary: fourth, hundred, thirds, thousand
New Signs and Symbols: None
New Signs and Symbols: + addition, = is equal to, × multiplication,
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.
Page 4-19
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
171 - 180
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
161 - 170
Understand Place Value, Counting, and Cardinality
Skills and Concepts to Develop (50% Probability*)
171 - 180
Understand Place Value, Counting, and Cardinality
Skills and Concepts to Introduce (27% Probability*)
181 - 190
Understand Place Value, Counting, and Cardinality
• Identifies whole numbers under 100 using base-10 blocks
• Identifies whole numbers 100 - 999 using base-10 blocks
• Identifies the numerical and written name for whole numbers 11 to 20
(e.g., 15 is fifteen, and vice versa)
• Identifies the numerical and written name for whole numbers 21 to 100
(e.g., 62 is sixty-two, and vice versa)
• Identifies the numeral and written name for whole numbers 101 to 999
(e.g., 342 is three hundred forty-two, and vice versa)
• Counts 1 to 10 objects
• Identifies the numeral and written name for whole numbers 101 to 999
(e.g., 342 is three hundred forty-two, and vice versa)
• Identifies missing numbers in a series through 100
• Recognizes and generates equivalent forms for the same number
using physical models for whole numbers 11 to 20
• Orders whole numbers less than 10
• Writes whole numbers in standard and expanded form through the tens
• Identifies missing numbers in a series through 100
• Identifies the numeral and written name for whole numbers to 1000 to
9999 (e.g., 3456 is three thousand, four hundred fifty-six, and vice versa)
• Identifies the numeral and written name for whole numbers 10,000 to
100,000
• Counts backwards from a given number (given number greater than
10)
• Compares whole numbers through 999
• Recognizes and generates equivalent forms for the same number
using physical models for whole numbers 11 to 20
• Rounds 3-digit whole numbers to the nearest hundred
• Compares sets of objects and identifies which is equal to, more than,
or less than the other (1 to 10 objects)
• Identifies whole numbers under 100 given place value terms (e.g., 3
tens and 4 ones = 34)
• Compares whole numbers through 999
• Counts objects that are grouped into tens and ones
• Identifies the place value and value of each digit in whole numbers
through the tens place
• Identifies the place value and value of each digit in whole numbers
through the tens place
• Identifies the place value and value of each digit in whole numbers
through the hundreds place
• Rounds 2- and 3- digit whole numbers to the nearest ten
• Counts objects that are grouped into tens and ones
• Identifies the place value and value of each digit in whole numbers
through the thousands
• Identifies the place value and value of each digit in whole numbers
through the hundred thousands
• Compares and orders decimals to the hundredths place (same number
of digits after decimal)
Number and Operations in Base Ten
Number and Operations in Base Ten
Number and Operations in Base Ten
• Uses models to calculate whole number sums through 99
• Uses models to calculate whole number sums through 999
• Adds two or three 2-digit number with regrouping
• Adds multiple 1-digit numbers
• Uses strategies for addition facts (e.g., compatible numbers, counting
on, doubles, neighbors, making tens)
• Adds 3-digit numbers, with regrouping, with sums under 1000
• Adds two or three 2-digit number with regrouping
• Uses strategies for addition facts (e.g., compatible numbers, counting
on, doubles, neighbors, making tens)
• Performs mental computation with 2, 3, or 4 addends
• Adds 1-digit to multiple-digit number with no regrouping
• Adds 1- and/or 2-digit numbers with sums under 100
• Adds two 3- and/or 4-digit numbers, with regrouping, with sums over
1000
• Adds 1-digit to multiple-digit number with regrouping
• Adds 3-digit numbers with no regrouping
• Adds multiple-digit numbers, with regrouping, with sums over 1000
• Adds 2-digit numbers with no regrouping
• Adds 3-digit numbers, with regrouping, with sums under 1000
• Uses models to calculate differences through 100 (whole numbers)
• Subtracts two 1-digit numbers horizontally
• Subtracts a 2-digit number from a 2-digit number, with no regrouping
• Subtracts a 2-digit number from a 2-digit number, with regrouping
• Subtracts a 2-digit number from a 2-digit number, with no regrouping
• Subtracts 2- and/or 3-digit numbers with no regrouping
• Uses strategies for sums and differences with 2-digit numbers (e.g.,
decomposing, compatible, compensation, partial sums, counting on)
• Subtracts 2- and/or 3-digit numbers with no regrouping
• Subtracts 3- or 4-digit numbers with regrouping
• Performs mental subtraction with numbers under 1000
• Subtracts multiple-digit numbers with no regrouping
• Multiplies a 2-digit number by a 1-digit number with regrouping
• Multiplies a 2-digit number by a 2-digit number with no regrouping
• Adds decimals to the hundredths place (same number of digits)
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.
Page 4-20
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
171 - 180
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
161 - 170
Number and Operations in Base Ten
Skills and Concepts to Develop (50% Probability*)
171 - 180
Number and Operations in Base Ten
Skills and Concepts to Introduce (27% Probability*)
181 - 190
Number and Operations in Base Ten
• Identifies the number that is "1 less than" a given number
• Compares whole numbers through 9999
Number and Operations - Fractions
Number and Operations - Fractions
Number and Operations - Fractions
• Represents 1/2 with a diagram or model
• Represents 3/4 with a diagram or model
• Represents 1/4 with a diagram or model
• Identifies 1/2 from a region or set
• Identifies one-half from a region or set
• Identifies one-half from a region or set
• Identifies 1/4 from a region or set
• Identifies 2/4, 3/4, or 4/4 from a region or set
• Identifies 2/3 or 3/3 from a region or set
• Identifies tenths from a region or set
• Identifies eighths from a region or set
• Identifies a fraction (denominators other than 2, 3, 4, 8, 10) from a
region or set
New Vocabulary: None
New Vocabulary: fourth, hundred, thirds, thousand
New Signs and Symbols: + addition, = is equal to, × multiplication,
variable
New Signs and Symbols: None
New Vocabulary: closest, digit, hundreds, million, nearest, one, ten
thousand
New Signs and Symbols: { } set notation, $ dollar sign, - 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.
Page 4-21
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
181 - 190
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
171 - 180
Understand Place Value, Counting, and Cardinality
Skills and Concepts to Develop (50% Probability*)
181 - 190
Understand Place Value, Counting, and Cardinality
Skills and Concepts to Introduce (27% Probability*)
191 - 200
Understand Place Value, Counting, and Cardinality
• Identifies whole numbers 100 - 999 using base-10 blocks
• Identifies the numeral and written name for whole numbers 101 to 999
(e.g., 342 is three hundred forty-two, and vice versa)
• Identifies whole numbers over 999 using base-10 blocks
• Identifies the numerical and written name for whole numbers 21 to 100
(e.g., 62 is sixty-two, and vice versa)
• Identifies the numeral and written name for whole numbers 101 to 999
(e.g., 342 is three hundred forty-two, and vice versa)
• Identifies the numeral and written name for whole numbers to 1000 to
9999 (e.g., 3456 is three thousand, four hundred fifty-six, and vice versa)
• Identifies missing numbers in a series through 100
• Identifies the numeral and written name for whole numbers 10,000 to
100,000
• Counts backwards from a given number (given number greater than 10)
• Compares whole numbers through 999
• Recognizes and generates equivalent forms for the same number
using physical models for whole numbers 11 to 20
• Rounds 2- and 3- digit whole numbers to the nearest ten
• Compares sets of objects and identifies which is equal to, more than,
or less than the other (1 to 10 objects)
• Counts objects that are grouped into tens and ones
• Compares whole numbers through 999
• Counts objects that are grouped into tens and ones
• Identifies the place value and value of each digit in whole numbers
through the tens place
• Rounds 3-digit whole numbers to the nearest hundred
• Identifies whole numbers under 100 given place value terms (e.g., 3
tens and 4 ones = 34)
• Identifies the place value and value of each digit in whole numbers
through the tens place
• Identifies the place value and value of each digit in whole numbers
through the hundreds place
• Identifies the place value and value of each digit in whole numbers
through the thousands
• Identifies the place value and value of each digit in whole numbers
through the hundred thousands
• Compares and orders decimals to the hundredths place (same number
of digits after decimal)
• Identifies the numeral and written name for whole numbers with a zero
between digits to the ten thousands place
• Identifies the numeral and written name for whole numbers 10,000 to
100,000
• Identifies the numeral and written name for whole numbers over
100,000
• Compares whole numbers to 100, using the symbols for 'less than',
'equal to', or 'greater than' (<, =, >)
• Compares whole numbers through the thousands using the symbols <,
>, or =
• Rounds 2- and 3- digit whole numbers to the nearest ten
• Rounds 3-digit whole numbers to the nearest hundred
• Identifies whole numbers under 100 given place value terms (e.g., 3
tens and 4 ones = 34)
• Identifies the place value and value of each digit in whole numbers
through the thousands
• Identifies the place value and value of each digit in whole numbers
through the hundred thousands
• Writes whole numbers in standard and expanded form through the
hundreds
• Writes whole numbers in standard and expanded form through the
thousands
Number and Operations in Base Ten
Number and Operations in Base Ten
Number and Operations in Base Ten
• Uses models to calculate whole number sums through 999
• Adds two or three 2-digit number with regrouping
• Uses strategies for addition facts (e.g., compatible numbers, counting
on, doubles, neighbors, making tens)
• Adds 3-digit numbers, with regrouping, with sums under 1000
• Uses rounding to estimate answers to addition and subtraction
problems (whole numbers only)
• Adds two or three 2-digit number with regrouping
• Adds 1- and/or 2-digit numbers with sums under 100
• Adds two 3- and/or 4-digit numbers, with regrouping, with sums over
1000
• Adds 3-digit numbers with no regrouping
• Adds multiple-digit numbers, with regrouping, with sums over 1000
• Adds multiple-digit numbers with sums under 1000
• Adds 3-digit numbers, with regrouping, with sums under 1000
• Uses models to calculate differences through 100 (whole numbers)
• Subtracts 1-digit number from a 2-digit number with regrouping
• Subtracts a 2-digit number from a 2-digit number, with no regrouping
• Subtracts a 2-digit number from a 2-digit number, with regrouping
• Subtracts a 2-digit number from a 2-digit number, with regrouping
• Subtracts 2- and/or 3-digit numbers with no regrouping
• Uses strategies for sums and differences with 2-digit numbers (e.g.,
decomposing, compatible, compensation, partial sums, counting on)
• Uses strategies for sums and differences with 2-digit numbers (e.g.,
decomposing, compatible, compensation, partial sums, counting on)
• Subtracts 2- and/or 3-digit numbers with no regrouping
• Subtracts a 2-digit number from a 3-digit number with a single
regrouping
• Performs mental computation with 2, 3, or 4 addends
• Subtracts 3- or 4-digit numbers with regrouping
• Performs mental subtraction with numbers under 1000
• Subtracts multiple-digit numbers with no regrouping
• Multiplies a 2-digit number by a 1-digit number with regrouping
• Multiplies a 2-digit number by a 2-digit number with no regrouping
• Adds two 3- and/or 4-digit numbers, with regrouping, with sums over
1000
• Adds multiple-digit numbers, with regrouping, with sums over 1000
• Subtracts 3- or 4-digit numbers with regrouping
• Performs mental subtraction with numbers under 1000
• Subtracts multiple-digit numbers with no regrouping
• Multiplies a 2- or 3-digit number by a 1-digit number with no regrouping
• Multiplies a 2-digit number by a 1-digit number with regrouping
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.
Page 4-22
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
181 - 190
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
171 - 180
Number and Operations in Base Ten
Skills and Concepts to Develop (50% Probability*)
181 - 190
Number and Operations in Base Ten
Skills and Concepts to Introduce (27% Probability*)
191 - 200
Number and Operations in Base Ten
• Adds decimals to the hundredths place (same number of digits)
• Multiplies a 3- or 4-digit number by a 1-digit number
• Identifies the number that is "1 less than" a given number
• Multiplies a 2-digit number by a 2-digit number with no regrouping
• Compares whole numbers through 9999
• Performs mental computation with multiplication
• Divides a 2-digit number by a 1-digit number with no remainder
• Adds decimals to the hundredths place (same number of digits)
• Adds decimals to the hundredths place in vertical format (not same
number of digits)
• Adds decimals to the thousandths place vertically with and without
regrouping
• Subtracts decimals to the hundredths place (same number of digits)
with regrouping
• Multiplies a decimal by whole number
Number and Operations - Fractions
Number and Operations - Fractions
Number and Operations - Fractions
• Represents 1/2 with a diagram or model
• Represents 3/4 with a diagram or model
• Represents 1/4 with a diagram or model
• Identifies 1/2 from a region or set
• Uses models to add and subtract fractions and connect the actions to
algorithms
• Identifies one-half from a region or set
• Identifies one-half from a region or set
• Subtracts fractions with like denominators without reducing
• Identifies 1/4 from a region or set
• Solves real-world 1-step problems involving addition and subtraction of
fractions with like denominators
• Identifies 2/4, 3/4, or 4/4 from a region or set
• Identifies 2/3 or 3/3 from a region or set
• Solves real-world 1-step problems involving multiplication or division of
a whole number by a fraction
• Identifies tenths from a region or set
• Represents 1/3 with a diagram or model
• Identifies eighths from a region or set
• Represents fractions with denominators other than 2, 3, 4 with a
diagram or model
• Identifies a fraction (denominators other than 2, 3, 4, 8, 10) from a
region or set
• Identifies 1/4 from a region or set
• Identifies 1/3 from a region or set
• Identifies 2/3 or 3/3 from a region or set
• Identifies tenths from a region or set
• Identifies a fraction (denominators other than 2, 3, 4, 8, 10) from a
region or set
• Identifies equivalent fractions using visual representations
• Matches numeric and visual representation of equivalent fractions
• Explains different interpretations of fractions (e.g., parts of a whole,
parts of a set, and division of whole numbers by whole numbers)
• Writes the missing number in a proportion using basic facts
New Vocabulary: fourth, hundred, thirds, thousand
New Signs and Symbols: None
New Vocabulary: closest, digit, hundreds, million, nearest, one, ten
thousand
New Vocabulary: billion, hundred million, quintillion, standard numeral,
trillion
New Signs and Symbols: { } set notation, $ dollar sign, - subtraction
New Signs and Symbols: °F degrees Fahrenheit, > greater than, < less
than, long division symbol, R remainder
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.
