56 crackers are divided equally among 8 children. How many each? ()
- Each child gets 48 crackers
- Each child gets 8 crackers
- Each child gets 7 crackers (correct answer)
- Each child gets 56 crackers
Explanation: This question tests interpreting division as equal shares or equal groups (CCSS.3.OA.2), specifically understanding that a÷b can mean (1) a objects divided into b equal shares (partition), or (2) a objects with b per group, how many groups (measurement). Division has two interpretations. Partition (equal shares): When you have a total and need to divide it into a specific number of shares, asking "how many in each share?" For example, 24÷6 can mean "24 cookies divided equally among 6 children—how many does each child get?" Answer: 4 cookies per child. Measurement (equal groups): When you have a total and put a specific amount in each group, asking "how many groups?" For example, 24÷6 can also mean "24 cookies, put 6 in each bag—how many bags needed?" Answer: 4 bags. Both use 24÷6=4 but ask different questions. In this problem, 56 crackers are divided equally among 8 children, asking how many each child gets. This represents partition division, asking for the number in each share. Choice B is correct because 56÷8=7, meaning each child gets 7 crackers when 56 crackers are divided among 8 children. This accurately interprets the division as partition: objects per share. Choice A is incorrect because it states each child gets 8 crackers, which confuses partition with measurement by giving the number of shares instead of objects per share. This error occurs when students don't understand the two interpretations of division. To help students interpret division: Teach both meanings explicitly using the same numbers (24÷6 as partition: 6 shares of 4 each; as measurement: 4 groups of 6 each). Use concrete materials (counters, cubes) to physically divide and group. Draw pictures showing both interpretations. Connect to real contexts: sharing food (partition), packaging items (measurement). Language cues: "divided among" or "each person gets" suggests partition; "put X in each" or "per group" suggests measurement. Practice writing story problems for division expressions. Connect to multiplication: If 8×7=56, then 56÷8=7 and 56÷7=8.