# Transforming 2D Figures

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to:

- Describe in words the transformation that maps an object to a transformed image.
- Given a geometric figure and a rotation, reflection or translation, draw the transformed figure (or the original figure if the image is given.)
- Describe transformations as algebraic functions that take points in the plane as inputs and give other points as outputs.

## Introduction

The lesson unit is structured in the following way:

- Before the lesson, students work individually on a task designed to reveal their current understanding and difficulties. You then review their solutions and create questions for students to consider in order to improve their work.
- After a whole-class introduction, students work in pairs or threes on a collaborative task, describing transformations and completing the transformed image/original figure for a given transformation. The lesson ends with a whole-class discussion of the work.
- In a follow-up lesson, students work alone on a new assessment task, or return to the original task and try to improve their responses.

## Materials required

- Each individual student will need a copy of
*Figure to Figure*and*Figure to Figure (revisited)*, a mini-whiteboard, pen, and eraser. - Each small group of students will need the cut-up
*Card Set:**Transformations*, a glue stick, a marker pen, and a large sheet of poster paper. Tracing paper should be made available on request. - There is a projector resource to support whole-class discussions.

## Time needed

15 minutes before the lesson, a 90-minute lesson (or two 50-minute lessons), and 15 minutes in a follow-up lesson. Timings are approximate and will depend on the needs of the class.

## Lesson Type

## Mathematical Practices

This lesson involves a range of *mathematical practices* from the standards, with emphasis on:

- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP3: Construct viable arguments and critique the reasoning of others
- MP4: Model with mathematics
- MP5: Use appropriate tools strategically
- MP6: Attend to precision
- MP7: Look for and make use of structure
- MP8: Look for and express regularity in repeated reasoning

## Mathematical Content Standards

This lesson asks students to select and apply mathematical content from across the grades, including the *content standards:*

- H.A-SSE: Interpret the structure of expressions
- H.G-CO: Experiment with transformations in the plane
- H.G-CO: Understand congruence in terms of rigid motions