PROBLEM SOLVINGPROBLEM SOLVINGThursday October 25, 2007 Ms. ManaktolaThursday October 25, 2007 Ms. Manaktola

The Coin ProblemThe 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.

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.

The Coin ProblemThe 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

The Coin ProblemThe 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

The Coin ProblemThe 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)

The Coin ProblemThe 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

That means there will be 7 dimes, and 15 nickels.

Let’s check our answer:7(0.10) + 15(0.05) = $1.45

The Card ProblemThe 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.

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.

The Card ProblemThe Card Problem

# of Student

s in Class

Diagram # of Cards Each

Person Gives

Total # of Cards

Exchanged

2 1 2

3 2 6

4 3 12

The Card ProblemThe 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.

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.

The Pyramid ProblemThe Pyramid Problem

Layer # of Rows Cans in Each Row

Total Cans in Layer

1 2 3 6

2 4 6 24

3 8 12 96

The Pyramid ProblemThe Pyramid Problem

Can we use an algebraic expression to describe the pattern?

Can we use an algebraic expression to describe the pattern?

HomeworkHomework

Textbook: Page 138, #4-11

Monday October 29: Problem Solving QUIZ

Textbook: Page 138, #4-11

Monday October 29: Problem Solving QUIZ