# Describing and Defining Triangles

## Mathematical goals

This lesson unit is intended to help you assess how students reason about geometry, and in particular, how well they are able to:

- Recall and apply triangle properties.
- Sketch and construct triangles with given conditions.
- Determine whether a set of given conditions for the measures of angle and/or sides of a triangle describe a unique triangle, more than one possible triangle or do not describe a possible triangle.

## Introduction

This lesson unit is structured in the following way:

- Before the lesson, students work individually on an assessment task designed to reveal their current understanding and ability to reason using geometrical properties. You then review their responses and create questions for students to consider when improving their work.
- After a whole-class introduction, students work in pairs or threes on a collaborative task, determining whether sets of conditions describe possible triangles (unique or otherwise) or whether it is impossible to draw a triangle with these conditions. Throughout their work, students justify and explain their thinking and reasoning. They then compare their categorizations with their peers before reviewing their work and what they have learned in a whole-class discussion.
- In a follow-up lesson, students review their initial work on the assessment task and work alone on a similar task to the introductory task.

## Materials required

- Each student will need a copy of the tasks
*Triangles or Not?*and*Triangles or Not? (revisited),*some plain paper to work on, a mini-whiteboard, pen, and eraser. - Each small group of students will need the
*Card Set:**Possible Triangles?*(cut-up), a pencil, a marker, some poster paper, and a glue stick. Rules, protractors and compasses should be made available.

## Time needed

15 minutes before the lesson, a 90-minute lesson (or two 50-minute lessons), and 20 minutes in a follow-up lesson. Exact timings will depend on the needs of your students.

## 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
- 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:*