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Warm UpOBJECTIVE: SWBAT solve ratio problems by using a tape diagram.Language Objective: SWBAT discuss ratio problem solving with a partner and in groups.

Agenda1

Write each ratio as a fraction in lowest terms.

What is the ratio of…1. Girls to boys?2. People wearing pants to

people who are not?3. People wearing white to

people who are in jeans?4. Write a sentence about what your answer to #2 means.

1:1

4:1

3:2

Launch

Agenda2

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.

Launch

Agenda3

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?

Launch

Agenda4

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.

Here’s the definition:

http://www.bbc.co.uk/skillswise/video/ratio-and-proportion

http://www.bbc.co.uk/skillswise/video/ratio-and-proportion

Launch – Think, Pair, Share

Agenda5


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

Explore – Strategize

Agenda6

Zack bought 24 cups of red paint.

How much yellow paint will Zack need to buy to make his shade of orange paint?

Write down in your notes any ideas you have about how to answer this question.

Explore – Mini-Lesson

Agenda7

Before we solve Zack’s problem, let’s look at some simpler problems to get ready. Read this problem.

1. If there are 4 boys in the class, how many girls are there?

Example 1) The ratio of boys to girls in a class is 2 to 3.


Agenda8

Let’s learn about a helpful tool for ratio problems that could help you with all sorts of ratio problems.




Agenda9

We can use a tape diagram to solve ratio math problems.



Each box represents a number in the original ratio.

Now let’s look at the question.

New Tool: Tape Diagram

boys

girls


Agenda10



boys

girls



If this tape shows 4 boys then…


Agenda11



boys


girls 2


How many students are in one box? 2 2 This tape is 4 boys.So we put 4 above the tape.

4


Agenda12



boys


girls


Important Rule:The number in each box must be the same for every tape.

2 22 2 2

4

?

We don’t yet know the number of girls so we put a ? for the length of that tape.


Agenda13



boys


girls

Now we can answer the question.


4

?

2 22 2 2


Agenda14

Let’s try another one.


2. If there are 8 girls in the class, how many boys are there?

First, draw the tapes.

Now let’s look at the question.


boys

girls

We can label what we know. 8 girls.We can put a question mark for what we don’t know.8

?


Agenda15



boys


4 4girls

How many students does each box represent? 4


This makes 8 girls.

?

8


Agenda16



boys 4


4

4 4girls

Remember:Every box must have the same quantity.

4

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.

?

8

Explore

Agenda17

Check this out for more about how tape diagrams work:

Click “Watch video” for a demonstration.

Tape Diagrams can be a helpful tool for solving problems.

http://www.thinkingblocks.com/tb_ratios/ratios.html

Practice

Agenda18

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.

Discuss

Agenda19

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.

Discuss

Agenda20

Let’s look at questions 3 and 4. Check to see if you and your partner completed the tape diagrams in the same way.

If you and your partner cannot agree on a diagram, put a star next to the problem.

Agenda21

6 6 6 6

66 sour oranges

4 4 4

4 48 red marbles

Discuss Answers

6

8

Discuss

Agenda22

Did you and your partner complete the tape diagrams the same way? Did you get the same answers?

Discuss

Agenda

23

apples

oranges

playing

resting

8

8

8 8 8

24

24 children playing

15

10 apples

5 5

55 5

Did you and your partner complete the tape diagrams the same way? Did you get the same answers?

Agenda

10

Summary – Write in your notebook

Agenda24

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?

Exit Ticket

Agenda25

Now that you learned a new tool use it to solve Zack’s paint problem.


Use tape diagrams as a tool to find out how much yellow paint Zack will need to buy to make his orange paint.


Remember:

He bought 24 cups of red paint.

Exit Ticket

Agenda26

Let’s solve this problem using a tape diagram. 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.

This is a 3:5 ratio of red to yellow.

Let’s draw the tapes.red

yellow

Let’s label the diagram.24

Now we can figure out how many cups each box represents. If 3 boxes are 24 then…

?

8 8 8

The question is: How many cups of yellow paint does Zack need to make his shade of orange paint?

Since every box must have the same quantity…

8 8 8 8 8

That means the answer is:

Assessment

27

Agenda

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.

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