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

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

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

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

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