Mathematical goals

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

• Use the properties of exponents, including rational exponents and manipulate algebraic statements involving radicals.
• Discriminate between equations and identities.

In this lesson there is also the (optional) opportunity to consider the role of the imaginary number .

Introduction

The unit is structured in the following way:

• Before the lesson, students work alone on an assessment task designed to reveal their current understanding. You review their work, creating questions to help students improve their solutions.
• During the lesson, students first work in small groups on a collaborative discussion task. After sharing their solutions with another group, students extend and generalize the math.
• An optional collaborative task focuses on imaginary numbers.
• During a whole-class discussion, students review the main mathematical concepts of the lesson.
• In a follow-up lesson, students review their initial solutions and then use what they have learned to revise the same introductory assessment task and complete a second, similar task.

Materials required

• Each student will need a copy of Operations with Radicals and Operations with Radicals (revisited), a mini-whiteboard, pen, and eraser.
• Each small group of students will need the Card Set: Always, Sometimes, or Never True?, scissors, glue, and a large sheet of poster paper. To begin with, cut Cards G and H off the sheet, but do not cut up the rest of the cards.
• There is a projector resource to support whole-class discussions. You may also want to copy the cards onto transparencies to be used on an overhead projector to support discussions.

Time needed

15 minutes before the lesson, a 95-minute lesson (or two 50-minute lessons) (more if introducing imaginary numbers), and 20 minutes in a follow-up lesson. Exact timings will depend on the class.