## Which Way Am I Walking?

### Ramon Pedraja

#### Description

Students learn the concept of inverses through a real-world example, then relate it specifically to multiplication and division.

#### Objectives

The student explains and demonstrates the inverse nature of multiplication and division, with particular attention to multiplication by a fraction (for example, multiplying by 1/4 yields the same result as dividing by 4).

#### Materials

-PowerPoint Software/Projector (Transparencies as a backup)
-Computer
-Markers
-Clean Board/Eraser
-Paper (printed problems on it)

#### Preparations

1. Prepare 30 PowerPoint slides
2. Select practice problems
3. Create practice problem sheets and make copies for all students.
4. Select explanation problems.

#### Procedures

1. Call for a volunteer.

2. Ask the volunteer to walk across the room.

3. Ask the class which way is the person walking?

5. Ask the new volunteer to walk across the room, but this time backwards.

6. Ask the class which way is the person walking?

7. Did the second person get to the same place as the first walker?

8. Tell students they are going to learn about inverse operations.Tell them it is similar to giving directions….turning right from one way is the same as turning left from the opposite direction.

9. Ask them if they can think of any other instances of inverse operations.

10. Explain how multiplication and division are inverse operations.

11. Work through several multiplication and division statements, calling on students randomly. Write the mathmatical statements on the board and model to the students.

12. Give students a practice problem sheet with five multiplication statements and have them write similar division statements.

13. Give students a practice problem sheet with five division statements and have them write similar multiplication statements.

14. Review the answers on the board with the students when they have all attempted the activity.

15. Using a PowerPoint (or Transparencies) presentation, have each slide show a multiplication or division statement. Call on each one of the students, then he or she will have to provide three responses:
1. What is the original number?
2. Will the answer be smaller or larger than the original number?

Examples: 8 / 2 =
1. -What is the original number?- Answer- -8-
2. -Will the answer be smaller or larger than the original number?- Answer- -Smaller-

8 x 1/2 =
1. -8-
2. -Smaller-
3. -4-

-We get the same answer because dividing by a number is the same as multiplying by its inverse-

Other examples: 8 x 2 = AND 8 / (1/2) =

#### Assessments

Have a student performance roster (checklist with student names) and as the students answer the questions from the PowerPoint presentation, tally the correct responses for each student.

The student must complete four correct responses(two multiplication, two division) in a row to demonstrate mastery. Students not answering four will have multiple opportunities to do so, however, when they miss one of the four, the teacher will call on a different student and come back to them. The class will be encouraged to applaud the successful efforts of each student.

(The performance roster will be a list of the students in the class with a space for tally marks for each of the four responses.)

#### Attached Files

Problems to be used on the PowerPoint slides and for Assessment purposes.     File Extension:  pdf