# Classifying Proportion and Non-Proportion Situations

## Mathematical goals

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

- Identify when two quantities vary in direct proportion to each other.
- Distinguish between direct proportion and other functional relationships.
- Solve proportionality problems using efficient methods.

## Introduction

This lesson unit is structured in the following way:

- Before the lesson, students work individually on a task designed to reveal their current levels of understanding. You review their solutions and write questions to help them improve their work.
- At the beginning of the lesson, there is a whole-class discussion about key features of direct proportionality.
- Students then work in small groups on a task related to the assessment task. They write and solve their own questions on direct proportion, exchange questions with another group, assess each other’s work, and write suggestions for improvement.
- In a whole-class discussion, students share their questions and solution methods, generalizing to identify criteria for identifying direct proportion.
- In a follow-up lesson, students use their learning and your questions to review their work.

## Materials required

- Each individual student will need a calculator, a mini-whiteboard, a pen, an eraser, a copy of the assessment task,
*Getting Things in Proportion,*and a copy of the review task,*Getting Things in Proportion (revisited).* - Each small group of students will need a copy of the lesson tasks,
*Direct Proportion or Not?*and*Swapping Questions*.

## Time needed

15 minutes before the lesson, a 60-minute lesson, and 15 minutes in a follow-up lesson. These timings are approximate: exact timings 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:*