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Curriculum / Math / 7th Grade / Unit 1: Proportional Relationships / Lesson 4
Proportional Relationships
Lesson 4 of 18
Criteria for Success
Tips for teachers, anchor problems, problem set, target task, additional practice.
Write equations for proportional relationships presented in tables.
Common Core Standards
Core standards.
The core standards covered in this lesson
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.
7.RP.A.2.C — Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
Foundational Standards
The foundational standards covered in this lesson
Expressions and Equations
6.EE.B.7 — Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
- Determine the constant of proportionality from a table.
- Write an equation for a proportional relationship in the form $$y=kx$$ where $$k$$ represents the constant of proportionality.
- Explain what the constant of proportionality means in context of a situation.
- Explain the role of the constant of proportionality in an equation.
- Use an equation to solve problems and determine additional values for the situation.
- Decontextualize situations to represent them as equations and re-contextualize equations to explain their meanings as they relate to situations (MP.2).
Suggestions for teachers to help them teach this lesson
Lessons 4 and 5 focus on representing proportional relationships as equations. Equations are abstract and can be challenging for some students to grasp. Encourage students to return to the table to show the relationship between the two quantities, either adding a column to show the constant of proportionality or drawing an arrow across rows and indicating the multiplication. Ensure that students know what the variables in the equation represent to keep the context connected to the abstract form.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Felix worked at a music shop during the summer. The table below shows some of Felix’s hours and earnings. The amount of money he earned is proportional to the number of hours he worked.
| 1 | |
| 2 | 18 |
| 3 | |
| 5 | 45 |
| 10 | |
| 15 | 135 |
| 20 | 180 |
a. Fill in the rest of the table and then write an equation that represents the relationship.
b. If Felix worked 35 hours, then how much money did he earn?
c. If Felix earned $198, then how many hours did he work?
Guiding Questions
The table below shows measurement conversions between cups and ounces.
| 3 | 24 |
| 5 | 40 |
| 8 | 64 |
Let $$x$$ represent the number of cups and $$y$$ represent the number of ounces. Write an equation that represents this relationship.
The students in Ms. Baca’s art class were mixing yellow and blue paint. She told them that two mixtures will be the same shade of green if the blue and yellow paint are in the same ratio.
The table below shows the different mixtures of paint that the students made.
| 1 part | 2 parts | 3 parts | 4 parts | 5 parts | 6 parts | |
| 2 parts | 3 parts | 6 parts | 6 parts | 8 parts | 9 parts |
a. How many different shades of paint did the students make?
b. Write an equation that relates $$y$$ , the number of parts of yellow paint, and $$b$$ , the number of parts of blue paint for each of the different shades of paint the students made.
Art Class, Variation 2 , accessed on Aug. 1, 2017, 3:07 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0 . For further information, contact Illustrative Mathematics .
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
A lemonade is made by mixing flavored powder, $$p$$ , with water, $$w$$ . The chart below shows some measurements that can be used to make different amounts of lemonade.
| ) | ) |
| $$\frac{1}{2}$$ | $$2$$ |
| $$2$$ | $$8$$ |
| $$3\frac{1}{2}$$ | $$14$$ |
| $$4$$ | $$16$$ |
a. Which equation represents this relationship?
a. $$p=4w$$
b. $$w=4p$$
c. $$w=4+p$$
d. $$p=4\div w$$
b. What is the constant of proportionality, and what does it mean in this example?
Student Response
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.
- Batches of recipe ingredients
- Distance, time, speed
- Miles per gallon
- Unit prices
- Unit conversions
- Paint or other mixtures
- Include problems where students explain the relationship between the table, constant of proportionality, and equation in context.
- EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic B > Lesson 8 — Example 1 only
- EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic B > Lesson 9 — Example 2, Problem Set 2 and 4
Topic A: Representing Proportional Relationships in Tables, Equations, and Graphs
Solve ratio and rate problems using double number lines, tables, and unit rate.
7.RP.A.1 7.RP.A.2
Represent proportional relationships in tables, and define the constant of proportionality.
7.RP.A.2 7.RP.A.2.B
Determine the constant of proportionality in tables, and use it to find missing values.
7.RP.A.2.A 7.RP.A.2.B
7.RP.A.2.B 7.RP.A.2.C
Write equations for proportional relationships from word problems.
7.RP.A.2 7.RP.A.2.C
Represent proportional relationships in graphs.
7.RP.A.2 7.RP.A.2.A 7.RP.A.2.D
Interpret proportional relationships represented in graphs.
7.RP.A.2 7.RP.A.2.D
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Topic B: Non-Proportional Relationships
Compare proportional and non-proportional relationships.
Determine if relationships are proportional or non-proportional.
Topic C: Connecting Everything Together
Make connections between the four representations of proportional relationships (Part 1).
7.RP.A.2 7.RP.A.2.A 7.RP.A.2.B 7.RP.A.2.C 7.RP.A.2.D
Make connections between the four representations of proportional relationships (Part 2).
Use different strategies to represent and recognize proportional relationships.
Topic D: Solving Ratio & Rate Problems with Fractions
Find the unit rate of ratios involving fractions.
Find the unit rate and use it to solve problems.
7.RP.A.1 7.RP.A.3
Solve ratio and rate problems by setting up a proportion.
Solve ratio and rate problems by setting up a proportion, including part-part-whole problems.
Solve multi-step ratio and rate problems using proportional reasoning, including fractional price increase and decrease, commissions, and fees.
Use proportional reasoning to solve real-world, multi-step problems.
7.RP.A.1 7.RP.A.2 7.RP.A.3
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