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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?