Page 4-23
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
191 - 200
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
181 - 190
Understand Place Value, Counting, and Cardinality
Skills and Concepts to Develop (50% Probability*)
191 - 200
Understand Place Value, Counting, and Cardinality
Skills and Concepts to Introduce (27% Probability*)
201 - 210
Understand Place Value, Counting, and Cardinality
• Identifies the numeral and written name for whole numbers 101 to 999
(e.g., 342 is three hundred forty-two, and vice versa)
• Identifies whole numbers over 999 using base-10 blocks
• Identifies whole numbers over 999 using base-10 blocks
• Identifies the numeral and written name for whole numbers with a zero
between digits to the ten thousands place
• Identifies the numeral and written name for whole numbers with a zero
between digits to the ten thousands place
• Identifies the numeral and written name for whole numbers 10,000 to
100,000
• Identifies the numeral and written name for whole numbers over
100,000
• Identifies the numeral and written name for whole numbers over
100,000
• Compares whole numbers through the billions using the symbols <, >,
or =
• Compares whole numbers to 100, using the symbols for 'less than',
'equal to', or 'greater than' (<, =, >)
• Orders whole numbers a million or greater using < or > symbols
• Compares whole numbers through the thousands using the symbols <,
>, or =
• Rounds 4-, 5-, and 6-digit whole numbers to the nearest hundred
• Identifies the numeral and written name for whole numbers to 1000 to
9999 (e.g., 3456 is three thousand, four hundred fifty-six, and vice versa)
• Identifies the numeral and written name for whole numbers 10,000 to
100,000
• Compares whole numbers through 999
• Rounds 2- and 3- digit whole numbers to the nearest ten
• Rounds 3-digit whole numbers to the nearest hundred
• Counts objects that are grouped into tens and ones
• Identifies whole numbers under 100 given place value terms (e.g., 3
tens and 4 ones = 34)
• Identifies the place value and value of each digit in whole numbers
through the tens place
• Identifies the place value and value of each digit in whole numbers
through the hundreds place
• Identifies the place value and value of each digit in whole numbers
through the thousands
• Identifies the place value and value of each digit in whole numbers
through the hundred thousands
• Compares and orders decimals to the hundredths place (same number
of digits after decimal)
• Rounds 2- and 3- digit whole numbers to the nearest ten
• Rounds 3-digit whole numbers to the nearest hundred
• Identifies whole numbers under 100 given place value terms (e.g., 3
tens and 4 ones = 34)
• Rounds 4-, 5-, and 6-digit whole numbers to the nearest ten
• Rounds 4-, 5-, and 6-digit whole numbers to the nearest thousand
• Rounds whole numbers to the nearest hundred thousand
• Rounds wholes numbers to the nearest billion
• Explains the rules for rounding
• Identifies the place value and value of each digit in whole numbers
through the thousands
• Writes equivalent forms of whole numbers using place value (e.g., 54
= 4 tens and 14 ones)
• Identifies the place value and value of each digit in whole numbers
through the hundred thousands
• Identifies the place value and value of each digit in whole numbers
through the billions
• Writes whole numbers in standard and expanded form through the
hundreds
• Writes whole numbers in standard and expanded form through the
hundred thousands
• Writes whole numbers in standard and expanded form through the
thousands
• Applies base ten place value concepts with whole numbers to solve
problems
• Writes whole numbers using place value terms and vice versa
• Rounds decimals to the nearest whole number
Number and Operations in Base Ten
Number and Operations in Base Ten
Number and Operations in Base Ten
• Adds two or three 2-digit number with regrouping
• Uses rounding to estimate answers to addition and subtraction
problems (whole numbers only)
• Uses rounding to estimate answers to addition and subtraction
problems (whole numbers only)
• Adds two 3- and/or 4-digit numbers, with regrouping, with sums over
1000
• Adds multiple-digit numbers, with regrouping, with sums over 1000
• Adds multiple-digit numbers, with regrouping, with sums over 1000
• Performs mental computation with more than 4 addends
• Adds multiple-digit numbers, with regrouping, with sums over 1000
• Adds multiple-digit numbers with sums under 1000
• Subtracts 3- or 4-digit numbers with regrouping
• Uses models to calculate differences through 100 (whole numbers)
• Subtracts 1-digit number from a 2-digit number with regrouping
• Subtracts numbers with 5 digits or more with regrouping
• Subtracts a 2-digit number from a 2-digit number, with regrouping
• Subtracts a 2-digit number from a 2-digit number, with regrouping
• Instantly recalls basic multiplication and division facts in a table
• Uses strategies for sums and differences with 2-digit numbers (e.g.,
decomposing, compatible, compensation, partial sums, counting on)
• Uses strategies for sums and differences with 2-digit numbers (e.g.,
decomposing, compatible, compensation, partial sums, counting on)
• Multiplies a 2-digit number by a 1-digit number with regrouping
• Subtracts 2- and/or 3-digit numbers with no regrouping
• Subtracts a 2-digit number from a 3-digit number with a single
regrouping
• Multiplies multiple 1-digit numbers
• Adds 3-digit numbers, with regrouping, with sums under 1000
• Performs mental computation with 2, 3, or 4 addends
• Adds two 3- and/or 4-digit numbers, with regrouping, with sums over
1000
• Subtracts 3- or 4-digit numbers with regrouping
• Performs mental subtraction with numbers under 1000
• Subtracts multiple-digit numbers with no regrouping
• Multiplies a 2-digit number by a 1-digit number with regrouping
• Adds multiple-digit numbers with sums under 1000
• Multiplies a 3- or 4-digit number by a 1-digit number
• Subtracts 3- or 4-digit numbers with regrouping
• Multiplies a 2-digit number by a 2-digit number with regrouping
• Performs mental subtraction with numbers under 1000
• Multiplies a 3-digit number by a 2-digit number with regrouping
• Subtracts multiple-digit numbers with no regrouping
• Performs mental computation with 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.
Page 4-24
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
191 - 200
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
181 - 190
Number and Operations in Base Ten
Skills and Concepts to Develop (50% Probability*)
191 - 200
Number and Operations in Base Ten
Skills and Concepts to Introduce (27% Probability*)
201 - 210
Number and Operations in Base Ten
• Multiplies a 2-digit number by a 2-digit number with no regrouping
• Multiplies a 2- or 3-digit number by a 1-digit number with no regrouping
• Multiplies a 2- or 3-digit number by multiples of 10 or 100
• Adds decimals to the hundredths place (same number of digits)
• Multiplies a 2-digit number by a 1-digit number with regrouping
• Multiplies a 3-digit number by a 3-digit number
• Identifies the number that is "1 less than" a given number
• Multiplies a 3- or 4-digit number by a 1-digit number
• Divides a 2-digit number by a 1-digit number with no remainder
• Compares whole numbers through 9999
• Multiplies a 2-digit number by a 2-digit number with no regrouping
• Performs mental computation with multiplication
• Divides a 2-digit number or a 3-digit number by a 1-digit number with a
remainder
• Divides a 2-digit number by a 1-digit number with no remainder
• Divides a 3-digit number by a 1-digit number with no remainder
• Adds decimals to the hundredths place (same number of digits)
• Divides a 4-digit number by a 1-digit number with no remainder
• Adds decimals to the hundredths place in vertical format (not same
number of digits)
• Divides a 3-digit number by a multiple of 10
• Adds decimals to the thousandths place vertically with and without
regrouping
• Adds decimals to the thousandths place horizontally with and without
regrouping
• Subtracts decimals to the hundredths place (same number of digits)
with regrouping
• Subtracts decimals to the hundredths place (same number of digits)
with regrouping
• Multiplies a decimal by whole number
• Multiplies a decimal by whole number
Number and Operations - Fractions
Number and Operations - Fractions
Number and Operations - Fractions
• Represents 3/4 with a diagram or model
• Uses models to add and subtract fractions and connect the actions to
algorithms
• Adds fractions with like denominators without reducing
• Identifies 1/2 from a region or set
• Identifies one-half from a region or set
• Subtracts fractions with like denominators without reducing
• Identifies 1/4 from a region or set
• Solves real-world 1-step problems involving addition and subtraction of
fractions with like denominators
• Uses models to add and subtract fractions and connect the actions to
algorithms
• Divides a 4-digit number by a 2-digit number
• Divides decimal by a whole number
• Identifies 2/4, 3/4, or 4/4 from a region or set
• Adds whole numbers and fractions
• Subtracts fractions with like denominators without reducing
• Identifies 2/3 or 3/3 from a region or set
• Solves real-world 1-step problems involving multiplication or division of
a whole number by a fraction
• Identifies tenths from a region or set
• Represents 1/3 with a diagram or model
• Identifies eighths from a region or set
• Solves real-world 1-step problems involving addition and subtraction of
fractions with like denominators
• Represents fractions with denominators other than 2, 3, 4 with a
diagram or model
• Multiplies a fraction by a fraction without reducing to simplest form
(simple problem)
• Identifies 1/4 from a region or set
• Identifies halves of a region using nonadjacent parts
• Identifies 1/3 from a region or set
• Identifies equivalent fractions using visual representations
• Identifies 2/3 or 3/3 from a region or set
• Expresses "1" in many different ways (e.g., 3/3, 4/4)
• Identifies tenths from a region or set
• Converts a basic fractional numeral to lowest terms (e.g., halves,
thirds, quarters)
• Identifies a fraction (denominators other than 2, 3, 4, 8, 10) from a
region or set
• Identifies a fraction (denominators other than 2, 3, 4, 8, 10) from a
region or set
• Identifies equivalent fractions using visual representations
• Matches numeric and visual representation of equivalent fractions
• Explains different interpretations of fractions (e.g., parts of a whole,
parts of a set, and division of whole numbers by whole numbers)
• Writes the missing number in a proportion using basic facts
• Subtracts mixed fractions with like denominators with no regrouping
• Writes mixed numbers as improper fractions and improper fractions as
mixed numbers
• Compares fractions (e.g., common denominator, 1 in the numerator,
denominator is 2, 3, 4, 6, 8, 10)
• Orders fractions on a number line
• Explains different interpretations of fractions (e.g., parts of a whole,
parts of a set, and division of whole numbers by whole numbers)
• Writes a terminating decimal as a fraction or mixed 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.
Page 4-25
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
191 - 200
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
181 - 190
Number and Operations - Fractions
Skills and Concepts to Develop (50% Probability*)
191 - 200
Number and Operations - Fractions
Skills and Concepts to Introduce (27% Probability*)
201 - 210
Number and Operations - Fractions
• Expresses the equivalent form of a fraction, decimal, and/or percent
(simple fraction)
• Writes the missing number in a proportion using basic facts
New Vocabulary: closest, digit, hundreds, million, nearest, one, ten
thousand
New Vocabulary: billion, hundred million, quintillion, standard numeral,
trillion
New Signs and Symbols: { } set notation, $ dollar sign, - subtraction
New Signs and Symbols: °F degrees Fahrenheit, > greater than, < less
than, long division symbol, R remainder
New Vocabulary: biggest, expanded numeral
New Signs and Symbols: ¢ cent 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.
Page 4-26
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
201 - 210
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
191 - 200
Understand Place Value, Counting, and Cardinality
Skills and Concepts to Develop (50% Probability*)
201 - 210
Understand Place Value, Counting, and Cardinality
Skills and Concepts to Introduce (27% Probability*)
211 - 220
Understand Place Value, Counting, and Cardinality
• Identifies whole numbers over 999 using base-10 blocks
• Identifies whole numbers over 999 using base-10 blocks
• Identifies the numeral and written name for whole numbers with a zero
between digits to the ten thousands place
• Identifies the numeral and written name for whole numbers with a zero
between digits to the ten thousands place
• Predicts the relative size of the answer when computing with 10's,
100's, 1000's
• Identifies the numeral and written name for whole numbers 10,000 to
100,000
• Identifies the numeral and written name for whole numbers over
100,000
• Rounds 4-, 5-, and 6-digit whole numbers to the nearest thousand
• Identifies the numeral and written name for whole numbers over
100,000
• Compares whole numbers through the billions using the symbols <, >,
or =
• Rounds wholes numbers to the nearest billion
• Compares whole numbers to 100, using the symbols for 'less than',
'equal to', or 'greater than' (<, =, >)
• Orders whole numbers a million or greater using < or > symbols
• Compares whole numbers through the thousands using the symbols <,
>, or =
• Rounds 4-, 5-, and 6-digit whole numbers to the nearest hundred
• Represents a decimal to the hundredths place (e.g., three hundredths
= 0.03)
• Rounds 4-, 5-, and 6-digit whole numbers to the nearest thousand
• Compares and orders decimals past the thousandths place
• Rounds whole numbers to the nearest hundred thousand
• Rounds decimals to the nearest whole number
• Rounds wholes numbers to the nearest billion
• Rounds decimals to the nearest tenth
• Explains the rules for rounding
• Applies base ten place value concepts to solve problems using
decimals
• Rounds 2- and 3- digit whole numbers to the nearest ten
• Rounds 3-digit whole numbers to the nearest hundred
• Identifies whole numbers under 100 given place value terms (e.g., 3
tens and 4 ones = 34)
• Rounds 4-, 5-, and 6-digit whole numbers to the nearest ten
• Identifies the place value and value of each digit in whole numbers
through the thousands
• Writes equivalent forms of whole numbers using place value (e.g., 54
= 4 tens and 14 ones)
• Identifies the place value and value of each digit in whole numbers
through the hundred thousands
• Identifies the place value and value of each digit in whole numbers
through the billions
• Writes whole numbers in standard and expanded form through the
hundreds
• Writes whole numbers in standard and expanded form through the
hundred thousands
• Writes whole numbers in standard and expanded form through the
thousands
• Applies base ten place value concepts with whole numbers to solve
problems
• Rounds 4-, 5-, and 6-digit whole numbers to the nearest hundred
• Rounds 4-, 5-, and 6-digit whole numbers to the nearest ten thousand
• Writes whole numbers in standard and expanded form through the
hundred thousands
• Writes whole numbers using place value terms and vice versa
• Rounds decimals to the nearest whole number
Number and Operations in Base Ten
Number and Operations in Base Ten
Number and Operations in Base Ten
• Uses rounding to estimate answers to addition and subtraction
problems (whole numbers only)
• Uses rounding to estimate answers to addition and subtraction
problems (whole numbers only)
• Uses rounding to estimate answers to difficult multiplication and
division problems (whole numbers only)
• Adds two 3- and/or 4-digit numbers, with regrouping, with sums over
1000
• Adds multiple-digit numbers, with regrouping, with sums over 1000
• Subtracts numbers with 5 digits or more with regrouping
• Adds multiple-digit numbers with sums under 1000
• Instantly recalls basic multiplication and division facts in a table
• Adds multiple-digit numbers, with regrouping, with sums over 1000
• Performs mental computation with more than 4 addends
• Multiplies a 2-digit number by a 2-digit number with regrouping
• Adds multiple-digit numbers with sums under 1000
• Subtracts 3- or 4-digit numbers with regrouping
• Multiplies a 3-digit number by a 2-digit number with regrouping
• Subtracts 1-digit number from a 2-digit number with regrouping
• Subtracts numbers with 5 digits or more with regrouping
• Performs mental computation with multiplication
• Subtracts a 2-digit number from a 2-digit number, with regrouping
• Instantly recalls basic multiplication and division facts in a table
• Uses strategies for sums and differences with 2-digit numbers (e.g.,
decomposing, compatible, compensation, partial sums, counting on)
• Multiplies a 2-digit number by a 1-digit number with regrouping
• Uses multiplication strategies to explain computation (e.g., doubles, 9patterns, decomposing, partial products)
• Multiplies a 3- or 4-digit number by a 1-digit number
• Multiplies a 3-digit number by a 3-digit number
• Subtracts a 2-digit number from a 3-digit number with a single
regrouping
• Multiplies multiple 1-digit numbers
• Multiplies a 4- or more digit number by multiples of 100 or 1000
• Subtracts 3- or 4-digit numbers with regrouping
• Multiplies a 2-digit number by a 2-digit number with regrouping
• Multiplies multiple-digit numbers
• Performs mental subtraction with numbers under 1000
• Multiplies a 3-digit number by a 2-digit number with regrouping
• Subtracts multiple-digit numbers with no regrouping
• Performs mental computation with multiplication
• Divides a 2-digit number or a 3-digit number by a 1-digit number with a
remainder
• Divides a 4-digit number by a 1-digit number with no remainder
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.
