# Defining Lines by Points, Slopes and Equations

## Mathematical goals

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

- Find the slopes and equations of linear graphs defined by pairs of coordinates.
- Calculate the slope and
*y*-intercept of a straight line. - Use the slope and
*y*-intercept of a straight line to derive its equation. - Students may use the properties of similar triangles to achieve these goals.

## Introduction

- Before the lesson, students work individually on an assessment task designed to reveal their current understanding. You then review their responses and create questions for students to consider when improving their work.
- After a whole-class introduction, students work in small groups on a collaborative discussion task, matching cards that describe the same line. Throughout their work, students justify and explain their thinking and reasoning.
- Students review their work by comparing their matches with those of their peers.
- In a whole-class discussion, students discuss what they have learned.
- In a follow-up lesson, students revisit 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 mini-whiteboard, pen, and wipe, and a copy of the assessment tasks
*Lines, Slopes and Equations*and*Lines, Slopes and Equations**(revisited).* - Each small group of students will need a cut-up copy of the
*Card Set:**Lines*, a pencil, a marker, a large sheet of poster paper and a glue stick.

## Time needed

15 minutes before the lesson, an 90-minute lesson (or split into two shorter ones), and 15 minutes in a follow-up lesson (or for homework). These timings are not exact. 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:*