1. Set Theory: Using Mathematics to Classify Objects
Chapter 1
Set Theory: Using Mathematics to Classify Objects

2. Section 1.1
Problem Solving

3. Objective of Lesson
To be able to solve problems using the organization of the four-step problem solving process.

4. Problem Solving Strategies
Finding What Is Missing
Finding What Is Unnecessary
Applying the Four-Step Procedure
Understand the problem.
Devise a plan.
Carry out the plan and solve the problem.
Look back and check the answer.
Solving a Problem by Making a List
Solving a Problem by Using a Diagram

5. Example 1: Finding What Is Missing
A man purchased five shirts, each at the same discount price. How much did he pay for them?

6. Example 2: Finding What Is Unnecessary
A roll of E-Z Wipe paper towels contains 100 sheets and costs $1.38. A comparable brand, Kwik-Clean, contains five dozen sheets per roll and costs $ If you need 3 rolls of paper towels, which brand is the better value?

7. Example 3: Applying the Four-Step Procedure
By paying $100 cash up front and the balance at $20 a week, how long will it take to pay for a bicycle costing $680?
Step 1: Understand the problem

8. Example 3: Applying the Four-Step Procedure
By paying $100 cash up front and the balance at $20 a week, how long will it take to pay for a bicycle costing $680?
Step 2: Devise a plan

9. Example 3: Applying the Four-Step Procedure
By paying $100 cash up front and the balance at $20 a week, how long will it take to pay for a bicycle costing $680?
Step 3: Carry out plan & solve problem

10. Example 3: Applying the Four-Step Procedure
By paying $100 cash up front and the balance at $20 a week, how long will it take to pay for a bicycle costing $680?
Step 4: Look back & check answer

11. Example 4: Solving a Problem by Making a List
Suppose you are an engineer programming an automatic gate for a 50-cent toll. The gate should except exact change only. It should not accept pennies. How many coin combinations must you program the gate to accept?

12. Example 4: Solving a Problem by Making a List
Half-Dollars
Quarters
Dimes
Nickels 1 2 3 5 4 6 8 10

13. Example 5: Solving a Problem by Using a Diagram
Four runners are in a one-mile race: Maria, Aretha, Thelma, and Debbie. Points are awarded only to the women finishing first or second. The first-place winner gets more points than the second-place winner. How many different arrangements of first- and second-place winners are possible?
Maria
Aretha
Thelma
Debbie

14. Example 5: Solving a Problem by Using a Diagram
Maria
Aretha
Thelma
Debbie
Aretha
Maria
Thelma
Debbie
Thelma
Maria
Aretha
Debbie
Debbie
Maria
Aretha
Thelma

15. Assignments: Class work: Homework: Handout
To receive credit, you must show ALL work.
Homework: