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

Created Feb. 7, 2024 by MSDE Admin, Linda Schoenbrodt, Chelsea Davies

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.

Jamil's Sandwich.
three_sixths_sandwich.JPGJamil's Sandwich.

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.
three_fourths_sandwich.JPGHassan's Sandwich. 

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.

Enter your answer and your work or explanation in the space provided.


Student Copy


Download: 3.NF.A.3d__Sandwiches_for_Lunch__tMwhFxZ.docx



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. 


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