Beacon Lesson Plan Library
Simplifying Square Roots
Johnny Wolfe
Santa Rosa District Schools
Description
The square root of a positive integer is in simplest form if the radicand has no perfect square factor other than one.
Standards
Florida Sunshine State Standards
MA.A.1.4.4
Understands that numbers can be represented in a variety of equivalent forms using integers, fractions, decimals, and percents, scientific notation, exponents, radicals, absolute value, or logarithms.
Florida Process Standards
Numeric Problem Solvers
03 Florida students use numeric operations and concepts to describe, analyze, communicate, synthesize numeric data, and to identify and solve problems.
Materials
-Overhead transparencies for Simplifying Square Roots (see attached file)
-Marking pens (for overhead)
-Simplifying Square Roots Examples (see attached file)
-Simplifying Square Roots Worksheet (see attached file)
-Simplifying Square Roots Checklist (see attached file)
Preparations
1. Prepare transparencies for Simplifying Square Roots Examples if using as an overhead transparency. (See attached file.)
2. Have marking pens (for overhead).
3. Have Simplifying Square Roots Examples prepared and ready to demonstrate to students. (See attached file.)
4. Have enough copies of Simplifying Square Roots Worksheet for each student. (See attached file.)
5. Have enough copies of Simplifying Square Roots Checklist for each student. (See attached file.)
Procedures
Prior Knowledge: Students should be familiar with basic operation skills, such as addition, subtraction, multiplication, division, exponents, fractions, decimals, distributive property, prime factorization, absolute value, and factoring. NOTE: This lesson does not address fractions, decimals, percents, scientific notation, and logarithms for SSS MA.A.1.4.4.
1. Go over the definition for a simplified form for a square root. (See #1 on attached file: Simplifying Square Roots Examples.)
2. Have students analyze different forms of a square root. (See #2 on attached file: Simplifying Square Roots Examples.) Make sure that students understand that each of the forms names the same number.
3. Go over the Product Property of Square Roots. (See #3 on attached file: Simplifying Square Roots Examples.)
4. Work example #4. (See attached file: Simplifying Square Roots Examples.) Answer students' questions and comments.
5. Work example #5. (See attached file: Simplifying Square Roots Examples.) Answer students' questions and comments.
6. Discuss principal square root and nonnegative results. Introduce the need for absolute values on some terms. (See #6 on attached file: Simplifying Square Roots Examples.)
7. Discuss the rule of odd and even exponents as it deals with absolute value. (See #7 on attached file: Simplifying Square Roots Examples.)
8. Work example #8. (See attached file: Simplifying Square Roots Examples.) Answer students' questions and comments.
9. Work example #9. (See attached file: Simplifying Square Roots Examples.) Answer students' questions and comments.
10. Work example #10. (See attached file: Simplifying Square Roots Examples.) Answer students' questions and comments.
11. Distribute the Simplifying Square Roots Worksheet. (See attached file.)
12. Distribute the Simplifying Square Roots Checklist. (See attached file.)
13. The student will write their responses on the Worksheet.
14. The teacher will move from student to student observing the students work and lending assistance.
15. The teacher will assess the activity.
Assessments
The student Worksheet will be collected and scored according to the Simplifying Square Roots Checklist. (See attached file.)
Extensions
Have students find the area of rectangles whose length and width involve square roots
Web Links
Web supplement for Simplifying Square Roots MATH FORUM ASK DR. MATH
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