Two students, Carter and Jamie, had a picnic with their teacher Mrs. Duval. Mrs. Duval brought three sandwiches of equal size, cutting the first into thirds, the second into fourths, and the third into sixths. Carter ate two pieces of the first sandwich, which was cut into thirds, so he ate 2/3 of that sandwich. Jamie ate two pieces of the second sandwich, which was cut into fourths, so he ate 2/4 of that sandwich. Mrs. Duval ate three pieces of the third sandwich, which was cut into sixths, so she ate 3/6 of that sandwich.

1. Dayana Duval
RED6545
February 9th, 2014
Christine Joseph
MACC.3.NF.1.3A – Explain equivalence of fractions in special cases, and
compare fractions by reasoning about their size. Understand two fractions as
equivalent (equal) if they are the same size, or the same point on a number line.

2. Two students in 3rd grade were rewarded for
their good behavior by having a special picnic
with their teacher, Mrs. Duval.

3. Mrs. Duval bought three sandwiches that were
the same size. She cut the first one into thirds.
She cut the second one into fourths and the third
one into sixths. Each whole sandwich was
divided into equal parts.



When you have something such as a sandwich or a cake, how do you share it?
How do you know each person gets the same amount?
If you were to cut a sandwich in half, how would you do it?

4. Mrs. Duval cut the first sandwich into thirds. How many equal
parts is that? Help Mrs. Duval cut the sandwich into thirds
by dragging the lines.
 In your notebook, draw a model of the sandwich cut
into thirds.

5. One of the students in Mrs. Duval’s class, Carter, ate
two pieces of the first sandwich. The first sandwich
was cut into ________ equal pieces. Carter ate
__________ pieces of the sandwich.
 Refer to the model in your notebook and shade in the
part that Carter ate.
What fraction of the sandwich did
Carter eat?
_____
Label the numerator and denominator.

6. Mrs. Duval cut the second sandwich into fourths. How
many equal parts is that? Help Mrs. Duval cut the sandwich into
fourths by dragging the lines.
 In your notebook, draw a model of the sandwich cut
into fourths.

7.  How else could Mrs. Duval have cut this sandwich? Draw a different
model in your notebook.
 Are the 4 equal parts of this sandwich the same shape as the 4 equal
parts of the new sandwich?
 Are the 4 equal parts of this sandwich the same size as the equal parts
of the new sandwich? Explain.

Possible explanation: Yes, you have two sandwiches that are the same size and you divide each of
them into four equal parts. So an equal part of one sandwich is the same size as an equal part of the
other sandwich.

8. Another student, Jamie, ate 2 pieces of the second
sandwich. The second sandwich was cut into ________
equal pieces. Jamie ate ________ pieces of the
sandwich.
 Refer to the model in your notebook and shade in the
part that Jamie ate.
What fraction of the sandwich did
Jamie eat?
Explain what the numerator
and denominator represent.

9. Mrs. Duval cut the third sandwich into sixths.
How many
equal parts is that? If the sandwich is divided into six unequal parts, is the shape divided into sixths?
Explain.
Help Mrs. Duval cut the sandwich into sixths by
dragging the lines.
 In your notebook, draw a model of the sandwich cut
into sixths.

10. Mrs. Duval ate three pieces of the third sandwich. The
third sandwich was cut into ________ equal pieces.
Mrs. Duval ate ________ pieces of the sandwich.
 Refer to the model in your notebook and shade in the
part that Mrs. Duval ate.
What fraction of the sandwich did Mrs.
Duval eat?

11. After lunch was over, Mrs. Duval, Carter, and Jamie
compared the pieces of sandwich they each ate.
Carter
2/3
Jamie
2/4
Mrs. Duval
3/6
Shade in the portions that each person ate. Who ate the most of their
sandwich? Did anyone eat the same portion? How can you tell?
How do you know which fractions are equivalent?