WorkBackwards - mate sem2

8/6/2019 WorkBackwards - mate sem2

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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

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WorkBackwards - mate sem2