1. Introduction to Tape Diagrams

2. Warm Up Write each ratio as a fraction in lowest terms.
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…
Girls to boys?
People wearing pants to people who are not?
People wearing white to people who are in jeans?
1:1
4:1
4. Write a sentence about what your answer to #2 means.
3:2
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 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

5. 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

6. Launch – Think, Pair, Share
Think for one minute about an answer to these questions:
What is a job that uses a ratio?
How was a ratio useful in that job?
Lefty share your answers with Righty.
Now Righty share your answers with Lefty.
Does anyone want to share what their
partner told them?
Agenda

7. Launch – Think, Pair, Share
Zack’s orange paint is made by mixing
3 cups of red for every 5 cups of yellow.
Lefty – Tell Righty the ratio of red to yellow in Zack’s orange paint.
3:5
Righty – Tell Lefty the ratio of yellow to red in Zack’s orange paint.
Class – What is the ratio of red to yellow in Zack’s orange paint?
Partner Share
3 to 5
or 3:5
or 3 5
Agenda

8. 3:5 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?
3:5
Write down in your notes any ideas you have about how to answer this question.
Agenda

9. 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

10. 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

11. New Tool: Tape Diagram
Explore – Mini-Lesson
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

12. New Tool: Tape Diagram
Explore – Mini-Lesson
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.
If this tape shows 4 boys then…
boys
girls
1. If there are 4 boys in the class, how many girls are there?
Agenda

13. New Tool: Tape Diagram
Explore – Mini-Lesson
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
This tape is 4 boys.
So we put 4 above the tape.
How many students are in one box? 2 2
boys
girls 2
1. If there are 4 boys in the class, how many girls are there?
Agenda

14. The number in each box must be the same for every tape.
New Tool: Tape Diagram
Explore – Mini-Lesson
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
We don’t yet know the number of girls so we put a ? for the length of that tape. 2 2
Important Rule:
The number in each box must be the same for every tape.
boys 2 2 2
girls ?
1. If there are 4 boys in the class, how many girls are there?
Agenda

15. New Tool: Tape Diagram
Explore – Mini-Lesson
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 2 2
Now we can answer the question.
boys 2 2 2
girls ?
1. If there are 4 boys in the class, how many girls are there? 6
Agenda

16. ? 8 Explore – Mini-Lesson Let’s try another one.
New Tool: Tape Diagram
Explore – Mini-Lesson
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 know. 8 girls.
boys
girls
First, draw the tapes.
We can put a question mark for what we don’t know. 8
2. If there are 8 girls in the class, how many boys are there?
Now let’s look at the question.
Agenda

17. 4 ? 8 Explore – Mini-Lesson Let’s try another one.
New Tool: Tape Diagram
Explore – Mini-Lesson
Let’s try another one.
Example 2) The ratio of boys to girls in a class is 3 to 2. ?
How many students does each box represent?
boys
This makes 8 girls. 4 4
girls 4 8
2. If there are 8 girls in the class, how many boys are there?
Agenda

18. Every box must have the same quantity.
New Tool: Tape Diagram
Explore – Mini-Lesson
Let’s try another one.
Example 2) The ratio of boys to girls in a class is 3 to 2. ?
Remember:
Every box must have the same quantity.
boys 4 4 4 4 4
girls 8
2. If there are 8 girls in the class, how many boys are there? 12
Can you answer the question using the diagram?
Advanced: Think of one way you could prove that the numbers in each box should be 4. Tell your partner.
Agenda

19. 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

20. New Tool: Tape Diagram
Exit Ticket
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

21. 24 8 8 8 8 8 8 8 8 ? 40 cups of yellow paint Exit Ticket
New Tool: Tape Diagram
Exit Ticket
Let’s solve this problem using a tape diagram.
The question is: How many cups of yellow paint does Zack need to make his shade of orange paint?
We know: Zack’s orange paint is made by mixing
3 cups of red for every 5 cups of yellow.
And, we know: he bought 24 cups of red paint.
Since every box must have the same quantity…
Now we can figure out how many cups each box represents. If 3 boxes are 24 then…
This is a 3:5 ratio of red to yellow. 24
Let’s label the diagram.
red
yellow 8 8 8
Let’s draw the tapes. 8 8 8 8 8 ?
40 cups of yellow paint
That means the answer is:
Agenda

22. 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
strawberries 20 20 20 20 20
Answer: So the number of grapes is 20.
Agenda