Mathematical goals

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

• Recognize the differences between equations and identities.
• Substitute numbers into algebraic statements in order to test their validity in special cases.
• Resist common errors when manipulating expressions such as 2(x – 3) = 2x – 3; (x + 3)² = x² + 3².
• Carry out correct algebraic manipulations.

It also aims to encourage discussion on some common misconceptions about algebra.

Introduction

The lesson unit is structured in the following way:

• Before the lesson, students work individually on an assessment task that is designed to reveal their current understanding and difficulties. You then review their work and create questions for students to answer in order to improve their solutions.
• After a whole-class introduction, students work in small groups on a collaborative discussion task.
• Students return to their original task and try to improve their own responses.

Materials required

• Each student will need two copies of the assessment task Equations and Identities, a mini-whiteboard, a pen, and an eraser.
• Each small group of students will need Card Set: Always, Sometimes, or Never True? (cut into cards before the lesson), a marker pen, a glue stick, and a large sheet of paper for making a poster.
• There is a projector resource to support the whole-class introduction.

Time needed

15 minutes before the lesson, a 1-hour lesson, and 15 minutes in a follow-up lesson. Timings given are approximate and will depend on the needs of the class.