problem-solving strategies i

8/8/2019 Problem-Solving Strategies I

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Problem SolvingProblem SolvingStrategies IStrategies I

Problem SolvingProblem SolvingStrategies IStrategies I

Guess & CheckGuess & Check

Draw a diagramDraw a diagramWorking backwardsWorking backwards


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Problem 1

You are required to usenumerals 1, 2, 3, 4, 5, 6,7 and 8 only to be putinside the 8 squares.

The condition is thatthe neighboringnumbers must not beput next to each other,

either above, below,left, right or diagonally.


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Problem 2 How would you place these digits 1, 2, 3,4, 5 and 6 in the circles as below such

that the sum at all the sides of thetriangle is 11 or 12.


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3 ways of Guess &

Check Guess & check at random

Systematic guess & check

Guess & check by inference

Step 1 : understand the problem


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Guess & check at random

Step 2 : Make a plan Take 6 pieces of paper Write the digits 1 to 6

Step 3 : Implement the plan Arrange the 6 pieces of paper in an

equilateral triangle

Check if the total at all the sides Arrange until you get 12 at all the sides


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Systematic guess & check

Step 2 : Make a plan Put the 3 smaller numbers at the verticesStep 3 : Implement the plan Put 1, 2 & 3 at the vertices

Total at all the sides are too small Try 1, 2 & 4 and so on Until you put 4, 5 & 6 at the vertices

Alternative:Put 3 bigger numbers at the vertices


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Guess & check by inference

Step 2 : Make a plan/conjecture

A particular number must be at the top of thetriangle

Investigate possibilities that arise

Step 3 : Implement the plan If 1 is put there, then we need 11 to form 12

on two of the sides

Only one combination that gives 11, i.e. 5 & 6 So 1 cannot be put there

What if 2? 3? 4?


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Step 4 : Looking back

Is the solution correct?

Is there easier way to get the

solution?


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Problem 3

Mary hits the dartboard shown belowwith 4 darts. Each dart hits adifferent number. Her total scorewas 60. How might she have scored60?

15 7 19

10 31 17

9 25 5


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Guess & Check

Guess & check by random is usually used asa start in solving a problem

But it requires too many trials and can be

confusing or misleading Guess & check systematically enables us to

expand a scheme to try all possibilities Guess & check by inference saves time &

gives more information about all thepossible solutions


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Find the maximum product

8x


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Problem 4

A

B

Cylinder A can be used to contain exactly9 liters of water. Cylinder B can be usedto contain exactly 4 liters of water.

By using cylinders A and B only, explainhow can you measure exactly 6 liters ofwater?


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Working Backwards A strategy that is used when the outcome

of a situation is known, and the initialconditions are required

When we work backwards, the operationsrequired by the original action will have tobe reversed

Example: subtraction replaces addition,division replaces multiplication, and viceversa


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Problem 5 Jimmy was trying a number trick on

Sally. He told her to pick a number,

add 5 to it, multiply the sum by 3,then subtract 10 and double theresult

Sallys final answer was 28

What number did Sally start with?


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Problem 6 Freddy Frog is at the bottom of a

well 10m deep. Each hour he climbs

up 1m and then falls back 0.5m. Howlong is it before Freddy is out of thewell?


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Draw a diagram Paper and pencil simulation of the

action described in a problem

Enable students to convert a verbalsituation into a visual representation

Remove destructors, recognize facts,

understand relationships in theproblem


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Problem 7 If posts are spaced 10m apart, how

many posts are needed for 100m of

straight-line fence?


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Problem 8 Sylvia dropped a tennis ball from a balcony

16 feet above the side walk. Each time

the ball bounced, it travelled half as highon the previous bounce. Sylvias brothercaught the ball when it bounced exactly 1foot from the sidewalk. How many times

did the ball bounced?

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