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:
Launch – Think, Pair, Share
Agenda5
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.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.
Explore – Mini-Lesson
Agenda8
Let’s learn about a helpful tool for ratio problems that could help you with all sorts of ratio problems.
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.
Explore – Mini-Lesson
Agenda9
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.
1. If there are 4 boys in the class, how many girls are there?
Each box represents a number in the original ratio.
Now let’s look at the question.
New Tool: Tape Diagram
boys
girls
Explore – Mini-Lesson
Agenda10
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
1. If there are 4 boys in the class, how many girls are there?
New Tool: Tape Diagram
If this tape shows 4 boys then…
Explore – Mini-Lesson
Agenda11
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
1. If there are 4 boys in the class, how many girls are there?
girls 2
New Tool: Tape Diagram
How many students are in one box? 2 2 This tape is 4 boys.So we put 4 above the tape.
4
Explore – Mini-Lesson
Agenda12
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
1. If there are 4 boys in the class, how many girls are there?
girls
New Tool: Tape Diagram
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.
Explore – Mini-Lesson
Agenda13
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
1. If there are 4 boys in the class, how many girls are there?
girls
Now we can answer the question.
New Tool: Tape Diagram
4
?
2 22 2 2
Explore – Mini-Lesson
Agenda14
Let’s try another one.
Example 2) The ratio of boys to girls in a class is 3 to 2.
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.
New Tool: Tape Diagram
boys
girls
We can label what we know. 8 girls.We can put a question mark for what we don’t know.8
?
Explore – Mini-Lesson
Agenda15
Let’s try another one.
Example 2) The ratio of boys to girls in a class is 3 to 2.
boys
2. If there are 8 girls in the class, how many boys are there?
4 4girls
How many students does each box represent? 4
New Tool: Tape Diagram
This makes 8 girls.
?
8
Explore – Mini-Lesson
Agenda16
Let’s try another one.
Example 2) The ratio of boys to girls in a class is 3 to 2.
boys 4
2. If there are 8 girls in the class, how many boys are there?
4
4 4girls
Remember:Every box must have the same quantity.
4
Can you answer the question using the diagram?
New Tool: Tape 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.
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.
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.
Zack’s orange paint is made by mixing 3 cups of red for every 5 cups of yellow.
Use tape diagrams as a tool to find out how much yellow paint Zack will need to buy to make his orange paint.
New Tool: Tape Diagram
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.
New Tool: Tape Diagram
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.