MAFS.8.G.1.1Archived Standard

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

Type: Educational Game

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

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

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

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

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 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

Students are introduced to isometric transformations using patty paper. Translations, reflections, and rotations will be explained and practiced, emphasizing the properties preserved during those transformations and, without sacrificing precision, allowing students to differentiate between these isometries. The lesson can also be taught using GeoGebra free software.

Type: Lesson Plan

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

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

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

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

The task is intended for instructional purposes and assumes that students know the properties of rigid transformations. 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.

Type: Problem-Solving Task

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