# 3.NF.A.3d Comparing Fractions Flawed Reasoning_Aiden's Work

## 3.NF.A.3d Comparing Fractions (Flawed Reasoning)

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 corrected reasoning. (For example, some flawed student reasoning is presented and the task is to correct and improve it.)

### Aiden's Work

Aiden thinks that ¼ = ½. He drew the number lines below to show that ¼ = ½. This image shows two number lines of different lengths.  The longer number line is partitioned into fourths with one-fourth labeled. The shorter number line is partitioned into halves with one-half labeled.  The zero is at the same point and one-half and one-fourth are at the same point on both number lines.

• Explain why Aiden’s thinking is incorrect.
• Write the correct comparison for 1/4 and 1/2 using  < or >.

## Scoring Rubric

### Score 2

Student response includes the following 2 elements.

• Reasoning component = 1 points
• The student explains that Aiden did not compare the fractions correctly because the length of the number lines was not equal. In order to compare fractions the wholes must be equal.
• Computation component = 1 point
• The student provides the correct comparison, ¼ < ½ or ½ > ¼.

### Score 1

Student response includes 1 of the above elements.

### Score 0

Student response is incorrect or irrelevant.