# Evaluating Statements about Radicals

## 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)*, - 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.

## 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

## Mathematical Content Standards

This lesson asks students to select and apply mathematical content from across the grades, including the *content standards:*

- H.A-REI: Understand solving equations as a process of reasoning and explain the reasoning
- H.N-CN: Perform arithmetic operations with complex numbers.
- H.N-RN: Extend the properties of exponents to rational exponents