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Work Backwards
Problem Solving Strategy
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Work Backwards
Working backwards is another strategy that requires you to
change your focus. Youll consider the whole problem inreverse. Once you reach a solution, check it by working itforward from your solution to make sure it indeed reachesthe desired solution.
Consider planning a vacation to Europe. Once you find a
flight, you need to work backwards to plan the beginningof your tripwhen do you need to arrive at the airport andthen when must you leave your house to arrive at theairport at that time, etc.
Many problems that can be solved by working backwards
can also be solved using guess and check. But, whenthere is a way to work backwards, it is more efficient to doso. If it is hard to figure out how to begin a problem withthe working backwards strategy, use guess and check tofind a place to start and then work backwards.
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Strategy: Work Backwards
Write out the steps in order. Work from the end to the
beginning.
Draw diagrams as needed. Perhaps act it out.
Use algebra or other tools to getfrom one step to the previous one.
Check from the beginning to the
end.
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How many M&Ms ?
After dinner, three friends leaving arestaurant noticed a bowl of M&Ms on thefront counter.
Steven took one-fourth of the M&Ms butreturned four because he had a momentarypang of guilt.
Aakash then took one-third of what was leftbut returned three for similar reasons.
Eugene then took half the remainder but threwtwo green ones back.
The bowl had only 17 M&Ms left after the boyshelped themselves. How many mints wereoriginally in the bowl?
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Write down the story steps in order
Begin.Steven took 1/3 of the M&Ms.
Steven returned 4.
Aakash took 1/4 of what was left.Aakash returned 3.
Eugene took half the remainder.
Eugene threw 2 back.The bowl had 17 M&Ms
left.
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Work backwards from theend to the beginning.
Bowl is full.
Steven took 1/3 of theM&Ms.
Steven returned 4.
Aakash took 1/4 of
what was left.
Aakash returned 3.
Eugene took half the
remainder. Eugene threw 2 back.
The bowl had 17 M&Msleft.
17 in the bowl
15 in the bowl
30 in the bowl
27 in the bowl
36 in the bowl
32 in the bowl
48 in the bowl !
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Check from beginningto end.
Bowl is full.
Steven took 1/3 of theM&Ms.
Steven returned 4.
Aakash took 1/4 of
what was left.
Aakash returned 3.
Eugene took half the
remainder. Eugene threw 2 back.
The bowl had 17 M&Msleft.
48 16
32 + 4
36 9
27 + 3
30 15
15 + 2
17 it works!
48 in the bowl
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Now itsyour turn
Open your problem solving book and go tothe section on Work BackwardsWork Backwards (page 27).
Print off a problem solving sheet and do acomplete solution to a problem from this
sectiondo one and submit it or do more forextra fun. (Dad's Wallet and the ATM, Crossing the River,and/or Golf Clubs )
Email your complete solution, with your stepsclearly shown to [email protected] orput them in Nancy Powells mail box!
Have fun and Problem Solve!Have fun and Problem Solve!
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Now itsyour turn
Jack walked from Santa Clara to Palo
Alto. It took 1 hour 25 minutes to walk
from Santa Clara to LosA
ltos. Then ittook 25 minutes to walk from Los Altos
to Palo Alto. He arrived in Palo Alto at
2:45 P.M. At what time did he leave
Santa Clara?
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Now itsyour turn
Joe forgot to check how much money he
began the day with. During the day, he
spent $8.00 on breakfast, withdrew $40.00
from the ATM, got his dry cleaning for $12.00,
bought 5 shirts for $22.00 a piece (plus 8%
sales tax).A
t the end of the day, he had$100.00, how much did he start the day
with?
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Now itsyour turn
J
oe gives Nick and Tom as many peanuts aseach already has. Then Nick gives Joe and
Tom as many peanuts as each of them then
has. Finally, Tom gives Nick and Joe as
many peanuts as each has. If at the end
each has sixteen peanuts, how many
peanuts did each have at the beginning?
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Now itsyour turn
The grid represents a section of townwith only 2-way streets. You want togo from point A to point B withoutbacktracking. How many different
routes are possible? (You can only gonorth or east at each intersection.)
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After Melody returned from
shopping, she had $4.00. She had
spent $5.25 for lunch and $13.75 on anew music CD. How much money did
she have when she began her
shopping trip?
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Rujukan .
http://www.mathstories.com/strategies_working_backward.htm
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remember Work Backwards
Problem Solving Strategy
Owner :
Siti Zulaikha binti Abdu RahimFarahatun Nailah binti Mansor