Linear Relationships

Lesson 1

Math

Unit 5

8th Grade

Lesson 1 of 15

Objective


Review representations of proportional relationships.

Common Core Standards


Core Standards

  • 8.EE.B.5 — Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

Foundational Standards

  • 7.RP.A.2

Criteria for Success


  1. Represent proportional situations involving speed as equations, graphs, tables, and descriptions.
  2. Understand that the constant of proportionality is the same as the rate of change in a proportional relationship.
  3. Understand that the rate of change in a situation is the same as the slope of the graph that represents the situation. 

Tips for Teachers


  • This lesson is approaching 8.EE.5 and reviews concepts from seventh grade Ratios and Proportions standards and from Unit 4 of eighth grade using the context of speed. In Lesson 2, students will draw graphs of proportional relationships and continue to make connections between the different representations. This will prepare students for Lessons 3 and 4, where students will compare across proportional relationships.
  • The term slope is introduced in this lesson. Students learn that the rate of change is the same as the slope of the graph. The concept of slope will be developed more thoroughly in later lessons in the unit. 
  • Throughout the unit, students may want to use graph paper and/or rulers.
Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

25-30 minutes


Problem 1

Asia is training for a 10K road race that will take place in October. She starts her training in July and runs every weekend. On her first run, she ran at a constant pace and covered 5.5 miles in 60 minutes. On her last run before the race, she ran at a constant pace and covered 10.2 miles in 1$$\frac{1}{2}$$ hours.

a.   What were Asia's speeds, in miles per hour, on her first and last runs?

b.   Write an equation to represent Asia's distance ran as a function of time for her first run and for her last run.

c.   A 10K road race is approximately 6.2 miles. If Asia ran at her beginning pace, how long would it take her to finish the road race? How long would it take her if she ran at her end pace?

d.   Determine which graph below represents Asia’s first run and her last run. Explain your reasoning.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem 2

The graph below shows the relationship between the distance an airplane has covered and the amount of time it has been flying. 

a.   What is the speed of the airplane in miles per hour?

b.   What is the rate of change in the relationship?

c.   What is the slope of the graph?

d.   What equation represents the relationship?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

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


Four representations are shown below. Three of the four representations match. 

Which one does not belong? Explain your reasoning.

Graph: 

Equation:

$${y=2x}$$

 

 

 

 

 

 

Table:

$$x$$ 2 4 6 8
$$y$$ 1 2 3 4

Description:

A caterpillar moves at a constant speed of $$\frac{1}{2}$$ inch per second. Let $$x$$ represent the time in seconds and $$y$$ represent the distance traveled in inches.

Student Response

Upgrade to Fishtank Plus to view Sample 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 are given a proportional graph and asked to find the slope of the graph (or rate of change in situation) and write the equation.

Next

Graph proportional relationships and interpret slope as the unit rate.

Lesson 2
icon/arrow/right/large

Lesson Map

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

Topic A: Comparing Proportional Relationships

Topic B: Slope and Graphing Linear Equations

Topic C: Writing Linear Equations

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free