Warm Up
OBJECTIVE: SWBAT solve ratio problems by using a tape diagram.
Language Objective: SWBAT discuss ratio problem solving with a
partner and in groups.
Write each ratio as a fraction
in lowest terms.
What is the ratio of…
1. Girls to boys? 1:1
2. People wearing pants to
people who are not? 4:1
3. People wearing white to
people who are in jeans?
4. Write a sentence about what your answer to #2 means. 3:2
Agenda
1
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
2
Launch
Zack’s orange paint is made by mixing
3 cups of red for every 5 cups of yellow.
This sounds like a ratio.
What are ratios again?
Agenda
3
Launch
Here’s the definition:
A ratio is a relationship between two or more
quantities.
But, why would I want to use or think about a ratio?
Here’s a short video that will
show how ratios are used in a
few real life situations. 
Agenda
4
Launch – Think, Pair, Share
Zack’s orange paint is made by mixing
3 cups of red for every 5 cups of yellow.
3:
Lefty – Tell Righty the ratio of red to yellow in
Zack’s orange paint.
Righty – Tell Lefty the ratio of yellow to red in
Zack’s orange paint.
Partner
Share
Class – What is the ratio of red to
yellow in Zack’s orange paint?
3 to 5 or 3:5 or 3
5
Agenda
5
Explore – Strategize
Zack bought 24 cups of red paint.
How much yellow paint will Zack need to
buy to make his shade of orange paint?
3:
Write down in your notes any
ideas you have about how to
answer this question.
Agenda
6
Explore – Mini-Lesson
Before we solve Zack’s problem, let’s look at some
simpler problems to get ready. Read this problem.
Example 1) The ratio of boys to girls in a class is 2 to 3.
1. If there are 4 boys in the class, how many girls are
there?
Agenda
7
Explore – Mini-Lesson
Let’s learn about a helpful tool for ratio problems that
could help you with all sorts of ratio problems.
Example 1) The ratio of boys to girls in a class is 2 to 3.
1. If there are 4 boys in the class, how many girls are
there?
Agenda
8
Explore – Mini-Lesson
New Tool: Tape Diagram
We can use a tape diagram to solve ratio math problems.
Example 1) The ratio of boys to girls in a class is 2 to 3.
boys
girls
Each box represents a
number in the original
ratio.
1. If there are 4 boys in the class, how many girls are
there?
Now let’s look at the question.
Agenda
9
Explore – Mini-Lesson
New Tool: Tape Diagram
We can use a tape diagram to solve ratio math problems.
Example 1) The ratio of boys to girls in a class is 2 to 3.
boys
If this tape shows 4
boys then…
girls
1. If there are 4 boys in the class, how many girls are
there?
Agenda
10
Explore – Mini-Lesson
New Tool: Tape Diagram
We can use a tape diagram to solve ratio math problems.
Example 1) The ratio of boys to girls in a class is 2 to 3.
4
boys
girls
2
2
This tape
How
manyisstudents
4 boys.
arewe
So
in one
put 4box?
above
the tape.
2
1. If there are 4 boys in the class, how many girls are
there?
Agenda
11
Explore – Mini-Lesson
New Tool: Tape Diagram
We can use a tape diagram to solve ratio math problems.
Example 1) The ratio of boys to girls in a class is 2 to 3.
4
boys
girls
2
2
2
2
?
2
Rule:
We Important
don’t yet
know
Thethe
number
in each
number
of box
girlsmust
be the same for every tape.
so we put a ? for the
length of that tape.
1. If there are 4 boys in the class, how many girls are
there?
Agenda
12
Explore – Mini-Lesson
New Tool: Tape Diagram
We can use a tape diagram to solve ratio math problems.
Example 1) The ratio of boys to girls in a class is 2 to 3.
4
boys
girls
2
2
2
2
?
2
Now we can answer
the question.
1. If there are 4 boys in the class, how many girls are
there?
6
Agenda
13
Explore – Mini-Lesson
New Tool: Tape Diagram
Let’s try another one.
