Chapter 1Set Theory: Using Mathematics to Classify Objects

Section 1.1Problem Solving

Objective of Lesson

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

Problem Solving Strategies1. Finding What Is Missing

2. Finding What Is Unnecessary

3. Applying the Four-Step Procedurei. Understand the problem.

ii. Devise a plan.

iii. Carry out the plan and solve the problem.

iv. Look back and check the answer.

4. Solving a Problem by Making a List

5. Solving a Problem by Using a Diagram

Example 1: Finding What Is Missing

A man purchased five shirts, each at the same discount price. How much did he pay for them?

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 $1.23. If you need 3 rolls of paper towels, which brand is the better value?

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

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

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

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

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?

Example 4:Solving a Problem by Making a List

Half-Dollars Quarters Dimes Nickels

1 0 0 0

0 2 0 0

0 1 2 1

0 1 1 3

0 1 0 5

0 0 5 0

0 0 4 2

0 0 3 4

0 0 2 6

0 0 1 8

0 0 0 10

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

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

Assignments:

Class work:Handout

• To receive credit, you must show ALL work.

Homework:Handout

• To receive credit, you must show ALL work.