problem solving thursday october 25, 2007 ms. manaktola
TRANSCRIPT
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