Math

Finding Pattern

One of most frequently used problem solving strategies is that a recognizing an extending a pattern. As we shall see, there are many times that this is used a strategy in conjunction with other problem solving strategies. For this discussion, though, we look at some problems that can be solved by identifying a pattern in given and simply applying that pattern to the problem situation.

Operation #

Suppose that there is a mathematical operation called #, in which each of the following statements is true.

2 # 5 = 9

5 # 3 = 13

3 # 5 = 11

8 # 7 = 23

What is the value of 7 # 3 ?

Do you observe any pattern that applies to all the given examples? The statements 2#4=8 may lead you think that the pattern is one of multiplication, but you can soon see that this does not apply to the other examples. The fact that 5#3 does not have the same value as 3#5 indicates that the order of the numbers make a difference. Pause to consider whether a cpmbination of operations might be involved. Try doubling the firs number. Did you conclude that operation # consist of doubling the firs number then adding the second number to that result.

So the answer 7#3=2×7+3=17

QUIZ

TEST 1

4 # 2 = 8

5 # 3 = 11

3 # 5 = 13

1 # 7 = 15

4 # 3 = ?

TEST2

3 # 1 = 9

1 # 3 = 9

2 # 2 = 12

5 # 1 = 15

? # 3 = 18

source :
Lenchner, George .“Creative Problem Solving in School Mathematics”.New York: Glenwood Publoication Inc.h22-23

Solution :Draw A Model

Sheila and Muthu have 80 marbles altogether. Sheila and Alice have 50 marbles altogether. Alice has as many marbles as Muthu. How many marbles does Sheila have?

Find the Answer!

1. The total of two numbers is 51. Their difference is 9. What are the two numbers?

2. 1/4 of a number is 120. What is 70% of the number?

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