Table 1 The tasks used in three diagnostic tests
Exam | Name | Problem situation | Problem structure | Two solutions | Source |
|---|---|---|---|---|---|
Pretest | Mango | Mr. Levin’s students are tasting foods grown in rainforests. He put 5 pieces of mango on each plate and put 2 plates on each table. There are 3 tables. How many pieces of mango are there? | 3 tables of 2 plates of 5 mangos | (3 × 2) × 5 = 3 × (2 × 5) | Houghton Mifflin—3rd grade |
Posttest I (mid-term exam) | String | Upright bass strings come in sets of 4. Suppose one box holds 2 sets of strings. If a musician orders 3 boxes, how many strings will there be? | 3 boxes of 2 sets of 4 strings | (3 × 2) × 4 = 3 × (2 × 4) | Houghton Mifflin—4th grade |
Posttest II (final exam) | Cup | Each cup costs $5. Mom wants to purchase 4 boxes of cups with each box holds 3 cups. How much does mom need to pay? | 3 cups of 4 boxes of $5 | (4 × 3) × 5 = 4 × (3 × 5) | Chinese 3rd grade textbook (adapted) |