Mathematics Alignment Lesson
Grade 5 Quarter 3 Day 119
Common Core State Standard(s)
5.NF.7 Apply and extend previous
understandings of division to divide unit
fractions by whole numbers and whole
numbers by unit fractions.
b. Interpret division of a whole number
by a unit fraction, and compute such
quotients.
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.
Standards for Mathematical Practice
Standard 4 Model with mathematics.
Standard 7 Look for and make use of structure.
Materials Needed:
Transparencies/Blackline Masters“Divide Whole Numbers by Unit
Fractions”, “Divide Whole
Numbers by Unit Fractions
Continued”
Cardstock – “Divide Whole Numbers by
Unit Fractions Memory”
Assessment
Ask students: “How does your drawing
and/or the equation you wrote support your
answer?”
Homework
Alignment Lesson
Divide Whole Number by Unit Fraction
Note: To maximize instructional time, have sets of Memory
cards pre-cut and in individual baggies.
1. Display Transparency “Divide Whole Numbers by Unit
Fractions”, read the question aloud and allow students to
work on solving it, either independently or with a partner.
When students have finished, select student leaders to share
the various strategies they used to solve the problem. During
this discussion, be sure to ask “Why is the quotient larger than
the dividend?” (When you divide a whole number by a unit
fraction, you are splitting the whole into smaller parts. The
quotient is the total number of smaller parts you have so it
will be more than the whole number.) Also, discuss the
related multiplication equations for the division equations
students write as part of their answer. This will reinforce
using multiplication to check their answers and connect to
existing knowledge about fractions.
2. Display Transparency “Divide Whole Numbers by Unit
Fractions Continued” and repeat the process described in Step
1.
3. Explain to students that they will have the rest of the class
period to play a game of Memory to practice dividing whole
numbers by unit fractions. Display/ distribute
Transparency/Blackline Master “Divide Whole Numbers by
Unit Fractions Memory” and read over the rules with the
students. Once the directions are clear, have students get in
groups of 2 or 3 and give them cards so they can begin
playing. As students play the game, circulate to check for
misunderstandings.
4. Once all groups have finished playing Memory, have the class
come back together and review what you learned about
dividing whole numbers by unit fractions. (Students may
notice: the quotient is always larger than the dividend; the
quotient can be found by multiplying the whole number by
the denominator of the unit fraction)
Blackline Master, “Divide Whole Numbers
by Unit Fractions Journal Prompt”
Vocabulary
None
Source: DPI Unpacking Document (some questions) ,
Teacher Created
Wake County Public School System, 2012
Transparency/Blackline Master
Grade 5
Day 119
Standards 5.NF.7b, 5.NF.7c
Divide Whole Numbers by Unit Fractions
Percy has 6 pears and plans to divide them by ½ to
share with his friends. How many friends can he
share the pears with?
Directions: Use the space below to draw a picture or diagram to
solve the problem. Write an equation to support your
answer.
Wake County Public School System, 2012
Answer Key Grade 5
Day 119
Standards 5.NF.7b, 5.NF.7c
Divide Whole Numbers by Unit Fractions – Answer Key
Percy has 6 pears and plans to divide them by ½ to share with his
friends. How many friends can he share the pears with?
Directions: Use the space below to draw a picture or diagram to
solve the problem. Write an equation to support your
answer.
To find the answer, I drew a picture of 6 pears. I know I am dividing
by ½ so that means I need to split each pear in half. Next, I counted
the number of halves there are and I got 12. This means Percy can
share the pears with 12 friends. The equation that supports my work
is 6 ÷ ½ = 12. I remember that multiplication is the inverse of
division so to check my work, I wrote a related multiplication equation
12 x ½ = 6. I know that ½ of 12 is 6 so my answer is correct.
Wake County Public School System, 2012
Transparency/Blackline Master
Grade 5
Day 119
Standards 5.NF.7b, 5.NF.7c
Divide Whole Numbers by Unit Fractions Continued
Ann’s fish bowl holds 5 liters of water. If she used a scoop that
holds 1/6 of a liter, how many scoops will she need in order to
fill the entire bowl?
Directions: Use the space below to draw a picture or diagram to
solve the problem. Write an equation to support your
answer.
NC DPI Unpacking Document
Wake County Public School System, 2012
Answer Key Grade 5
Day 119
Standards 5.NF.7b, 5.NF.7c
Divide Whole Numbers by Unit Fractions Continued –
Answer Key
Ann’s fish bowl holds 5 liters of water. If she used a scoop that holds 1/6 of a
liter, how many scoops will she need in order to fill the entire bowl?
Directions: Use the space below to draw a picture or diagram to solve the problem. Write
an equation to support your answer.
I created 5 boxes, each box represents 1 liter of water. I then divided each box into sixths
to represent the size of the scoop. My answer is the number of small boxes I now have,
which is 30. The equation that supports my work is 5 ÷ 1/6 = 30. I can use multiplication
to check my work. 30 x 1/6 = 5 so I know my answer is correct.
