DIVISION 5.NF.7
Division of Whole Numbers by Unit Fractions
Purpose:
Materials:
To illustrate and compute division of whole numbers by unit fractions
Fraction Bars, Tower of Bars activity sheet (attached), pencils and paper
TEACHER MODELING/STUDENT COMMUNICATION
Activity 1 Division of whole numbers by unit fractions
1. Pose the following problem.
pencils
and paper
Fraction Bars
 If a chef uses 1/6 of a pound of hamburger for each burger patty, how many patties
can be obtained from 4 pounds of hamburger?
a. One possibility for illustrating this information with a visual fraction model is
to represent each pound of hamburger by using the backs of red bars for whole
bars and to represent 1/6 of a pound of hamburger with a 1/6 bar.
b. How many times does the shaded amount of the 1/6 bar fit into a whole bar? (6 times)
c. How many times does the shaded amount of the 1/6 bar fit into 4 whole bars? (24 times)
d. How many patties can the chef make from 4 pounds of hamburger? (24 patties)
e. Write a division equation to express 4 divided by 1/6. (4 ÷ 1/6 = 24)
f. In the solution to this problem we determined how many times 1/6 of a bar "fits into" or
goes into a whole bar. This is the same idea we used for division of whole numbers when
we ask, "How many times does 3 go into 15?" In both dividing by fractions and dividing by
whole numbers, we are comparing two amounts to determine how many times greater one
amount is than another.
pencils
and paper
Fraction Bars
2. Ask students how to use a visual fraction model to represent the following information.
 Max cooks a small batch of pancakes each day, and each batch requires 1/3 cup of
milk. How many days can a batch of pancakes be made, if 2 cups of milk are available?
This information can be represented by two whole bars and a 1/3 bar. The bars show that
Max can make pancakes for 6 days and this information is expressed by 2 ÷ 1/3 = 6.
Activity 2 Relating division of unit fractions to multiplication
pencils
and paper
1. You may have noticed in this lesson, as in the previous lesson involving division of a unit
fraction by a whole number, that dividing a whole number by a unit fraction also can be
found by using multiplication. Here are two examples from this lesson:
4÷
1
5
= 20 because
1
5
× 20 = 4, and 2 ÷
1
3
= 6 because
1
3
×6 = 2
2. Apply this relationship between division and multiplication to complete the following
equations.
a. 5 ÷
1
4
=
b. 7 ÷
1
3
=
c. 8 ÷
1
5
=
Activity 3 Patterns involving unit fractions
Tower of Bars
activity sheet
1. Distribute copies of Tower of Bars (page 3).
a. Shade (or X-out) the first part of each
one of the bars below the whole bar and
write its unit fraction next to the bar.
b. What do you notice about the shaded
amounts of these bars? (Answers will vary:
The shaded amounts of the bars decrease
from top to bottom; The unit fractions for
these bars get smaller from top to bottom.
c. We can use division to say that the shaded
amount of the ½ bar "fits into" the shaded
amount of the whole bar 2 times. Or, we can
use multiplication to say that the whole bar is
2 times the shaded amount of the ½ bar. Use
such descriptions to compare the 1/3 bar or
the ¼ bar, etc. to the whole bar. (The shaded
amount of the 1/3 bar fits into the shaded
amount of a whole bar 3 times; etc.)
Activity 4 Creating story problems
1. The comparisons with the Tower of Bars can be used to create word problems. For
example: A whole candy bar is how many times the size of 1/6 of a bar? (6 times) Or, if
each bite is 1/6 of a whole bar, how many bites can be taken? (6 bites)
2. Ask each student to write questions involving one whole bar being divided by the
shaded amount of a unit fraction. Examples could involve: one whole candy bar; one
whole bar of chocolate; one stick of butter; one whole bottle of maple syrup; etc.
INDEPENDENT PRACTICE and ASSESSMENT
Worksheet 5.NF.7 #2