# 3.NF.A.3d- Compare Fractions Using Models_Comparing Sandwiches

## 3.NF.A.3d- Compare Fractions Using Models

Evidence Statement 3.C.3-1  Base arithmetic explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in their response), connecting the diagram (s) to the written (symbolic method.

### Sandwiches for Lunch

Hassan and his brother Jamil each ate a sandwich for lunch. The image shows the fraction of a sandwich each boy ate.

A square divided into six equal pieces. Three of the pieces are shaded in to represent Jamil eating them.

Hassan's Sandwich. A square divided into four equal pieces. Three of the pieces are shaded in to represent Hassan eating them.

# Part A

Write the fraction of a sandwich each boy ate in the space provided.

# Part B

• Which boy ate the greatest part of their sandwich?
• Write an inequality to compare the two fractions.
• Explain why your reasoning is correct.

# Scoring Rubric Part A

Score of 1- Student response includes a correct fraction for each sandwich that was eaten.

Sample Response: Hassan  and Jamil

Score of 0- Student response is incorrect or irrelevant.

# Scoring Rubric Part B

Score of 3- Student response includes the following 3 elements.

• Computation Component = 1 point.  The student provides a correct inequality to compare Hassan and Jamil’s sandwich.

• Computation Component = 1 point. The student correct identifies which boy at the greatest part of their sandwich. Correct response is Hassan.

•  Reasoning Component = 1 point. The student explains why their reasoning is correct.

• Sample Response- I know that Hassan at the greatest part of his sandwich because  is greater than . I know this because when fractions of the same sized whole have the same numerator you compare using the denominator. The larger the denominator is the smaller the parts are. 6 is greater than 4 so Jamil’s sandwich was divided up into smaller pieces than Hassan’s sandwich.

Score of 2- Student response includes 2 of the elements.

Score of 1- Student response includes 1 of the elements.

Score of 0- Student response is incorrect or irrelevant.