Using Tape Diagrams with PartWhole Ratio Problems
1
Lesson Target
Content Objective: SWBAT solve partwhole ratio problems by using a tape
diagram.
Learning Target: SWBAT identify the
ratio in a word problem and translate
the words into a tape diagram.
2
Warm Up
OBJECTIVE: SWBAT solve part-whole ratio problems by using a
tape diagram. Language Objective: SWBAT identify the ratio in a
word problem and translate the words into a tape diagram.
Crystal and her brother Marcus have some cookies.
I have 9
cookies.
But I
have 6.
1. If there are 5 chocolate chips in
each cookie, how many chips are in
all the cookies? 9 x 5 + 6 x 5 = 75 chips
2. What part of a dozen cookies does
Crystal have? Hint: A dozen is 12!
¾ dozen
Crystal
Marcus
3. If Crystal ate one cookie
each day, how many weeks
would her cookies last?
1 2/7 weeks
Agenda
3
Launch
Abby and Zack are mixing red
and yellow paint to make an
orange color to paint their
kitchen table. They each
think they have the perfect
shade of orange.
Agenda
4
Launch – Think, Pair, Share
Righty – Tell Lefty the ratio of red to
total in Abby’s orange paint.
Lefty – Tell Righty the ratio of yellow to
total in Zack’s orange paint.
Abby’s orange paint
is made by mixing 1
cup of red for every 3
cups of yellow.
Zack’s orange paint is
made by mixing 3 cups
of red for every 5 cups
of yellow.
Agenda
5
Explore – Predict
They will need a gallon of orange paint for the project.
Hint: A gallon is 16 cups.
1. How can Abby make enough of her orange paint for
the project?
2. How can Zack make enough of his orange paint for
the project?
Write down in your notes
any ideas you have about
how to answer these
questions.
Agenda
6
Explore – Mini-Lesson
Tape Diagram Tool
Follow along by filling out the whiteboard as we go.
Agenda
7
Explore – Mini-Lesson
New Tool: Tape Diagram
TOTAL
Example 1) A recipe for fruit punch says to use 5 ounces
of orange juice for every 3 ounces of grape juice.
Janice’s punch bowl can hold 80 ounces of punch. How
much orange juice is that? How much grape juice?
50
All
of
these
?
We don’t
boxes
from
What is10
the
ratio
in
the
problem?
know
the
Orange
80
10 draw
10the 10
First, let’s
tapes. 10
both
tapes
Orange to grape is 5:3. So…
amounts
Grape 10 10 10
make
80
ofoz.
each
of
30
? Because 80 ÷ 8 = ounces
juice
so…
10
punch.
Now
can equals
see that
orange
juice
is… 50 oz
So,
if 8we
boxes
80the
ounces,
then
each
Orgiven.
algebraically: 8b = 80
Now let’s Why
look 10?
at what’s
box
Andis…
the grape juice is … 30 oz
So…
b = 10
Agenda
8
Explore – Guided Practice
Tape Diagram Tool
Let’s practice this next one together.
Continue to
put your
work on
your
whiteboard
Agenda
9
Explore – Guided Practice
Tape Diagram Tool
A florist makes Mother’s Day bouquets of a dozen roses
with a ratio of 1 pink rose to every 2 yellow roses. How
many yellow roses are needed for 1 bouquet?
Hint: A dozen is 12.
Guided Practice #1
Here are the tapes:
_____________
What is the ratio in the problem?
_____________
Pink
to yellow is 1:2.
What is a
bouquet? 
10
Vocabulary:
Now
Let’sYou:
see how
Labeldid!
the tape
you
diagram with
the information
from the
problem.
Agenda
Vocabulary
Back to Lesson
Bouquet - a pretty collection of flowers
sometimes with a bow usually given as a
gift to someone.
Roses
Agenda
11
Explore – Guided Practice
Tape Diagram Tool
A florist makes Mother’s Day bouquets of a dozen roses
with a ratio of 1 pink rose to every 2 yellow roses. How
many yellow roses are needed for 1 bouquet?
Hint: A dozen is 12.
Guided Practice #1
?
4
4
yellow
4
12
4
?