Page 4-27
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
201 - 210
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
191 - 200
Number and Operations in Base Ten
Skills and Concepts to Develop (50% Probability*)
201 - 210
Number and Operations in Base Ten
Skills and Concepts to Introduce (27% Probability*)
211 - 220
Number and Operations in Base Ten
• Multiplies a 2- or 3-digit number by a 1-digit number with no regrouping
• Multiplies a 2- or 3-digit number by multiples of 10 or 100
• Divides a 3-digit number by a 2-digit number
• Multiplies a 2-digit number by a 1-digit number with regrouping
• Multiplies a 3-digit number by a 3-digit number
• Divides a 4-digit number by a 2-digit number
• Multiplies a 3- or 4-digit number by a 1-digit number
• Divides a 2-digit number by a 1-digit number with no remainder
• Multiplies a 2-digit number by a 2-digit number with no regrouping
• Adds decimals to the hundredths place in horizontal format (not same
number of digits)
• Performs mental computation with multiplication
• Divides a 2-digit number or a 3-digit number by a 1-digit number with a
remainder
• Divides a 2-digit number by a 1-digit number with no remainder
• Divides a 3-digit number by a 1-digit number with no remainder
• Adds decimals to the thousandths place horizontally with and without
regrouping
• Adds decimals to the hundredths place (same number of digits)
• Divides a 4-digit number by a 1-digit number with no remainder
• Adds decimals through the hundred-thousandths place
• Adds decimals to the hundredths place in vertical format (not same
number of digits)
• Divides a 3-digit number by a multiple of 10
• Multiplies a decimal by a decimal, vertical form (factors to tenths or
hundredths)
• Adds decimals to the thousandths place vertically with and without
regrouping
• Adds decimals to the thousandths place horizontally with and without
regrouping
• Subtracts decimals to the hundredths place (same number of digits)
with regrouping
• Subtracts decimals to the hundredths place (same number of digits)
with regrouping
• Multiplies a decimal by whole number
• Multiplies a decimal by whole number
Number and Operations - Fractions
Number and Operations - Fractions
Number and Operations - Fractions
• Uses models to add and subtract fractions and connect the actions to
algorithms
• Adds fractions with like denominators without reducing
• Adds fractions with like denominators without reducing
• Adds whole numbers and fractions
• Subtracts fractions with like denominators without reducing
• Uses models to add and subtract fractions and connect the actions to
algorithms
• Adds fractions with like denominators with reducing or converting to a
mixed fraction
• Divides a 4-digit number by a 2-digit number
• Multiplies a decimal by a decimal (factors to hundredths)
• Divides decimal by a whole number
• Divides decimal by a whole number
• Solves real-world 1-step problems involving addition and subtraction of
fractions with like denominators
• Adds fractions with unlike denominators without reducing
• Subtracts mixed fractions with like denominators with no regrouping
• Adds simple mixed fractions with unlike denominators (e.g., halves,
thirds, fourths, eighths)
• Represents 1/3 with a diagram or model
• Solves real-world 1-step problems involving addition and subtraction of
fractions with like denominators
• Subtracts simple fractions with unlike denominators without reducing
(e.g., halves, quarters, thirds, eighths)
• Represents fractions with denominators other than 2, 3, 4 with a
diagram or model
• Multiplies a fraction by a fraction without reducing to simplest form
(simple problem)
• Subtracts fractions with unlike denominators without reducing
• Identifies 1/4 from a region or set
• Identifies halves of a region using nonadjacent parts
• Subtracts mixed fractions with unlike denominators with no regrouping
• Identifies 1/3 from a region or set
• Identifies equivalent fractions using visual representations
• Identifies 2/3 or 3/3 from a region or set
• Expresses "1" in many different ways (e.g., 3/3, 4/4)
• Solves real-world problems involving addition and subtraction of
fractions where converting one denominator is necessary
• Identifies tenths from a region or set
• Converts a basic fractional numeral to lowest terms (e.g., halves,
thirds, quarters)
• Uses models to multiply and divide fractions and connect the actions
to algorithms
• Writes mixed numbers as improper fractions and improper fractions as
mixed numbers
• Multiplies a fraction by a fraction where reducing to simplest form is
necessary
• Compares fractions (e.g., common denominator, 1 in the numerator,
denominator is 2, 3, 4, 6, 8, 10)
• Multiplies a fraction by a whole number
• Solves real-world 1-step problems involving multiplication or division of
a whole number by a fraction
• Identifies a fraction (denominators other than 2, 3, 4, 8, 10) from a
region or set
• Identifies equivalent fractions using visual representations
• Matches numeric and visual representation of equivalent fractions
• Explains different interpretations of fractions (e.g., parts of a whole,
parts of a set, and division of whole numbers by whole numbers)
• Writes the missing number in a proportion using basic facts
• Subtracts fractions with like denominators without reducing
• Orders fractions on a number line
• Subtracts mixed fractions with like denominators with no regrouping
• Solves 1-step real-world problems involving fractions with
multiplication and division
• Explains different interpretations of fractions (e.g., parts of a whole,
parts of a set, and division of whole numbers by whole numbers)
• Solves 1-step problems involving proportions
• Writes a terminating decimal as a fraction or mixed number
• Identifies a fractions in lowest terms from a region or set
• Identifies equivalent fractions using visual representations
• Identifies eighths, reduced to lowest terms, from a region or set
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.
Page 4-28
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
201 - 210
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
191 - 200
Number and Operations - Fractions
Skills and Concepts to Develop (50% Probability*)
201 - 210
Number and Operations - Fractions
Skills and Concepts to Introduce (27% Probability*)
211 - 220
Number and Operations - Fractions
• Expresses the equivalent form of a fraction, decimal, and/or percent
(simple fraction)
• Determines simple equivalent fractions using multiples
• Writes the missing number in a proportion using basic facts
• Writes mixed numbers as improper fractions and improper fractions as
mixed numbers
• Converts fractions to lowest terms
• Compares fractions on a number line
• Compares fractions greater than or less than a given fraction using
visual representations
• Compares fractions and mixed numbers
• Compares fractions and mixed numbers using symbols
• Orders fractions on a number line
• Explains different interpretations of fractions (e.g., parts of a whole,
parts of a set, and division of whole numbers by whole numbers)
• Expresses a simple fraction as a decimal
• Writes a fraction or mixed number as a decimal when the denominator
is a multiple of 10
• Expresses the equivalent form of a fraction, decimal, and/or percent
(simple fraction)
New Vocabulary: billion, hundred million, quintillion, standard numeral,
trillion
New Vocabulary: biggest, expanded numeral
New Vocabulary: lowest term, lowest terms, reduce, triple
New Signs and Symbols: ¢ cent sign
New Signs and Symbols: ≠ not equal to
New Signs and Symbols: °F degrees Fahrenheit, > greater than, < less
than, long division symbol, R remainder
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.
Page 4-29
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
211 - 220
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
201 - 210
Understand Place Value, Counting, and Cardinality
Skills and Concepts to Develop (50% Probability*)
211 - 220
Understand Place Value, Counting, and Cardinality
Skills and Concepts to Introduce (27% Probability*)
221 - 230
Understand Place Value, Counting, and Cardinality
• Identifies whole numbers over 999 using base-10 blocks
• Predicts the relative size of the answer when computing with 10's,
100's, 1000's
• Multiplies a decimal by 10, 100, 1000
• Rounds 4-, 5-, and 6-digit whole numbers to the nearest hundred
• Determines the relative magnitude of whole numbers
• Identifies the numeral and written name for whole numbers over
100,000
• Rounds 4-, 5-, and 6-digit whole numbers to the nearest thousand
• Rounds whole numbers to the nearest million
• Rounds 4-, 5-, and 6-digit whole numbers to the nearest ten thousand
• Compares whole numbers through the billions using the symbols <, >,
or =
• Rounds wholes numbers to the nearest billion
• Writes equivalent forms of whole numbers using place value (numbers
100 or greater) (e.g., 253 = 2 hundreds, 5 tens, and 3 ones)
• Identifies the numeral and written name for whole numbers with a zero
between digits to the ten thousands place
• Orders whole numbers a million or greater using < or > symbols
• Rounds 4-, 5-, and 6-digit whole numbers to the nearest ten
• Writes whole numbers in standard and expanded form through the
hundred thousands
• Divides a decimal by 10, 100, 1000
• Writes whole numbers in standard and exponential form
• Represents a decimal to thousandths place (e.g., three thousandths =
0.003)
• Rounds 4-, 5-, and 6-digit whole numbers to the nearest hundred
• Represents a decimal to the hundredths place (e.g., three hundredths
= 0.03)
• Rounds 4-, 5-, and 6-digit whole numbers to the nearest thousand
• Compares and orders decimals past the thousandths place
• Rounds whole numbers to the nearest hundred thousand
• Rounds decimals to the nearest whole number
• Rounds wholes numbers to the nearest billion
• Rounds decimals to the nearest tenth
• Compares and orders decimals to the hundredths place (not same
number of digits after decimal)
• Explains the rules for rounding
• Applies base ten place value concepts to solve problems using
decimals
• Compares and orders decimals to the thousandths place (not same
number of digits after decimal)
• Writes equivalent forms of whole numbers using place value (e.g., 54 =
4 tens and 14 ones)
• Represents a decimal to the hundred thousandths place - (e.g., three
hundred thousandths = 0. 00003)
• Compares and orders decimals past the thousandths place
• Identifies the place value and value of each digit in whole numbers
through the billions
• Rounds decimals to the nearest hundredth
• Writes whole numbers in standard and expanded form through the
hundred thousands
• Identifies the place value and value of each digit to the hundredths and
thousandths
• Applies base ten place value concepts with whole numbers to solve
problems
• Applies base ten place value concepts to solve problems using
decimals
• Rounds decimals to nearest thousandth
• Writes whole numbers using place value terms and vice versa
• Rounds decimals to the nearest whole number
Number and Operations in Base Ten
Number and Operations in Base Ten
Number and Operations in Base Ten
• Uses rounding to estimate answers to addition and subtraction
problems (whole numbers only)
• Uses rounding to estimate answers to difficult multiplication and
division problems (whole numbers only)
• Multiplies multiple-digit numbers
• Adds multiple-digit numbers, with regrouping, with sums over 1000
• Subtracts numbers with 5 digits or more with regrouping
• Adds multiple-digit numbers with sums under 1000
• Instantly recalls basic multiplication and division facts in a table
• Adds decimals to the hundredths place in horizontal format (not same
number of digits)
• Performs mental computation with more than 4 addends
• Multiplies a 2-digit number by a 2-digit number with regrouping
• Adds decimals through the hundred-thousandths place
• Subtracts 3- or 4-digit numbers with regrouping
• Multiplies a 3-digit number by a 2-digit number with regrouping
• Subtracts decimals to the hundredths place (not same number of digits)
• Subtracts numbers with 5 digits or more with regrouping
• Performs mental computation with multiplication
• Subtracts a decimal from a whole number, horizontally
• Instantly recalls basic multiplication and division facts in a table
• Multiplies a 2-digit number by a 1-digit number with regrouping
• Uses multiplication strategies to explain computation (e.g., doubles, 9patterns, decomposing, partial products)
• Multiplies a decimal by a decimal, vertical form (factors to tenths or
hundredths)
• Multiplies a 3- or 4-digit number by a 1-digit number
• Multiplies a 3-digit number by a 3-digit number
• Multiplies a decimal by a decimal (factors to hundredths)
• Multiplies multiple 1-digit numbers
• Multiplies a 4- or more digit number by multiples of 100 or 1000
• Multiplies a decimal by a decimal (factors to thousandths)
• Multiplies a 2-digit number by a 2-digit number with regrouping
• Multiplies multiple-digit numbers
• Divides a decimal by a decimal
• Multiplies a 3-digit number by a 2-digit number with regrouping
• Divides a 2-digit number or a 3-digit number by a 1-digit number with a
remainder
• Performs mental computation with multiplication
• Divides a 4-digit number by a 2-digit number
• Divides a 4-digit number by a 1-digit number with no remainder
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.
Page 4-30
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
211 - 220
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
201 - 210
Number and Operations in Base Ten
Skills and Concepts to Develop (50% Probability*)
211 - 220
Number and Operations in Base Ten
• Multiplies a 2- or 3-digit number by multiples of 10 or 100
• Divides a 3-digit number by a 2-digit number
• Multiplies a 3-digit number by a 3-digit number
• Divides a 4-digit number by a 2-digit number
• Divides a 2-digit number by a 1-digit number with no remainder
• Adds decimals to the hundredths place in horizontal format (not same
number of digits)
• Divides a 2-digit number or a 3-digit number by a 1-digit number with a
remainder
• Divides a 3-digit number by a 1-digit number with no remainder
• Adds decimals to the thousandths place horizontally with and without
regrouping
• Divides a 4-digit number by a 1-digit number with no remainder
• Adds decimals through the hundred-thousandths place
• Divides a 3-digit number by a multiple of 10
• Multiplies a decimal by a decimal, vertical form (factors to tenths or
hundredths)
• Divides a 4-digit number by a 2-digit number
• Adds decimals to the thousandths place horizontally with and without
regrouping
Skills and Concepts to Introduce (27% Probability*)
221 - 230
Number and Operations in Base Ten
• Multiplies a decimal by a decimal (factors to hundredths)
• Divides decimal by a whole number
• Subtracts decimals to the hundredths place (same number of digits)
with regrouping
• Multiplies a decimal by whole number
• Divides decimal by a whole number
Number and Operations - Fractions
Number and Operations - Fractions
Number and Operations - Fractions
• Adds fractions with like denominators without reducing
• Adds fractions with like denominators without reducing
• Adds whole numbers and fractions
• Adds fractions with like denominators with reducing or converting to a
mixed fraction
• Adds fractions with like denominators with reducing or converting to a
mixed fraction
• Uses models to add and subtract fractions and connect the actions to
algorithms
• Adds fractions with unlike denominators without reducing
• Adds fractions with unlike denominators without reducing
• Adds fractions with unlike denominators with reducing or converting to
a mixed fraction
• Subtracts mixed fractions with like denominators with no regrouping
• Adds simple mixed fractions with unlike denominators (e.g., halves,
thirds, fourths, eighths)
• Solves real-world 1-step problems involving addition and subtraction of
fractions with like denominators
• Subtracts simple fractions with unlike denominators without reducing
(e.g., halves, quarters, thirds, eighths)
• Multiplies a fraction by a fraction without reducing to simplest form
(simple problem)
• Subtracts fractions with unlike denominators without reducing
• Adds mixed fractions where converting from improper fractions is
necessary
• Subtracts mixed fractions with like denominators with no regrouping
• Subtracts fractions with like denominators with reducing
• Identifies halves of a region using nonadjacent parts
• Subtracts mixed fractions with unlike denominators with no regrouping
• Subtracts fractions with unlike denominators without reducing
• Identifies equivalent fractions using visual representations
• Subtracts fractions with unlike denominators with reducing
• Expresses "1" in many different ways (e.g., 3/3, 4/4)
• Solves real-world problems involving addition and subtraction of
fractions where converting one denominator is necessary
• Converts a basic fractional numeral to lowest terms (e.g., halves,
thirds, quarters)
• Uses models to multiply and divide fractions and connect the actions
to algorithms
• Subtracts whole numbers, fractions, and mixed fractions
• Writes mixed numbers as improper fractions and improper fractions as
mixed numbers
• Multiplies a fraction by a fraction where reducing to simplest form is
necessary
• Compares fractions (e.g., common denominator, 1 in the numerator,
denominator is 2, 3, 4, 6, 8, 10)
• Multiplies a fraction by a whole number
• Solves real-world problems involving addition and subtraction of
fractions where converting one denominator is necessary
• Solves 1-step real-world problems involving fractions with
multiplication and division
• Uses models to multiply and divide fractions and connect the actions
to algorithms
• Explains different interpretations of fractions (e.g., parts of a whole,
parts of a set, and division of whole numbers by whole numbers)
• Solves 1-step problems involving proportions
• Multiplies a fraction by a fraction without reducing to simplest form
(complex problem)
• Writes a terminating decimal as a fraction or mixed number
• Identifies a fractions in lowest terms from a region or set
• Subtracts fractions with like denominators without reducing
• Orders fractions on a number line
• Identifies equivalent fractions using visual representations
• Identifies eighths, reduced to lowest terms, from a region or set
• Adds simple mixed fractions with unlike denominators (e.g., halves,
thirds, fourths, eighths)
• Subtracts mixed fractions with unlike denominators with no regrouping
• Subtracts whole numbers, fractions, and mixed fractions with
regrouping
• Multiplies a fraction by a fraction where reducing to simplest form is
necessary
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.
Page 4-31
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
211 - 220
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
201 - 210
Number and Operations - Fractions
Skills and Concepts to Develop (50% Probability*)
211 - 220
Number and Operations - Fractions
Skills and Concepts to Introduce (27% Probability*)
221 - 230
Number and Operations - Fractions
• Expresses the equivalent form of a fraction, decimal, and/or percent
(simple fraction)
• Determines simple equivalent fractions using multiples
• Multiplies a fraction by a whole number
• Converts fractions to lowest terms
• Multiplies mixed fractions
• Writes the missing number in a proportion using basic facts
• Writes mixed numbers as improper fractions and improper fractions as
mixed numbers
• Divides a mixed fraction by a fraction
• Compares fractions on a number line
• Solves 1-step real-world problems involving fractions with
multiplication and division
• Compares fractions greater than or less than a given fraction using
visual representations
• Solves 2- or more step real-world problems involving fractions with
multiplication and division
• Compares fractions and mixed numbers
• Compares fractions and mixed numbers using symbols
• Solves problems involving fractions (e.g., multiple operations,
conversions)
• Orders fractions on a number line
• Solves 1-step problems involving proportions
• Explains different interpretations of fractions (e.g., parts of a whole,
parts of a set, and division of whole numbers by whole numbers)
• Identifies a fractions in lowest terms from a region or set
• Expresses a simple fraction as a decimal
• Determines equivalent fractions using multiples
• Writes a fraction or mixed number as a decimal when the denominator
is a multiple of 10
• Compares fractions (e.g., comparing numerators and denominators)
• Expresses the equivalent form of a fraction, decimal, and/or percent
(simple fraction)
• Writes a decimal for a shaded region to the hundredths place
• Determines simple equivalent fractions using multiples
• Uses alternative algorithms to explain the meaning of "fraction"
• Writes a fraction or mixed number as a decimal when the denominator
is a multiple of 10
New Vocabulary: biggest, expanded numeral
New Vocabulary: lowest term, lowest terms, reduce, triple
New Vocabulary: short, ten million
New Signs and Symbols: ¢ cent sign
New Signs and Symbols: ≠ not equal to
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.
