### Johnny WolfeSanta Rosa District Schools

#### Description

Solving quadratic equations using the Complete the Square form.

#### Objectives

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 Is Your Square Complete? (see attached file).
- Is Your Square Complete? Examples (see attached file).
- Is Your Square Complete? Worksheet (see attached file).
- Is Your Square Complete? Checklist (see attached file).

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for Is Your Square Complete? Examples (see attached file).

2. Have marking pens (for overhead).

3. Have Is Your Square Complete? Examples (see attached file) prepared and ready to demonstrate to students.

4. Have enough copies of Is Your Square Complete? Worksheet (see attached file) for each student.

5. Have enough copies of Is Your Square Complete? 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.

1. Illustrate to students how to solve to a quadratic of the form x
2 – b
2 using inverse operations (see # 1 on attached file Is Your Square Complete? Examples). Answer student questions and comments.

2. Work example # 2 (see attached file Is Your Square Complete? Examples). Explain to students that the quadratic expression must be a perfect square in order to use this method. If it is not a perfect square then we must make it a perfect square using a method called “completing the square.” Answer student questions and comments.

3. Work example # 3 (see attached file Is Your Square Complete? Examples). Ask students if they notice a pattern (if students cannot pick out the pattern suggest that they half the middle term and then square). Answer student questions and comments.

4. Go over the three steps for completing the square of a quadratic equation of the form x
2 + bx (see # 4 on attached file Is Your Square Complete? Examples). Answer student questions and comments.

5. Work example # 5 (see attached file Is Your Square Complete? Examples}. Emphasize that the “c” term is half the middle term squared. Answer student questions and comments.

6. Work example # 6 (see attached file Is Your Square Complete? Examples). Point out to students that this quadratic is not a perfect square. Therefore we must rewrite the equation so that it becomes a perfect square. Answer student questions and comments.

7. Work example # 7 (see attached file Is Your Square Complete? Examples). Point out to students that to complete the square the coefficient of x
2 must be 1. Therefore we will divide each side of the equation by the coefficient of x
2. Then complete the 3 steps for completing the square. Answer student questions and comments. Note: If roots involve radicals, they come in conjugate pairs.

8. Distribute the Is Your Square Complete? Worksheet[see attached file).

9. Distribute the Is Your Square Complete? Checklist (see attached file). Describe what constitutes an “A,” “B,” “C,” “D,” and an “F” in the Checklist.

10. The student will write their responses on the worksheet.

11. Move from student to student observing the student's work and lending assistance.

#### Assessments

The student worksheet will be collected and scored according to the Is Your Square Complete? Checklist (see attached file).

#### Extensions

Give students the roots of a quadratic equation and have them build a perfect square quadratic.