8
Vocabulary
12
TOTAL
pink
And
thethat 3
I know
answer:
That
boxesmakes
is equal
Yellow
rosesso
the
pink
to 12
roses
needed
equal
to is...
each box
has…
4
Answer:
4 roses
roses
8 roses
Agenda
Explore – Guided Practice
Tape Diagram Tool
Try the next one on your own.
Remember
to put your
work on
the
worksheet.
Agenda
13
Explore – Guided Practice
Tape Diagram Tool
Mrs. Stanford is having a class pizza party. She has found
that students prefer pepperoni pizza to cheese pizza in a
ratio of 3 to 1. If she needs 48 slices of pizza in total,
how many slices of pepperoni will she need?
Identify the
Let’s
how
you did!
ratio.see
Draw
the
Istapes.
there anyone ____________
who
The ratio of pepperoni
________
Then
fill out
Ok,
let’s
see diagram
what
it
to
cheese
is
3:1.
can
draw
the
____________
thefind
diagram
should
look
and
the like.
answer?
and find the
answer.
Agenda
14
Explore – Guided Practice
Tape Diagram Tool
Mrs. Stanford is having a class pizza party. She has found
that students prefer pepperoni pizza to cheese pizza in a
ratio of 3 to 1. If she needs 48 slices of pizza in total,
how many slices of pepperoni will she need?
36
12
12
12
12
48 slices
________
Answer:
slices
1236slices
Agenda
15
TOTAL
If all
four
boxes
So
the
amount
equals
48 slices,
of
pepperoni
____________
then that means pepperoni
pizza is…
that each box is ____________
cheese
equal to …
Explore – Independent Practice
Tape Diagram
There are two more tape diagram ratio problems for
you to solve on your own on your worksheet. Show
your work. Circle your answer.
Answer #3
Answer #4
Challenge
Answers
Agenda
16
Explore – Independent Practice Answers
Independent Practice #3
The ratio of orange to brown candies in a bag of M & Ms is 4:1. If there
are 45 orange and brown candies in the bag of M & Ms altogether then
how many brown candies are there?
Ratio of orange to brown is 4:1
9
brown
9
9
9
9
45
TOTAL
orange
9
Answer: 9 brown candies
Agenda
17
Explore – Independent Practice Answers
Independent Practice #4
For every eraser in a pencil box there are 2 pencils. If there are 14
pencils in the box, then how many pencils and erasers are there
altogether?
Ratio of pencils to erasers is 2:1
14
7
eraser
7
7
?
TOTAL
pencils
Answer: 21 pencils & erasers
Agenda
18
Explore – Independent Practice Challenge Answers
Challenge Practice #5
To make the Perfectly Pink paint color you use 8 parts of white paint for
every one part of red paint. If 27 cups of Perfectly Pink paint is mixed up
in a bucket, then how many cups of red paint were used?
Answer: 3 cups red paint
Challenge Practice #6
The ratio of flour to sugar in a cake recipe is 7 to 5. If the recipe calls for
20 tablespoons of sugar, then how many tablespoons of flour and sugar
will be required in total?
Answer: 48 tablespoons total
Agenda
19
Explore – Independent Practice Challenge Answers
Challenge Practice #7
A water molecule has a ratio of 2 Hydrogen atoms for every 1 Oxygen
atom. If there are 27 atoms that make up some water, then how many
Hydrogen atoms are there?
Answer: 18 atoms of H
Challenge Practice #8
The ratio of flour to sugar in a cake recipe is 7 to 5. If the recipe calls for
20 tablespoons of sugar, then how many tablespoons of flour and sugar
will be required in total? Extension: For the problem above:
If 4 tablespoons equals ¼ cup, then how many cups of flour and how
many cups of sugar are required for the cake?
Answer:
20 tbsp sugar ÷ 4 = 5 quarter cups or 1 ¼ cups sugar
28 tbsp flour ÷ 4 = 7 quarter cups or 1 ¾ cups flour
Agenda
20
Exit Ticket – use the half sheet of paper
provided
The painting project will require a gallon of orange paint .
Hint: A gallon is 16 cups.
1. How many cups of red paint and yellow paint will Abby need
to make enough of her orange paint for the project?
2. How many cups of red paint and yellow paint will Zack
need to make enough of her orange paint for the project?
Use tape diagrams to
determine how much red and
how much yellow paint each
child needs.
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