Page 4-32
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
221 - 230
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
211 - 220
Understand Place Value, Counting, and Cardinality
Skills and Concepts to Develop (50% Probability*)
221 - 230
Understand Place Value, Counting, and Cardinality
Skills and Concepts to Introduce (27% Probability*)
231 - 240
Understand Place Value, Counting, and Cardinality
• Predicts the relative size of the answer when computing with 10's,
100's, 1000's
• Multiplies a decimal by 10, 100, 1000
• Divides numbers by powers of 10
• Divides a decimal by 10, 100, 1000
• Multiplies a decimal by 10, 100, 1000
• Rounds 4-, 5-, and 6-digit whole numbers to the nearest hundred
• Determines the relative magnitude of whole numbers
• Divides a decimal by 10, 100, 1000
• Rounds 4-, 5-, and 6-digit whole numbers to the nearest thousand
• Rounds whole numbers to the nearest million
• Determines the relative magnitude of whole numbers
• Rounds 4-, 5-, and 6-digit whole numbers to the nearest ten thousand
• Writes equivalent forms of whole numbers using place value (numbers
100 or greater) (e.g., 253 = 2 hundreds, 5 tens, and 3 ones)
• Writes whole numbers in standard and exponential form
• Rounds wholes numbers to the nearest billion
• Writes whole numbers in standard and expanded form through the
hundred thousands
• Represents a decimal to the hundredths place (e.g., three hundredths
= 0.03)
• Compares and orders decimals past the thousandths place
• Rounds decimals to the nearest whole number
• Rounds decimals to the nearest hundredth
• Writes whole numbers in standard and exponential form
• Represents a decimal to thousandths place (e.g., three thousandths =
0.003)
• Represents a decimal to the hundred thousandths place - (e.g., three
hundred thousandths = 0. 00003)
• Rounds decimals to the nearest tenth
• Compares and orders decimals to the hundredths place (not same
number of digits after decimal)
• Applies base ten place value concepts to solve problems using
decimals
• Compares and orders decimals to the thousandths place (not same
number of digits after decimal)
• Compares and orders decimals past the thousandths place
• Rounds decimals to the nearest hundredth
• Rounds decimals to nearest thousandth
• Identifies the place value and value of each digit to the hundredths and
thousandths
• Applies base ten place value concepts to solve problems using
decimals
Number and Operations in Base Ten
Number and Operations in Base Ten
Number and Operations in Base Ten
• Uses rounding to estimate answers to difficult multiplication and
division problems (whole numbers only)
• Multiplies multiple-digit numbers
• Subtracts a decimal from a whole number, horizontally
• Divides a 4-digit number by a 2-digit number
• Divides a whole number by a decimal
• Subtracts numbers with 5 digits or more with regrouping
• Divides a decimal by a decimal
• Instantly recalls basic multiplication and division facts in a table
• Adds decimals to the hundredths place in horizontal format (not same
number of digits)
• Multiplies a 2-digit number by a 2-digit number with regrouping
• Adds decimals through the hundred-thousandths place
• Multiplies a 3-digit number by a 2-digit number with regrouping
• Subtracts decimals to the hundredths place (not same number of digits)
• Performs mental computation with multiplication
• Subtracts a decimal from a whole number, horizontally
• Uses multiplication strategies to explain computation (e.g., doubles, 9patterns, decomposing, partial products)
• Multiplies a decimal by a decimal, vertical form (factors to tenths or
hundredths)
• Multiplies a 3-digit number by a 3-digit number
• Multiplies a decimal by a decimal (factors to hundredths)
• Multiplies a 4- or more digit number by multiples of 100 or 1000
• Multiplies a decimal by a decimal (factors to thousandths)
• Multiplies multiple-digit numbers
• Divides a decimal by a decimal
• Divides a 2-digit number or a 3-digit number by a 1-digit number with a
remainder
• Divides a 4-digit number by a 1-digit number with no remainder
• Divides a 3-digit number by a 2-digit number
• Divides a 4-digit number by a 2-digit 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.
Page 4-33
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
221 - 230
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
211 - 220
Number and Operations in Base Ten
Skills and Concepts to Develop (50% Probability*)
221 - 230
Number and Operations in Base Ten
Skills and Concepts to Introduce (27% Probability*)
231 - 240
Number and Operations in Base Ten
Number and Operations - Fractions
Number and Operations - Fractions
Number and Operations - Fractions
• Adds fractions with like denominators without reducing
• Adds fractions with like denominators with reducing or converting to a
mixed fraction
• Adds fractions with unlike denominators with reducing or converting to
a mixed fraction
• Adds fractions with unlike denominators without reducing
• Adds simple mixed fractions with unlike denominators (e.g., halves,
thirds, fourths, eighths)
• Adds decimals to the hundredths place in horizontal format (not same
number of digits)
• Adds decimals to the thousandths place horizontally with and without
regrouping
• Adds decimals through the hundred-thousandths place
• Multiplies a decimal by a decimal, vertical form (factors to tenths or
hundredths)
• Multiplies a decimal by a decimal (factors to hundredths)
• Divides decimal by a whole number
• Adds fractions with like denominators with reducing or converting to a
mixed fraction
• Adds fractions with unlike denominators without reducing
• Adds simple mixed fractions with unlike denominators (e.g., halves,
thirds, fourths, eighths)
• Subtracts simple fractions with unlike denominators without reducing
(e.g., halves, quarters, thirds, eighths)
• Adds fractions with unlike denominators with reducing or converting to
a mixed fraction
• Adds simple mixed fractions with unlike denominators (e.g., halves,
thirds, fourths, eighths)
• Adds mixed fractions where converting from improper fractions is
necessary
• Subtracts whole numbers, fractions, and mixed fractions
• Subtracts fractions with unlike denominators without reducing
• Adds mixed fractions where converting from improper fractions is
necessary
• Subtracts whole numbers, fractions, and mixed fractions with
regrouping
• Subtracts mixed fractions with like denominators with no regrouping
• Subtracts fractions with like denominators with reducing
• Subtracts mixed fractions with unlike denominators with no regrouping
• Subtracts fractions with unlike denominators without reducing
• Solves real-world problems involving addition and subtraction of
fractions where converting both denominators is necessary
• Solves real-world problems involving addition and subtraction of
fractions where converting one denominator is necessary
• Subtracts fractions with unlike denominators with reducing
• Uses models to multiply and divide fractions and connect the actions to
algorithms
• Subtracts whole numbers, fractions, and mixed fractions
• Multiplies a fraction by a fraction where reducing to simplest form is
necessary
• Subtracts mixed fractions with unlike denominators with no regrouping
• Subtracts whole numbers, fractions, and mixed fractions with
regrouping
• Multiplies a fraction by a whole number
• Solves real-world problems involving addition and subtraction of
fractions where converting one denominator is necessary
• Solves 1-step real-world problems involving fractions with multiplication
and division
• Uses models to multiply and divide fractions and connect the actions
to algorithms
• Solves 1-step problems involving proportions
• Multiplies a fraction by a fraction without reducing to simplest form
(complex problem)
• Identifies equivalent fractions using visual representations
• Identifies a fractions in lowest terms from a region or set
• Identifies eighths, reduced to lowest terms, from a region or set
• Determines simple equivalent fractions using multiples
• Converts fractions to lowest terms
• Writes mixed numbers as improper fractions and improper fractions as
mixed numbers
• Compares fractions on a number line
• Multiplies a fraction by a fraction where reducing to simplest form is
necessary
• Uses models to multiply and divide fractions and connect the actions
to algorithms
• Multiplies mixed fractions
• Uses models to multiply and divide fractions and mixed fractions and
connect the actions to algorithms
• Divides a fraction by a whole number
• Divides a whole number by a fraction
• Divides a mixed fraction by a fraction
• Solves 2- or more step real-world problems involving fractions with
multiplication and division
• Solves problems involving fractions (e.g., multiple operations,
conversions)
• Compares fractions (e.g., comparing numerators and denominators)
• Multiplies a fraction by a whole number
• Writes a fraction as a decimal and vice versa
• Multiplies mixed fractions
• Compares and orders decimal and fractional coordinates on a number
line
• Divides a mixed fraction by a fraction
• Solves 1-step real-world problems involving fractions with
multiplication and division
• Solves 2- or more step real-world problems involving fractions with
multiplication and division
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.
Page 4-34
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
221 - 230
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
211 - 220
Number and Operations - Fractions
Skills and Concepts to Develop (50% Probability*)
221 - 230
Number and Operations - Fractions
• Compares fractions greater than or less than a given fraction using
visual representations
• Solves problems involving fractions (e.g., multiple operations,
conversions)
• Compares fractions and mixed numbers
• Solves 1-step problems involving proportions
• Compares fractions and mixed numbers using symbols
• Identifies a fractions in lowest terms from a region or set
• Orders fractions on a number line
• Determines simple equivalent fractions using multiples
• Explains different interpretations of fractions (e.g., parts of a whole,
parts of a set, and division of whole numbers by whole numbers)
• Determines equivalent fractions using multiples
• Expresses a simple fraction as a decimal
• Uses alternative algorithms to explain the meaning of "fraction"
• Writes a fraction or mixed number as a decimal when the denominator
is a multiple of 10
• Writes a decimal for a shaded region to the hundredths place
• Expresses the equivalent form of a fraction, decimal, and/or percent
(simple fraction)
Skills and Concepts to Introduce (27% Probability*)
231 - 240
Number and Operations - Fractions
• Compares fractions (e.g., comparing numerators and denominators)
• Writes a fraction or mixed number as a decimal when the denominator
is a multiple of 10
New Vocabulary: lowest term, lowest terms, reduce, triple
New Vocabulary: short, ten million
New Vocabulary: None
New Signs and Symbols: ≠ not equal to
New Signs and Symbols: None
New Signs and Symbols: ÷ division
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.
Page 4-35
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
231 - 240
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
221 - 230
Understand Place Value, Counting, and Cardinality
Skills and Concepts to Develop (50% Probability*)
231 - 240
Understand Place Value, Counting, and Cardinality
• Multiplies a decimal by 10, 100, 1000
• Divides numbers by powers of 10
• Divides a decimal by 10, 100, 1000
• Multiplies a decimal by 10, 100, 1000
• Determines the relative magnitude of whole numbers
• Divides a decimal by 10, 100, 1000
• Rounds whole numbers to the nearest million
• Determines the relative magnitude of whole numbers
• Writes equivalent forms of whole numbers using place value (numbers
100 or greater) (e.g., 253 = 2 hundreds, 5 tens, and 3 ones)
• Writes whole numbers in standard and exponential form
Skills and Concepts to Introduce (27% Probability*)
> 240
Understand Place Value, Counting, and Cardinality
• Rounds decimals to the nearest hundredth
• Writes whole numbers in standard and exponential form
• Represents a decimal to thousandths place (e.g., three thousandths =
0.003)
• Represents a decimal to the hundred thousandths place - (e.g., three
hundred thousandths = 0. 00003)
• Compares and orders decimals to the hundredths place (not same
number of digits after decimal)
• Compares and orders decimals to the thousandths place (not same
number of digits after decimal)
• Compares and orders decimals past the thousandths place
• Rounds decimals to the nearest hundredth
• Rounds decimals to nearest thousandth
• Identifies the place value and value of each digit to the hundredths and
thousandths
• Applies base ten place value concepts to solve problems using
decimals
Number and Operations in Base Ten
Number and Operations in Base Ten
• Multiplies multiple-digit numbers
• Subtracts a decimal from a whole number, horizontally
• Divides a 4-digit number by a 2-digit number
• Divides a whole number by a decimal
• Adds decimals to the hundredths place in horizontal format (not same
number of digits)
• Divides a decimal by a decimal
Number and Operations in Base Ten
• Adds decimals through the hundred-thousandths place
• Subtracts decimals to the hundredths place (not same number of digits)
• Subtracts a decimal from a whole number, horizontally
• Multiplies a decimal by a decimal, vertical form (factors to tenths or
hundredths)
• Multiplies a decimal by a decimal (factors to hundredths)
• Multiplies a decimal by a decimal (factors to thousandths)
• Divides a decimal by a decimal
Number and Operations - Fractions
Number and Operations - Fractions
Number and Operations - Fractions
• Adds fractions with like denominators with reducing or converting to a
mixed fraction
• Adds fractions with unlike denominators with reducing or converting to
a mixed fraction
• Solves open sentences with fractions
• Adds fractions with unlike denominators without reducing
• Adds simple mixed fractions with unlike denominators (e.g., halves,
thirds, fourths, eighths)
• Identifies the least common multiple of whole 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.
Page 4-36
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
231 - 240
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
221 - 230
Number and Operations - Fractions
Skills and Concepts to Develop (50% Probability*)
231 - 240
Number and Operations - Fractions
• Adds fractions with unlike denominators with reducing or converting to
a mixed fraction
• Adds mixed fractions where converting from improper fractions is
necessary
• Adds simple mixed fractions with unlike denominators (e.g., halves,
thirds, fourths, eighths)
• Subtracts whole numbers, fractions, and mixed fractions
• Adds mixed fractions where converting from improper fractions is
necessary
• Subtracts fractions with like denominators with reducing
• Subtracts fractions with unlike denominators without reducing
• Subtracts whole numbers, fractions, and mixed fractions with
regrouping
• Solves real-world problems involving addition and subtraction of
fractions where converting both denominators is necessary
• Subtracts fractions with unlike denominators with reducing
• Uses models to multiply and divide fractions and connect the actions
to algorithms
• Subtracts mixed fractions with unlike denominators with no regrouping
• Multiplies mixed fractions
• Subtracts whole numbers, fractions, and mixed fractions
• Uses models to multiply and divide fractions and mixed fractions and
connect the actions to algorithms
• Subtracts whole numbers, fractions, and mixed fractions with
regrouping
• Divides a fraction by a whole number
• Solves real-world problems involving addition and subtraction of
fractions where converting one denominator is necessary
• Divides a whole number by a fraction
• Uses models to multiply and divide fractions and connect the actions to
algorithms
• Solves 2- or more step real-world problems involving fractions with
multiplication and division
• Multiplies a fraction by a fraction without reducing to simplest form
(complex problem)
• Solves problems involving fractions (e.g., multiple operations,
conversions)
• Multiplies a fraction by a fraction where reducing to simplest form is
necessary
• Compares fractions (e.g., comparing numerators and denominators)
• Multiplies a fraction by a whole number
• Compares and orders decimal and fractional coordinates on a number
line
• Multiplies mixed fractions
Skills and Concepts to Introduce (27% Probability*)
> 240
Number and Operations - Fractions
• Divides a mixed fraction by a fraction
• Writes a fraction as a decimal and vice versa
• Divides a mixed fraction by a fraction
• Solves 1-step real-world problems involving fractions with multiplication
and division
• Solves 2- or more step real-world problems involving fractions with
multiplication and division
• Solves problems involving fractions (e.g., multiple operations,
conversions)
• Solves 1-step problems involving proportions
• Identifies a fractions in lowest terms from a region or set
• Determines simple equivalent fractions using multiples
• Determines equivalent fractions using multiples
• Compares fractions (e.g., comparing numerators and denominators)
• Uses alternative algorithms to explain the meaning of "fraction"
• Writes a decimal for a shaded region to the hundredths place
• Writes a fraction or mixed number as a decimal when the denominator
is a multiple of 10
New Vocabulary: short, ten million
New Vocabulary: None
New Vocabulary: None
New Signs and Symbols: None
New Signs and Symbols: ÷ division
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.
