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: 4 4 3 4 0 15/5=3.0

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 OOOOOO Princess OOOOOOOOO Prince OOOOOOOOOOOO Queen OOOOOOOOOOOOOOO King OOOOOOOOOOOOOOOOOO
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.