1. SOLVE RATIO AND RATE PROBLEMS USING TAPE DIAGRAMS
OBJECTIVE: 6RP3 Use ratio and rate reasoning to solve real world problems using tape diagrams.
SOLVE RATIO AND RATE PROBLEMS USING TAPE DIAGRAMS

2. Activator: Let’s review what we know about Tape Diagrams.
New Tool: Tape Diagram
2 Minute Talk
Partner 1: Tell Partner 2 one thing you
Remember about tape diagrams from yesterday.
Partner 2: Tell Partner 1 one thing you remember about tape diagrams from yesterday.
Share.

3. 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.

4. 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

5. 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
How many students are in one box?
This tape is 4 boys.
So we put 4 above the tape. 2 2
boys
girls 2
1. If there are 4 boys in the class, how many girls are there?

6. 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?

7. 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

8. ? 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?
(Time on this slide – 2 min) Time passed 26 min
In-Class Notes
Make sure students realize that this is a different problem.
Now let’s look at the question.

9. 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? a

10. 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?

11. Explore Go to Student Share Drive Purcell Thinking Blocks Link
Tape Diagrams can be a helpful tool for solving problems.
For the next 10 minutes, use this computer program to practice tape diagrams.

12. Practice: Work with a partner to try it on paper.

13. 6 8 Discuss: Did you and your partner get the same answers? 6 6 6 6 6
6 sour oranges 6 4 4 4 4 4
8 red marbles 8

14. 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 10
playing 8 8 8
apples 5 5
resting 8
oranges 5 5 5
Agenda 8 15
Agenda

15. TOTD: Error Analysis
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? Answer: The number of strawberries is 20.
grapes
strawberries 20 20 20 20 20
What is the mistake? What is the correct answer?

16. Summary – Let’s Talk About It
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?