**Number:**MA.8.GR.2

**Title:**Understand similarity and congruence using models and transformations.

**Type:**Standard

**Subject:**Mathematics (B.E.S.T.)

**Grade:**8

**Strand:**Geometric Reasoning

## Related Benchmarks

## Related Access Points

## Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Idea

## Problem-Solving Tasks

## Student Resources

## Problem-Solving Tasks

Students' first experience with transformations is likely to be with specific shapes like triangles, quadrilaterals, circles, and figures with symmetry. Exhibiting a sequence of transformations that shows that two generic line segments of the same length are congruent is a good way for students to begin thinking about transformations in greater generality.

Type: Problem-Solving Task

This task has two goals: first to develop student understanding of rigid motions in the context of demonstrating congruence. Secondly, student knowledge of reflections is refined by considering the notion of orientation in part (b). Each time the plane is reflected about a line, this reverses the notions of ''clockwise'' and ''counterclockwise.''

Type: Problem-Solving Task

In this resource, students experiment with the reflection 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 the effect of a single transformation on two-dimensional figures. 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 two-dimensional figures are found by reflecting individual points.

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

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

## Parent Resources

## Problem-Solving Tasks

Students' first experience with transformations is likely to be with specific shapes like triangles, quadrilaterals, circles, and figures with symmetry. Exhibiting a sequence of transformations that shows that two generic line segments of the same length are congruent is a good way for students to begin thinking about transformations in greater generality.

Type: Problem-Solving Task

This task has two goals: first to develop student understanding of rigid motions in the context of demonstrating congruence. Secondly, student knowledge of reflections is refined by considering the notion of orientation in part (b). Each time the plane is reflected about a line, this reverses the notions of ''clockwise'' and ''counterclockwise.''

Type: Problem-Solving Task

In this resource, students experiment with the reflection 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 the effect of a single transformation on two-dimensional figures. 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 two-dimensional figures are found by reflecting individual points.

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

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