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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: Described solution step-by-step with pictures.
REASONABLE RESULT: This student did not show us that she checked her
answer.
SCORE:
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4
4
3
4
0
15/5=3.0
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Step 1 - The King, Queeen, Prince, Princess and Dog all ate a fraction of
the mangoes. How many mangoes were there originally.
Step 2
- King ate 1/6
- Queen ate 1/5
- Prince ate 1/4
- Princess ate 1/3
- dog ate 1/2
- 3 are left
Step 3 - Strategy - work backwards, pictures
| Basket | OOO |
| Dog | OOO
OOO |
| Princess | OOO
OOO
OOO |
| Prince | OOOO
OOOO
OOOO |
| Queen | OOOOO
OOOOO
OOOOO |
| King | OOOOOO
OOOOOO
OOOOOO |
Step 4 - To find the answer I made a picture while working backwards. I
knew that the dog ate half of the mangoes so the 3 mangoes had to be
doubled. Then to follow the pattern I kept adding three.
Step 5 - Everyone ate three mangoes. Then we knew that there was 18
mangoes in the basket.
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