## The Case of the Missing Middle Term

### Johnny WolfeSanta Rosa District Schools

#### Description

You can use the difference of squares to factor binomials of the form “a" squared minus “b” squared.

#### Objectives

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

Describes, analyzes and generalizes relationships, patterns, and functions using words, symbols, variables, tables and graphs.

#### Materials

-Overhead transparencies (if examples are to be worked on overhead) for THE CASE OF THE MISSING MIDDLE TERM (See attached file)
-THE CASE OF THE MISSING MIDDLE TERM EXAMPLES (See attached file)
-THE CASE OF THE MISSING MIDDLE TERM WORKSHEET (See attached file)
-THE CASE OF THE MISSING MIDDLE TERM CHECKLIST (See attached file)

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for THE CASE OF THE MISSING MIDDLE TERM EXAMPLES. (See attached file.)

2. Have marking pens (for overhead).

3. Have THE CASE OF THE MISSING MIDDLE TERM EXAMPLES prepared and ready to demonstrate to students. (See attached file.)

4. Have enough copies of THE CASE OF THE MISSING MIDDLE TERM WORKSHEET for each student. (See attached file.)

5. Have enough copies of THE CASE OF THE MISSING MIDDLE TERM 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, area, distributive property, multiplying binomials, and FOIL method. Note: Tables and graphs will not be assessed.

1. Draw the two squares from examples 1 and 2. (See attached file: THE CASE OF THE MISSING MIDDLE TERM EXAMPLES.) Ask the students to determine the area of each square.

2. Ask the students what the area would be if you cut away the “square b” area from “square a”? Get their responses and make sure they understand that it will be ("a" squared minus "b" squared).

3. Manipulate the squares as shown in example 3. (See attached file: THE CASE OF THE MISSING MIDDLE TERM EXAMPLES.) (It may be helpful to have students cut out squares on paper to visualize the relationship. This way they can manipulate the pieces of paper and grasp the concept).

4. Have students multiply the binomials from example 4. (See attached file: THE CASE OF THE MISSING MIDDLE TERM EXAMPLES.) If students are unsure of the products, review the “FOIL” method in example 13).

5. Have students make comments about the pattern that is being developed. (See example 5 in the attached file: THE CASE OF THE MISSING MIDDLE TERM EXAMPLES.)

6. Introduce the “Difference of Squares” equation. (See example 6 in attached file: THE CASE OF THE MISSING MIDDLE TERM EXAMPLES.)

7. Go over example 7. (See attached file: THE CASE OF THE MISSING MIDDLE TERM EXAMPLES).

8. Go over example 8. (See attached file: THE CASE OF THE MISSING MIDDLE TERM EXAMPLES.)

9. Go over example 9. (See attached file: THE CASE OF THE MISSING MIDDLE TERM EXAMPLES.)

10. Go over example 10. (See attached file: THE CASE OF THE MISSING MIDDLE TERM EXAMPLES.)

11. Go over example 11. (See attached file: THE CASE OF THE MISSING MIDDLE TERM EXAMPLES.)

12. Go over example 12. (See attached file: THE CASE OF THE MISSING MIDDLE TERM EXAMPLES.)

13. Review “FOIL” method if not mentioned earlier.

14. Reinforce “why” there are no middle terms in the “difference of squares” model. (See number 14 on attached file: THE CASE OF THE MISSING MIDDLE TERM EXAMPLES.)

15. Go over example 15. (See attached file: THE CASE OF THE MISSING MIDDLE TERM EXAMPLES.)

16. Distribute THE CASE OF THE MISSING MIDDLE TERM WORKSHEET. (See attached file.)

17. Distribute the CASE OF THE MISSING MIDDLE TERM CHECKLIST. (See attached file). Describe what constitutes an “A,” “B,” “C,” “D,” and an “F” in the CHECKLIST.

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

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

#### Assessments

Student worksheets will be taken up and evaluated using THE CASE OF THE MISSING MIDDLE TERM CHECKLIST.

#### Extensions

Have a “math bee” (similar to a spelling bee) where you call out binomials (those that fit the difference of square model), and the students call out the factored form.