## How Simple Is Your Rational Expression?

### Johnny WolfeSanta Rosa District Schools

#### Description

Rational expressions are algebraic expressions whose numerator and denominator are polynomials. This lesson simplifies such expressions and identifies values of the variable that must be excluded.

#### 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 "How Simple Is Your Rational Expression?"(see attached file).

- "How Simple Is Your Rational Expression?" Examples (see attached file).

- "How Simple Is Your Rational Expression?" Worksheet (see attached file).

- "How Simple Is Your Rational Expression?" Checklist (see attached file).

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for "How Simple Is Your Rational Expression?" Examples (see attached file).

2. Have marking pens (for overhead).

3. Have "How Simple Is Your Rational Expression?" Examples (see attached file) prepared and ready to demonstrate to students.

4. Have enough copies of "How Simple Is Your Rational Expression?" Worksheet (see attached file) for each student.

5. Have enough copies of "How Simple Is Your Rational Expression?" 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 does not address percents, scientific notation, radicals, absolute value, and radicals; does not address square roots and appropriate inverse relationships; nor does it address square roots.

1. Define rational expressions (see # 1 on attached file "How Simple Is Your Rational Expression?" Examples). Answer student questions and comments.

2. Discuss why zero cannot be in the denominator of a rational expression (see # 2 on attached file "How Simple Is Your Rational Expression?" Examples).

3. Discuss why some solutions must be excluded from the solution set (see # 3 on attached file "How Simple Is Your Rational Expression?" Examples). Answer student questions and comments.

4. Go over examples of exclusion (see # 4 on attached file "How Simple Is Your Rational Expression?" Examples). Answer student questions and comments.

5. Work example # 5 (see attached file "How Simple Is Your Rational Expression?" Examples). Answer student questions and comments.

6. Work example # 6 (see attached file "How Simple Is Your Rational Expression?" Examples). Answer student questions and comments.

7. Discuss simplifying common factors by using the GCF (Greatest Common Factor) (see # 7 on attached file "How Simple Is Your Rational Expression?" Examples). Answer student questions and comments.

8. Work example # 8 (see attached file "How Simple Is Your Rational Expression?" Examples). Answer student questions and comments.

9. Work example # 9 (see attached file "How Simple Is Your Rational Expression?" Examples). Answer student questions and comments.

10. Distribute the "How Simple Is Your Rational Expression?" Worksheet (see attached file).

11. Distribute the "How Simple Is Your Rational Expression?" Checklist (see attached file). Describe what constitutes an “A,” “B,” “C,” “D,” and an “F” in the Checklist.

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

13. 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 "How Simple Is Your Rational Expression?" Checklist (see attached file).

#### Extensions

Give students particular limits to stay within and have them build a rational expression. For example, the roots are 2 and 3 with exclusion of 1.