Proportional Relationships

Lesson 4

Math

Unit 1

7th Grade

Lesson 4 of 18

Objective


Write equations for proportional relationships presented in tables.

Common Core Standards


Core Standards

  • 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

  • 6.EE.B.7
  • 6.RP.A.3

Criteria for Success


  1. Determine the constant of proportionality from a table. 
  2. Write an equation for a proportional relationship in the form $$y=kx$$ where $$k$$ represents the constant of proportionality.
  3. Explain what the constant of proportionality means in context of a situation.
  4. Explain the role of the constant of proportionality in an equation.
  5. Use an equation to solve problems and determine additional values for the situation.
  6. Decontextualize situations to represent them as equations and re-contextualize equations to explain their meanings as they relate to situations (MP.2).

Tips for Teachers


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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Anchor Problems

25-30 minutes


Problem 1

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.

# hours worked Amount earned ($)
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

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Student Response

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Problem 2

The table below shows measurement conversions between cups and ounces.

Cups 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.

Guiding Questions

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Student Response

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Problem 3

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.

  A B C D E F
Yellow 1 part 2 parts 3 parts 4 parts 5 parts 6 parts
Blue 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.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Art Class, Variation 2

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.

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.

Target Task

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.

Amount of powder (tsp, $$p$$) Amount of water (cups, $$w$$)
$$\frac{1}{2}$$ $$2$$
$$2$$ $$8$$
$$3\frac{1}{2}$$ $$14$$
$$4$$ $$16$$

 

a.    Which equation represents this relationship?

  1. a.   $$p=4w$$

  2. b.   $$w=4p$$

  3. c.   $$w=4+p$$

  4. d.   $$p=4\div w$$

b.   What is the constant of proportionality, and what does it mean in this example?

Student Response

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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 examples where students are given a table and must determine the equation that represents the proportional relationship. Some example contexts include:
    • 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.

Next

Write equations for proportional relationships from word problems.

Lesson 5
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Representing Proportional Relationships in Tables, Equations, and Graphs

Topic B: Non-Proportional Relationships

Topic C: Connecting Everything Together

Topic D: Solving Ratio & Rate Problems with Fractions

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