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):
 
 
 How does change in dimensions affect transformations, similar figures and scale drawings?
   
Concept:  Similar Figures
Concept: Change in dimensions
Concept: Scale Drawings
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)
Lesson Essential Question(s):

How do I use a ratio in making a scale model?  (A)
Vocabulary:

Concept: Transformations
Concept:
Concept:
Lesson Essential Question(s):

How do you translate a figure in a coordinate plane?
(A)
How can you tell when one figure is a reflection of another figure?  (A)
How do you determine the coordinates of the image of rotated figure in a coordinate plane?  (A)
Lesson Essential Question(s):
Lesson Essential Question(s):
Vocabulary:

Vocabulary:

Additional Information:

 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.
Content Limits
  • Items may include graphic representations of three-dimensional objects, but the similar figures being assessed must be two-dimensional figures.
  • Items may include diagonals of two-dimensional 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 real-world or mathematical context.
  • Items that are set in real-world 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.
MA.7.A.1.6 from item specifications (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.1.6 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 real-world 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.
MA.7.G.4.1 from item specifications (see item specs for specific problems)
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 right-rectangular prisms and right-circular cylinders.
  • Items will not assess changes in surface area.

Stimulus Attributes
  • Items should be set in a real-world or mathematical context.
  • Items that are set in real-world 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.
MA.7.G.4.2 from item specifications (see item specs for specific problems)
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 two-dimensional figure.
  • Students will identify the transformations that were performed on a two-dimensional 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 two-dimensional 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 real-world 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:

Vocabulary Report

  • Similar Figures - Figures that have the same shape but not necessarily the same size
  • Scale Drawing - a proportional two-dimensional drawing of an object
  • Transformation - changes a figure into another figure
  • Indirect Measurement - uses similar figures to find a missing measure that is
    difficult to find directly.
  • Scale Model - a proportional three-dimensional model of an object
  • Translation - a transformation in which a figure slides but does not turn.
  • scale - the ratio that compares the measurements of the drawing or model with the actual measurements.
  • Reflection - a transformation in which a figure is reflected in a line called the line of reflection
  • Rotation - a turn angle of rotation center of rotation transformation in which a figure is rotated about a point called the center of rotation.