Page 4-37
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
> 240
Goal: Number and Operations
Skills and concepts to Enhance (73% Probability*)
231 - 240
Understand Place Value, Counting, and Cardinality
Skills and Concepts to Develop (50% Probability*)
> 240
Understand Place Value, Counting, and Cardinality
• Divides numbers by powers of 10
• Multiplies a decimal by 10, 100, 1000
• Divides a decimal by 10, 100, 1000
• Determines the relative magnitude of whole numbers
• Writes whole numbers in standard and exponential form
• Rounds decimals to the nearest hundredth
Number and Operations in Base Ten
Number and Operations in Base Ten
• Subtracts a decimal from a whole number, horizontally
• Divides a whole number by a decimal
• Divides a decimal by a decimal
Number and Operations - Fractions
Number and Operations - Fractions
• Adds fractions with unlike denominators with reducing or converting to
a mixed fraction
• Solves open sentences with fractions
• Adds simple mixed fractions with unlike denominators (e.g., halves,
thirds, fourths, eighths)
• Identifies the least common multiple of whole numbers
• Adds mixed fractions where converting from improper fractions is
necessary
• Subtracts whole numbers, fractions, and mixed fractions
• Subtracts whole numbers, fractions, and mixed fractions with
regrouping
• Solves real-world problems involving addition and subtraction of
fractions where converting both denominators is necessary
• Uses models to multiply and divide fractions and connect the actions to
algorithms
• Multiplies mixed fractions
• Uses models to multiply and divide fractions and mixed fractions and
connect the actions to algorithms
• Divides a fraction by a whole number
• Divides a whole number by a fraction
• Divides a mixed fraction by a fraction
• Solves 2- or more step real-world problems involving fractions with
multiplication and division
• Solves problems involving fractions (e.g., multiple operations,
conversions)
• Compares fractions (e.g., comparing numerators and denominators)
• Writes a fraction as a decimal and vice versa
• Compares and orders decimal and fractional coordinates on a number
line
New Vocabulary: None
New Vocabulary: None
New Signs and Symbols: ÷ division
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.
Page 4-38
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
< 161
Goal: Measurement and Data
Skills and Concepts to Develop (50% Probability*)
< 161
Geometric Measurement and Problem Solving
Skills and Concepts to Introduce (27% Probability*)
161 - 170
Geometric Measurement and Problem Solving
• Compares objects (shorter, longer)
• Estimates and measures length of an object to the nearest inch using
a picture of a ruler
• Measures length with customary measures to the inch mark
• Measures length with metric measures to the centimeter mark
• Identifies time of day (e.g., morning, afternoon)
• Tells time to the nearest hour
• Tells time to the nearest half hour
Represent and Interpret Data
Represent and Interpret Data
• Reads a simple pictograph - comparisons (e.g., largest smallest, most
often, least often)
• Reads a chart or table - numbers
• Reads a simple pictograph - comparisons (e.g., largest smallest, most
often, least often)
• Displays data appropriately - bar graph - scale is 1 to 1
• Reads a simple bar graph - comparisons (e.g., largest, smallest, most
often, least often)
• Compares data from simple graphs (e.g., largest, smallest, most often,
least often)
New Vocabulary: None
New Vocabulary: dollar, longest, shortest
New Signs and Symbols: None
New Signs and Symbols: = is equal to, : used with 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.
Page 4-39
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
161 - 170
Goal: Measurement and Data
Skills and concepts to Enhance (73% Probability*)
< 161
Geometric Measurement and Problem Solving
Skills and Concepts to Develop (50% Probability*)
161 - 170
Geometric Measurement and Problem Solving
Skills and Concepts to Introduce (27% Probability*)
171 - 180
Geometric Measurement and Problem Solving
• Compares objects (shorter, longer)
• Identifies the value of a collection of coins to $1.00 (with pictures of
coins)
• Estimates and measures length of an object to the nearest inch using
a picture of a ruler
• Measures length with customary measures to the inch mark
• Measures length with metric measures to the centimeter mark
• Identifies time of day (e.g., morning, afternoon)
• Tells time to the nearest hour
• Tells time to the nearest half hour
• Identifies the value of a collection of coins and bills to $10.00 by
"counting on" (with picture of money)
• Estimates and measures length of an object to the nearest centimeter
using a picture of a ruler
• Measures length with customary measures to the inch mark
• Tells time to the nearest hour
• Tells time to the nearest half hour
• Tells time to the nearest 5 minutes
• Computes simple conversions among units of time (minutes in an
hour, half hour, quarter hour)
• Connects money with place value
• Determines the area of irregular shapes by counting square units
Represent and Interpret Data
Represent and Interpret Data
Represent and Interpret Data
• Reads a simple pictograph - comparisons (e.g., largest smallest, most
often, least often)
• Reads a chart or table - numbers
• Reads a chart or table - comparisons
• Reads a simple pictograph - comparisons (e.g., largest smallest, most
often, least often)
• Reads a chart or table - numbers
• Displays data appropriately - bar graph - scale is 1 to 1
• Reads a simple pictograph - comparisons (e.g., largest smallest, most
often, least often)
• Reads a simple bar graph - comparisons (e.g., largest, smallest, most
often, least often)
• Compares data from simple graphs (e.g., largest, smallest, most often,
least often)
• Interprets simple graphs or tables
• Solves simple problems based on data from pictographs
• Reads a simple bar graph - comparisons (e.g., largest, smallest, most
often, least often)
• Reads a simple bar graph - numbers (e.g., how many)
• Solves simple problems based on data from bar graphs
• Compares data from simple graphs (e.g., largest, smallest, most often,
least often)
New Vocabulary: None
New Vocabulary: dollar, longest, shortest
New Vocabulary: morning
New Signs and Symbols: None
New Signs and Symbols: = is equal to, : used with time
New Signs and Symbols: a.m., ¢ cent sign, $ dollar sign, p.m.
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.
Page 4-40
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
171 - 180
Goal: Measurement and Data
Skills and concepts to Enhance (73% Probability*)
161 - 170
Geometric Measurement and Problem Solving
Skills and Concepts to Develop (50% Probability*)
171 - 180
Geometric Measurement and Problem Solving
Skills and Concepts to Introduce (27% Probability*)
181 - 190
Geometric Measurement and Problem Solving
• Compares objects (shorter, longer)
• Identifies the value of a collection of coins to $1.00 (with pictures of
coins)
• Identifies the value of a collection of coins to $1.00 (without picture of
coins)
• Identifies the value of a collection of coins and bills to $10.00 by
"counting on" (with picture of money)
• Adds money with regrouping
• Estimates and measures length of an object to the nearest inch using a
picture of a ruler
• Measures length with customary measures to the inch mark
• Measures length with metric measures to the centimeter mark
• Identifies time of day (e.g., morning, afternoon)
• Tells time to the nearest hour
• Tells time to the nearest half hour
• Estimates and measures length of an object to the nearest centimeter
using a picture of a ruler
• Identifies the value of a collection of coins and bills to $10.00 by
"counting on" (with picture of money)
• Finds equivalent combinations of coins with the same value
• Measures length with customary measures to the inch mark
• Combines a collection of coins and identifies the correct notation
• Tells time to the nearest hour
• Makes change to $1.00 by "counting on" or subtracting
• Tells time to the nearest half hour
• Tells time to the nearest 5 minutes
• Computes with dollars and cents up to and including $5.00 and
converts to decimals (addition/subtraction only)
• Computes simple conversions among units of time (minutes in an
hour, half hour, quarter hour)
• Computes 1 operation on addition or subtraction real-world problems
involving money up to $5.00
• Connects money with place value
• Selects and uses the appropriate type and size of unit in customary
system (length)
• Determines the area of irregular shapes by counting square units
• Uses a variety of non-standard units to measure the same length
• Determines more capacity or less capacity
• Identifies the correct time, given the words, and vice versa
• Determines elapsed clock time
• Determines elapsed time under 1 hour or to the hour
• Determines elapsed time involving whole hours, whole days, whole
years
• Tells time to the nearest 5 minutes
• Computes simple conversions among units of time (days, weeks)
• Determines the perimeter of a figure where all sides are labeled
• Determines the area of irregular shapes by counting square units
Represent and Interpret Data
Represent and Interpret Data
Represent and Interpret Data
• Reads a chart or table - numbers
• Reads a chart or table - comparisons
• Measures length with customary measures to the half-inch mark
• Reads a simple pictograph - comparisons (e.g., largest smallest, most
often, least often)
• Reads a chart or table - numbers
• Interprets simple graphs or tables
• Interprets simple graphs or tables
• Reads and interprets data from a pictograph
• Displays data appropriately - bar graph - scale is 1 to 1
• Reads a simple pictograph - comparisons (e.g., largest smallest, most
often, least often)
• Solves simple problems based on data from pictographs
• Reads a simple bar graph - comparisons (e.g., largest, smallest, most
often, least often)
• Solves simple problems based on data from pictographs
• Compares data from simple graphs (e.g., largest, smallest, most often,
least often)
• Reads a simple bar graph - comparisons (e.g., largest, smallest, most
often, least often)
• Reads a simple bar graph - numbers (e.g., how many)
• Reads a simple bar graph - numbers (e.g., how many)
• Interprets a simple bar graph - calculation required
• Solves simple problems based on data from bar graphs
• Solves simple problems based on data from bar graphs
• Compares data from simple graphs (e.g., largest, smallest, most often,
least often)
• Reads data in a line graph - no calculations
• Reads a simple bar graph - comparisons (e.g., largest, smallest, most
often, least often)
• Reads and interprets data from a bar graph
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.
Page 4-41
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
171 - 180
Goal: Measurement and Data
Skills and concepts to Enhance (73% Probability*)
161 - 170
New Vocabulary: dollar, longest, shortest
Skills and Concepts to Develop (50% Probability*)
171 - 180
New Vocabulary: morning
New Signs and Symbols: = is equal to, : used with time
New Signs and Symbols: a.m., ¢ cent sign, $ dollar sign, p.m.
Skills and Concepts to Introduce (27% Probability*)
181 - 190
New Vocabulary: changed, clock, estimation, half past, how much time,
left over, lowest, millimeter, noon, o'clock, pennies, quarter past, quarter
to, what time
New Signs and Symbols: : used with time, : used with 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.
Page 4-42
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
181 - 190
Goal: Measurement and Data
Skills and concepts to Enhance (73% Probability*)
171 - 180
Geometric Measurement and Problem Solving
Skills and Concepts to Develop (50% Probability*)
181 - 190
Geometric Measurement and Problem Solving
Skills and Concepts to Introduce (27% Probability*)
191 - 200
Geometric Measurement and Problem Solving
• Identifies the value of a collection of coins to $1.00 (with pictures of
coins)
• Identifies the value of a collection of coins to $1.00 (without picture of
coins)
• Identifies the value of a collection of coins to $1.00 (without picture of
coins)
• Identifies the value of a collection of coins and bills to $10.00 by
"counting on" (with picture of money)
• Adds money with regrouping
• Adds money with regrouping
• Identifies the value of a collection of coins and bills to $10.00 by
"counting on" (with picture of money)
• Identifies the value of a collection of coins and bills to $10.00 by
"counting on" (without picture of money)
• Estimates and measures length of an object to the nearest centimeter
using a picture of a ruler
• Finds equivalent combinations of coins with the same value
• Finds equivalent combinations of coins with the same value
• Measures length with customary measures to the inch mark
• Combines a collection of coins and identifies the correct notation
• Makes change to $1.00 by "counting on" or subtracting
• Tells time to the nearest hour
• Makes change to $1.00 by "counting on" or subtracting
• Tells time to the nearest half hour
• Solves real-world problems involving decimals (not money) using
addition and subtraction
• Tells time to the nearest 5 minutes
• Computes with dollars and cents up to and including $5.00 and
converts to decimals (addition/subtraction only)
• Computes simple conversions among units of time (minutes in an hour,
half hour, quarter hour)
• Computes 1 operation on addition or subtraction real-world problems
involving money up to $5.00
• Connects money with place value
• Selects and uses the appropriate type and size of unit in customary
system (length)
• Determines the area of irregular shapes by counting square units
• Uses a variety of non-standard units to measure the same length
• Determines more capacity or less capacity
• Identifies the correct time, given the words, and vice versa
• Determines elapsed clock time
• Computes with dollars and cents up to and including $5.00 and
converts to decimals (addition/subtraction only)
• Computes 1 operation on real-world problems involving money over
$5.00 (addition/subtraction only)
• Computes half price (multiplication/division)
• Computes with dollars and cents up to and including $5.00 and
converts to decimals (multiplication/division)
• Computes 1 operation on real-world problems involving money over
$5.00 (multiplication/division)
• Determines elapsed time under 1 hour or to the hour
• Selects and uses the appropriate type and size of unit in customary
system (length)
• Determines elapsed time involving whole hours, whole days, whole
years
• Computes basic operations with units of weight/mass
• Tells time to the nearest 5 minutes
• Computes simple conversions among units of time (days, weeks)
• Determines the perimeter of a figure where all sides are labeled
• Determines the area of irregular shapes by counting square units
• Converts between cups and pints
• Converts between cups, pints, and quarts
• Identifies the correct time, given the words, and vice versa
• Determines elapsed clock time
• Tells time to the nearest quarter hour
• Determines elapsed time involving whole hours, whole days, whole
years
• Tells time to the nearest 1 minute
• Computes simple conversions among units of time (minutes, hours)
• Solves simple problems involving elapsed time, with the conversion of
hours
• Solves simple problems involving miles/kilometers per hour
• Determines the perimeter of a figure where all sides are labeled
• Determines the perimeter of a figure where some sides are labeled
• Solves simple problems involving the perimeter of squares, rectangles,
or triangles
• Estimates the area of rectangles using square units
Represent and Interpret Data
Represent and Interpret Data
Represent and Interpret Data
• Reads a chart or table - comparisons
• Measures length with customary measures to the half-inch mark
• Reads and interprets data from a pictograph
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.
Page 4-43
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
181 - 190
Goal: Measurement and Data
Skills and concepts to Enhance (73% Probability*)
171 - 180
Represent and Interpret Data
Skills and Concepts to Develop (50% Probability*)
181 - 190
Represent and Interpret Data
Skills and Concepts to Introduce (27% Probability*)
191 - 200
Represent and Interpret Data
• Reads a chart or table - numbers
• Interprets simple graphs or tables
• Interprets a pictograph - calculation required
• Interprets simple graphs or tables
• Reads and interprets data from a pictograph
• Reads and interprets data from a bar graph
• Reads a simple pictograph - comparisons (e.g., largest smallest, most
often, least often)
• Solves simple problems based on data from pictographs
• Reads and interprets dual bar graphs
• Reads a simple bar graph - comparisons (e.g., largest, smallest, most
often, least often)
• Interprets a simple bar graph - calculation required
• Solves simple problems based on data from pictographs
• Reads a simple bar graph - comparisons (e.g., largest, smallest, most
often, least often)
• Reads a simple bar graph - numbers (e.g., how many)
• Reads a simple bar graph - numbers (e.g., how many)
• Interprets a simple bar graph - calculation required
• Solves simple problems based on data from bar graphs
• Solves simple problems based on data from bar graphs
• Compares data from simple graphs (e.g., largest, smallest, most often,
least often)
• Reads data in a line graph - no calculations
New Vocabulary: morning
New Signs and Symbols: a.m., ¢ cent sign, $ dollar sign, p.m.
• Reads data in a line graph - no calculations
• Reads and interprets data from a bar graph
New Vocabulary: changed, clock, estimation, half past, how much time,
left over, lowest, millimeter, noon, o'clock, pennies, quarter past, quarter
to, what time
New Vocabulary: decade, deposit, longer, miles per hour
New Signs and Symbols: °F degrees Fahrenheit, ft feet, g gram, in. inch,
lb pound, m meter/metre, min minute, yd yard
New Signs and Symbols: : used with time, : used with 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.
