Grade 5 Mathematics: Division of Fractions
California
Common Core
State Standards
Mathematics
CCSS.Math.Content.5.NF.7: Apply and extend previous understandings
of division to divide unit fractions by whole numbers and whole numbers
by unit fractions
CCSS.Math.Content.5.NF.7.B: Interpret division of a whole
number by a unit fraction, and compute such quotients. For
example, create a story context for 4 ÷ (1/5), and use a visual
fraction model to show the quotient. Use the relationship between
multiplication and division to explain that 4 ÷ (1/5) = 20 because
20 × (1/5) = 4.
CCSS.Math.Content.5.NF.7.C: Solve real-world problems
involving division of unit fractions by non-zero whole numbers
and division of whole numbers by unit fractions, e.g., by using
visual fraction models and equations to represent the problem. For
example, how much chocolate will each person get if 3 people
share 1/2 lb of chocolate equally? How many 1/3-cup servings are
in 2 cups of raisins?
Common Core
Math Practice
Standards
CCSS.MATH.PRACTICE.MP4 Model with mathematics.
Specific Learning
Objectives
Students will divide a whole number by a fraction using fraction models.
CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.
Students will apply their learning to a real world problem.
Materials
Lesson Plan
Engage
Concept/Learning
Goal:
Students will
activate prior
knowledge of
division.
•
•
•
Math Journals
Pencil
Different colored pen/pencil
Teacher asks/says/does:
1. Write the expression 8 ÷ 2
under the ELMO and ask
students to discuss with a
partner what the expression
means to them and how they
would find the answer.
2. Ask students to volunteer their
thinking.
Student asks/says/does:
1. Students will share their
thinking with their partner.
2. Students will volunteer answers
to the whole class.
3. Students will review objective
and agenda for the lesson.
3. Draw eight circles. Ask students
how they would show 8 ÷ 2 in
the picture.
4. Review objective and agenda
with students by saying,
“Today, you are going to use
what you already know about
division, fractions, and fraction
models in order to divide a
fraction by a whole number.”
Instructional
Strategies Used
(with rationale):
Partner Share: All students engage with the material when they are
required to discuss their thinking with a partner.
Modeling: The picture helps connect the concept of division with the
numerical expression.
Scaffolding: The lesson begins with a simple division problem to help
students make the connection between new and previous learning.
How is student
participation
ensured?
Partner Share
Questions and
Levels of
Questioning
(Blooms) Used:
What does 8 ÷ 2 mean?
These questions will help students
recall previous learning and
How many groups of 2 are in 8? demonstrate understanding of the
concept of division.
How can I show 8 ÷ 2 in a
picture?
How can I use multiplication to
check my answer?
Explore
Concept/Learning
Goal:
Students will
connect division of a
whole number by a
fraction to their
understanding of
!
1. Write the expression 1 ÷ !
under the ELMO. Ask
students how they should
interpret this expression
based on their previous
work thinking about 8 ÷ 2.
2. Ask students how many
halves are in one whole.
1. Students will record their thinking
in their notebook throughout the
remaining portion of the lesson.
2. Students are selected via volunteers
or equity sticks to help answer
questions about the steps to
!
simplify and explain 1 ÷ !.
division of whole
numbers.
3. Use the ELMO to draw the
fraction model to determine
the answer. Note the
differences between the
picture of 8 ÷ 2 and 1 ÷
!
!.
3. Students work independently and
with a partner to simplify and
!
explain 1 ÷ ! .
!
4. Write 1 ÷ ! on the ELMO.
Have students think about
the problem independently
for two minutes before
discussing with a partner.
Pick students to discuss
their reasoning with the
class.
Instructional
Strategies Used
(with rationale):
Modeling: Students will use fraction models to develop their
understanding of a whole number divided by a fraction.
Private Think Time: Students are provided an opportunity to attend to the
material on their own before hearing ideas from their partner. This
increases students’ ability to discuss with their partner.
How is student
participation
ensured?
Private Think Time
Partner Share
Questions and
Levels of
Questioning
(Blooms) Used:
What does ½ mean?
!
What does 1 ÷ ! mean?
Students will demonstrate
understanding of division of a whole
number by a fraction. Students will
apply their learning to a new problem.
How many ½ “groups” are in
1?
What does ½ look like in my
picture?
How can I use this same
!
thinking to determine 1 ÷ !?
