# 3.NF.A.3d Comparing Fractions_Rosina's Reasoning

## 3.NF.A.3d Comparing Fractions

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

### Rosina's Reasoning

Rosina was explaining how to compare 2/6 and 3/6 her friend.  She drew the rectangles below to help her explain.

This image shows a large rectangle partitioned into 6 equal parts with 2 parts shaded and a small rectangle partitioned into 6 parts with 3 parts shaded.

Rosina tells her friend that 2/6 > 3/6.

• Explain why Rosina’s thinking is incorrect.
• Explain how to correct Rosina’s thinking.
• Write the correct comparison for 2/6 and 3/6 using  < or >.

## Scoring Rubric

### Score 3

Student response includes the following 2 elements.

• Reasoning component = 2 points

• The student explains that Rosina did not compare the fractions correctly because the rectangles were not the same size.

• The student explains that in order to compare fractions the wholes must be equal.

• Computation component = 1 point

• The student provides the comparison, 2/6 < 3/6.

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.