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Work Backwards Problem Solving Strategy

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Work Backwards A strategy that requires you to change your focus. Consider the whole problem in reverse. Check by working it forward from your solution to make sure it is correct. EXAMPLE: Consider planning a vacation to Disneyworld. Once you find a flight, you need to work backwards to plan the beginning of your trip…when do you need to arrive at the airport and then when must you leave your house to arrive at the airport at that time, etc.

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How many M&M’s ? After dinner, three friends leaving a restaurant noticed a bowl of M&M’s on the front counter. Eddie took one-third of the M&Ms but returned four because he had a momentary pang of guilt. Cole then took one-fourth of what was left but returned three for similar reasons. Adam then took half the remainder but threw two green ones back. The bowl had only 17 M&M’s left after the boys helped themselves. How many M&Ms were originally in the bowl?

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Write down the story steps in order Begin. Eddie took 1/3 of the M&Ms. Eddie returned 4. Cole took 1/4 of what was left. Cole returned 3. Adam took half the remainder. Adam threw 2 back. The bowl had 17 M&Ms left.

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Work backwards from the end to the beginning. Bowl is full. Eddie took 1/3 of the M&Ms. Eddie returned 4. Cole took 1/4 of what was left. Cole returned 3. Adam took half the remainder. Adam threw 2 back. The bowl had 17 M&Ms left. 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 beginning to end. Bowl is full. Eddie took 1/3 of the M&Ms. Eddie returned 4. Cole took 1/4 of what was left. Cole returned 3. Adam took half the remainder. Adam threw 2 back. The bowl had 17 M&Ms left. 48 – 16 32 + 4 36 – 9 27 + 3 30 – 15 15 + 2 17 – it works! 48 in the bowl

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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. Check from the beginning to the end.

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