The Mangoes Problem
The Mangoes Problem Sample ResponseThe 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).
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.