1.3 Problem Solving. p.22. Polya’s 4 Steps in Problem Solving. Understand the problem . a. Read the problem several times. b. Write down what you know and what you need to know. Polya’s 4 Steps in Problem Solving. Devise a plan . Choose a problem solving strategy:
1.3 Problem Solving p.22
Polya’s 4 Steps in Problem Solving • Understand the problem. a. Read the problem several times. b. Write down what you know and what you need to know.
Polya’s 4 Steps in Problem Solving • Devise a plan. Choose a problem solving strategy: a. Look for a pattern b. Make a list or table c. Make and educated guess d. Work backwards e. Use trial and error f. Make a drawing g. try expressing it as a simpler problem h. Use elimination I. Use common sense. Is the answer too obvious? It could be a trick. j. relate the problem to one you’ve worked before.
Polya’s 4 Steps in Problem Solving • Carry out the plan a. solve the problem using one or more of the problem solving methods
Polya’s 4 Steps in Problem Solving • Check your answer a. Did you answer the question asked? b. Does your answer make sense? c. Recheck your work
Example 1: What information is missing? • A man purchased five shirts, each at the same discount price. How much did he pay for them? • The bill for your meal totaled $20.36, including tax. How much change should you receive?
Example 2: Find the unnecessary information. Then solve the problem. • A roll of E-Z Wipe paper towels contains 100 sheets and costs $1.38. A comparable brand contains five-dozen sheets per roll and costs $1.23. If you need three rolls of paper towels, which brand is the better value?
Unit price • Unit price is the total price divided by the total units. • To compare prices, the best value is the brand with the lowest unit price.
Example 3 • A manufacturer packages apple juice in boxes and in bottles. A 128-ounce bottle costs $5.39 and a 9-pack of 6.75 boxes costs $3.15. Which is the better value?
Example 4: Use Polya’s method to solve • By paying cash up front and the balance at $20 a week, how long will it take to pay for a bicycle costing $680?
Example 5: • Suppose you are an engineer programming the automatic gate for a 30-cent toll. The gate should accept exact change only. It cannot accept pennies. How many coin combinations must you program the gate to accept? (use a table)
Example: Use a diagram • You have two pair of pants (blue and black) and three shirts (red, yellow and white) that you can where to work. How many different outfits can you form?
Ch. review • P.36 1.3/27,28,31 • P.36 Chapter 1 Test/6-11,13,16