Page 4-44
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
191 - 200
Goal: Measurement and Data
Skills and concepts to Enhance (73% Probability*)
181 - 190
Geometric Measurement and Problem Solving
Skills and Concepts to Develop (50% Probability*)
191 - 200
Geometric Measurement and Problem Solving
Skills and Concepts to Introduce (27% Probability*)
201 - 210
Geometric Measurement and Problem Solving
• Identifies the value of a collection of coins to $1.00 (without picture of
coins)
• Identifies the value of a collection of coins to $1.00 (without picture of
coins)
• Computes the value of multiple bills and coins (addition/subtraction
only)
• Adds money with regrouping
• Adds money with regrouping
• Identifies the value of a collection of coins and bills to $10.00 by
"counting on" (with picture of money)
• Identifies the value of a collection of coins and bills to $10.00 by
"counting on" (without picture of money)
• Computes with dollars and cents up to and including $5.00 and
converts to decimals (multiplication/division)
• Finds equivalent combinations of coins with the same value
• Finds equivalent combinations of coins with the same value
• Combines a collection of coins and identifies the correct notation
• Makes change to $1.00 by "counting on" or subtracting
• Makes change to $1.00 by "counting on" or subtracting
• Solves real-world problems involving decimals (not money) using
addition and subtraction
• Computes with dollars and cents up to and including $5.00 and
converts to decimals (addition/subtraction only)
• Computes 1 operation on addition or subtraction real-world problems
involving money up to $5.00
• Computes with dollars and cents up to and including $5.00 and
converts to decimals (addition/subtraction only)
• Computes addition and subtraction on multiple-step real-world
problems involving money
• Computes money problems with multiple operations (addition/
subtraction only)
• Computes addition, subtraction, multiplication, and division on multiplestep, real-world problems involving money
• Uses the appropriate unit of measure for length
• Computes 1 operation on real-world problems involving money over
$5.00 (addition/subtraction only)
• Knows the approximate size of a yard
• Computes half price (multiplication/division)
• Converts between inches and feet
• Computes with dollars and cents up to and including $5.00 and
converts to decimals (multiplication/division)
• Knows the approximate size of a pound
• Computes 1 operation on real-world problems involving money over
$5.00 (multiplication/division)
• Converts between cups and pints
• Determines elapsed time under 1 hour or to the hour
• Selects and uses the appropriate type and size of unit in customary
system (length)
• Computes simple conversions among units of time (hours, days)
• Determines elapsed time involving whole hours, whole days, whole
years
• Computes basic operations with units of weight/mass
• Computes more difficult conversions among units of time
• Converts between cups and pints
• Solves problems involving measurement of time
• Converts between cups, pints, and quarts
• Applies dimensional analysis to simple real-world problems (time)
• Identifies the correct time, given the words, and vice versa
• Solves simple problems involving elapsed time, with the conversion of
hours
• Selects and uses the appropriate type and size of unit in customary
system (length)
• Uses a variety of non-standard units to measure the same length
• Determines more capacity or less capacity
• Identifies the correct time, given the words, and vice versa
• Determines elapsed clock time
• Tells time to the nearest 5 minutes
• Computes simple conversions among units of time (days, weeks)
• Determines the perimeter of a figure where all sides are labeled
• Determines the area of irregular shapes by counting square units
• Determines elapsed clock time
• Tells time to the nearest quarter hour
• Determines elapsed time involving whole hours, whole days, whole
years
• Tells time to the nearest 1 minute
• Computes simple conversions among units of time (minutes, hours)
• Solves simple problems involving elapsed time, with the conversion of
hours
• Measures length to the nearest centimeter
• Knows the approximate size of a gram
• Converts between cups, pints, and quarts
• Solves simple problems involving miles per gallon
• Solves simple problems involving miles/kilometers per hour
• Estimates the measure of acute, right, and obtuse angles using 45 and
90 degrees as referents
• Determines the perimeter of a figure where some sides are labeled
• Estimates the area of rectangles using square units
• Determines the area of irregular shapes with partial square units
• Solves simple problems involving miles/kilometers per hour
• Identifies situations where it is appropriate to calculate area
• Determines the perimeter of a figure where all sides are labeled
• Estimates and finds volume of a figure using cubic units
• Determines the perimeter of a figure where some sides are labeled
• Uses basic indirect methods to estimate measurements (grids for area
of irregular figures)
• Solves simple problems involving the perimeter of squares, rectangles,
or triangles
• Estimates the area of rectangles using square units
Represent and Interpret Data
Represent and Interpret Data
Represent and Interpret Data
• Measures length with customary measures to the half-inch mark
• Reads and interprets data from a pictograph
• Solves problems using pictographs
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.
Page 4-45
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
191 - 200
Goal: Measurement and Data
Skills and concepts to Enhance (73% Probability*)
181 - 190
Represent and Interpret Data
Skills and Concepts to Develop (50% Probability*)
191 - 200
Represent and Interpret Data
Skills and Concepts to Introduce (27% Probability*)
201 - 210
Represent and Interpret Data
• Interprets simple graphs or tables
• Interprets a pictograph - calculation required
• Organizes data to create simple bar graphs
• Reads and interprets data from a pictograph
• Reads and interprets data from a bar graph
• Solves problems using bar graphs
• Solves simple problems based on data from pictographs
• Reads and interprets dual bar graphs
• Solves problems using dual bar graphs
• Reads a simple bar graph - comparisons (e.g., largest, smallest, most
often, least often)
• Interprets a simple bar graph - calculation required
• Draws conclusions from data - bar graphs
• Reads data in a line graph - no calculations
• Reads a simple bar graph - numbers (e.g., how many)
• Reads and interprets data from a bar graph
• Interprets a simple bar graph - calculation required
• Solves simple problems based on data from bar graphs
• Reads data in a line graph - no calculations
New Vocabulary: changed, clock, estimation, half past, how much time,
left over, lowest, millimeter, noon, o'clock, pennies, quarter past, quarter
to, what time
New Vocabulary: decade, deposit, longer, miles per hour
New Vocabulary: bar graph, cubic centimeter, cubic unit, larger
New Signs and Symbols: °F degrees Fahrenheit, ft feet, g gram, in. inch,
lb pound, m meter/metre, min minute, yd yard
New Signs and Symbols: cm centimeter/centimetre,
variable
New Signs and Symbols: : used with time, : used with 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.
Page 4-46
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
201 - 210
Goal: Measurement and Data
Skills and concepts to Enhance (73% Probability*)
191 - 200
Geometric Measurement and Problem Solving
Skills and Concepts to Develop (50% Probability*)
201 - 210
Geometric Measurement and Problem Solving
Skills and Concepts to Introduce (27% Probability*)
211 - 220
Geometric Measurement and Problem Solving
• Identifies the value of a collection of coins to $1.00 (without picture of
coins)
• Computes the value of multiple bills and coins (addition/subtraction
only)
• Computes the value of multiple bills and coins (addition/subtraction
only)
• Adds money with regrouping
• Computes with dollars and cents up to and including $5.00 and
converts to decimals (multiplication/division)
• Analyzes and computes 1 operation on real-world problems involving
money over $5.00 (addition/subtraction only)
• Computes addition and subtraction on multiple-step real-world
problems involving money
• Analyzes and computes 1 operation on real-world problems involving
money over $5.00 (multiplication/division)
• Computes money problems with multiple operations (addition/
subtraction only)
• Computes with dollars and cents over $5.00 and converts to decimals
(multiplication/division)
• Computes addition, subtraction, multiplication, and division on multiplestep, real-world problems involving money
• Computes addition and subtraction on multiple-step real-world
problems involving money
• Uses the appropriate unit of measure for length
• Computes 1 operation on real-world problems involving money over
$5.00 (addition/subtraction only)
• Knows the approximate size of a yard
• Computes addition, subtraction, multiplication, and division on multiplestep, real-world problems involving money
• Measures length to the nearest centimeter
• Uses the appropriate unit of measure for length
• Computes half price (multiplication/division)
• Converts between inches and feet
• Knows the approximate size of a millimeter
• Computes with dollars and cents up to and including $5.00 and
converts to decimals (multiplication/division)
• Knows the approximate size of a pound
• Converts between inches and feet
• Knows the approximate size of a gram
• Converts between inches, feet, and yards
• Computes 1 operation on real-world problems involving money over
$5.00 (multiplication/division)
• Converts between cups and pints
• Selects and uses the appropriate type and size of unit in metric system
(mass)
• Selects and uses the appropriate type and size of unit in customary
system (length)
• Computes simple conversions among units of time (hours, days)
• Identifies the value of a collection of coins and bills to $10.00 by
"counting on" (without picture of money)
• Finds equivalent combinations of coins with the same value
• Makes change to $1.00 by "counting on" or subtracting
• Solves real-world problems involving decimals (not money) using
addition and subtraction
• Computes with dollars and cents up to and including $5.00 and
converts to decimals (addition/subtraction only)
• Converts between cups, pints, and quarts
• Computes basic operations with units of weight/mass
• Computes more difficult conversions among units of time
• Converts between cups and pints
• Solves problems involving measurement of time
• Converts between cups, pints, and quarts
• Applies dimensional analysis to simple real-world problems (time)
• Identifies the correct time, given the words, and vice versa
• Solves simple problems involving elapsed time, with the conversion of
hours
• Determines elapsed clock time
• Solves simple problems involving miles per gallon
• Tells time to the nearest quarter hour
• Determines elapsed time involving whole hours, whole days, whole
years
• Tells time to the nearest 1 minute
• Computes simple conversions among units of time (minutes, hours)
• Solves simple problems involving elapsed time, with the conversion of
hours
• Solves simple problems involving miles/kilometers per hour
• Estimates the measure of acute, right, and obtuse angles using 45 and
90 degrees as referents
• Determines the perimeter of a figure where some sides are labeled
• Estimates the area of rectangles using square units
• Converts between cups, pints, quarts, and gallons
• Apply dimensional analysis to simple real-world problems (capacity)
• Computes more difficult conversions among units of time
• Applies dimensional analysis to simple real-world problems (time)
• Solves difficult problems involving elapsed time, with the conversion of
hours
• Solves simple problems involving miles per gallon
• Solves problems involving rates
• Estimates the measure of acute, right, and obtuse angles using 45 and
90 degrees as referents
• Measures angles using a protractor
• Determines the perimeter of a figure using non-standard units
• Determines the area of irregular shapes with partial square units
• Solves problems involving the perimeter of squares, rectangles, or
triangles
• Solves simple problems involving miles/kilometers per hour
• Identifies situations where it is appropriate to calculate area
• Finds the perimeter of a polygon using a formula
• Determines the perimeter of a figure where all sides are labeled
• Estimates and finds volume of a figure using cubic units
• Determines the perimeter of a figure where some sides are labeled
• Uses basic indirect methods to estimate measurements (grids for area
of irregular figures)
• Describes the change in perimeter when dimensions of an object are
altered
• Solves simple problems involving the perimeter of squares, rectangles,
or triangles
• Determines the area of irregular shapes with partial square units
• Estimates and finds volume of a figure using cubic units
• Estimates the area of rectangles using square units
• Identifies properties of angles
Represent and Interpret Data
Represent and Interpret Data
Represent and Interpret Data
• Reads and interprets data from a pictograph
• Solves problems using pictographs
• Solves problems using pictographs
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.
Page 4-47
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
201 - 210
Goal: Measurement and Data
Skills and concepts to Enhance (73% Probability*)
191 - 200
Represent and Interpret Data
Skills and Concepts to Develop (50% Probability*)
201 - 210
Represent and Interpret Data
Skills and Concepts to Introduce (27% Probability*)
211 - 220
Represent and Interpret Data
• Interprets a pictograph - calculation required
• Organizes data to create simple bar graphs
• Solves problems using bar graphs
• Reads and interprets data from a bar graph
• Solves problems using bar graphs
• Reads and interprets data in line plots
• Reads and interprets dual bar graphs
• Solves problems using dual bar graphs
• Interprets a simple bar graph - calculation required
• Draws conclusions from data - bar graphs
• Reads data in a line graph - no calculations
New Vocabulary: decade, deposit, longer, miles per hour
New Vocabulary: bar graph, cubic centimeter, cubic unit, larger
New Vocabulary: century, coin, how long
New Signs and Symbols: °F degrees Fahrenheit, ft feet, g gram, in. inch,
lb pound, m meter/metre, min minute, yd yard
New Signs and Symbols: cm centimeter/centimetre, variable
New Signs and Symbols: $ dollar sign, hr hour, ↓ measurement span
down, ← measurement span left, → measurement span right, ↑
measurement span up
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.
Page 4-48
© 2006-2013 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
Common
Core 3.4.1
1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
211 - 220
Goal: Measurement and Data
Skills and concepts to Enhance (73% Probability*)
201 - 210
Geometric Measurement and Problem Solving
Skills and Concepts to Develop (50% Probability*)
211 - 220
Geometric Measurement and Problem Solving
Skills and Concepts to Introduce (27% Probability*)
221 - 230
Geometric Measurement and Problem Solving
• Computes the value of multiple bills and coins (addition/subtraction
only)
• Computes the value of multiple bills and coins (addition/subtraction
only)
• Computes with dollars and cents over $5.00 and converts to decimals
(multiplication/division)
• Computes with dollars and cents up to and including $5.00 and
converts to decimals (multiplication/division)
• Analyzes and computes 1 operation on real-world problems involving
money over $5.00 (addition/subtraction only)
• Computes the value of multiple bills and coins (multiplication/division)
• Computes addition and subtraction on multiple-step real-world
problems involving money
• Analyzes and computes 1 operation on real-world problems involving
money over $5.00 (multiplication/division)
• Converts between inches, feet, and yards
• Computes money problems with multiple operations (addition/
subtraction only)
• Computes with dollars and cents over $5.00 and converts to decimals
(multiplication/division)
• Computes addition, subtraction, multiplication, and division on multiplestep, real-world problems involving money
• Computes addition and subtraction on multiple-step real-world
problems involving money
• Uses the appropriate unit of measure for length
• Converts between ounces, pounds, and tons
• Knows the approximate size of a yard
• Computes addition, subtraction, multiplication, and division on multiplestep, real-world problems involving money
• Measures length to the nearest centimeter
• Uses the appropriate unit of measure for length
• Converts within the metric system
• Converts between inches and feet
• Knows the approximate size of a millimeter
• Apply dimensional analysis to simple real-world problems (capacity)
• Knows the approximate size of a pound
• Converts between inches and feet
• Computes 2-step conversions between units of time
• Knows the approximate size of a gram
• Converts between inches, feet, and yards
• Applies dimensional analysis to simple real-world problems (time)
• Converts between cups and pints
• Selects and uses the appropriate type and size of unit in metric system
(mass)
• Solves difficult problems involving elapsed time, with the conversion of
hours
• Converts between cups, pints, quarts, and gallons
• Solves complex problems involving miles/kilometers per hour
• Apply dimensional analysis to simple real-world problems (capacity)
• Solves problems involving rates
• Computes more difficult conversions among units of time
• Determines the perimeter of a figure using non-standard units
• Applies dimensional analysis to simple real-world problems (time)
• Solves problems involving the perimeter of squares, rectangles, or
triangles
• Converts between cups, pints, and quarts
• Computes simple conversions among units of time (hours, days)
• Computes more difficult conversions among units of time
• Solves problems involving measurement of time
• Applies dimensional analysis to simple real-world problems (time)
• Solves simple problems involving elapsed time, with the conversion of
hours
• Solves simple problems involving miles per gallon
• Solves simple problems involving miles/kilometers per hour
• Estimates the measure of acute, right, and obtuse angles using 45 and
90 degrees as referents
• Determines the perimeter of a figure where some sides are labeled
• Estimates the area of rectangles using square units
• Solves difficult problems involving elapsed time, with the conversion of
hours
• Solves simple problems involving miles per gallon
• Converts between millimeters, centimeters, meters, and kilometers
• Solves problems involving length in the customary system and
converts to larger or smaller units
• Converts between ounces and pounds
• Converts between cups, pints, quarts, and gallons
• Solves problems involving the perimeter of irregular or complex shapes
• Solves problems involving rates
• Solves problems involving perimeter and converts to larger or smaller
units
• Estimates the measure of acute, right, and obtuse angles using 45 and
90 degrees as referents
• Describes the change in perimeter when dimensions of an object are
altered
• Measures angles using a protractor
• Calculates the area of a rectangle, given labeled sides (customary
units)
• Determines the perimeter of a figure using non-standard units
• Determines the area of irregular shapes with partial square units
• Solves problems involving the perimeter of squares, rectangles, or
triangles
• Identifies situations where it is appropriate to calculate area
• Finds the perimeter of a polygon using a formula
• Estimates and finds volume of a figure using cubic units
• Describes the change in perimeter when dimensions of an object are
altered
• Uses basic indirect methods to estimate measurements (grids for area
of irregular figures)
• Measures length to the nearest millimeter
• Determines the length or width of a rectangle, given the area (metric
units)
• Determines the area of irregular shapes (customary units)
• Calculates area and perimeter of a rectangle (customary units)
• Calculates the volume of rectangular solids
• Determines the area of irregular shapes with partial square units
• Estimates and finds volume of a figure using cubic units
• Identifies properties of angles
Represent and Interpret Data
Represent and Interpret Data
Represent and Interpret Data
• Solves problems using pictographs
• Solves problems using pictographs
• Determines appropriate intervals and/or scale for a bar graph
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.
