curriculum Geometry 6 12

Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into 
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
1
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
< 161
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Develop (50% Probability*)
< 161
Skills and Concepts to Introduce (27% Probability*)
161 - 170
Geometric Measurement and Relationships
Geometric Measurement and Relationships
• Identifies and names a circle
• Identifies spatial sense concepts (e.g., outside, inside, between, over, 
under, above, below, behind, in front, middle)
• 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 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
• Compares open and closed figures
• Sorts solid figures and objects according to attributes
• Identifies position of shapes (e.g., inside, outside, between)
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
• Identifies figures that are the same size and shape
• Identifies figures that are the same size and shape
New Vocabulary: None
New Signs and Symbols: None
New Vocabulary: corner, flat
New Signs and Symbols: None


Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into 
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
2
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
161 - 170
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
< 161
Skills and Concepts to Develop (50% Probability*)
161 - 170
Skills and Concepts to Introduce (27% Probability*)
171 - 180
Geometric Measurement and Relationships
Geometric Measurement and Relationships
Geometric Measurement and Relationships
• Identifies and names a circle
• Identifies spatial sense concepts (e.g., outside, inside, between, over, 
under, above, below, behind, in front, middle)
• 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 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
• Compares open and closed figures
• Sorts solid figures and objects according to attributes
• Identifies position of shapes (e.g., inside, outside, between)
• 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
• Determines the area of irregular shapes by counting square units
• Identifies and names a triangle
• Identifies and names a square
• Identifies and names a cube
• Recognizes geometric shapes in real-world objects
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
• Identifies figures that are the same size and shape
• Identifies figures that are the same size and shape
• Identifies figures that are similar
New Vocabulary: None
New Signs and Symbols: None
New Vocabulary: corner, flat
New Signs and Symbols: None
New Vocabulary: geometric figure, similar
New Signs and Symbols: None


Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into 
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
3
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
171 - 180
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
161 - 170
Skills and Concepts to Develop (50% Probability*)
171 - 180
Skills and Concepts to Introduce (27% Probability*)
181 - 190
Geometric Measurement and Relationships
Geometric Measurement and Relationships
Geometric Measurement and Relationships
• 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 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
• Compares open and closed figures
• Sorts solid figures and objects according to attributes
• Identifies position of shapes (e.g., inside, outside, between)
• 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
• Determines the area of irregular shapes by counting square units
• Identifies and names a triangle
• Identifies and names a square
• Identifies and names a cube
• Recognizes geometric shapes in real-world objects
• Selects and uses the appropriate type and size of unit in customary 
system (length)
• Measures length with customary measures to the half-inch mark
• Uses a variety of non-standard units to measure the same length
• Determines more capacity or less capacity
• Determines the perimeter of a figure where all sides are labeled
• Determines the area of irregular shapes by counting square units
• Classifies polygons by sides and vertices
• Identifies and names a cube
• Identifies and names a sphere
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
• Identifies figures that are the same size and shape
• Identifies figures that are similar
• Identifies congruent figures
• Identifies figures that are similar
• Identifies plane figures with line symmetry
• Identifies transformations of plane figures (rotations/turns)
New Vocabulary: corner, flat
New Signs and Symbols: None
New Vocabulary: geometric figure, similar
New Signs and Symbols: None
New Vocabulary: estimation, millimeter, symmetry
New Signs and Symbols: None


Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into 
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
4
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
181 - 190
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
171 - 180
Skills and Concepts to Develop (50% Probability*)
181 - 190
Skills and Concepts to Introduce (27% Probability*)
191 - 200
Geometric Measurement and Relationships
Geometric Measurement and Relationships
Geometric Measurement and Relationships
• 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
• Determines the area of irregular shapes by counting square units
• Identifies and names a triangle
• Identifies and names a square
• Identifies and names a cube
• Recognizes geometric shapes in real-world objects
• Selects and uses the appropriate type and size of unit in customary 
system (length)
• Measures length with customary measures to the half-inch mark
• Uses a variety of non-standard units to measure the same length
• Determines more capacity or less capacity
• Determines the perimeter of a figure where all sides are labeled
• Determines the area of irregular shapes by counting square units
• Classifies polygons by sides and vertices
• Identifies and names a cube
• Identifies and names a sphere
• Selects and uses the appropriate type and size of unit in customary 
system (length)
• 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
• Identifies lines
• Identifies parallel lines
• Uses models to compare angles relative to right angles
• Identifies right angles
• Identifies corners (vertices) of cubes
• Identifies the number of faces on rectangular prisms
• Identifies and names a cylinder
• Identifies and names a sphere
• Sorts 2-D shapes and objects according to their attributes
• Creates a new shape by combining different shapes, or identifies the 
different shapes that were used to make the original shape
• Explores maps and relates them to measurements of real distances, 
using the scale
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
• Identifies figures that are similar
• Identifies congruent figures
• Identifies figures that are similar
• Identifies plane figures with line symmetry
• Identifies transformations of plane figures (rotations/turns)
• Identifies congruent figures
• Identifies congruent polygons and their corresponding sides and angles
• Identifies plane figures with line symmetry
• Identifies the number of lines of symmetry in plane figures
• Identifies transformations of plane figures (reflections/flips)
New Vocabulary: geometric figure, similar
New Signs and Symbols: None
New Vocabulary: estimation, millimeter, symmetry
New Signs and Symbols: None
New Vocabulary: face, intersect, large, parallel, vertical line
New Signs and Symbols: $ dollar sign, ft feet, in. inch, m meter/metre, yd 
yard


Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into 
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
5
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
191 - 200
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
181 - 190
Skills and Concepts to Develop (50% Probability*)
191 - 200
Skills and Concepts to Introduce (27% Probability*)
201 - 210
Geometric Measurement and Relationships
Geometric Measurement and Relationships
Geometric Measurement and Relationships
• Selects and uses the appropriate type and size of unit in customary 
system (length)
• Measures length with customary measures to the half-inch mark
• Uses a variety of non-standard units to measure the same length
• Determines more capacity or less capacity
• Determines the perimeter of a figure where all sides are labeled
• Determines the area of irregular shapes by counting square units
• Classifies polygons by sides and vertices
• Identifies and names a cube
• Identifies and names a sphere
• Selects and uses the appropriate type and size of unit in customary 
system (length)
• 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
• Identifies lines
• Identifies parallel lines
• Uses models to compare angles relative to right angles
• Identifies right angles
• Identifies corners (vertices) of cubes
• Identifies the number of faces on rectangular prisms
• Identifies and names a cylinder
• Identifies and names a sphere
• Sorts 2-D shapes and objects according to their attributes
• Creates a new shape by combining different shapes, or identifies the 
different shapes that were used to make the original shape
• Explores maps and relates them to measurements of real distances, 
using the scale
• Uses the appropriate unit of measure for length
• Knows the approximate size of a yard
• Measures length to the nearest centimeter
• Knows the approximate size of a pound
• Knows the approximate size of a gram
• 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
• Describes the change in area of a triangle when 1 dimension of an 
object is altered (metric units)
• Estimates the area of rectangles using square units
• Determines the area of irregular shapes with partial square units
• Identifies situations where it is appropriate to calculate area
• Estimates and finds volume of a figure using cubic units
• Uses basic indirect methods to estimate measurements (grids for area 
of irregular figures)
• Identifies parallel lines
• Uses models to compare angles relative to right angles
• Identifies and names a parallelogram
• Identifies and names a trapezoid
• Identifies and names a hexagon
• Classifies polygons by number of sides
• 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 a cube from a net
• Identifies and names a cylinder
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
• Identifies congruent figures
• Identifies figures that are similar
• Identifies plane figures with line symmetry
• Identifies transformations of plane figures (rotations/turns)
• Identifies congruent figures
• Identifies congruent polygons and their corresponding sides and angles
• Identifies plane figures with line symmetry
• Identifies the number of lines of symmetry in plane figures
• Identifies transformations of plane figures (reflections/flips)
• Identifies congruent polygons and their corresponding sides and angles
• Classifies plane figures by the number of lines of symmetry
New Vocabulary: estimation, millimeter, symmetry
New Signs and Symbols: None
New Vocabulary: face, intersect, large, parallel, vertical line
New Signs and Symbols: $ dollar sign, ft feet, in. inch, m meter/metre, yd 
yard
New Vocabulary: cubic centimeter, cubic unit, edge, larger, parallel line, 
regular polygon, trapezoid
New Signs and Symbols: cm centimeter/centimetre, ° degrees, g gram


Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into 
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
6
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
201 - 210
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
191 - 200
Skills and Concepts to Develop (50% Probability*)
201 - 210
Skills and Concepts to Introduce (27% Probability*)
211 - 220
Geometric Measurement and Relationships
Geometric Measurement and Relationships
Geometric Measurement and Relationships
• Selects and uses the appropriate type and size of unit in customary 
system (length)
• 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
• Identifies lines
• Identifies parallel lines
• Uses models to compare angles relative to right angles
• Identifies right angles
• Identifies corners (vertices) of cubes
• Identifies the number of faces on rectangular prisms
• Identifies and names a cylinder
• Identifies and names a sphere
• Sorts 2-D shapes and objects according to their attributes
• Creates a new shape by combining different shapes, or identifies the 
different shapes that were used to make the original shape
• Explores maps and relates them to measurements of real distances, 
using the scale
• Uses the appropriate unit of measure for length
• Knows the approximate size of a yard
• Measures length to the nearest centimeter
• Knows the approximate size of a pound
• Knows the approximate size of a gram
• 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
• Describes the change in area of a triangle when 1 dimension of an 
object is altered (metric units)
• Estimates the area of rectangles using square units
• Determines the area of irregular shapes with partial square units
• Identifies situations where it is appropriate to calculate area
• Estimates and finds volume of a figure using cubic units
• Uses basic indirect methods to estimate measurements (grids for area 
of irregular figures)
• Identifies parallel lines
• Uses models to compare angles relative to right angles
• Identifies and names a parallelogram
• Identifies and names a trapezoid
• Identifies and names a hexagon
• Classifies polygons by number of sides
• 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 a cube from a net
• Identifies and names a cylinder
• Uses the appropriate unit of measure for length
• Knows the approximate size of a millimeter
• Selects and uses the appropriate type and size of unit in metric system 
(mass)
• Solves simple problems involving capacity
• 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
• 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
• Determines the diameter, given the radius, and vice versa
• Describes the change in area of a triangle when 1 dimension of an 
object is altered (metric units)
• Determines the area of irregular shapes with partial square units
• Estimates and finds volume of a figure using cubic units
• Calculates the volume of a rectangular prism, and converts to a 
different measurement scale (customary units)
• Identifies rays
• Identifies properties of angles
• Identifies acute angles
• Identifies obtuse angles
• Identifies and names a trapezoid
• Identifies and names a rhombus
• Identifies and names a quadrilateral
• Classifies polygons by type of angle
• Identifies corners (vertices) of cubes
• Identifies the net which makes a cube-like (open box) figure
• Identifies the number of edges on rectangular prisms
• Predicts and verifies the effects of combining or subdividing basic 
shapes
• Determines an appropriate scale for representing a distance on a map
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
• Identifies congruent figures
• Identifies congruent polygons and their corresponding sides and angles
• Identifies plane figures with line symmetry
• Identifies congruent polygons and their corresponding sides and angles
• Classifies plane figures by the number of lines of symmetry
• Identifies similar and congruent triangles
• Uses similar figures to construct ratios and solve for a missing side
• Identifies geometric transformations (rotations)


Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into 
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
7
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
201 - 210
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
191 - 200
Skills and Concepts to Develop (50% Probability*)
201 - 210
Skills and Concepts to Introduce (27% Probability*)
211 - 220
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
• Identifies the number of lines of symmetry in plane figures
• Identifies transformations of plane figures (reflections/flips)
• Identifies geometric transformations (translations)
New Vocabulary: face, intersect, large, parallel, vertical line
New Signs and Symbols: $ dollar sign, ft feet, in. inch, m meter/metre, yd 
yard
New Vocabulary: cubic centimeter, cubic unit, edge, larger, parallel line, 
regular polygon, trapezoid
New Signs and Symbols: cm centimeter/centimetre, ° degrees, g gram
New Vocabulary: acute angle, congruent angle, cord, dilation, obtuse 
angle, straight angle, transformation
New Signs and Symbols: ∠ angle, angle marker (arc), ↓ measurement 
span down, ← measurement span left, → measurement span right, ↑ 
measurement span up, mm millimeter/millimetre, ∙ point, right angle 
marker, : 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.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
8
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
211 - 220
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
201 - 210
Skills and Concepts to Develop (50% Probability*)
211 - 220
Skills and Concepts to Introduce (27% Probability*)
221 - 230
Geometric Measurement and Relationships
Geometric Measurement and Relationships
Geometric Measurement and Relationships
• Uses the appropriate unit of measure for length
• Knows the approximate size of a yard
• Measures length to the nearest centimeter
• Knows the approximate size of a pound
• Knows the approximate size of a gram
• 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
• Describes the change in area of a triangle when 1 dimension of an 
object is altered (metric units)
• Estimates the area of rectangles using square units
• Determines the area of irregular shapes with partial square units
• Identifies situations where it is appropriate to calculate area
• Estimates and finds volume of a figure using cubic units
• Uses basic indirect methods to estimate measurements (grids for area 
of irregular figures)
• Identifies parallel lines
• Uses models to compare angles relative to right angles
• Identifies and names a parallelogram
• Identifies and names a trapezoid
• Identifies and names a hexagon
• Classifies polygons by number of sides
• 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 a cube from a net
• Identifies and names a cylinder
• Uses the appropriate unit of measure for length
• Knows the approximate size of a millimeter
• Selects and uses the appropriate type and size of unit in metric system 
(mass)
• Solves simple problems involving capacity
• 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
• 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
• Determines the diameter, given the radius, and vice versa
• Describes the change in area of a triangle when 1 dimension of an 
object is altered (metric units)
• Determines the area of irregular shapes with partial square units
• Estimates and finds volume of a figure using cubic units
• Calculates the volume of a rectangular prism, and converts to a 
different measurement scale (customary units)
• Identifies rays
• Identifies properties of angles
• Identifies acute angles
• Identifies obtuse angles
• Identifies and names a trapezoid
• Identifies and names a rhombus
• Identifies and names a quadrilateral
• Classifies polygons by type of angle
• Identifies corners (vertices) of cubes
• Identifies the net which makes a cube-like (open box) figure
• Identifies the number of edges on rectangular prisms
• Predicts and verifies the effects of combining or subdividing basic 
shapes
• Determines an appropriate scale for representing a distance on a map
• Determines coordinates of geometric figures in the first quadrant
• Measures length to the nearest millimeter
• 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
• Describes the change in perimeter when dimensions of an object are 
altered
• Describes the change in area of a triangle when 1 dimension of an 
object is altered (metric 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)
• Solves simple problems involving the area of a square or rectangle
• Calculates the base or height of a parallelogram, given the area and 
formula (metric)
• Determines the area of irregular shapes (customary units)
• Calculates area and perimeter of a rectangle (customary units)
• Calculates the volume of rectangular solids
• Calculates the volume of a rectangular prism, and converts to a 
different measurement scale (customary units)
• Identifies rays
• Determines which lines are perpendicular (analysis)
• Identifies and determines missing angle measures for supplementary 
angles
• Identifies acute angles
• Classifies equilateral triangles
• Identifies and names a rhombus
• Identifies and names a quadrilateral
• Compares polygons by properties
• Identifies properties of quadrilaterals
• Classifies polygons by type of angle
• Identifies the number of edges on rectangular prisms
• Uses similarity to solve problems using scale drawings
• Determines an appropriate scale for representing an object in a scale 
drawing
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
• Identifies congruent polygons and their corresponding sides and angles
• Classifies plane figures by the number of lines of symmetry
• Identifies similar and congruent triangles
• Uses similar figures to construct ratios and solve for a missing side
• Identifies properties of parallel and perpendicular lines
• Recognizes the interior angle relationships of triangles


Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into 
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
9
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
211 - 220
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
201 - 210
Skills and Concepts to Develop (50% Probability*)
211 - 220
Skills and Concepts to Introduce (27% Probability*)
221 - 230
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
• Identifies geometric transformations (rotations)
• Identifies geometric transformations (translations)
• Uses similar figures to construct ratios and solve for a missing side
• Uses similar triangles to construct ratios and solve for a missing side
• Identifies geometric transformations (rotations)
• Identifies geometric transformations (translations)
• Identifies geometric transformations (reflections)
New Vocabulary: cubic centimeter, cubic unit, edge, larger, parallel line, 
regular polygon, trapezoid
New Signs and Symbols: cm centimeter/centimetre, ° degrees, g gram
New Vocabulary: acute angle, congruent angle, cord, dilation, obtuse 
angle, straight angle, transformation
New Signs and Symbols: ∠ angle, angle marker (arc), ↓ measurement 
span down, ← measurement span left, → measurement span right, ↑ 
measurement span up, mm millimeter/millimetre, ∙ point, right angle 
marker, : used with time
New Vocabulary: cubic meter, interior angle, long, scale factor
New Signs and Symbols: ( ) ordered pair, ′ feet, h height, ″ inches, = is 
equal to, = is equal to, l length, × multiplication, : ratio, V volume, w width


Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into 
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
10
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
221 - 230
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
211 - 220
Skills and Concepts to Develop (50% Probability*)
221 - 230
Skills and Concepts to Introduce (27% Probability*)
231 - 240
Geometric Measurement and Relationships
Geometric Measurement and Relationships
Geometric Measurement and Relationships
• Uses the appropriate unit of measure for length
• Knows the approximate size of a millimeter
• Selects and uses the appropriate type and size of unit in metric system 
(mass)
• Solves simple problems involving capacity
• 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
• 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
• Determines the diameter, given the radius, and vice versa
• Describes the change in area of a triangle when 1 dimension of an 
object is altered (metric units)
• Determines the area of irregular shapes with partial square units
• Estimates and finds volume of a figure using cubic units
• Calculates the volume of a rectangular prism, and converts to a 
different measurement scale (customary units)
• Identifies rays
• Identifies properties of angles
• Identifies acute angles
• Identifies obtuse angles
• Identifies and names a trapezoid
• Identifies and names a rhombus
• Identifies and names a quadrilateral
• Classifies polygons by type of angle
• Identifies corners (vertices) of cubes
• Identifies the net which makes a cube-like (open box) figure
• Identifies the number of edges on rectangular prisms
• Predicts and verifies the effects of combining or subdividing basic 
shapes
• Determines an appropriate scale for representing a distance on a map
• Determines coordinates of geometric figures in the first quadrant
• Measures length to the nearest millimeter
• 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
• Describes the change in perimeter when dimensions of an object are 
altered
• Describes the change in area of a triangle when 1 dimension of an 
object is altered (metric 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)
• Solves simple problems involving the area of a square or rectangle
• Calculates the base or height of a parallelogram, given the area and 
formula (metric)
• Determines the area of irregular shapes (customary units)
• Calculates area and perimeter of a rectangle (customary units)
• Calculates the volume of rectangular solids
• Calculates the volume of a rectangular prism, and converts to a 
different measurement scale (customary units)
• Identifies rays
• Determines which lines are perpendicular (analysis)
• Identifies and determines missing angle measures for supplementary 
angles
• Identifies acute angles
• Classifies equilateral triangles
• Identifies and names a rhombus
• Identifies and names a quadrilateral
• Compares polygons by properties
• Identifies properties of quadrilaterals
• Classifies polygons by type of angle
• Identifies the number of edges on rectangular prisms
• Uses similarity to solve problems using scale drawings
• Determines an appropriate scale for representing an object in a scale 
drawing
• Measures length to the nearest millimeter
• 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 circumference when given the diameter or radius (or 
vice versa)
• Determines the circumference when given the area of a circle (or vice 
versa)
• Knows the relationship between radius, diameter, and circumference
• Compares area of numerous triangles
• Determines the area of a triangle drawn on a grid
• Determines the area of a triangle, given the formula
• Calculates the area of a rectangle, given labeled sides (customary 
units)
• Determines the length or width of a rectangle, given the area (metric 
units)
• Describes the change in area of a rectangle when dimensions of an 
object are altered
• Solves simple problems involving the area of a square or rectangle
• Determines the area of a parallelogram, given a labeled diagram
• Calculates the base or height of a parallelogram, given the area and 
formula (metric)
• Determines the area of a trapezoid, given the formula (metric units)
• Solves problems comparing areas of different polygons
• Determines the area of irregular shapes (customary units)
• Understands the procedure for finding the area and surface area of 
figures
• Calculates the volume of rectangular solids
• Calculates the length, width, or height of a rectangular prism, given the 
area (customary units)
• Calculates the volume of a rectangular prism, and converts to a 
different measurement scale (customary units)
• Determines which lines are perpendicular (analysis)
• Classifies isosceles triangles
• Classifies scalene triangles
• Identifies properties of circles
• Compares polygons by properties
• Identifies properties of quadrilaterals
• Uses similarity to solve problems using scale drawings


Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into 
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
11
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
221 - 230
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
211 - 220
Skills and Concepts to Develop (50% Probability*)
221 - 230
Skills and Concepts to Introduce (27% Probability*)
231 - 240
Geometric Measurement and Relationships
Geometric Measurement and Relationships
Geometric Measurement and Relationships
• Explores maps and relates them to measurements of real distances, 
using proportional reasoning
• Determines an appropriate scale for representing an object in a scale 
drawing
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
• Identifies similar and congruent triangles
• Uses similar figures to construct ratios and solve for a missing side
• Identifies geometric transformations (rotations)
• Identifies geometric transformations (translations)
• Identifies properties of parallel and perpendicular lines
• Recognizes the interior angle relationships of triangles
• Uses similar figures to construct ratios and solve for a missing side
• Uses similar triangles to construct ratios and solve for a missing side
• Identifies geometric transformations (rotations)
• Identifies geometric transformations (translations)
• Identifies geometric transformations (reflections)
• Identifies and determines a missing angle measure in corresponding, 
vertical, and alternate exterior/interior angles
• Recognizes the interior angle relationships of triangles
• Identifies properties of congruent triangles
• Solves problems involving properties of congruent triangles
• Uses similar triangles to construct ratios and solve for a missing side
• Identifies geometric transformations (dilations)
• Identifies geometric transformations (reflections)
• Determines whether a given pair of figures on a coordinate plane 
represents a translation, reflection, rotation, or dilation
New Vocabulary: acute angle, congruent angle, cord, dilation, obtuse 
angle, straight angle, transformation
New Signs and Symbols: ∠ angle, angle marker (arc), ↓ measurement 
span down, ← measurement span left, → measurement span right, ↑ 
measurement span up, mm millimeter/millimetre, ∙ point, right angle 
marker, : used with time
New Vocabulary: cubic meter, interior angle, long, scale factor
New Signs and Symbols: ( ) ordered pair, ′ feet, h height, ″ inches, = is 
equal to, = is equal to, l length, × multiplication, : ratio, V volume, w width
New Vocabulary: None
New Signs and Symbols: ( ) order of operations, + addition, C 
circumference, congruent segment symbol, d diameter, × multiplication, P 
perimeter, π pi, r radius


Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into 
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
12
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
231 - 240
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
221 - 230
Skills and Concepts to Develop (50% Probability*)
231 - 240
Skills and Concepts to Introduce (27% Probability*)
241 - 250
Geometric Measurement and Relationships
Geometric Measurement and Relationships
Geometric Measurement and Relationships
• Determines coordinates of geometric figures in the first quadrant
• Measures length to the nearest millimeter
• 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
• Describes the change in perimeter when dimensions of an object are 
altered
• Describes the change in area of a triangle when 1 dimension of an 
object is altered (metric 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)
• Solves simple problems involving the area of a square or rectangle
• Calculates the base or height of a parallelogram, given the area and 
formula (metric)
• Determines the area of irregular shapes (customary units)
• Calculates area and perimeter of a rectangle (customary units)
• Calculates the volume of rectangular solids
• Calculates the volume of a rectangular prism, and converts to a 
different measurement scale (customary units)
• Identifies rays
• Determines which lines are perpendicular (analysis)
• Identifies and determines missing angle measures for supplementary 
angles
• Identifies acute angles
• Classifies equilateral triangles
• Identifies and names a rhombus
• Identifies and names a quadrilateral
• Compares polygons by properties
• Identifies properties of quadrilaterals
• Classifies polygons by type of angle
• Identifies the number of edges on rectangular prisms
• Uses similarity to solve problems using scale drawings
• Determines an appropriate scale for representing an object in a scale 
drawing
• Measures length to the nearest millimeter
• 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 circumference when given the diameter or radius (or 
vice versa)
• Determines the circumference when given the area of a circle (or vice 
versa)
• Knows the relationship between radius, diameter, and circumference
• Compares area of numerous triangles
• Determines the area of a triangle drawn on a grid
• Determines the area of a triangle, given the formula
• Calculates the area of a rectangle, given labeled sides (customary 
units)
• Determines the length or width of a rectangle, given the area (metric 
units)
• Describes the change in area of a rectangle when dimensions of an 
object are altered
• Solves simple problems involving the area of a square or rectangle
• Determines the area of a parallelogram, given a labeled diagram
• Calculates the base or height of a parallelogram, given the area and 
formula (metric)
• Determines the area of a trapezoid, given the formula (metric units)
• Solves problems comparing areas of different polygons
• Determines the area of irregular shapes (customary units)
• Understands the procedure for finding the area and surface area of 
figures
• Calculates the volume of rectangular solids
• Calculates the length, width, or height of a rectangular prism, given the 
area (customary units)
• Calculates the volume of a rectangular prism, and converts to a 
different measurement scale (customary units)
• Determines which lines are perpendicular (analysis)
• Classifies isosceles triangles
• Classifies scalene triangles
• Identifies properties of circles
• Compares polygons by properties
• Identifies properties of quadrilaterals
• Uses similarity to solve problems using scale drawings
• Determines slope from an equation (analysis)
• Determines the midpoint of a line on a coordinate grid
• Determines the figure when plotting ordered pairs
• Computes and interprets the midpoint, given a set of ordered pairs 
(horizontal and vertical lines)
• Determines the circumference when given the diameter or radius (or 
vice versa)
• Determines the circumference when given the area of a circle (or vice 
versa)
• Determines the area of a triangle without the formula
• Determines the area of a figure when plotting ordered pairs without a 
grid
• Solves problems involving area of a rectangle and converts to larger or 
smaller units (customary)
• Describes the change in area of a rectangle when dimensions of an 
object are altered
• Determines the area of a parallelogram, given a labeled diagram
• Solves problems involving area of a circle
• Determines the diameter or radius when given the area of a circle 
(metric units)
• Solves problems comparing areas of different polygons
• Determines the area of irregular shapes (customary units)
• Calculates the area of irregular shapes (metric units)
• Solves complex problems involving inscribed figures
• Determines the surface area of rectangular solids
• Determines the effects of changing dimensions on volume (no units)
• Identifies and determines missing angle measures for complementary 
angles
• Recognizes that the sum of the measures of two sides of a triangle 
must be greater than the measure of the third side


Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into 
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
13
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
231 - 240
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
221 - 230
Skills and Concepts to Develop (50% Probability*)
231 - 240
Skills and Concepts to Introduce (27% Probability*)
241 - 250
Geometric Measurement and Relationships
Geometric Measurement and Relationships
Geometric Measurement and Relationships
• Explores maps and relates them to measurements of real distances, 
using proportional reasoning
• Determines an appropriate scale for representing an object in a scale 
drawing
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
• Identifies properties of parallel and perpendicular lines
• Recognizes the interior angle relationships of triangles
• Uses similar figures to construct ratios and solve for a missing side
• Uses similar triangles to construct ratios and solve for a missing side
• Identifies geometric transformations (rotations)
• Identifies geometric transformations (translations)
• Identifies geometric transformations (reflections)
• Identifies and determines a missing angle measure in corresponding, 
vertical, and alternate exterior/interior angles
• Recognizes the interior angle relationships of triangles
• Identifies properties of congruent triangles
• Solves problems involving properties of congruent triangles
• Uses similar triangles to construct ratios and solve for a missing side
• Identifies geometric transformations (dilations)
• Identifies geometric transformations (reflections)
• Determines whether a given pair of figures on a coordinate plane 
represents a translation, reflection, rotation, or dilation
• Uses an indirect method to measure the height of an inaccessible 
object
• Identifies and determines a missing angle measure in corresponding, 
vertical, and alternate exterior/interior angles
• Identifies corresponding and alternate exterior/interior angles
• Uses properties of angles to solve mathematical problems
• Recognizes the exterior angle relationships of triangles
• Uses the Pythagorean theorem to solve problems
• Uses Pythagorean triplets to solve problems
• Determines whether a given pair of figures on a coordinate plane 
represents a translation, reflection, rotation, or dilation
• Determines the coordinates of the dilation of a figure on a coordinate 
graph
• Determines the new coordinates of a transformed geometric figure
New Vocabulary: cubic meter, interior angle, long, scale factor
New Signs and Symbols: ( ) ordered pair, ′ feet, h height, ″ inches, = is 
equal to, = is equal to, l length, × multiplication, : ratio, V volume, w width
New Vocabulary: None
New Signs and Symbols: ( ) order of operations, + addition, C 
circumference, congruent segment symbol, d diameter, × multiplication, P 
perimeter, π pi, r radius
New Vocabulary: y-axis
New Signs and Symbols: A area, b base, km kilometer/kilometre, ↔ line 
symbol, - negative number, parallel symbol, segment overbar, sq square, 
△ triangle


Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into 
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
14
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
241 - 250
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
231 - 240
Skills and Concepts to Develop (50% Probability*)
241 - 250
Skills and Concepts to Introduce (27% Probability*)
251 - 260
Geometric Measurement and Relationships
Geometric Measurement and Relationships
Geometric Measurement and Relationships
• Measures length to the nearest millimeter
• 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 circumference when given the diameter or radius (or 
vice versa)
• Determines the circumference when given the area of a circle (or vice 
versa)
• Knows the relationship between radius, diameter, and circumference
• Compares area of numerous triangles
• Determines the area of a triangle drawn on a grid
• Determines the area of a triangle, given the formula
• Calculates the area of a rectangle, given labeled sides (customary 
units)
• Determines the length or width of a rectangle, given the area (metric 
units)
• Describes the change in area of a rectangle when dimensions of an 
object are altered
• Solves simple problems involving the area of a square or rectangle
• Determines the area of a parallelogram, given a labeled diagram
• Calculates the base or height of a parallelogram, given the area and 
formula (metric)
• Determines the area of a trapezoid, given the formula (metric units)
• Solves problems comparing areas of different polygons
• Determines the area of irregular shapes (customary units)
• Understands the procedure for finding the area and surface area of 
figures
• Calculates the volume of rectangular solids
• Calculates the length, width, or height of a rectangular prism, given the 
area (customary units)
• Calculates the volume of a rectangular prism, and converts to a 
different measurement scale (customary units)
• Determines which lines are perpendicular (analysis)
• Classifies isosceles triangles
• Classifies scalene triangles
• Identifies properties of circles
• Compares polygons by properties
• Identifies properties of quadrilaterals
• Uses similarity to solve problems using scale drawings
• Determines slope from an equation (analysis)
• Determines the midpoint of a line on a coordinate grid
• Determines the figure when plotting ordered pairs
• Computes and interprets the midpoint, given a set of ordered pairs 
(horizontal and vertical lines)
• Determines the circumference when given the diameter or radius (or 
vice versa)
• Determines the circumference when given the area of a circle (or vice 
versa)
• Determines the area of a triangle without the formula
• Determines the area of a figure when plotting ordered pairs without a 
grid
• Solves problems involving area of a rectangle and converts to larger or 
smaller units (customary)
• Describes the change in area of a rectangle when dimensions of an 
object are altered
• Determines the area of a parallelogram, given a labeled diagram
• Solves problems involving area of a circle
• Determines the diameter or radius when given the area of a circle 
(metric units)
• Solves problems comparing areas of different polygons
• Determines the area of irregular shapes (customary units)
• Calculates the area of irregular shapes (metric units)
• Solves complex problems involving inscribed figures
• Determines the surface area of rectangular solids
• Determines the effects of changing dimensions on volume (no units)
• Identifies and determines missing angle measures for complementary 
angles
• Recognizes that the sum of the measures of two sides of a triangle 
must be greater than the measure of the third side
• Determines slope from an equation (analysis)
• Using the slope of an equation, identifies parallel and perpendicular 
lines
• Determines the slope of perpendicular lines
• Determines the midpoint of a line on a coordinate grid
• Determines an endpoint of a line segment on a coordinate grid, given 
the midpoint and the other endpoint
• Determines the circumference when given the area of a circle (or vice 
versa)
• Determines the area of a figure when plotting ordered pairs without a 
grid
• Determines the area of a parallelogram, given a labeled diagram
• Calculate the height of a trapezoid, given the area, without the formula 
given (metric)
• Determines the diameter or radius when given the area of a circle 
(metric units)
• Solves problems involving complex figures (e.g., triangle, 
parallelogram)
• Solves complex problems involving inscribed figures
• Solves real-world problems involving surface area
• Calculates the length of one side of a cube, given the volume 
(customary units)
• Determines the volume of a cylinder
• Calculates the radius of a sphere, given the volume and formula 
(metric units)
• Solves real-world problems comparing volumes of figures
• Recognizes that the sum of the measures of two sides of a triangle 
must be greater than the measure of the third side
• Classifies polygons by properties


Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into 
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
15
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
241 - 250
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
231 - 240
Skills and Concepts to Develop (50% Probability*)
241 - 250
Skills and Concepts to Introduce (27% Probability*)
251 - 260
Geometric Measurement and Relationships
Geometric Measurement and Relationships
Geometric Measurement and Relationships
• Explores maps and relates them to measurements of real distances, 
using proportional reasoning
• Determines an appropriate scale for representing an object in a scale 
drawing
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
• Identifies and determines a missing angle measure in corresponding, 
vertical, and alternate exterior/interior angles
• Recognizes the interior angle relationships of triangles
• Identifies properties of congruent triangles
• Solves problems involving properties of congruent triangles
• Uses similar triangles to construct ratios and solve for a missing side
• Identifies geometric transformations (dilations)
• Identifies geometric transformations (reflections)
• Determines whether a given pair of figures on a coordinate plane 
represents a translation, reflection, rotation, or dilation
• Uses an indirect method to measure the height of an inaccessible 
object
• Identifies and determines a missing angle measure in corresponding, 
vertical, and alternate exterior/interior angles
• Identifies corresponding and alternate exterior/interior angles
• Uses properties of angles to solve mathematical problems
• Recognizes the exterior angle relationships of triangles
• Uses the Pythagorean theorem to solve problems
• Uses Pythagorean triplets to solve problems
• Determines whether a given pair of figures on a coordinate plane 
represents a translation, reflection, rotation, or dilation
• Determines the coordinates of the dilation of a figure on a coordinate 
graph
• Determines the new coordinates of a transformed geometric figure
• Determines the distance between two points
• Uses reasoning to verify properties of parallel and perpendicular lines
• Identifies corresponding and alternate exterior/interior angles
• Uses properties of angles to solve mathematical problems
• Recognizes the exterior angle relationships of triangles
• Solves problems involving properties of triangles
• Uses the Pythagorean theorem to solve problems
• Uses Pythagorean triplets to solve problems
• Verifies congruency of triangles using ASA, SAS, SSS, or AAS
• Solves problems involving similar polygons (not triangles)
• Solves problems involving properties of similar triangles (e.g., using 
geometric mean, Triangle Proportionality Theorem)
• Uses picture representations to identify symmetry of plane figures with 
respect to a point or line
• Determines the coordinates of the dilation of a figure on a coordinate 
graph
New Vocabulary: None
New Signs and Symbols: ( ) order of operations, + addition, C 
circumference, congruent segment symbol, d diameter, × multiplication, P 
perimeter, π pi, r radius
New Vocabulary: y-axis
New Signs and Symbols: A area, b base, km kilometer/kilometre, ↔ line 
symbol, - negative number, parallel symbol, segment overbar, sq square, 
△ triangle
New Vocabulary: rotational symmetry
New Signs and Symbols: AAS angle angle side, ASA angle side angle, ° 
degrees, ≅ is congruent to,  perpendicular to, SAS side angle side, 
square root symbol, SSA side side angle, SSS side side side, - 
subtraction


Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into 
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
16
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
251 - 260
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
241 - 250
Skills and Concepts to Develop (50% Probability*)
251 - 260
Skills and Concepts to Introduce (27% Probability*)
261 - 270
Geometric Measurement and Relationships
Geometric Measurement and Relationships
Geometric Measurement and Relationships
• Determines slope from an equation (analysis)
• Determines the midpoint of a line on a coordinate grid
• Determines the figure when plotting ordered pairs
• Computes and interprets the midpoint, given a set of ordered pairs 
(horizontal and vertical lines)
• Determines the circumference when given the diameter or radius (or 
vice versa)
• Determines the circumference when given the area of a circle (or vice 
versa)
• Determines the area of a triangle without the formula
• Determines the area of a figure when plotting ordered pairs without a 
grid
• Solves problems involving area of a rectangle and converts to larger or 
smaller units (customary)
• Describes the change in area of a rectangle when dimensions of an 
object are altered
• Determines the area of a parallelogram, given a labeled diagram
• Solves problems involving area of a circle
• Determines the diameter or radius when given the area of a circle 
(metric units)
• Solves problems comparing areas of different polygons
• Determines the area of irregular shapes (customary units)
• Calculates the area of irregular shapes (metric units)
• Solves complex problems involving inscribed figures
• Determines the surface area of rectangular solids
• Determines the effects of changing dimensions on volume (no units)
• Identifies and determines missing angle measures for complementary 
angles
• Recognizes that the sum of the measures of two sides of a triangle 
must be greater than the measure of the third side
• Determines slope from an equation (analysis)
• Using the slope of an equation, identifies parallel and perpendicular 
lines
• Determines the slope of perpendicular lines
• Determines the midpoint of a line on a coordinate grid
• Determines an endpoint of a line segment on a coordinate grid, given 
the midpoint and the other endpoint
• Determines the circumference when given the area of a circle (or vice 
versa)
• Determines the area of a figure when plotting ordered pairs without a 
grid
• Determines the area of a parallelogram, given a labeled diagram
• Calculate the height of a trapezoid, given the area, without the formula 
given (metric)
• Determines the diameter or radius when given the area of a circle 
(metric units)
• Solves problems involving complex figures (e.g., triangle, 
parallelogram)
• Solves complex problems involving inscribed figures
• Solves real-world problems involving surface area
• Calculates the length of one side of a cube, given the volume 
(customary units)
• Determines the volume of a cylinder
• Calculates the radius of a sphere, given the volume and formula 
(metric units)
• Solves real-world problems comparing volumes of figures
• Recognizes that the sum of the measures of two sides of a triangle 
must be greater than the measure of the third side
• Classifies polygons by properties
• Determines slope from an equation (analysis)
• Using the slope of an equation, identifies parallel and perpendicular 
lines
• Determines the slope of perpendicular lines
• Defines pi and knows common estimates (3.14 and 22/7)
• Solves problems involving complex figures (e.g., triangle, 
parallelogram)
• Solves real-world problems involving surface area
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
• Uses an indirect method to measure the height of an inaccessible 
object
• Identifies and determines a missing angle measure in corresponding, 
vertical, and alternate exterior/interior angles
• Identifies corresponding and alternate exterior/interior angles
• Uses properties of angles to solve mathematical problems
• Recognizes the exterior angle relationships of triangles
• Uses the Pythagorean theorem to solve problems
• Uses Pythagorean triplets to solve problems
• Determines the distance between two points
• Uses reasoning to verify properties of parallel and perpendicular lines
• Identifies corresponding and alternate exterior/interior angles
• Uses properties of angles to solve mathematical problems
• Recognizes the exterior angle relationships of triangles
• Solves problems involving properties of triangles
• Uses the Pythagorean theorem to solve problems
• Uses Pythagorean triplets to solve problems
• Verifies congruency of triangles using ASA, SAS, SSS, or AAS
• Determines sine of an angle in a given right triangle
• Determines cosine of an angle in a given right triangle
• Determines tangent of an angle in a given triangle
• Uses trigonometric methods to solve mathematical problems involving 
triangles
• Uses properties of angles to solve mathematical problems
• Uses the properties of 30-60-90 triangles 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.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
17
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
251 - 260
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
241 - 250
Skills and Concepts to Develop (50% Probability*)
251 - 260
Skills and Concepts to Introduce (27% Probability*)
261 - 270
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
• Determines whether a given pair of figures on a coordinate plane 
represents a translation, reflection, rotation, or dilation
• Determines the coordinates of the dilation of a figure on a coordinate 
graph
• Determines the new coordinates of a transformed geometric figure
• Solves problems involving similar polygons (not triangles)
• Solves problems involving properties of similar triangles (e.g., using 
geometric mean, Triangle Proportionality Theorem)
• Uses picture representations to identify symmetry of plane figures with 
respect to a point or line
• Determines the coordinates of the dilation of a figure on a coordinate 
graph
New Vocabulary: y-axis
New Signs and Symbols: A area, b base, km kilometer/kilometre, ↔ line 
symbol, - negative number, parallel symbol, segment overbar, sq square, 
△ triangle
New Vocabulary: rotational symmetry
New Signs and Symbols: AAS angle angle side, ASA angle side angle, ° 
degrees, ≅ is congruent to,  perpendicular to, SAS side angle side, 
square root symbol, SSA side side angle, SSS side side side, - 
subtraction
New Vocabulary: trigonometric relationship
New Signs and Symbols: cos cosine, sin sine, tan tangent


Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into 
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
18
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
261 - 270
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
251 - 260
Skills and Concepts to Develop (50% Probability*)
261 - 270
Skills and Concepts to Introduce (27% Probability*)
> 270
Geometric Measurement and Relationships
Geometric Measurement and Relationships
Geometric Measurement and Relationships
• Determines slope from an equation (analysis)
• Using the slope of an equation, identifies parallel and perpendicular 
lines
• Determines the slope of perpendicular lines
• Determines the midpoint of a line on a coordinate grid
• Determines an endpoint of a line segment on a coordinate grid, given 
the midpoint and the other endpoint
• Determines the circumference when given the area of a circle (or vice 
versa)
• Determines the area of a figure when plotting ordered pairs without a 
grid
• Determines the area of a parallelogram, given a labeled diagram
• Calculate the height of a trapezoid, given the area, without the formula 
given (metric)
• Determines the diameter or radius when given the area of a circle 
(metric units)
• Solves problems involving complex figures (e.g., triangle, 
parallelogram)
• Solves complex problems involving inscribed figures
• Solves real-world problems involving surface area
• Calculates the length of one side of a cube, given the volume 
(customary units)
• Determines the volume of a cylinder
• Calculates the radius of a sphere, given the volume and formula 
(metric units)
• Solves real-world problems comparing volumes of figures
• Recognizes that the sum of the measures of two sides of a triangle 
must be greater than the measure of the third side
• Classifies polygons by properties
• Determines slope from an equation (analysis)
• Using the slope of an equation, identifies parallel and perpendicular 
lines
• Determines the slope of perpendicular lines
• Defines pi and knows common estimates (3.14 and 22/7)
• Solves problems involving complex figures (e.g., triangle, 
parallelogram)
• Solves real-world problems involving surface area
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
• Determines the distance between two points
• Uses reasoning to verify properties of parallel and perpendicular lines
• Identifies corresponding and alternate exterior/interior angles
• Uses properties of angles to solve mathematical problems
• Recognizes the exterior angle relationships of triangles
• Solves problems involving properties of triangles
• Uses the Pythagorean theorem to solve problems
• Uses Pythagorean triplets to solve problems
• Verifies congruency of triangles using ASA, SAS, SSS, or AAS
• Solves problems involving similar polygons (not triangles)
• Determines sine of an angle in a given right triangle
• Determines cosine of an angle in a given right triangle
• Determines tangent of an angle in a given triangle
• Uses trigonometric methods to solve mathematical problems involving 
triangles
• Uses properties of angles to solve mathematical problems
• Uses the properties of 30-60-90 triangles to solve problems
• Uses trigonometric methods to solve mathematical problems involving 
triangles


Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into 
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
19
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
261 - 270
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
251 - 260
Skills and Concepts to Develop (50% Probability*)
261 - 270
Skills and Concepts to Introduce (27% Probability*)
> 270
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
• Solves problems involving properties of similar triangles (e.g., using 
geometric mean, Triangle Proportionality Theorem)
• Uses picture representations to identify symmetry of plane figures with 
respect to a point or line
• Determines the coordinates of the dilation of a figure on a coordinate 
graph
New Vocabulary: rotational symmetry
New Signs and Symbols: AAS angle angle side, ASA angle side angle, ° 
degrees, ≅ is congruent to,  perpendicular to, SAS side angle side, 
square root symbol, SSA side side angle, SSS side side side, - subtraction
New Vocabulary: trigonometric relationship
New Signs and Symbols: cos cosine, sin sine, tan tangent
New Vocabulary: None
New Signs and Symbols: None


Explanatory Notes
* At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into 
appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version.
Generated
8/7/14, 9:51:09 PM
© 2006-2014 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use.
Educational Standard: Common Core Mathematics K-12: 2010
Page
20
of
20
DesCartes: A Continuum of Learning®
Mathematics
RIT Score Range:
> 270
Statements Last Updated:  Aug 4, 2014
Goal: Geometry
Skills and Concepts to Enhance (73% Probability*)
261 - 270
Skills and Concepts to Develop (50% Probability*)
> 270
Geometric Measurement and Relationships
Geometric Measurement and Relationships
• Determines slope from an equation (analysis)
• Using the slope of an equation, identifies parallel and perpendicular 
lines
• Determines the slope of perpendicular lines
• Defines pi and knows common estimates (3.14 and 22/7)
• Solves problems involving complex figures (e.g., triangle, 
parallelogram)
• Solves real-world problems involving surface area
Congruence, Similarity, Right Triangles, & Trig
Congruence, Similarity, Right Triangles, & Trig
• Determines sine of an angle in a given right triangle
• Determines cosine of an angle in a given right triangle
• Determines tangent of an angle in a given triangle
• Uses trigonometric methods to solve mathematical problems involving 
triangles
• Uses properties of angles to solve mathematical problems
• Uses the properties of 30-60-90 triangles to solve problems
• Uses trigonometric methods to solve mathematical problems involving 
triangles
New Vocabulary: trigonometric relationship
New Signs and Symbols: cos cosine, sin sine, tan tangent
New Vocabulary: None
New Signs and Symbols: None