How can I use multiplication to
check my answer?
Explain
1. Discuss with students how
1. Students will write the expression
Concept/Learning
Goal:
Students extend their
learning to more
complex problems.
they can extend their
strategy for dividing 1 by a
fraction to dividing other
whole numbers by a
fraction. Ask students to
simplify the expression
!
3 ÷ !.
2. Draw a fraction model as
shown below.
1
1
2
1
1
2
1
2
in their own notebook. Students
will participate in a whole class
discussion of how to solve the
!
expression, 3 ÷ !
2. Have students turn to their neighbor
to discuss what happened. Use the
timer to allow time for discussion.
When timer beeps, select volunteers
or use equity sticks to have students
explain their thinking.
1
1
2
1
2
1
2
3. To find the quotient of
!
3 ÷ ! count the number of
one-halves. (To emphasize
this step in the drawing,
circle each half as shown
below. This may be
something that is skipped
once students understand the
concept). There are 6 halves
in three. Therefore, there are
6 one-halves in threewholes. Three divided by
one-half equals 6.
1
1
2
1
1
2
1
2
1
1
2
1
2
1
2
Instructional
Strategies Used
(with rationale):
Modeling: Students extend fraction models to more difficult expressions.
How is student
participation
ensured?
Whole Class Discussion
Partner Share
Questions and
How does the problem differ
Summarizing: Students are able to synthesize new material by discussing
what they just saw with their partner.
Students will analyze the new problem
Levels of
Questioning
(Blooms) Used:
!
!
from 1 ÷ ! and 1 ÷ !?
How can we represent this
difference in our fraction
model?
based on their understanding of the
previous problems. Students will
extend their understanding of a fraction
model to solve the new problem.
Can you tell your partner what
!
the expression 3 ÷ ! means?
How do we use our fraction
model to determine the answer?
Elaborate
Concept/Learning
Goal:
Students apply their
learning to real
world problems.
1. Provide students with
additional problems to solve
in their notebook. Provide
private think time before
asking students to share
with a partner.
Examples:
!
2 ÷ !
!
5 ÷ !
1. Students will practice the concept
by solving new problems through
private think time and then with a
partner.
2. Students will extend their thinking
by participating in a whole class
discussion of a word problem.
3. Students will work on their own to
solve a second world problem
2. Explain that can use division
before discussing with the class.
of a whole number by a
fraction to help solve realworld word problems.
Model for students how one
can use a fraction model to
answer the question below.
Example: Josh has 3 candy
bars. He cut each candy bar
!
into ! pieces to share with
his friends. How many
pieces does Josh have?
3. Provide students with an
additional word problem for
them to solve on their own.
Bring students back together
to discuss as a class.
Example: How many 1/3cup servings are in 2 cups of
raisins?
Instructional
Strategies Used
(with rationale):
Modeling: Students continue to use fraction models to solve problems.
How is student
participation
ensured?
Private Think Time
Partner Share
Whole Class Discussion
Questions and
Levels of
Questioning
(Blooms) Used:
How can I represent the word
problem by a fraction model?
Connecting Concept to Real World Problem: Some students might grasp
the concept more with the use of a real life example.
In the word problem, what
quantity is the whole number?
Students must apply their learning to
create a fraction model and write an
expression to represent a word
problem.
What fraction am I dividing the
whole number by?
What mathematical expression
represents the word problem?
Evaluate
Concept/Learning
Goal:
Students will
synthesize the
concepts addressed
in this lesson by
simplifying a new
expression.
1. Return to the objective.
Have students give a
“thumbs-up” to show if they
understand the objective, a
“thumbs-sideways” if they
think they got it but are not
sure; or a “thumbs-down” if
they don’t get it or feel lost.
1. Students will reflect on their
understanding of the objective.
2. Students will simplify and explain
a final problem on their own.
2. Provide students with 3x5
index card. Ask them to
write to their
parent(s)/guardian(s)
explaining how to simplify
!
2 ÷ !.
Instructional
Strategies Used
(with rationale):
Individual Work Time: Students are able to discuss with a partner
throughout the lesson. They will work on this last problem individually so
they can summarize their learning.
How is student
participation
Individual Activity
ensured?
Questions and
Levels of
Questioning
(Blooms) Used:
How would you explain to your
parent or another adult how to
!
simplify 2 ÷ !?
This closing question asks students to
summarize the key learning in the
lesson.