**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 - Archived

**Assessed:**Yes

**Assessment Limits :**

Coordinate values of ?? and ?? must be integers. The number of transformations should be no more than two. In items that require the student to draw a transformed figure using a dilation or a rotation, the center of the transformation must be given.**Calculator :**Neutral

**Context :**Allowable

**Test Item #:**Sample Item 1**Question:**Triangle ABC is translated 5 units to the right to create triangle A’B’C’.Use the Connect Line tool to draw triangle A’B’C’.

**Difficulty:**N/A**Type:**GRID: Graphic Response Item Display

**Test Item #:**Sample Item 2**Question:**Quadrilateral ABCD is rotated 90° clockwise about the origin to create quadrilateral A’B’C’D’.

Use the Connect Line tool to draw quadrilateral A’B’C’D’.

**Difficulty:**N/A**Type:**GRID: Graphic Response Item Display

**Test Item #:**Sample Item 3**Question:**A pentagon is shown.

The pentagon is translated 5 units to the left and then reflected over the x-axis.

Use the Connect Line tool to draw the pentagon after its transformations.

**Difficulty:**N/A**Type:**GRID: Graphic Response Item Display

## Related Courses

## Related Access Points

## Related Resources

## Educational Software / Tool

## Formative Assessments

## Lesson Plans

## Problem-Solving Tasks

## Student Center Activity

## Tutorial

## Virtual Manipulative

## MFAS Formative Assessments

Students are asked to dilate two-dimensional figures in the coordinate plane and identify the coordinates of the vertices of the images.

Students are asked to reflect two-dimensional figures in the coordinate plane and identify the coordinates of the vertices of the images.

Students are asked to rotate two-dimensional figures in the coordinate plane and identify the coordinates of the vertices of the images.

Students are asked to translate two-dimensional figures in the coordinate plane and identify the coordinates of the vertices of the images.

## Student Resources

## Educational Software / Tool

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

In this resource, students experiment with successive reflections of a triangle in a coordinate plane.

Type: Problem-Solving Task

The purpose of this task is for students to apply a reflection to a single point. The standard asks students to apply rigid motions to lines, line segments, and angles. Although this problem only applies a reflection to a single point, it has high cognitive demand if the students are prompted to supply a picture. This is because the coordinates of the point (1000,2012) are very large. If students try to plot this point and the line of reflection on the usual x-y coordinate grid, then either the graph will be too big or else the point will lie so close to the line of reflection that it is not clear whether or not it lies on this line. A good picture requires a careful choice of the appropriate region in the plane and the corresponding labels. Moreover, reflections of lines, line segments, and angles are all found by reflecting individual points.

Type: Problem-Solving Task

In this resource, students will decide how to use transformations in the coordinate plane to translate a triangle onto a congruent triangle. Exploratory examples are included to prompt analytical thinking.

Type: Problem-Solving Task

## Student Center Activity

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

This video demonstrates the effect of a dilation on the coordinates of a triangle.

Type: Tutorial

## Virtual Manipulative

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

## Problem-Solving Tasks

In this resource, students experiment with successive reflections of a triangle in a coordinate plane.

Type: Problem-Solving Task

The purpose of this task is for students to apply a reflection to a single point. The standard asks students to apply rigid motions to lines, line segments, and angles. Although this problem only applies a reflection to a single point, it has high cognitive demand if the students are prompted to supply a picture. This is because the coordinates of the point (1000,2012) are very large. If students try to plot this point and the line of reflection on the usual x-y coordinate grid, then either the graph will be too big or else the point will lie so close to the line of reflection that it is not clear whether or not it lies on this line. A good picture requires a careful choice of the appropriate region in the plane and the corresponding labels. Moreover, reflections of lines, line segments, and angles are all found by reflecting individual points.

Type: Problem-Solving Task

In this resource, students will decide how to use transformations in the coordinate plane to translate a triangle onto a congruent triangle. Exploratory examples are included to prompt analytical thinking.

Type: Problem-Solving Task