Page 4-49
© 2006-2013 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
Common
Core 3.4.1
1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
211 - 220
Goal: Measurement and Data
Skills and concepts to Enhance (73% Probability*)
201 - 210
Represent and Interpret Data
Skills and Concepts to Develop (50% Probability*)
211 - 220
Represent and Interpret Data
• Organizes data to create simple bar graphs
• Solves problems using bar graphs
• Solves problems using bar graphs
• Reads and interprets data in line plots
Skills and Concepts to Introduce (27% Probability*)
221 - 230
Represent and Interpret Data
• Solves problems using dual bar graphs
• Draws conclusions from data - bar graphs
New Vocabulary: bar graph, cubic centimeter, cubic unit, larger
New Vocabulary: century, coin, how long
New Vocabulary: cubic meter
New Signs and Symbols: cm centimeter/centimetre,
New Signs and Symbols: $ dollar sign, hr hour, ↓ measurement span
down, ← measurement span left, → measurement span right, ↑
measurement span up
New Signs and Symbols: h height, l length, mL milliliter/millilitre, mm
millimeter/millimetre, V volume, w width
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.
Page 4-50
© 2006-2013 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
Common
Core 3.4.1
1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
221 - 230
Goal: Measurement and Data
Skills and concepts to Enhance (73% Probability*)
211 - 220
Geometric Measurement and Problem Solving
Skills and Concepts to Develop (50% Probability*)
221 - 230
Geometric Measurement and Problem Solving
Skills and Concepts to Introduce (27% Probability*)
231 - 240
Geometric Measurement and Problem Solving
• Computes the value of multiple bills and coins (addition/subtraction
only)
• Computes with dollars and cents over $5.00 and converts to decimals
(multiplication/division)
• Measures length to the nearest millimeter
• Analyzes and computes 1 operation on real-world problems involving
money over $5.00 (addition/subtraction only)
• Computes the value of multiple bills and coins (multiplication/division)
• Apply dimensional analysis to simple real-world problems (length)
• Measures length to the nearest millimeter
• Analyzes and computes 1 operation on real-world problems involving
money over $5.00 (multiplication/division)
• Converts between inches, feet, and yards
• Solves problems involving length in the customary system and
converts to larger or smaller units
• Converts between millimeters, centimeters, meters, and kilometers
• Converts between grams and kilograms
• Solves problems involving length in the customary system and
converts to larger or smaller units
• Converts within the metric system
• Converts between ounces and pounds
• Computes with dollars and cents over $5.00 and converts to decimals
(multiplication/division)
• Computes addition and subtraction on multiple-step real-world
problems involving money
• Converts between millimeters, centimeters, meters, and kilometers
• Apply dimensional analysis to simple real-world problems (capacity)
• Computes addition, subtraction, multiplication, and division on multiplestep, real-world problems involving money
• Converts between ounces, pounds, and tons
• Solves problems involving capacity in the metric system and converts
to larger or smaller units
• Converts between cups, pints, quarts, and gallons
• Solves problems involving rates
• Uses the appropriate unit of measure for length
• Converts within the metric system
• Solves problems involving the perimeter of irregular or complex shapes
• Knows the approximate size of a millimeter
• Apply dimensional analysis to simple real-world problems (capacity)
• Converts between inches and feet
• Computes 2-step conversions between units of time
• Describes the change in perimeter when dimensions of an object are
altered
• Converts between inches, feet, and yards
• Applies dimensional analysis to simple real-world problems (time)
• Identifies the formula for perimeter with a variable
• Selects and uses the appropriate type and size of unit in metric system
(mass)
• Solves difficult problems involving elapsed time, with the conversion of
hours
• Determines the area of a triangle drawn on a grid
• Converts between cups, pints, quarts, and gallons
• Solves complex problems involving miles/kilometers per hour
• Apply dimensional analysis to simple real-world problems (capacity)
• Solves problems involving rates
• Computes more difficult conversions among units of time
• Determines the perimeter of a figure using non-standard units
• Applies dimensional analysis to simple real-world problems (time)
• Solves problems involving the perimeter of squares, rectangles, or
triangles
• Solves difficult problems involving elapsed time, with the conversion of
hours
• Solves simple problems involving miles per gallon
• Solves problems involving the perimeter of irregular or complex shapes
• Solves problems involving rates
• Solves problems involving perimeter and converts to larger or smaller
units
• Estimates the measure of acute, right, and obtuse angles using 45 and
90 degrees as referents
• Describes the change in perimeter when dimensions of an object are
altered
• Measures angles using a protractor
• Calculates the area of a rectangle, given labeled sides (customary
units)
• Determines the perimeter of a figure using non-standard units
• Solves problems involving the perimeter of squares, rectangles, or
triangles
• Finds the perimeter of a polygon using a formula
• Describes the change in perimeter when dimensions of an object are
altered
• Calculates the area of a rectangle, given labeled sides (customary
units)
• Determines the length or width of a rectangle, given the area (metric
units)
• Determines the area of irregular shapes (customary units)
• Calculates the volume of rectangular solids
• Calculates the length, width, or height of a rectangular prism, given the
area (customary units)
• Determines the length or width of a rectangle, given the area (metric
units)
• Determines the area of irregular shapes (customary units)
• Calculates area and perimeter of a rectangle (customary units)
• Calculates the volume of rectangular solids
• Determines the area of irregular shapes with partial square units
• Estimates and finds volume of a figure using cubic units
• Identifies properties of angles
Represent and Interpret Data
Represent and Interpret Data
Represent and Interpret Data
• Solves problems using pictographs
• Determines appropriate intervals and/or scale for a bar graph
• Determines appropriate intervals and/or scale for a bar graph
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.
Page 4-51
© 2006-2013 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
Common
Core 3.4.1
1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
221 - 230
Goal: Measurement and Data
Skills and concepts to Enhance (73% Probability*)
211 - 220
Represent and Interpret Data
Skills and Concepts to Develop (50% Probability*)
221 - 230
Represent and Interpret Data
• Solves problems using bar graphs
Skills and Concepts to Introduce (27% Probability*)
231 - 240
Represent and Interpret Data
• Interprets data given in horizontal and vertical bar graphs to solve
problems
• Reads and interprets data in line plots
New Vocabulary: century, coin, how long
New Vocabulary: cubic meter
New Vocabulary: None
New Signs and Symbols: $ dollar sign, hr hour, ↓ measurement span
down, ← measurement span left, → measurement span right, ↑
measurement span up
New Signs and Symbols: h height, l length, mL milliliter/millilitre, mm
millimeter/millimetre, V volume, w width
New Signs and Symbols: ( ) order of operations, + addition, kg kilogram,
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.
Page 4-52
© 2006-2013 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
Common
Core 3.4.1
1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
231 - 240
Goal: Measurement and Data
Skills and concepts to Enhance (73% Probability*)
221 - 230
Geometric Measurement and Problem Solving
Skills and Concepts to Develop (50% Probability*)
231 - 240
Geometric Measurement and Problem Solving
Skills and Concepts to Introduce (27% Probability*)
241 - 250
Geometric Measurement and Problem Solving
• Computes with dollars and cents over $5.00 and converts to decimals
(multiplication/division)
• Measures length to the nearest millimeter
• Apply dimensional analysis to simple real-world problems (length)
• Converts between millimeters, centimeters, meters, and kilometers
• Computes the value of multiple bills and coins (multiplication/division)
• Apply dimensional analysis to simple real-world problems (length)
• Solves problems involving capacity in the metric system and converts
to larger or smaller units
• Measures length to the nearest millimeter
• Converts between inches, feet, and yards
• Solves problems involving length in the customary system and
converts to larger or smaller units
• Solves problems involving area of a rectangle and converts to larger or
smaller units (customary)
• Converts between millimeters, centimeters, meters, and kilometers
• Converts between grams and kilograms
• Determines the area of irregular shapes (customary units)
• Solves problems involving length in the customary system and
converts to larger or smaller units
• Converts within the metric system
• Calculates the area of irregular shapes (metric units)
• Apply dimensional analysis to simple real-world problems (capacity)
• Solves complex problems involving inscribed figures
• Converts between ounces and pounds
• Uses properties of angles to solve mathematical problems
• Converts between ounces, pounds, and tons
• Solves problems involving capacity in the metric system and converts
to larger or smaller units
• Converts between cups, pints, quarts, and gallons
• Solves problems involving rates
• Converts within the metric system
• Solves problems involving the perimeter of irregular or complex shapes
• Apply dimensional analysis to simple real-world problems (capacity)
• Computes 2-step conversions between units of time
• Describes the change in perimeter when dimensions of an object are
altered
• Applies dimensional analysis to simple real-world problems (time)
• Identifies the formula for perimeter with a variable
• Solves difficult problems involving elapsed time, with the conversion of
hours
• Determines the area of a triangle drawn on a grid
• Solves complex problems involving miles/kilometers per hour
• Solves problems involving rates
• Determines the perimeter of a figure using non-standard units
• Solves problems involving the perimeter of squares, rectangles, or
triangles
• Solves problems involving the perimeter of irregular or complex shapes
• Solves problems involving perimeter and converts to larger or smaller
units
• Calculates the area of a rectangle, given labeled sides (customary
units)
• Determines the length or width of a rectangle, given the area (metric
units)
• Determines the area of irregular shapes (customary units)
• Calculates the volume of rectangular solids
• Calculates the length, width, or height of a rectangular prism, given the
area (customary units)
• Describes the change in perimeter when dimensions of an object are
altered
• Calculates the area of a rectangle, given labeled sides (customary
units)
• Determines the length or width of a rectangle, given the area (metric
units)
• Determines the area of irregular shapes (customary units)
• Calculates area and perimeter of a rectangle (customary units)
• Calculates the volume of rectangular solids
Represent and Interpret Data
Represent and Interpret Data
• Determines appropriate intervals and/or scale for a bar graph
• Determines appropriate intervals and/or scale for a bar graph
Represent and Interpret Data
• Interprets data given in horizontal and vertical bar graphs to solve
problems
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.
Page 4-53
© 2006-2013 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
Common
Core 3.4.1
1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
231 - 240
Goal: Measurement and Data
Skills and concepts to Enhance (73% Probability*)
221 - 230
New Vocabulary: cubic meter
Skills and Concepts to Develop (50% Probability*)
231 - 240
New Vocabulary: None
Skills and Concepts to Introduce (27% Probability*)
241 - 250
New Vocabulary: None
New Signs and Symbols: h height, l length, mL milliliter/millilitre, mm
millimeter/millimetre, V volume, w width
New Signs and Symbols: ( ) order of operations, + addition, kg kilogram,
P perimeter
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.
Page 4-54
© 2006-2013 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
Common
Core 3.4.1
1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
241 - 250
Goal: Measurement and Data
Skills and concepts to Enhance (73% Probability*)
231 - 240
Geometric Measurement and Problem Solving
Skills and Concepts to Develop (50% Probability*)
241 - 250
Geometric Measurement and Problem Solving
Skills and Concepts to Introduce (27% Probability*)
251 - 260
Geometric Measurement and Problem Solving
• Measures length to the nearest millimeter
• Apply dimensional analysis to simple real-world problems (length)
• Solves complex problems involving inscribed figures
• Converts between millimeters, centimeters, meters, and kilometers
• Apply dimensional analysis to simple real-world problems (length)
• Solves problems involving capacity in the metric system and converts
to larger or smaller units
• Calculates the length of one side of a cube, given the volume
(customary units)
• Solves problems involving length in the customary system and
converts to larger or smaller units
• Solves problems involving area of a rectangle and converts to larger or
smaller units (customary)
• Uses properties of angles to solve mathematical problems
• Converts between grams and kilograms
• Determines the area of irregular shapes (customary units)
• Converts within the metric system
• Calculates the area of irregular shapes (metric units)
• Apply dimensional analysis to simple real-world problems (capacity)
• Solves complex problems involving inscribed figures
• Solves problems involving capacity in the metric system and converts
to larger or smaller units
• Uses properties of angles to solve mathematical problems
• Solves problems involving rates
• Solves problems involving the perimeter of irregular or complex shapes
• Describes the change in perimeter when dimensions of an object are
altered
• Identifies the formula for perimeter with a variable
• Determines the area of a triangle drawn on a grid
• Calculates the area of a rectangle, given labeled sides (customary
units)
• Determines the length or width of a rectangle, given the area (metric
units)
• Determines the area of irregular shapes (customary units)
• Calculates the volume of rectangular solids
• Calculates the length, width, or height of a rectangular prism, given the
area (customary units)
Represent and Interpret Data
Represent and Interpret Data
Represent and Interpret Data
New Vocabulary: None
New Vocabulary: None
New Vocabulary: None
New Signs and Symbols: ( ) order of operations, + addition, kg kilogram,
P perimeter
New Signs and Symbols: × multiplication
New Signs and Symbols: None
• Determines appropriate intervals and/or scale for a bar graph
• Interprets data given in horizontal and vertical bar graphs to solve
problems
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.
Page 4-55
© 2006-2013 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
Common
Core 3.4.1
1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
251 - 260
Goal: Measurement and Data
Skills and concepts to Enhance (73% Probability*)
241 - 250
Geometric Measurement and Problem Solving
Skills and Concepts to Develop (50% Probability*)
251 - 260
Geometric Measurement and Problem Solving
Skills and Concepts to Introduce (27% Probability*)
> 260
Geometric Measurement and Problem Solving
• Apply dimensional analysis to simple real-world problems (length)
• Solves complex problems involving inscribed figures
• Uses properties of angles to solve mathematical problems
• Solves problems involving capacity in the metric system and converts
to larger or smaller units
• Calculates the length of one side of a cube, given the volume
(customary units)
• Solves problems involving area of a rectangle and converts to larger or
smaller units (customary)
• Uses properties of angles to solve mathematical problems
• Determines the area of irregular shapes (customary units)
• Calculates the area of irregular shapes (metric units)
• Solves complex problems involving inscribed figures
• Uses properties of angles to solve mathematical problems
Represent and Interpret Data
Represent and Interpret Data
Represent and Interpret Data
New Vocabulary: None
New Vocabulary: None
New Vocabulary: None
New Signs and Symbols: × multiplication
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.
Page 4-56
© 2006-2013 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
Common
Core 3.4.1
1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
> 260
Goal: Measurement and Data
Skills and concepts to Enhance (73% Probability*)
251 - 260
Geometric Measurement and Problem Solving
Skills and Concepts to Develop (50% Probability*)
> 260
Geometric Measurement and Problem Solving
• Solves complex problems involving inscribed figures
• Uses properties of angles to solve mathematical problems
• Calculates the length of one side of a cube, given the volume
(customary units)
• Uses properties of angles to solve mathematical problems
Represent and Interpret Data
Represent and Interpret Data
New Vocabulary: None
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.
