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PROBLEM SOLVING

PROBLEM SOLVING. Thursday October 25, 2007 Ms. Manaktola. The Coin Problem. Ludek has 22 coins in his pocket. The coins have a total value of $1.45. If the coins are nickels and dimes only, how many of each coin does Ludek have?

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PROBLEM SOLVING

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  1. PROBLEM SOLVING Thursday October 25, 2007 Ms. Manaktola

  2. The Coin Problem Ludek has 22 coins in his pocket. The coins have a total value of $1.45. If the coins are nickels and dimes only, how many of each coin does Ludek have? We are dealing with a MIXTURE of nickels and dimes, so let’s simplify the problem by only looking at one of the things in the mixture.

  3. The Coin Problem Pretend that Ludek only has nickels in his pocket. How many nickels would you need to make $1.45? $1.45 ÷ 0.05 = 29 nickels

  4. The Coin Problem BUT, the question tells us that Ludek only has 22 nickels in his pocket. How many EXTRA coins? 29 – 22 = 7 Remember: 2 nickels = 1 dime

  5. The Coin Problem Every time I trade nickels for dimes, the amount of coins I have decreases by one. So if I want to decrease the number of coins from 29 to 22, I will have to make 7 trades. (Demonstration using counters)

  6. The Coin Problem • That means there will be 7 dimes, and 15 nickels. • Let’s check our answer: 7(0.10) + 15(0.05) = $1.45

  7. The Card Problem There are 20 people in Susan’s class. Each person gives a card to everyone in the class. How many cards were exchanged? There are a lot of cards being exchanged in this problem. To make it simpler, let’s look at a smaller class.

  8. The Card Problem

  9. The Card Problem • What’s the pattern? In a group that has n number of classmates, each student gives (n-1) cards. In a class of 20, each student will give 19 cards. 20 x 19 = 380 cards are exchanged.

  10. The Pyramid Problem

  11. The Pyramid Problem Can we use an algebraic expression to describe the pattern?

  12. Homework Textbook: Page 138, #4-11 Monday October 29: Problem Solving QUIZ

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