Topic A: Proportional Relationships

Lesson 1An Experience in Relationships as

Measuring Rate

LEARNING TARGETLesson 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.

STANDARDS7.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

RatioRateUnit rate

Review Key Vocabulary

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

Example 1: How Fast is Our Class?Trial Number of

PapersTime

(in seconds)Ratio Rate Unit Rate

1

2

3

1. How will we measure our rate of passing out papers?2. What quantities will we use to describe our rate?

MODEL: Ratio Column

• Teacher: Trial 1• Class: Trial 2• Partner: Trial 3

Discussion

1. What was the ratio from the first trial?2. What was the ratio in the third trial?3. Are these two ratios equivalent? Explain.

Review Key Vocabulary

• A rate is a ratio of different units.Example: A unit rate is a rate with a denominator of 1. Example:

MODEL: Rate & Unit Rate Columns

• Teacher: Trial 1• Class: Trial 2• Partner: Trial 3

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?

Exit Ticket – Day 1

1. Describe the difference between the ratio and rate in Example 1.

2. Describe how we turned the rate into a unit rate in Example 1.

LEARNING TARGETLesson 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.

STANDARDS7.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 PracticeKEY VOCABULARY

RatioEquivalent ratios

Review Key Vocabulary

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

Example 2: Our Class by Gender

1. What are we comparing in this example?2. Are the units different? Explain.3. 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

MODEL: Ratio of Boys to Girls Column

• Teacher: Period 1• Class: Period 3• Partner: Period 5 & All

Discussion

1. Are the ratios of boys to girls in the three classes equivalent?

2. What could these ratios tell us? 3. What does the ratio of boys to girls in Period 1 to all

classes tell us? Are they equivalent? 4. 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?

5. How do we compare the ratios when we have varying sizes of quantities?

Review Key Vocabulary

Equivalent ratios have different numbers but represent the same relationship.Example:

Extension

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

Exit Ticket – Day 2

How do the equivalent ratios compare to the ratio of ALL boys: ALL girls? What does this mean?

LEARNING TARGETLesson 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.

STANDARDS7.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

RateUnit rate

Review Key Vocabulary

• A rate is a ratio of different units.Example: A unit rate is a rate with a denominator of 1. Example:

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 $4.77. Which is the better buy? How do you know?

Mathematical Practice: Reason abstractly and quantitatively

Critique Responses

Lesson Summary

How is finding a rate or unit rate helpful when making comparisons between quantities?

Problem Set 1 Point

(Unsatisfactory)2 Points

(Partially Proficient)

3 Points

(Proficient)

4 Points

(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

ExtensionWatch the video clip of Tillman the English Bulldog, the Guinness World Record holder for Fastest Dog on a Skateboard.

1. 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?

2. 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