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PROBLEM SOLVING STRATEGIES  
   
Problem Solvers Acknowledgements

The real obstacle when we are faced with an impossible problem is inside us. It is our experiences, mistaken assumptions, half-truths, misplaced generalities, and habits that keep us from brilliant solutions.

--Scott Thorpe
Strategies

1-Draw a Diagram

2-Make a List

3-Guess and Check

4-Divide and Conquer

5-Look for a Pattern

6-Start at the End

7-Mixed Problems

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STRATEGY 2: MAKE A LIST

There is a common saying, "Don't just stand there, do something!" When solving a problem, don't just think, write something! Draw a diagram or make a list!

It is often obvious when you should draw a diagram. And it is often obvious when you should make a list. Take a very simple example: putting things in order.

The letters ABCD, can be put into a different order: DCBA or BADC. How many different combinations of the letters ABCD can you make? To answer this question, obviously, you have to make a list.

Teach your students to make a SYSTEMATIC list. For example:

ABCD

ABDC

ACBD

ACDB

ADBC

ADCB

BACD

BADC

BCAD

BCDA

BDAC

BDCA

CABD

CADB

CBAD

CBDA

CDAB

CDBA

DABC

DACB

DBAC

DBCA

DCAB

DCBA

 

By making a SYSTEMATIC list, students will see every possible combination.

(Later, perhaps, they will learn that the number of permutations of size 4 taken from a set of 4 can be represented by the formula 4 * 3 * 2 * 1 = 24).

 

Problems:

Problem 1: Kisses

Problem 2: Linen Shop or Pizzeria

Problem 3: Dominoes

Problem 4: Get Well Soon

Problem 1: Kisses

Ten people arrive at a party.  As they arrive, each person kisses every other person twice, once on each cheek.  How many kisses are there?

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Problem 2: Linen Shop or Pizzeria

A linen shop sells sheets, duvet covers, and pillow cases. Linens from the Easirest company offer a choice in each color: a plain sheet or a sheet with a pattern, a plain duvet cover or a duvet cover with a pattern, plain pillow cases or pillow cases with a pattern. Customers may mix and match the plain or patterned sheets, duvet covers, and pillow cases in any combination they wish. To help the shop make its next order from the Easirest company, you have been asked to make a record of the different combinations that customers have chosen. How many different combinations are possible?

Some students might be more interested in pizza. The same problem might occur in a pizzeria.

 

 Solution -->

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Problem 3: Dominoes

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A tree diagram is a useful type of list. For example, the game of dominoes is played with black and white tiles. Each tile is divided into two halves and on each half a number from 0-6 is represented in the form of dots. Each tile contains a pair of numbers and each pair appears only once in a complete set. How many tiles are there in a complete set of tiles? The solution to this problem can take the form of a tree diagram.

 

Solution -->

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Problem 4: Get Well Soon

Melike and Funda are good friends. When Melike got the flu, her doctor wrote a prescription for twenty 30mg pills, and told her to take two a day, one after breakfast and one after dinner. Three days later, Funda also got the flu. Her doctor prescribed thirty 20mg pills, and told her to take a pill every four hours between 9:00 and 21:00. Whose medicine was finished first?

 

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PROBLEM SOLVING STRATEGIES

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