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. 

Write your answer and your explanation below. 

Student Copy

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.