# 3.OA.B.5-Properties of Operations_Yixuan's Problem

## 3.OA.B.5-Properties of Operations

Evidence Statement 3.C.4-1 Distinguish correct explanation/reasoning from that which is flawed, and if there is a flaw in the argument, present correcting reasoning. (For example, some flawed student reasoning is presented and the task is to correct it.

### Yixuan's Solution

Yixuan solved 7 × 8 by breaking it into two smaller problems.  He said the answer is 28.

(2 × 4) + (5 × 4)

8 + 20

28

Yixuan is incorrect in his reasoning.

• Explain why Yixuan is incorrect in his reasoning about breaking the expression apart.
• Write the correct solution to 7 × 8 by breaking it apart.
• Explain why your reasoning is correct.

## Scoring Rubric

### Score 3

Student response includes each of the following 3 elements.

• Reasoning component – 1 point. The student explains Yixuan's mistake about breaking the facts apart.
• Computation component- 1 point. The student provides a correct solution to break apart 7 x 8
• Reasoning component- The student provides an explanation why the expressions used to break apart 7 x 8 is correct.

Sample Student Response: Yixuan's reasoning is incorrect because he broke apart both factors in the expression 7 x 8. Yixuan could have broken 7 x 8 into (2 x 8) + (5 x 8). Then he could add 16 and 40 to get the correct solution of 56. I am correct because I broke the 7 into 2 and 5.  I did not break the 8.

### Score 2

Student response includes 2 of the above elements.

### Score 1

Student response includes 1 of the above elements.

### Score 0

Student response is incorrect or irrelevant.