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The Mangoes Problem
Sample Response
The following response was written by a student. We scored it using the
scoring guide as follows:
RIGHT ANSWER: 18 mangoes!
UNDERSTANDING: Noticed pattern--each person got 3 mangoes.
STRATEGY: Did not provide rationale for choice of strategy.
COMMUNICATION: Made a couple of grammmar/spelling errors.
REASONABLE RESULT: Checked by working forwards (same strategy in
reverse).
SCORE:
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4
4
3
3
3
17/5=3.4
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To begin, I started at the obvious starting point: 3 mangoes. Next, I
needed to work it backwards. The dog ate half, so three. 3 + 3 =
6. Now there is 6. The princess ate 1/3 of the mangoes. Now there is 9
left in the basket. By that time I noticed a pattern. As I went on, I
counted by threes, so it went: 12, 15, then lastly, 18. Then I had to
check it. This time I could work forwards: 1/6 of 18, then 1/5 of 15,
then 1/4 of 12, 1/3 of 9, 1/2 of 6, three. Now I knew my awnser was
correct.
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