1. Topic A: Proportional Relationships
Lesson 1
An Experience in Relationships as Measuring Rate

2. Lesson 1: An Experience in Relationships as Measuring Rate – Day 1
LEARNING TARGET
Lesson 1: An Experience in Relationships as Measuring Rate – Day 1
Today I can write a ratio and rate and compute a unit rate and explain their meaning in the context of the problem.
STANDARDS
7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
AGENDA
(5 min) Review Key Vocabulary: Ratio
(10 min) Example 1: How Fast is Our Class?
(5 min) MODEL: Ratio
(10 min) Discussion
(5 min) Review Key Vocabulary: Rate & Unit Rate
(5 min) MODEL: Rate
(5 min) MODEL: Unit Rate
(10 min) Extension
(5 min) Exit Ticket
(20-30 min) Online Practice
KEY VOCABULARY
Ratio
Rate
Unit rate

3. Review Key Vocabulary
A ratio is a comparison of two numbers by division. Example: 60 3 , 60: 3, 60 to 3

4. Example 1: How Fast is Our Class?
Trial
Number of Papers
Time
(in seconds)
Ratio
Rate
Unit Rate 1 2 3
How will we measure our rate of passing out papers?
What quantities will we use to describe our rate?

5. MODEL: Ratio Column
Teacher: Trial 1
Class: Trial 2
Partner: Trial 3

6. Discussion What was the ratio from the first trial?
What was the ratio in the third trial?
Are these two ratios equivalent? Explain.

7. Review Key Vocabulary A rate is a ratio of different units.
Example: 60 𝑚𝑖𝑙𝑒𝑠 3 ℎ𝑜𝑢𝑟𝑠
A unit rate is a rate with a denominator of 1. Example: 20 𝑚𝑖𝑙𝑒𝑠 1 ℎ𝑜𝑢𝑟

8. MODEL: Rate & Unit Rate Columns
Teacher: Trial 1
Class: Trial 2
Partner: Trial 3

9. Extension
Let’s say that in another class period students were able to pass 28 papers in 15 seconds. A third class period passed 18 papers in 10 seconds. How do these compare to our fastest unit rate?

10. Exit Ticket – Day 1
Describe the difference between the ratio and rate in Example 1.
Describe how we turned the rate into a unit rate in Example 1.

11. Lesson 1: An Experience in Relationships as Measuring Rate – Day 2
LEARNING TARGET
Lesson 1: An Experience in Relationships as Measuring Rate – Day 2
Today I can write ratios and equivalent ratios and explain their meaning in the context of the problem.
STANDARDS
7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
AGENDA
(5 min) Review Key Vocabulary: Ratio
(20 min) Example 2: Our Class by Gender
(10 min) MODEL: Ratio
(10 min) Discussion
(5 min) Review Key Vocabulary: Equivalent Ratios
(10 min) Extension
(5 min) Exit Ticket
(20-30 min) Online Practice
KEY VOCABULARY
Ratio
Equivalent ratios

12. Review Key Vocabulary
A ratio is a comparison of two numbers by division. Example: 60 3 , 60: 3, 60 to 3

13. Example 2: Our Class by Gender
What are we comparing in this example?
Are the units different? Explain.
Does it matter the order we write the ratio? Explain.
Class
Number of boys
Number of girls
Ratio of boys to girls
Period 1
Period 3
Period 5
All

14. MODEL: Ratio of Boys to Girls Column
Teacher: Period 1
Class: Period 3
Partner: Period 5 & All

15. Discussion
Are the ratios of boys to girls in the three classes equivalent?
What could these ratios tell us?
What does the ratio of boys to girls in Period 1 to all classes tell us? Are they equivalent?
If there is a larger ratio of boys to girls in one class than all classes, what does that mean must be true about the boy/girl ratio in other classes?
How do we compare the ratios when we have varying sizes of quantities?

16. Review Key Vocabulary
Equivalent ratios have different numbers but represent the same relationship.
Example: = 20 1

17. Extension
Write down two equivalent ratios comparing boys to girls from our class. Explain your process.

18. Exit Ticket – Day 2
How do the equivalent ratios compare to the ratio of ALL boys: ALL girls? What does this mean?

19. Lesson 1: An Experience in Relationships as Measuring Rate – Day 3
LEARNING TARGET
Lesson 1: An Experience in Relationships as Measuring Rate – Day 3
Today I can compute a unit rate and explain its meaning in the context of the problem.
STANDARDS
7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
AGENDA
(5 min) Review Key Vocabulary: Rate & Unit Rate
(15 min) Exercise 1: Which is the Better Buy?
(15 min) Critique Responses
(5 min) Lesson Summary
(25 min) Problem Set
(If Time) Extension
(15-20 min) Quiz: Lesson 1
KEY VOCABULARY
Rate
Unit rate

20. Review Key Vocabulary A rate is a ratio of different units.
Example: 60 𝑚𝑖𝑙𝑒𝑠 3 ℎ𝑜𝑢𝑟𝑠
A unit rate is a rate with a denominator of 1. Example: 20 𝑚𝑖𝑙𝑒𝑠 1 ℎ𝑜𝑢𝑟

21. Exercise 1: Which is the Better Buy?
Value-Mart is advertising a Back-to-School sale on pencils. A pack of 30 sells for $7.97 whereas a 12-pack of the same brand costs $ Which is the better buy? How do you know?
Mathematical Practice: Reason abstractly and quantitatively

22. Critique Responses

23. Lesson Summary
How is finding a rate or unit rate helpful when making comparisons between quantities?

24. Problem Set 1 Point (Unsatisfactory) 2 Points (Partially Proficient)
(Advanced)
Missing or incorrect answer and little evidence of reasoning
Missing or incorrect answer but evidence of some reasoning
A correct answer with some evidence of reasoning or an incorrect answer with substantial evidence
A correct answer supported by substantial evidence of solid reasoning

25. Extension
Watch the video clip of Tillman the English Bulldog, the Guinness World Record holder for Fastest Dog on a Skateboard.
At the conclusion of the video, your classmate takes out his or her calculator and says, “Wow that was amazing! That means the dog went about 5 meters in 1 second!” Is your classmate correct, and how do you know?
After seeing this video, another dog owner trained his dog, Lightning, to try to break Tillman’s skateboarding record. Lightning’s fastest recorded time was on a 75-meter stretch where it took him 15.5 seconds. Based on this data, did Lightning break Tillman’s record for fastest dog on a skateboard? Explain how you know.
Video Link