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.