# Exponential Expressions-Perfect Squares, Square Roots

#### Main Core Tie

Strand: EXPRESSIONS AND EQUATIONS (6.EE) Standard 6.EE.1

Strand: EXPRESSIONS AND EQUATIONS (8.EE) Standard 8.EE.2

Utah LessonPlans

### Summary

Identify and find the value of a perfect square. Find the square root of a perfect square.

### Background for Teachers

Enduring Understanding (Big Ideas):
Exponential numbers

Essential Questions:

• How do 2n and n² differ?
• What is the value of n²? Of √ n²?
• What is the relationship between a number squared and the square root of a number?

Skill Focus:
Find the value for perfect squares and square roots Explain the relationship. between a perfect square and its principle root.

Vocabulary Focus:
power, base, exponent, exponential expression, a number squared, square root, inverse relationship

Ways to Gain/Maintain Attention (Primacy):
Cooperative learning, manipulatives, recognizing patterns, Foldable Notes, making predictions.

### Instructional Procedures

#### Attachments

Starter:

1. Use prime factorization to find the GCF and the LCM for 9 and 12.
2. Find the value for each of the following:
1. 3 x 3
2. 3 + 3
3. 2 x 3
4. 6 x 6
5. 6 + 6
6. 2 x 6

Discuss the starter

Lesson Segment 1: How do 2n and n² differ?
Briefly review with students how to write a base number and an exponent. Students have used this notation since 5th grade. Show students how to use the key on a Ti-73 to write an exponential expression. Students will work in pairs to find a pattern value for the expressions using the Adding, Multiplying and Squaring Numbers (attached). Partners alternate roles with each problem having one partner being the Predictor and the other being the Checker. The predictor says what he/she believes the answer will be. The checker uses a calculator or pencil/paper to check. Both record on their own worksheets.

Lesson Segment 2: What is the relationship between n² and √ n²?
Use Building A Square Patio (attached), an investigation with Color Tiles to help students visualize the inverse relationship between squaring a number and taking the square root of that perfect square. Student pairs or teams can build each patio using the Color Tiles. Discuss each step as a class focusing on the relationship between the side length and the root, between the square and total tiles, and between the root and the square.

Lesson Segment 3: What is the value of n²? Of √n² ?
Journal:
A foldable is attached (front and back). Give each student a foldable. Holding the paper vertically, fold the paper on the dotted lines. Students should complete the foldable.

Do Pairs Compare at each team, where each person exchanges their foldable with a partner to check. After checking the pair should discuss how their answers and explanations are similar or how they differ.

Assign text practice as appropriate.