Topic A: Proportional Relationships

Lesson 4Identifying Proportional and

Non-Proportional Relationships in Table

Topic A Overview

Lesson 1: An Experience in Relationships as Measuring RateLesson 2: Proportional RelationshipsLessons 3-4: Identifying Proportional and Non-Proportional Relationships in TablesLessons 5-6: Identifying Proportional and Non-Proportional Relationships in Graphs

LEARNING TARGETLesson 4: Identifying Proportional & Non-Proportional Relationships in Tables

Today I can determine if data in a table represents a proportional or non-proportional relationship by determining if there’s a constant of proportionality for each set of x and y values.

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 – Day 1• (5 min) Review Key Vocabulary• (10 min) Warm-Up: Which Team Will Win

the Race?• (10 min) Share Solutions• (10 min) MODEL: Finding the Constant

of Proportionality• (10 min) Proportional or Non-

Proportional?• (10 min) Extension• (5 min) Exit Ticket• (30 min) Online Practice

KEY VOCABULARY

ProportionalConstantConstant of Proportionality

Review Key Vocabulary

• Proportional – when two quantities simplify to the same ratio.

• Constant – a quantity having a value that does not change or vary.

• Constant of Proportionality - a constant value of the ratio of two proportional quantities.

Warm-Up: Which Team Will Win the Race?You have decided to run in a long distance race. There are two teams that you can join. Team A runs at a constant rate of 2.5 miles per hour. Team B runs 4 miles the first hour and then 2 miles per hour after that. Task: Create a table for each team showing the distances that would be run for times of 1-6 hours.

Team A

Time (hrs) Distance (miles)

1

2

3

4

5

6

Team B

Time (hrs) Distance (miles)

1

2

3

4

5

6

MODEL: Finding the Constant of Proportionality

Team A runs at a constant rate of 2.5 miles per hour. Team A

Time (hrs) Distance (miles)

1

2

3

4

5

6

MODEL: Finding the Constant of Proportionality

Team B runs 4 miles the first hour and then 2 miles per hour after that.

Team B

Time (hrs) Distance (miles)

1

2

3

4

5

6

Proportional or Non-Proportional?

1. For which team is distance proportional to time? Explain your reasoning.

2. Explain how you know the distance for the other team is not proportional to time?

Extension

1. If the race were 2.5 miles long, which team would win? Explain.

2. If the race were 3.5 miles long, which team would win? Explain.

3. If the race were 4.5 miles long, which team would win? Explain.

Exit Ticket

The table below shows the relationship between the side lengths of a regular octagon and its perimeter.

1. Complete the table.2. If Gabby wants to make an octagon

with a side length of 20 inches using wire, how much wire does she need? Justify your reasoning with an explanation of whether perimeter is proportional to the side length.

Side Length, s(inches)

Perimeter, P(inches)

1 82 163 244 329

12

LEARNING TARGETLesson 3: Identifying Proportional & Non-Proportional Relationships in Tables

Today I can determine if data in a table represents a proportional or non-proportional relationship by determining if there’s a constant of proportionality for each set of x and y values.

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 – Day 2• (10 min) Warm-Up• (5 min) Review Key Vocabulary• (5 min) Review: Which Team Will Win the

Race?• (20 min) Discussion• (25 min) Lesson 4 Problem Set• (30 min) Lesson 4 Quiz

KEY VOCABULARY

ProportionalConstantConstant of Proportionality

Warm-Up: Day 2

Does the table show that y is proportional to x? Explain. X Y

1 42 83 124 16

Review Key Vocabulary

• Proportional – when two quantities simplify to the same ratio.

• Constant – a quantity having a value that does not change or vary.

• Constant of Proportionality - a constant value of the ratio of two proportional quantities.

Review: Which Team Will Win the Race?You have decided to run in a long distance race. There are two teams that you can join. Team A runs at a constant rate of 2.5 miles per hour. Team B runs 4 miles the first hour and then 2 miles per hour after that. Task: Create a table for each team showing the distances that would be run for times of 1-6 hours.

Team A

Time (hrs) Distance (miles)

1

2

3

4

5

6

Team B

Time (hrs) Distance (miles)

1

2

3

4

5

6

Discussion

1. For what length race would it be better to be on Team B than Team A? Explain.

2. Using the relationship, if the members on the team ran for 10 hours, how far would each member run on each team?

3. Will there always be a winning team, no matter what length of the course? Why or why not?

Discussion Continued…

4. If the race were 12 miles long, which team should you choose to be on if you wish to win? Why would you choose this team?

5. How much sooner would you finish on that team compared to the other team?

Lesson 4 – Problem Set1 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

Lesson 4 – Quiz1 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