MAFS.8.G.1.1

Verify experimentally the properties of rotations, reflections, and translations:
  1. Lines are taken to lines, and line segments to line segments of the same length.
  2. Angles are taken to angles of the same measure.
  3. Parallel lines are taken to parallel lines.
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
    Assessed with: 

     MAFS.8.G.1.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

    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.

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))
7912115: Fundamental Explorations in Mathematics 2 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.8.G.1.AP.1a: Perform rotations, reflections, and translations using pattern blocks.
MAFS.8.G.1.AP.1b: Draw rotations, reflections, and translations of polygons.

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

Sample 2 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth grade.

Type: Assessment

Sample 1 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth grade.

Type: Assessment

Educational Game

Transformation Complete:

Play this interactive game and determine whether the similar shapes have gone through rotations, translations, or reflections.

Type: Educational Game

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

Angle Transformations:

Students are given the opportunity to experimentally verify the properties of angle transformations (translations, reflections, and rotations).

Type: Formative Assessment

Segment Transformations:

Students are given the opportunity to experimentally verify the properties of segment transformations (translations, reflections, and rotations).

Type: Formative Assessment

Parallel Line Transformations:

Students are given the opportunity to experimentally verify the properties of parallel line transformations (translations, reflections, and rotations).

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

Triangles on a Lattice:

In this activity, students will use a 3x3 square lattice to study transformations of triangles whose vertices are part of the lattice. The tasks include determining whether two triangles are congruent, which transformations connect two congruent triangles, and the number of non-congruent triangles (with vertices on the lattice) that are possible.

Type: Lesson Plan

Rotations and Reflections of an Equilateral Triangle:

Students will apply simple transformations (rotation and reflection) to an equilateral triangle, then determine the result of the action of two successive transformations, eventually determining whether the action satisfies the commutative and associate properties.

Type: Lesson Plan

Transformations... Geometry in Motion:

Transformations... Geometry in Motion is designed for students to practice their knowledge of transformations. Students will represent transformations in the plane, compare transformations, and determine which have isometry. Students should have a basic understanding of the rules for each transformation as they will apply these rules in this activity. There is a teacher-led portion in this lesson followed by partner-activity. Students will be asked to explain and justify reasoning, as well.

Type: Lesson Plan

A Transformation's Adventure with Patty Paper: Exploring Translations, Reflections and Rotations.:

This lesson is an introduction to isometric transformations explained using patty paper. Meant for students with limited access to technology, it uses patty paper as a principal resource. Translations, reflections and rotations will be explained and practiced with this inexpensive element, emphasizing the properties preserved during those transformations and, without sacrificing precision, allowing students to differentiate between these isometries in a simple way.

Type: Lesson Plan

Identifying Similar Triangles:

This 105-minute lesson series helps teachers assess how students reason about geometry, including how they use facts about the angle sum and exterior angles of triangles to calculate missing angles, apply angle theorems to parallel lines cut by a transversal, and interpret geometrical diagrams using mathematical properties to identify similarity of triangles. In order to complete this lesson, students will need whiteboards, pens, wipes, copies of the assessment tasks, pencils, markers, scissors, glue sticks, and poster paper.

Type: Lesson Plan

Rotations and Reflections of an Equilateral Triangle:

Students will apply simple transformations (rotation and reflection) to an equilateral triangle, then determine the result of the action of two successive transformations, eventually determining whether the action satisfies the commutative and associate properties.

Type: Lesson Plan

Triangles on a Lattice:

In this activity, students will use a 3x3 square lattice to study transformations of triangles whose vertices are part of the lattice. The tasks include determining whether two triangles are congruent, which transformations connect two congruent triangles, and the number of non-congruent triangles (with vertices on the lattice) that are possible.

Type: Lesson Plan

Problem-Solving Tasks

Partitioning a Hexagon:

The purpose of this task is for students to find a way to decompose a regular hexagon into congruent figures. This is meant as an instructional task that gives students some practice working with transformations.

Type: Problem-Solving Task

Reflecting a Rectangle Over a Diagonal:

The task is intended for instructional purposes and assumes that students know the properties of rigid transformations described in . Note that the vertices of the rectangles in question do not fall exactly at intersections of the horizontal and vertical lines on the grid. This means that students need to approximate and this provides an extra challenge. Also providing a challenge is the fact that the grids have been drawn so that they are aligned with the diagonal of the rectangles rather than being aligned with the vertical and horizontal directions of the page. However, this choice of grid also makes it easier to reason about the reflections if they understand the descriptions of rigid motions indicated in MAFS.8.G.1.3.

Type: Problem-Solving Task

Virtual Manipulative

Rotation of a Point:

This virtual manipulative is an interactive visual presentation of the rotation of a point around the origin of the coordinate system. The original point can be dragged to different positions and the angle of rotation can be changed with a 90° increment.

Type: Virtual Manipulative

MFAS Formative Assessments

Angle Transformations:

Students are given the opportunity to experimentally verify the properties of angle transformations (translations, reflections, and rotations).

Parallel Line Transformations:

Students are given the opportunity to experimentally verify the properties of parallel line transformations (translations, reflections, and rotations).

Segment Transformations:

Students are given the opportunity to experimentally verify the properties of segment transformations (translations, reflections, and rotations).

Student Resources

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

Educational Game

Transformation Complete:

Play this interactive game and determine whether the similar shapes have gone through rotations, translations, or reflections.

Type: Educational Game

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

Problem-Solving Tasks

Partitioning a Hexagon:

The purpose of this task is for students to find a way to decompose a regular hexagon into congruent figures. This is meant as an instructional task that gives students some practice working with transformations.

Type: Problem-Solving Task

Reflecting a Rectangle Over a Diagonal:

The task is intended for instructional purposes and assumes that students know the properties of rigid transformations described in . Note that the vertices of the rectangles in question do not fall exactly at intersections of the horizontal and vertical lines on the grid. This means that students need to approximate and this provides an extra challenge. Also providing a challenge is the fact that the grids have been drawn so that they are aligned with the diagonal of the rectangles rather than being aligned with the vertical and horizontal directions of the page. However, this choice of grid also makes it easier to reason about the reflections if they understand the descriptions of rigid motions indicated in MAFS.8.G.1.3.

Type: Problem-Solving Task

Virtual Manipulative

Rotation of a Point:

This virtual manipulative is an interactive visual presentation of the rotation of a point around the origin of the coordinate system. The original point can be dragged to different positions and the angle of rotation can be changed with a 90° increment.

Type: Virtual Manipulative

Parent Resources

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

Problem-Solving Tasks

Partitioning a Hexagon:

The purpose of this task is for students to find a way to decompose a regular hexagon into congruent figures. This is meant as an instructional task that gives students some practice working with transformations.

Type: Problem-Solving Task

Reflecting a Rectangle Over a Diagonal:

The task is intended for instructional purposes and assumes that students know the properties of rigid transformations described in . Note that the vertices of the rectangles in question do not fall exactly at intersections of the horizontal and vertical lines on the grid. This means that students need to approximate and this provides an extra challenge. Also providing a challenge is the fact that the grids have been drawn so that they are aligned with the diagonal of the rectangles rather than being aligned with the vertical and horizontal directions of the page. However, this choice of grid also makes it easier to reason about the reflections if they understand the descriptions of rigid motions indicated in MAFS.8.G.1.3.

Type: Problem-Solving Task