 
How does change in dimensions affect transformations, similar figures and scale drawings?


3. Student Learning Map
 Topic:Unit 4: Similarity and Transformations
 Subject(s):
 Days:20
 Grade(s):
Key Learning:
Figures often transform. The transformations that occur not only affect
the dimensions of a figure but also affect perimeter and area.
Unit Essential Question(s):
Lesson Essential Question(s):
What must be true when determining if two
figures are similar? (A)
What information do you need to know to find the dimensions of a figure that is similar to another figure? (A)
Lesson Essential Question(s):
How do changes in dimensions of similar geometric figures affect the perimeters and areas of the figures? (A)
Additional Information:
Stimulus Attributes
Prior Knowledge
Reporting Category  Algebra
Standard Big Idea 1 Develop an understanding of and apply proportionality, including similarity.
Benchmark MA.7.A.1.6 Apply proportionality to measurement in multiple contexts, including scale drawings and constant speed. Item Type At Grade 7, this benchmark will be assessed using MC and GR items.
Benchmark Clarification
Content Limits
Stimulus Attributes
Prior Knowledge
Reporting Category Geometry and Measurement
Standard  Supporting Idea Geometry and Measurement
Benchmark MA.7.G.4.1 Determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and apply these relationships to solve problems.
Item Type  At Grade 7, this benchmark will be assessed using MC and GR items.
Benchmark Clarification
Content Limits
Stimulus Attributes
Prior Knowledge
Reporting Category Geometry and Measurement
Standard Supporting Idea Geometry and Measurement
Benchmark MA.7.G.4.2 Predict the results of transformations and draw transformed figures, with and without the coordinate plane.
Item Type At Grade 7, this benchmark will be assessed using MC items.
Benchmark Clarification
Content Limits
Stimulus Attributes
Prior Knowledge
Item Specification Document
MA.7.A.1.3 from item specification (see item specs for specific problems)
Reporting Category
Algebra
Standard  Big Idea 1 Develop an understanding of and apply proportionality, including similarity.
Benchmark MA.7.A.1.3 Solve problems involving similar figures.
Item Type At Grade 7, this benchmark
will be assessed using MC and GR items.
Benchmark Clarification
 Students will use proportional reasoning to solve problems involving similar figures.
 Students will identify conditions necessary to show two figures are similar.
 Items may include graphic representations of threedimensional objects, but the similar figures being assessed must be twodimensional figures.
 Items may include diagonals of twodimensional figures.
 Items will not require the use of the Pythagorean theorem.
 Items will not include circles.
 Items will not include how changes in dimensions affect perimeter, circumference, area, or volume.
Stimulus Attributes
 Graphics may be used in these items.
 Items should be set in a realworld or mathematical context.
 Items that are set in realworld context may use length and width as dimensions as well as base and height as dimensions.
Prior Knowledge
 Items may require the student to apply mathematical knowledge described in the Standards from lower grades. This benchmark requires prerequisite knowledge from MA.6.A.2.2.
Reporting Category  Algebra
Standard Big Idea 1 Develop an understanding of and apply proportionality, including similarity.
Benchmark MA.7.A.1.6 Apply proportionality to measurement in multiple contexts, including scale drawings and constant speed. Item Type At Grade 7, this benchmark will be assessed using MC and GR items.
Benchmark Clarification
 Students will solve problems by applying proportionality to measurement contexts.
 Students will determine the scale factor for a given situation or use a scale to determine a measurement.
Content Limits
 Measurements may be in either metric or customary units, but measurements from both systems may not be used in the same item.
 Items may include the concepts of average speed or constant speed. Items may include fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 24, 25, 32, or 50.
 Items may include decimals through the hundredths place. Items will not include circumference, perimeter, area, or volume. Items will not include percents of increase or decrease.
 Items will not include converting units between two derived units (e.g., converting miles per hour to feet per second).
Stimulus Attributes
 Items should be set in a realworld context or a mathematical context. Graphics should be used in some of these items, as appropriate.
Prior Knowledge
 Items may require the student to apply mathematical knowledge described in the Standards from lower grades. This benchmark requires prerequisite knowledge from MA.6.A.2.1 and MA.6.A.2.2.
Reporting Category Geometry and Measurement
Standard  Supporting Idea Geometry and Measurement
Benchmark MA.7.G.4.1 Determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and apply these relationships to solve problems.
Item Type  At Grade 7, this benchmark will be assessed using MC and GR items.
Benchmark Clarification
 Students will determine the effects of changing dimensions on perimeter, circumference, area, and volume.
 Students will solve problems involving the effects of changing dimensions on perimeter, circumference, area, and volume.
Content Limits
 Items that increase the dimensions of a figure should use scale factors that are whole numbers less than or equal to 25.
 Items that decrease the dimensions of a figure should use scale factors of 1/2, 1/3, 1/4, 1/5, 1/10, 10%, 20%, 25%, 50%. Distractors in MC items may exceed this limit.
 Items assessing change in volume should only include rightrectangular prisms and rightcircular cylinders.
 Items will not assess changes in surface area.
Stimulus Attributes
 Items should be set in a realworld or mathematical context.
 Items that are set in realworld context may use length and width as dimensions as well as base and height as dimensions.
 Graphics should be used in most of these items, as appropriate.
Prior Knowledge
 Items may require the student to apply mathematical knowledge described in the Standards from lower grades. This benchmark requires prerequisite knowledge from MA.3.G.5.1, MA.4.G.3.3, MA.5.G.3.2, MA.5.G.5.4, MA.6.G.4.1, and MA.6.G.4.2.
Reporting Category Geometry and Measurement
Standard Supporting Idea Geometry and Measurement
Benchmark MA.7.G.4.2 Predict the results of transformations and draw transformed figures, with and without the coordinate plane.
Item Type At Grade 7, this benchmark will be assessed using MC items.
Benchmark Clarification
 Students will identify the result of transformations on a twodimensional figure.
 Students will identify the transformations that were performed on a twodimensional figure, given the original figure and the resulting figure after the transformation.
 Students will determine the distance between two points, which are located on the same vertical or horizontal line.
 Students will determine the vertical and horizontal translations needed to get from one point to another on the coordinate plane.
Content Limits
 Items may include dilations, translations, reflections, and rotations of twodimensional figures.
 Items that include translations will be limited to horizontal or vertical moves. Items may include lines of reflection, which may or may not pass through the object being reflected. Items may include centers of rotation, which may or may not be on the object being rotated.
 Items may include clockwise and counterclockwise rotations, which are limited to 45°, 90°, 180°, 270°, and 360°.
 Items may present figures on coordinate grids, which may include all four quadrants.
 Items may include the concepts of symmetry or congruency. Items may include up to three translations.
Stimulus Attributes
 Items should be set in a realworld or mathematical context.
 Graphics should be used in most of these items, as appropriate.
Prior Knowledge
 Items may require the student to apply mathematical knowledge described in the Standards from lower grades.
 This benchmark requires prerequisite knowledge from MA.4.G.5.2.
Resources: