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PROBLEM SOLVING Thursday October 25, 2007 Ms. Manaktola

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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 lets simplify the problem by only looking at one of the things in the mixture. 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 lets simplify the problem by only looking at one of the things in the mixture.

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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 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

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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 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

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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) 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)

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

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The Card Problem There are 20 people in Susans 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, lets look at a smaller class. There are 20 people in Susans 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, lets look at a smaller class.

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The Card Problem # of Students in Class Diagram# of Cards Each Person Gives Total # of Cards Exchanged 212 326 4312

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The Card Problem Whats 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. Whats 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.

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The Pyramid Problem Layer # of RowsCans in Each Row Total Cans in Layer 1236 24624 381296

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

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

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