Objective
Represent proportional relationships in tables, and define the constant of proportionality.
Common Core Standards
Core Standards
The core standards covered in this lesson
7.RP.A.2— Recognize and represent proportional relationships between quantities.
Ratios and Proportional Relationships
7.RP.A.2— Recognize and represent proportional relationships between quantities.
7.RP.A.2.B— Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Ratios and Proportional Relationships
7.RP.A.2.B— Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Foundational Standards
The foundational standards covered in this lesson
6.RP.A.2
Ratios and Proportional Relationships
6.RP.A.2— Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.Expectations for unit rates in this grade are limited to non-complex fractions.For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."
6.RP.A.3
Ratios and Proportional Relationships
6.RP.A.3— Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
Criteria for Success
The essential concepts students need to demonstrate or understand to achieve the lesson objective
- Understand a proportional relationship between two quantities as a collection of equivalent ratios of those quantities.
- Understand the constant of proportionality as the constant value that tells how much of the second quantity is per 1 of the first quantity; the constant of proportionality is a constant multiplier between the two quantities.
- Describe a proportional relationship between two quantities shown in a table.
- Use unit rate and constant of proportionality to find missing values.
Tips for Teachers
Suggestions for teachers to help them teach this lesson
- The terms proportional relationships and constant of proportionality are introduced in this lesson. These terms will be used throughout the rest of the unit and students will have many more opportunities to understand and internalize their meanings. In this lesson, encourage students to make connections between these terms and their prior understandings of unit rate and equivalent ratios.
- In this lesson, students analyze tables as a way to understand the relationship between two quantities. They identify a numerical pattern (the unit rate or constant of proportionality) in the table (MP.8) and then contextualize that value to understand what it means about the two units involved (MP.2).
Fishtank Plus
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Anchor Problems
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Problem 1
A self-serve frozen yogurt store sells yogurt at a price based on weight. Each member of Isabelle’s family weighed their dish to determine the cost of their yogurt, as shown in the table below.
| Weight (ounces) | Cost ($) |
| 12 | 6 |
| 5 | 2.50 |
| 8 | 4 |
| 6 | 3 |
Is the cost of the yogurt proportional to the weight of the yogurt?
Guiding Questions
Create a free account or sign in to access the Guiding Questions for this Anchor Problem.
References
EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic A > Lesson 2—Example 1
Grade 7 Mathematics > Module 1 > Topic A > Lesson 2 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 USlicense.Accessed Dec. 2, 2016, 5:15 p.m..
Modified by Fishtank Learning, Inc.
Problem 2
The table below relates the number of gallons to number of quarts.
| Gallons | Quarts |
| 5 | 20 |
| 3 | 12 |
| 8 | 32 |
| 12 | 48 |
a.Describe the relationship between gallons and quarts.
b.What is the constant of proportionality for this relationship?
Guiding Questions
Create a free account or sign in to access the Guiding Questions for this Anchor Problem.
Problem Set
A set of suggested resources or problem types that teachers can turn into a problem set
Fishtank Plus Content
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
Target Task
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
A family took a road trip down the East coast. On average, they traveled at a constant speed, represented in miles and hours in the table below.
| Number of Hours | Number of Miles |
| $$\frac{1}{2}$$ | $$30$$ |
| $$2$$ | $$120$$ |
| $$5\frac{1}{2}$$ | $$330$$ |
| $$7\frac{1}{2}$$ | $$450$$ |
| $$9$$ | $$540$$ |
a.Describe the relationship between hours and miles.
b.How fast is the family driving?
c.What is the constant of proportionality? Explain what it means in this situation.
Student Response
Create a free account or sign in to view Student Response
Additional Practice
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
- Include problems where students practice using the new vocabulary, describing proportional relationships
- Include problems similar to Anchor Problem 2
- EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic B > Lesson 7—Examples and Problem Set
- EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic A > Lesson 2—Problem Set
- Open Up Resources Grade 7 Unit 2 Practice Problems—Lessons 2 and 3 (These can also be used in the next lesson)
Lesson 1
Lesson 3