Example 2) The ratio of boys to girls in a class is 3 to 2.
?
We can label what we
First,
the tapes.
know.draw
8 girls.
boys
We can put a question
girls
mark for what we
8
don’t know.
2. If there are 8 girls in the class, how many boys are
there?
Now let’s look at the question.
Agenda
14
Explore – Mini-Lesson
New Tool: Tape Diagram
Let’s try another one.
Example 2) The ratio of boys to girls in a class is 3 to 2.
?
boys
girls
4
4
8
How many students
does
each box
This makes
8 girls.
represent? 4
2. If there are 8 girls in the class, how many boys are
there?
Agenda
15
Explore – Mini-Lesson
New Tool: Tape Diagram
Let’s try another one.
Example 2) The ratio of boys to girls in a class is 3 to 2.
?
boys
4
4
girls
4
4
8
4
Remember:
Every box must have
the same quantity.
2. If there are 8 girls in the class, how many boys are
there?
Can you answer the question using
12 the diagram?
Advanced: Think of one way you could prove that the
numbers in each box should be 4. Tell your partner.
16
Agenda
Explore
Tape Diagrams can be a helpful tool for solving problems.
Check this out for more about how tape diagrams work:
Click “Watch video” for a demonstration.
Agenda
17
Practice
You will have 15 minutes to work on solving some ratio
problems using the tape diagrams tool. You might feel a
little confused and want to talk about it.
Don’t worry – you will discuss it when you are finished.
Agenda
18
Discuss
Check with a partner to see if you have the same
answers. See if you used your tape diagram tools in
the same way. You have 10 minutes.
Agenda
19
Discuss
If you and your partner cannot agree on a
diagram, put a star next to the problem.
Let’s look at questions 3 and 4. Check to
see if you and your partner completed the
tape diagrams in the same way.
Agenda
20
Discuss Answers
6
6 sour oranges
4
4
4
4
8
6
6
6
6
6
4
8 red marbles
Agenda
21
Discuss
Did you and your partner complete the tape diagrams
the same way? Did you get the same answers?
Agenda
22
Discuss
Did you and your partner complete the tape diagrams
the same way? Did you get the same answers?
24 children playing
10 apples
24
playing
8
resting
8
8
8
10
8
apples
5
5
oranges
5
5
15
5
Agenda
Agenda
23
Summary – Write in your notebook
What is one thing you like about the tape
diagrams as a tool?
What is one thing that is difficult?
Is there anything that is confusing about
using tape diagrams as a tool?
Agenda
24
Exit Ticket
New Tool: Tape Diagram
Now that you learned a new tool use it to solve Zack’s
paint problem.
Remember:
Zack’s orange paint is made by mixing
3 cups of red for every 5 cups of yellow.
He bought 24 cups of red paint.
Use tape diagrams as a tool to find out how much yellow
paint Zack will need to buy to make his orange paint.
Agenda
25
Exit Ticket
New Tool: Tape Diagram
Let’s solve this problem using a tape diagram.
Theknow:
question
is: How
many
cups
of yellow
paint does Zack
We
Zack’s
orange
paint
is
made
by
mixing
And, we know: he bought 24 cups of red paint.
hisevery
shade
of orange
paint?
3need
cupsto
ofmake
red for
5 cups
of yellow.
Since
Nowevery
we can
boxfigure
must have
out how
This is a 3:5 ratio of red to yellow.
themany
samecups
quantity…
each box
represents.
If 3the
boxes
are 24
Let’s label
diagram.
then…
red
yellow
8
8
24
8
8
8
8
?
Let’s draw the tapes.
8
8
That means the answer is: 40 cups of yellow paint
Agenda
26
Assessment
Carefully review the tape diagram tool and solution.
What is wrong here?
The ratio of grapes to strawberries in a fruit salad is 4 to 1. If
there are 20 grapes in the salad then how many strawberries
are there?
grapes
20
strawberries
20
20
20
20
Answer: So the number of grapes is 20.
Agenda
27