Page 4-57
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
< 161
Goal: Geometry
Skills and Concepts to Develop (50% Probability*)
< 161
Reason with Shapes, Attributes, & Coordinate Plane
Skills and Concepts to Introduce (27% Probability*)
161 - 170
Reason with Shapes, Attributes, & Coordinate Plane
• Identifies spatial sense concepts (e.g., outside, inside, between, over,
under, above, below, behind, in front, middle)
• Sorts solid figures and objects according to attributes
• Identifies and names a circle
• Identifies position of shapes (e.g., inside, outside, between)
• Compares open and closed figures
• Identifies and names a triangle
• Identifies and names a square
• Identifies and names a rectangle
• Identifies sides and vertices of polygons
• Identifies and names a cone
New Vocabulary: None
New Vocabulary: corner, flat
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.
Page 4-58
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
161 - 170
Goal: Geometry
Skills and concepts to Enhance (73% Probability*)
< 161
Reason with Shapes, Attributes, & Coordinate Plane
Skills and Concepts to Develop (50% Probability*)
161 - 170
Reason with Shapes, Attributes, & Coordinate Plane
Skills and Concepts to Introduce (27% Probability*)
171 - 180
Reason with Shapes, Attributes, & Coordinate Plane
• Identifies spatial sense concepts (e.g., outside, inside, between, over,
under, above, below, behind, in front, middle)
• Sorts solid figures and objects according to attributes
• Identifies and names a triangle
• Compares open and closed figures
• Recognizes geometric shapes in real-world objects
• Identifies and names a circle
• Identifies position of shapes (e.g., inside, outside, between)
• Identifies and names a cube
• Identifies and names a triangle
• Identifies and names a square
• Identifies and names a square
• Identifies and names a rectangle
• Identifies sides and vertices of polygons
• Identifies and names a cone
New Vocabulary: None
New Vocabulary: corner, flat
New Vocabulary: None
New Signs and Symbols: 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.
Page 4-59
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
171 - 180
Goal: Geometry
Skills and concepts to Enhance (73% Probability*)
161 - 170
Reason with Shapes, Attributes, & Coordinate Plane
Skills and Concepts to Develop (50% Probability*)
171 - 180
Reason with Shapes, Attributes, & Coordinate Plane
Skills and Concepts to Introduce (27% Probability*)
181 - 190
Reason with Shapes, Attributes, & Coordinate Plane
• Sorts solid figures and objects according to attributes
• Identifies and names a triangle
• Identifies and names a cube
• Compares open and closed figures
• Recognizes geometric shapes in real-world objects
• Identifies and names a sphere
• Identifies position of shapes (e.g., inside, outside, between)
• Identifies and names a cube
• Identifies equal parts by using models
• Identifies and names a triangle
• Identifies and names a square
• Identifies plane figures with line symmetry
• Identifies and names a square
• Classifies polygons by sides and vertices
• Identifies and names a rectangle
• Identifies sides and vertices of polygons
• Identifies and names a cone
New Vocabulary: corner, flat
New Vocabulary: None
New Vocabulary: fourths, symmetry
New Signs and Symbols: 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.
Page 4-60
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
181 - 190
Goal: Geometry
Skills and concepts to Enhance (73% Probability*)
171 - 180
Reason with Shapes, Attributes, & Coordinate Plane
Skills and Concepts to Develop (50% Probability*)
181 - 190
Reason with Shapes, Attributes, & Coordinate Plane
Skills and Concepts to Introduce (27% Probability*)
191 - 200
Reason with Shapes, Attributes, & Coordinate Plane
• Identifies and names a triangle
• Identifies and names a cube
• Identifies right angles
• Recognizes geometric shapes in real-world objects
• Identifies and names a sphere
• Identifies corners (vertices) of cubes
• Identifies and names a cube
• Identifies equal parts by using models
• Identifies the number of faces on rectangular prisms
• Identifies and names a square
• Identifies plane figures with line symmetry
• Identifies and names a cylinder
• Classifies polygons by sides and vertices
• Identifies and names a sphere
• Creates a new shape by combining different shapes, or identifies the
different shapes that were used to make the original shape
• Sorts 2-D shapes and objects according to their attributes
• Identifies the number of lines of symmetry in plane figures
• Identifies plane figures with line symmetry
• Determines and names locations in the first quadrant on a labeled grid
or coordinate system (e.g., map or graph)
• Identifies lines
• Identifies parallel lines
• Uses models to compare angles relative to right angles
New Vocabulary: None
New Vocabulary: fourths, symmetry
New Vocabulary: face, grid, intersect, large, parallel, vertical line
New Signs and Symbols: None
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.
Page 4-61
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
191 - 200
Goal: Geometry
Skills and concepts to Enhance (73% Probability*)
181 - 190
Reason with Shapes, Attributes, & Coordinate Plane
Skills and Concepts to Develop (50% Probability*)
191 - 200
Reason with Shapes, Attributes, & Coordinate Plane
Skills and Concepts to Introduce (27% Probability*)
201 - 210
Reason with Shapes, Attributes, & Coordinate Plane
• Identifies and names a cube
• Identifies right angles
• Uses models to compare angles relative to right angles
• Identifies and names a sphere
• Identifies corners (vertices) of cubes
• Graphs ordered pairs in the first quadrant
• Identifies equal parts by using models
• Identifies the number of faces on rectangular prisms
• Identifies plane figures with line symmetry
• Identifies and names a cylinder
• Determines and names locations in the first quadrant on a labeled grid
or coordinate system (e.g., map or graph)
• Classifies polygons by sides and vertices
• Identifies and names a sphere
• Creates a new shape by combining different shapes, or identifies the
different shapes that were used to make the original shape
• Sorts 2-D shapes and objects according to their attributes
• Identifies the number of lines of symmetry in plane figures
• Identifies plane figures with line symmetry
• Determines and names locations in the first quadrant on a labeled grid
or coordinate system (e.g., map or graph)
• Determines the distance between horizontal and vertical lines in the
first quadrant of a rectangular coordinate system
• Determines the distance between points, following grid lines, in the
first quadrant on a coordinate graph (as in city blocks)
• Locates the origin on a coordinate grid
• Identifies parallel lines
• Identifies and names a parallelogram
• Identifies and names a trapezoid
• Identifies lines
• Identifies and names a hexagon
• Identifies parallel lines
• Classifies polygons by number of sides
• Uses models to compare angles relative to right angles
• Classifies polygons by sides and angles
• Identifies corners (vertices) of cubes
• Classifies cubes by their properties (e.g., edges with equal lengths,
faces with equal areas and congruent shapes, right angle corners)
• Identifies and names a cylinder
• Classifies plane figures by the number of lines of symmetry
New Vocabulary: fourths, symmetry
New Vocabulary: face, grid, intersect, large, parallel, vertical line
New Signs and Symbols: None
New Signs and Symbols: ( ) ordered pair, ∙ point
New Vocabulary: coordinate point, edge, origin, parallel line, regular
polygon, trapezoid
New Signs and Symbols: ° degrees
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.
Page 4-62
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
201 - 210
Goal: Geometry
Skills and concepts to Enhance (73% Probability*)
191 - 200
Reason with Shapes, Attributes, & Coordinate Plane
Skills and Concepts to Develop (50% Probability*)
201 - 210
Reason with Shapes, Attributes, & Coordinate Plane
Skills and Concepts to Introduce (27% Probability*)
211 - 220
Reason with Shapes, Attributes, & Coordinate Plane
• Identifies right angles
• Uses models to compare angles relative to right angles
• Identifies and names a rhombus
• Identifies corners (vertices) of cubes
• Graphs ordered pairs in the first quadrant
• Identifies the number of faces on rectangular prisms
• Determines and names locations in the first quadrant on a labeled grid
or coordinate system (e.g., map or graph)
• Determines the distance between horizontal and vertical lines in the
first quadrant of a rectangular coordinate system
• Identifies and names a cylinder
• Identifies and names a sphere
• Creates a new shape by combining different shapes, or identifies the
different shapes that were used to make the original shape
• Sorts 2-D shapes and objects according to their attributes
• Identifies the number of lines of symmetry in plane figures
• Identifies plane figures with line symmetry
• Determines and names locations in the first quadrant on a labeled grid
or coordinate system (e.g., map or graph)
• Locates the origin on a coordinate grid
• Determines the distance between horizontal and vertical lines in the
first quadrant of a rectangular coordinate system
• Identifies rays
• Determines the distance between points, following grid lines, in the
first quadrant on a coordinate graph (as in city blocks)
• Identifies acute angles
• Locates the origin on a coordinate grid
• Identifies parallel lines
• Identifies and names a parallelogram
• Identifies and names a trapezoid
• Identifies perpendicular lines
• Identifies obtuse angles
• Identifies and names a quadrilateral
• Classifies polygons by type of angle
• Identifies corners (vertices) of cubes
• Identifies lines
• Identifies and names a hexagon
• Predicts and verifies the effects of combining or subdividing basic
shapes
• Identifies parallel lines
• Classifies polygons by number of sides
• Identifies the number of edges on rectangular prisms
• Uses models to compare angles relative to right angles
• Classifies polygons by sides and angles
• Identifies and names a trapezoid
• Identifies corners (vertices) of cubes
• Classifies cubes by their properties (e.g., edges with equal lengths,
faces with equal areas and congruent shapes, right angle corners)
• Identifies and names a cylinder
• Classifies plane figures by the number of lines of symmetry
New Vocabulary: face, grid, intersect, large, parallel, vertical line
New Signs and Symbols: ( ) ordered pair, ∙ point
New Vocabulary: coordinate point, edge, origin, parallel line, regular
polygon, trapezoid
New Vocabulary: acute angle, congruent angle, obtuse angle, straight
angle
New Signs and Symbols: ° degrees
New Signs and Symbols: ∠ angle, angle marker (arc)
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.
Page 4-63
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
211 - 220
Goal: Geometry
Skills and concepts to Enhance (73% Probability*)
201 - 210
Reason with Shapes, Attributes, & Coordinate Plane
Skills and Concepts to Develop (50% Probability*)
211 - 220
Reason with Shapes, Attributes, & Coordinate Plane
Skills and Concepts to Introduce (27% Probability*)
221 - 230
Reason with Shapes, Attributes, & Coordinate Plane
• Uses models to compare angles relative to right angles
• Identifies and names a rhombus
• Identifies properties of quadrilaterals
• Graphs ordered pairs in the first quadrant
• Determines the distance between horizontal and vertical lines in the
first quadrant of a rectangular coordinate system
• Determines coordinates of geometric figures in the first quadrant
• Locates the origin on a coordinate grid
• Determines which lines are perpendicular (analysis)
• Determines the distance between horizontal and vertical lines in the
first quadrant of a rectangular coordinate system
• Identifies rays
• Identifies acute angles
• Identifies perpendicular lines
• Determines the distance between points, following grid lines, in the first
quadrant on a coordinate graph (as in city blocks)
• Recognizes the interior angle relationships of triangles
• Identifies acute angles
• Classifies equilateral triangles
• Identifies obtuse angles
• Identifies and names a rhombus
• Identifies and names a quadrilateral
• Identifies and names a quadrilateral
• Classifies polygons by type of angle
• Compares polygons by properties
• Identifies corners (vertices) of cubes
• Classifies polygons by type of angle
• Identifies and names a hexagon
• Predicts and verifies the effects of combining or subdividing basic
shapes
• Identifies the number of edges on rectangular prisms
• Classifies polygons by number of sides
• Identifies the number of edges on rectangular prisms
• Classifies polygons by sides and angles
• Identifies and names a trapezoid
• Determines and names locations in the first quadrant on a labeled grid
or coordinate system (e.g., map or graph)
• Locates the origin on a coordinate grid
• Identifies parallel lines
• Identifies and names a parallelogram
• Identifies and names a trapezoid
• Identifies rays
• Identifies corners (vertices) of cubes
• Classifies cubes by their properties (e.g., edges with equal lengths,
faces with equal areas and congruent shapes, right angle corners)
• Identifies and names a cylinder
• Classifies plane figures by the number of lines of symmetry
New Vocabulary: coordinate point, edge, origin, parallel line, regular
polygon, trapezoid
New Vocabulary: acute angle, congruent angle, obtuse angle, straight
angle
New Signs and Symbols: ° degrees
New Signs and Symbols: ∠ angle, angle marker (arc)
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.
Page 4-64
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
221 - 230
Goal: Geometry
Skills and concepts to Enhance (73% Probability*)
211 - 220
Reason with Shapes, Attributes, & Coordinate Plane
Skills and Concepts to Develop (50% Probability*)
221 - 230
Reason with Shapes, Attributes, & Coordinate Plane
Skills and Concepts to Introduce (27% Probability*)
231 - 240
Reason with Shapes, Attributes, & Coordinate Plane
• Identifies and names a rhombus
• Identifies properties of quadrilaterals
• Identifies properties of circles
• Determines the distance between horizontal and vertical lines in the
first quadrant of a rectangular coordinate system
• Determines coordinates of geometric figures in the first quadrant
• Identifies properties of quadrilaterals
• Identifies rays
• Compares polygons by properties
• Locates the origin on a coordinate grid
• Determines which lines are perpendicular (analysis)
• Determines which lines are perpendicular (analysis)
• Identifies rays
• Identifies acute angles
• Recognizes the interior angle relationships of triangles
• Identifies perpendicular lines
• Recognizes the interior angle relationships of triangles
• Classifies isosceles triangles
• Identifies acute angles
• Classifies equilateral triangles
• Classifies scalene triangles
• Identifies obtuse angles
• Identifies and names a rhombus
• Identifies and names a quadrilateral
• Identifies and names a quadrilateral
• Classifies polygons by type of angle
• Compares polygons by properties
• Identifies corners (vertices) of cubes
• Classifies polygons by type of angle
• Predicts and verifies the effects of combining or subdividing basic
shapes
• Identifies the number of edges on rectangular prisms
• Identifies the number of edges on rectangular prisms
• Identifies and names a trapezoid
New Vocabulary: acute angle, congruent angle, obtuse angle, straight
angle
New Vocabulary: None
New Vocabulary: None
New Signs and Symbols: None
New Signs and Symbols: congruent segment symbol
New Signs and Symbols: ∠ angle, angle marker (arc)
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.
Page 4-65
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
231 - 240
Goal: Geometry
Skills and concepts to Enhance (73% Probability*)
221 - 230
Reason with Shapes, Attributes, & Coordinate Plane
Skills and Concepts to Develop (50% Probability*)
231 - 240
Reason with Shapes, Attributes, & Coordinate Plane
Skills and Concepts to Introduce (27% Probability*)
> 240
Reason with Shapes, Attributes, & Coordinate Plane
• Identifies properties of quadrilaterals
• Identifies properties of circles
• Determines the distance between two points
• Determines coordinates of geometric figures in the first quadrant
• Identifies properties of quadrilaterals
• Identifies rays
• Compares polygons by properties
• Uses picture representations to identify symmetry of plane figures with
respect to a point or line
• Determines which lines are perpendicular (analysis)
• Determines which lines are perpendicular (analysis)
• Classifies polygons by properties
• Identifies acute angles
• Recognizes the interior angle relationships of triangles
• Recognizes the interior angle relationships of triangles
• Classifies isosceles triangles
• Classifies equilateral triangles
• Classifies scalene triangles
• Identifies and names a rhombus
• Identifies and names a quadrilateral
• Compares polygons by properties
• Classifies polygons by type of angle
• Identifies the number of edges on rectangular prisms
New Vocabulary: None
New Vocabulary: None
New Vocabulary: None
New Signs and Symbols: None
New Signs and Symbols: congruent segment symbol
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.
Page 4-66
© 2006-2013 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
Common Core 3.4.1
DesCartes: A Continuum of Learning®
RIT Score Range:
Mathematics
> 240
Goal: Geometry
Skills and concepts to Enhance (73% Probability*)
231 - 240
Reason with Shapes, Attributes, & Coordinate Plane
Skills and Concepts to Develop (50% Probability*)
> 240
Reason with Shapes, Attributes, & Coordinate Plane
• Identifies properties of circles
• Determines the distance between two points
• Identifies properties of quadrilaterals
• Compares polygons by properties
• Uses picture representations to identify symmetry of plane figures with
respect to a point or line
• Determines which lines are perpendicular (analysis)
• Classifies polygons by properties
• Recognizes the interior angle relationships of triangles
• Classifies isosceles triangles
• Classifies scalene triangles
New Vocabulary: None
New Vocabulary: None
New Signs and Symbols: congruent segment symbol
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.
Page 4-67
© 2006-2013 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
Common Core 3.4.1