Beacon Lesson Plan Library
Doing Battle with Radical Equations
Johnny Wolfe
Santa Rosa District Schools
Description
Equations containing radicals with variables in the radicand are called radical equations. To solve such equations, first isolate the radical on one side of the equation and then square each side of the equation to eliminate the radical.
Standards
Florida Sunshine State Standards
MA.A.3.4.1
Understands and explains the effects of addition, subtraction, multiplication and division on real numbers, including square roots, exponents, and appropriate inverse relationships.
MA.A.3.4.3
Adds, subtracts, multiplies, and divides real numbers, including square roots and exponents using appropriate methods of computing (mental mathematics, paper-and-pencil, calculator).
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 (if examples are to be worked on overhead) for Doing Battle with Radical Equations (see attached file)
-Marking pens (for overhead)
-Doing Battle with Radical Eqautions EXAMPLES (see attached file)
-Doing Battle with Radical Equations WORKSHEET (see attached file)
-Doing Battle with Radical Equations CHECKLIST (see attached file)
Preparations
1. Prepare transparencies (if teacher uses overhead for examples) for Doing Battle with Radical Equations Examples. (See attached file.)
2. Gather marking pens for overhead.
3. Have Doing Battle with Radical Equations EXAMPLES prepared and ready to demonstrate to students. (See attached file.)
4. Have enough copies of Doing Battle wiht Radical Equations WORKSHEET for each student. (See attached file.)
5. Have enough copies of Doing Battle with Radical Equations 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, inverse operations, radicals, factoring, and solving equations.
1. Review inverse operations. (See #1 on attached file.) Answer students' questions and comments.
2. Have students do Warm-up activity. Go through this activity with students making sure they understand the concept of inverse operations. (See #2 on attached file.) Answer students' questions and comments.
3. Discuss squaring and square roots with students. Make sure that the students understand that squaring and square roots are inverse operations. (See #3 on attached file.) Answer students' questions and comments.
4. Describe the terminology that will be used (radicand, radicals, and radical equations). Also describe how we are going to solve an equation involving radicals. (See #4 on attached file.) Answer students' questions and comments.
5. Have the students work the four examples on #5. (See attached file.) Pay special attention to the use of squaring with inverse operations. Answer students' questions and comments.
6. Discuss the importance of checking solutions. (See #6 on attached file.) Answer students' questions and comments.
7. Work example #7. (See attached file.) Answer students' questions and comments.
8. Work example #8. (See attached file.) Answer students' questions and comments.
9. Work example #9. (See attached file.) Answer students' questions and comments.
10. Work example #10. (See attached file.) Answer students' questions and comments.
11. Work example #11. (See attached file.) Answer students' questions and comments.
12. Discuss why you must check solutions. (See #12 on attached file.) Answer students' questions and comments.
13. Discuss extraneous values. (See #13 on attached file.) Answer students' questions and comments.
14. Discuss the importance of isolating the radical. Show an example. (See #14 on attached file.) Answer students' questions and comments.
15. Distribute the Doing Battle with Radical Equations Worksheet. (See attached file.)
16. Distribute the Doing Battle with Radical Equations Checklist. (See attached file.)
17. The students will write their responses on the worksheet.
18. Move from student to student observing the students' work and lending assistance.
19. Assess the activity.
Assessments
The student worksheet will be collected and scored according to the Doing Battle with Radical Equations CHECKLIST. (See attached file.)
Extensions
Give students real-world application problems involving radicals. Have students solve these problems and determine if the solution is reasonable. (See #15 on attached file.)
Web Links
Web supplement for Doing Battle With Radical Equations RADICAL EQUATIONSWeb supplement for Doing Battle With Radical Equations EQUATIONS INVOLVING A RADICAL
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