## Topsy-Turvy Math With Rational Numbers

### Johnny WolfeSanta Rosa District Schools

#### Description

To find the quotient of two rational numbers, you multiply by the reciprocal of the second rational number.

#### Objectives

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.

Understands and explains the effects of addition, subtraction, multiplication and division on real numbers, including square roots, exponents, and appropriate inverse relationships.

Adds, subtracts, multiplies, and divides real numbers, including square roots and exponents using appropriate methods of computing (mental mathematics, paper-and-pencil, calculator).

#### Materials

- Overhead transparencies (if examples are to be worked on overhead) for "Topsey Turvey Math With Rational Numbers" (see attached file).

- "Topsey Turvey Math With Rational Numbers" Examples (see attached file).

- "Topsey Turvey Math With Rational Numbers" Worksheet (see attached file).

- "Topsey Turvey Math With Rational Numbers" Checklist (see attached file).

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for "Topsey Turvey Math With Rational Numbers" Examples (see attached file).

2. Have marking pens (for overhead).

3. Have "Topsey Turvey Math With Rational Numbers" Examples (see attached file) prepared and ready to demonstrate to students.

4. Have enough copies of "Topsey Turvey Math With Rational Numbers" Worksheet (see attached file) for each student.

5. Have enough copies of "Topsey Turvey Math With Rational Numbers" Checklist (see attached file) for each student.

#### Procedures

Prior Knowledge: Students should be familiar with basic operation skills such as addition, subtraction, multiplication, division, exponents, fractions, decimals, solving quadratic equations, and factoring. NOTE: This lesson did not address decimals, percents, scientific notation, radicals, absolute value or logarithms. This lesson did not address square roots.

1. Ask the students to study the products in Example # 1 (have students discuss the pattern of the factors) (see attached file "Topsey Turvey Math With Rational Numbers" Examples). Answer student questions and comments.

2. Go over definition of multiplicative inverses and reciprocals (see # 2 on attached file "Topsey Turvey Math With Rational Numbers" Examples). Answer student questions and comments.

3. Discuss how to find the quotient of two fractions (see # 3 attached file "Topsey Turvey Math With Rational Numbers" Examples). Discuss GCF and reducing fractions to simplest form. Answer student questions and comments.

4. Go over the equation that describes dividing rational numbers (see # 4 on attached file "Topsey Turvey Math With Rational Numbers" Examples). Answer student questions and comments.

5. Compare division of fractions to rational numbers (see # 5 on attached file "Topsey Turvey Math With Rational Numbers" Examples). Answer student questions and comments.

6. Do Example # 6 (see attached file "Topsey Turvey Math With Rational Numbers" Examples). Answer student questions and comments.

7. Do Example # 7 (on attached file "Topsey Turvey Math With Rational Numbers" Examples). Stress that each polynomial must be written in factored form and then simplified. Answer student questions and comments.

8. Warn students about finding the reciprocal of a polynomial (see # 8 on attached file "Topsey Turvey Math With Rational Numbers" Examples). Answer student questions and comments.

9. Distribute the "Topsey Turvey Math With Rational Numbers" Worksheet (see attached file).

10. Distribute the "Topsey Turvey Math With Rational Numbers" Checklist (see attached file). Describe what constitutes an A, B, C, D, and an F in the Checklist.

11. The student will write their response on the worksheet.

12. The teacher will move from student to student observing the students work and lending assistance.

#### Assessments

The student worksheet will be collected and scored according to the "Topsey Turvey Math With Rational Numbers" Checklist (see attached file).

#### Extensions

Give the students the area of a rectangle using a rational expression. Give the measure of the length of the rectangle and have students find the width.