MAFS.8.G.1.4

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
General Information
Subject Area: Mathematics
Grade: 8
Domain-Subdomain: Geometry
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications
    Also Assessed:

    MAFS.8.G.1.1 Verify experimentally the properties of rotations, reflections, and translations:

    MAFS.8.G.1.1a Lines are taken to lines, and line segments to line segments of the same length.

    MAFS.8.G.1.1b Angles are taken to angles of the same measure.

    MAFS.8.G.1.1c Parallel lines are taken to parallel lines.

  • Assessment Limits :
    Items should not include the coordinate plane as the coordinate plane is needed in MAFS.8.G.1.3. Limit the sequence to no more than two transformations. Two-dimensional figures are limited to no more than seven sides. A pre-image and image should not include apostrophe notation as this would give away the identification of similarity and congruence. No reference to the definition of congruence or symbols relating to the definition should be used (HS Geometry).
  • Calculator :

    Neutral

  • Context :

    Allowable

Sample Test Items (1)
  • Test Item #: Sample Item 1
  • Question:

    Which sequence of transformations results in figures that are similar but not congruent?

     

  • Difficulty: N/A
  • Type: MC: Multiple Choice

Related Courses

This benchmark is part of these courses.
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022 (current), 2022 and beyond)
1205070: M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7812030: Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.8.G.1.AP.4a: Recognize congruent and similar figures.
MAFS.8.G.1.AP.4b: Identify two-dimensional figures as similar or congruent given coordinate plane representations.
MAFS.8.G.1.AP.4c: Compare area and volume of similar figures.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Assessments

Sample 4 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth grade.

Type: Assessment

Sample 3 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth grade.

Type: Assessment

Educational Software / Tool

Transformations Using Technology:

This virtual manipulative can be used to demonstrate and explore the effect of translation, rotation, and/or reflection on a variety of plane figures. A series of transformations can be explored to result in a specified final image.

Type: Educational Software / Tool

Formative Assessments

Similarity - 2:

Students are asked to describe a sequence of transformations to show that two polygons are similar.

Type: Formative Assessment

Similarity - 1:

Students are asked to describe a sequence of transformations to show that two polygons are similar.

Type: Formative Assessment

Similarity - 3:

Students are asked to describe a sequence of transformations that demonstrates two polygons are similar.

Type: Formative Assessment

Proving Similarity:

Students are asked to explain similarity in terms of transformations.

Type: Formative Assessment

Lesson Plans

Coding Geometry Challenge #23 & 24:

This set of geometry challenges focuses on using transformations to show similarity and congruence of polygons and circles. Students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Type: Lesson Plan

Dilly Dallying with Dilations:

Students will understand the concept of dilation by constructing similar polygons on a coordinate grid using coordinate notation of dilation left parenthesis x comma y right parenthesis space rightwards arrow space left parenthesis k x comma k y right parenthesis. students use similar figures to determine the scale factor. students use proportions to determine side lengths of similar figures.

Type: Lesson Plan

Original Student Tutorial

Home Transformations:

Learn to describe a sequence of transformations that will produce similar figures. This interactive tutorial will allow you to practice with rotations, translations, reflections, and dilations.

Type: Original Student Tutorial

Perspectives Video: Professional/Enthusiast

All Circles Are Similar- Especially Circular Pizza!:

What better way to demonstrate that all circles are similar then to use pizzas! Gaines Street Pies explains how all pizza pies are similar through transformations.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Student Center Activity

Edcite: Mathematics Grade 8:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

Tutorial

Testing Similarity Through Transformations:

This video shows testing for similarity through transformations.

Type: Tutorial

MFAS Formative Assessments

Proving Similarity:

Students are asked to explain similarity in terms of transformations.

Similarity - 1:

Students are asked to describe a sequence of transformations to show that two polygons are similar.

Similarity - 2:

Students are asked to describe a sequence of transformations to show that two polygons are similar.

Similarity - 3:

Students are asked to describe a sequence of transformations that demonstrates two polygons are similar.

Original Student Tutorials Mathematics - Grades 9-12

Home Transformations:

Learn to describe a sequence of transformations that will produce similar figures. This interactive tutorial will allow you to practice with rotations, translations, reflections, and dilations.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorial

Home Transformations:

Learn to describe a sequence of transformations that will produce similar figures. This interactive tutorial will allow you to practice with rotations, translations, reflections, and dilations.

Type: Original Student Tutorial

Educational Software / Tool

Transformations Using Technology:

This virtual manipulative can be used to demonstrate and explore the effect of translation, rotation, and/or reflection on a variety of plane figures. A series of transformations can be explored to result in a specified final image.

Type: Educational Software / Tool

Student Center Activity

Edcite: Mathematics Grade 8:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

Tutorial

Testing Similarity Through Transformations:

This video shows testing for similarity through transformations.

Type: Tutorial

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.