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Chapter 1

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

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Chapter 1

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  1. 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 $1.23. 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

  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?

  14. Example 5:Solving a Problem by Using a Diagram

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

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