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 >.

Enter your explanation and answer below.

Student Copy

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.