Topic A: Proportional Relationships

Lesson 3Identifying 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 3: Identifying Proportional & Non-Proportional Relationships in Tables

Today I can determine if data in a table represents a proportional or non-proportional relationship and explain my reasoning.

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• (10 min) Warm-Up• (5 min) Review Key Vocabulary• (10 min) Warm-Up: Babysitting• (10 min) Discussion• (5 min) Teacher Model: Example 1• (10 min) Class Model: Example 2• (10 min) Partner Model: Example 3• (10 min) Discussion• (10 min) Partner Model: Example 4• (10 min) Discussion• (5 min) Exit Ticket

KEY VOCABULARY

ProportionalConstantConstant of Proportionality

Warm-Up: Day 1

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.

Exercise: BabysittingYou have been hired by your neighbors to babysit their children on Friday night. You are paid $8 per hour. Complete the table relating your pay to the number of hours you worked. Hours Worked Pay ($)

1

2

3

4

4.5

5

6

6.5

Discussion

1. Describe the relationship between the amount of money earned and the number of hours worked in this example.

2. How can multiplication and division be used to show the earnings are proportional to number of hours worked?

Discussion

1. Explain how you completed the table.2. How did you determine the pay for 4 ½ hours?3. How could you use the information to determine

the pay for a week in which you worked 20 hours?4. How many other ways can the answer be

determined? 5. If the quantities in the table were graphed, would

the point (0, 0) be on the graph? What would mean in the context of the problem.

TEACHER MODEL: Example 1

Determine if y is proportional to x. Justify your answer.The table below represents the amount of snow fall in 5 countries (in inches) to hours of a recent winter storm. x

Time (hrs)y

Snowfall (in)2 10

6 12

8 16

2.5 5

7 14

CLASS MODEL: Example 2

Determine if y is proportional to x. Justify your answer.The table below shows the relationship between cost of renting a movie to the number of days on rent. x

Number of Daysy

Cost6 2

9 3

24 8

3 1

PARTNER MODEL: Example 3

Determine if y is proportional to x. Justify your answer.The table below shows the relationship between the amount of candy (pounds) bought and the total cost. x

Poundsy

Cost5 10

4 8

6 12

8 16

10 20

Discussion

1. When looking at ratios that describe two quantities that are proportional in the same order, do the ratios always have to be equivalent?

2. For example, if the quantities in the table were graphed, would point (0,0) be on the graph? Describe what the point (0,0) would represent in each table.

3. Do the x and y values need to go up at a constant rate? In other words, when the x and y values both go up at constant rate, does this always indicate the relationship is proportional?

PARTNER MODEL: Example 4

Randy is planning to drive from New Jersey to Florida. Randy recorded the distance traveled and the total number of gallons used every time he stopped for gas. Assume miles driven is proportional to Gallons Consumed in order to complete the table.

Gallons Consumed

2 4 8 10 12

Miles Driven 54 189 216

Discussion

1. Why is it important for you to know that miles are proportional to the gallons used?

2. Describe the approach you used to complete the table.

3. What is the value of the constant? Explain how the constant was determined.

4. Explain how to use multiplication and division to complete the table.

Exit Ticket – Day 1

1. Explain how we found the constant of proportionality?

2. Explain how we used the constant of proportionality to find missing values in the table.

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 and explain my reasoning.

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• (5 min) Review Key Vocabulary• (10 min) Warm-Up: Price of Roses• (10 min) Lesson Summary• (25 min) Lesson 3 Problem Set• (30 min) Lesson 3 Quiz

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: Price of Roses

The table below shows the price for the number of roses indicated.

Number of Roses 3 6 7 12 15

Price (Dollars) 9 18 27 36 45

1. Is the price proportional to the number of roses? How do you know?

2. Find the cost of purchasing 30 roses.

Lesson Summary

One quantity is proportional to a second if a constant (number) exists such that each measure in the first quantity multiplied by this constant gives the corresponding measure in the second quantity. Steps to determine if two quantities in a table are proportional to each other:

1. For each given measure of Quantity A and Quantity B, find the value of .

2. If the value of is the same for each pair of numbers, then the quantities are proportional to each other.

Lesson 3 - 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

Lesson 3 - 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