## Objective

Interpret proportional relationships represented in graphs.

## 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.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.

### Ratios and Proportional Relationships

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

The foundational standards covered in this lesson

6.RP.A.3.A

### Ratios and Proportional Relationships

6.RP.A.3.A— Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

## Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

- Identify the constant of proportionality in a graph by finding the value of $$y/x$$from coordinate point $$(x,y)$$.
- Identify the constant of proportionality or unit rate as the value
*$$r$$*, when*$$x$$*is $$1$$, represented by the coordinate point $$(1,r)$$. - Explain the meaning of$$(0, 0)$$ in context of the situation.

## Tips for Teachers

Suggestions for teachers to help them teach this lesson

Students reason abstractly as they represent proportional situations using tables and graphs, and interpret the information to identify the constant of proportionality and write an equation. Given a graph of a proportional relationship, students re-contextualize information represented in coordinate points to explain what$$ (0, 0)$$ and$$ (0, r)$$ mean in context of the problem (MP.2).

### Lesson Materials

- Graph Paper (1 per student)
- Ruler (2-3 sheets per student)

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## Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

25-30 minutes

### Problem 1

In a video game, for every 3 coins you collect, you earn 4 points.

a.Create a table of values to represent the relationship.

b.Graph the relationship.

c.Determine the equation that represents the relationship.

#### Guiding Questions

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#### Student Response

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### Problem 2

Three toy cars race down a straight path. The distance each car traveled, in meters, over time, measured in seconds, is shown in the graph below.

a.At what speed is each car traveling? Where can you see each speed in the graph?

b.Explain the significance of the coordinate point $$(1, r)$$. What do you think the “$$r$$” represents?

#### Guiding Questions

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#### Student Response

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### Problem 3

The graph below shows the number of gallons of gasoline used by a car over a given number of miles.

a.Explain what each point A, B, and C means in the context of the situation.

b.Plot the point that represents the unit rate. Explain how you determined your answer, and what it means in context of the situation.

c.Does this car get more or less miles per gallon of gasoline than a car that gets 30 miles per gallon?

#### Guiding Questions

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#### Student Response

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## Problem Set

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.

## Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

5-10 minutes

A souvenir shop sells magnets, 2 for $3. The graph below shows the proportional relationship.

Which statements below are true? For each false statement, correct it so that the statement reads true.

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#### 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.

- Illustrative Mathematics
*Robot Races* - Illustrative Mathematics
*Buying Coffee* - RDA Performance Task Bank
*Grade 7 Mathematics Sample TE Item* - RDA Performance Task Bank
*Grade 7 Mathematics Sample SR Item* - EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic B > Lesson 10—Problem Set

Lesson 6

Lesson 8