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

Section 1.1 Problem Solving

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

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

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 2 3 5 4 6 8 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: Homework: Handout To receive credit, you must show ALL work. Homework: