# Creating a Measure of Slope

## Mathematical goals

This lesson unit is intended to assess students’ understanding of the four quadrants of the coordinate plane, while at the same time introducing them to a mathematical understanding of slope. The task helps students to link their intuitive understandings of steepness to a more precise, calculated measure of slope.

## Introduction

This lesson unit is structured in the following way:

- Before the lesson, students work individually on an assessment task,
*Steepness*, which is designed to reveal their current understanding with regard to slope. You then review their work and create questions for students to answer in order to improve their solutions. - In the lesson, students work in small groups on a collaborative task in which they put line segments into order of slope. They then examine some sample student work and critique the measures of slope used there.
- Then students try to construct a better measure of slope.
- In a follow-up lesson, students receive your comments on the assessment task and use these to attempt the similar task, approaching it with insights that they have gained from the lesson.

## Materials Required

- Each student will need a copy of the task sheets
*Steepness*and*Steepness (revisited)*and a*Grid**Paper*sheet. - Each small group of students will need copies of the cut-up
*Card Set*, the four*Sample Responses to Discuss*, - Have protractors, tracing paper, and squared paper or graph paper available on request.
- There is a projector resource to support whole-class discussions.

## Time needed

15 minutes before the lesson, a 100-minute lesson (or two 55-minute lessons), and 15 minutes in a follow-up lesson. Timings given are approximate and will depend on the needs of your 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
- 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:*