Proportional Relationships

Lesson 11

Math

Unit 1

7th Grade

Lesson 11 of 18

Objective


Make connections between the four representations of proportional relationships (Part 2).

Common Core Standards


Core Standards

  • 7.RP.A.2 — Recognize and represent proportional relationships between quantities.
  • 7.RP.A.2.A — 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.
  • 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.
  • 7.RP.A.2.D — Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Foundational Standards

  • 6.RP.A.3

Criteria for Success


  1. Represent and analyze proportional relationships in graphs, equations, and tables.
  2. Given one representation of a proportional relationship, create other representations.

Tips for Teachers


The Problem Set Guidance describes a possible activity to help students make connections between the representations. This is a good opportunity for students to showcase their collective work and look at the work of others, via posters, a gallery walk, or in small groups.

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Anchor Problems


Problem 1

A proportional relationship is shown in the graph below. 

a.   Describe a situation that could be represented with this graph.

b.   Write an equation for the relationship. Explain what each part of the equation represents.

Guiding Questions

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Problem 2

Jonathan and his brother Jeffrey went on a long run to prepare for an upcoming road race. Jonathan ran 18 miles in 4 hours. It took Jeffrey 6 hours to run the same route as his brother. Both brothers ran at a constant speed.

a.   Draw a graph to represent the relationship between distance and time for the two brothers. Label each line with the brother’s name.

b.   Explain what the graph tells you about the speed of each brother.

c.   The road race is a marathon and is 26.2 miles long. If Jonathan and Jeffrey each run at the same constant speed as they did in their preparation run, then how long will it take each brother to finish the road race?

Guiding Questions

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Problem Set

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Target Task


Patrice makes a spicy salsa by adding red pepper flakes to a chunky tomato mix in proportional amounts. For example, she mixes $$\frac{1}{2}$$ teaspoon of red pepper flakes to 2 cups of tomato mix.

Represent the relationship between red pepper flakes, in teaspoons, to tomato mix, in cups, in two different ways (table, graph, or equation). In your work, define any variables that you use.

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.

  • Have students create one representation of a proportional relationship (a table, written description, graph, or equation). Then have students swap their work with other students who add a new representation to the one already provided. This can be repeated so that, after 4 students have worked on each situation, all four representations of the proportional relationship are shown.
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Lesson 10

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Lesson 12

Lesson Map

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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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