NC DPI Unpacking Document
Wake County Public School System, 2012
Transparency/Blackline Master
Grade 5
Day 119
Standards 5.NF.7b, 5.NF.7c
Divide Whole Numbers by Unit Fractions Memory
Directions:
1. Divide students into pairs (or groups of 3 if needed).
2. Give each pair/group a set of the memory cards.
3. Have each group lay the cards facedown in a 4 by 4 square.
4. Player 1 will flip over a card. If the card has a word problem on it, each
group member should solve it independently. The group should then
agree on the answer and Player 1 flips over a second card to try to locate
the answer. If there is not a match, Player 1 flips both cards facedown
again and play continues. If there is a match, Player 1 collects the two
cards and keeps them as a pair. It will then be the next player’s turn.
5. If a player turns over two cards that have answers on them, then there is
no match. Both cards should be turned facedown again and it is the next
player’s turn.
6. If a player turns over two cards with word problems on them, the group
members will solve both problems independently then agree on the
answers. They will then turn both cards facedown again and it will be the
next player’s turn.
7. Play continues until all word problems have been matched with an
answer.
8. When your group thinks you’ve matched all of the cards, your teacher
will check to be sure you are correct.
Wake County Public School System, 2012
Cardstock Grade 5
Day 119
Standards 5.NF.7b, 5.NF.7c
Divide Whole Numbers by Unit Fractions Memory Cards
Angelo has 4 pounds
of peanuts. He wants How many 1/3-cup
to give each of his
servings are there
friends 1/5 lb. How
in 2 cups of
many friends can
raisins?
receive 1/5 lb of
peanuts?
90
9
Max is building a tree
Justin has 8 large
house. He has a
pizzas. Each of his
piece of wood that is friends wants to eat ¼
4 feet long. How
of a pizza. How
many 1/6 ft pieces of
many friends can
wood can he cut from Justin feed with the 8
this piece of wood?
pizzas he has?
20
33
24
32
6
30
How many 1/10cup servings are
there in 9 cups of
trail mix?
Darius’s fish tank
holds 15 gallons of
water. If he fills it
using a ½-gallon
container, how many
times will he have to
fill the container in
order to completely
fill the fish tank?
Mia has 3 hours to
work on her projects
How many 1/3
tonight. If she
servings are there
decides to spend 1/3 in 11 cartons of ice
of an hour on each
cream?
project, how many
projects can she work
on tonight?
NC DPI Unpacking Document
Wake County Public School System, 2012
Answer Key Grade 5
Day 119
Standards 5.NF.7b, 5.NF.7c
Divide Whole Numbers by Unit Fractions Memory Cards –
Answer Key
Question
Angelo has 4 pounds of
peanuts. He wants to
give each of his friends
1/5 lb. How many
friends can receive 1/5 lb
of peanuts?
Max is building a tree
house. He has a piece of
wood that is 4 feet long.
How many 1/6 ft pieces
of wood can he cut from
this piece of wood?
How many 1/10-cup
servings are there in 9
cups of trail mix?
Mia has 3 hours to work
on her projects tonight.
If she decides to spend
1/3 of an hour on each
project, how many
projects can she work on
tonight?
NC DPI Unpacking Document
Wake County Public School System, 2012
Answer
Question
Answer
20
How many 1/3-cup
servings are there in 2
cups of raisins?
6
24
90
9
Justin has 8 large
pizzas. Each of his
friends wants to eat ¼
of a pizza. How many
friends can Justin feed
with the 8 pizzas he
has?
Darius’s fish tank
holds 15 gallons of
water. If he fills it
using a ½-gallon
container, how many
times will he have to
fill the container in
order to completely
fill the fish tank?
How many 1/3
servings are there in
11 cartons of ice
cream?
32
30
33
Answer Key Grade 5
Day 119
Standards 5.NF.7b, 5.NF.7c
Name: _________________________________
Date: __________________________________
Divide Whole Numbers by Unit Fractions Journal Prompt
Why is the quotient larger than the dividend
when dividing by a unit fraction? Use an
example to support your explanation.
Wake County Public School System, 2012
Answer Key Grade 5
Day 119
Standards 5.NF.7b, 5.NF.7c
Name: _________________________________
Date: __________________________________
Divide Whole Numbers by Unit Fractions Journal Prompt –
Answer Key
Why is the quotient larger than the dividend
when dividing by a unit fraction? Use an
example to support your explanation.
When you divide a non-zero whole number by a unit fraction, the
quotient is always larger than the dividend. This is true because
you are taking a whole number and breaking it into smaller
sections (based on the fraction) and the number of small sections
is the answer. For example, if you have 7 ÷ 1/3 , you are taking 7
wholes and dividing each one into three equal sections. Then to
get the answer, you count how many total sections (thirds) result
from this , which is 21. To check you can use multiplication, 21 x
1/3 = 7 so I know the answer is correct.
Wake County Public School System, 2012