Curriculum  /  Math  /  8th Grade  /  Unit 4: Functions  /  Lesson 9

Functions

Lesson 9

Math

Unit 4

8th Grade

Lesson 9 of 12

Objective

Compare functions represented in different ways (Part 1).

Common Core Standards

Core Standards

  • 8.F.A.2 — Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

Foundational Standards

  • 7.RP.A.2.B
  • 7.RP.A.2.C
  • 7.RP.A.2.D

Criteria for Success

  1. Interpret and compare functions in context of the situation described.
  2. Identify rate of change in graphs, tables, equations, and verbal descriptions and compare across representations.
  3. Identify initial value in graphs, tables, equations, and verbal descriptions and compare across representations. 

Tips for Teachers

  • Lessons 9 and 10 bring together the concepts and skills from the previous lessons in the unit in order to interpret and compare functions presented in different formats. 
  • Students continue to re-contextualize information they gather from tables and graphs in order to make comparisons and conclusions (MP.2).
Fishtank Plus

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

Anchor Problems

25-30 minutes

Problem 1

Mari and Lewis both have cell phone plans that give them each 10 gigabytes (GB) of data each month. The graph and table below show the remaining amount of data that Mari and Lewis have after each week in the month. 

Lewis's Phone Data Usage
Week Number 0 1 2 3 4
Data Remaining (GB) 10 9.6 7.4 4.9 1.6

a.   Who used more data after 2 weeks? 

b.   Between weeks 2 and 3, who used more data?  

c.   Who had more data remaining after 3 weeks? By how much?

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

At the Atkinson Farm, you can pick your own vegetables. You pay a small fee to enter the farm, and then you pay a price per pound of vegetables you pick. The graph below shows the total cost as a function of pounds of vegetables. 

The Jackson Farm also allows you to pick your own vegetables. You pay an entry fee of $15 and then $2.50 per each pound of vegetables you pick.

a.   Which farm charges the higher entry fee? 

b.   Which farm charges more per pound of vegetables?

c.   If you plan on buying 4 pounds of vegetables, which farm has the better deal?

d.   If you plan on buying 10 pounds of vegetables, which farm has the better deal? 

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 3

Two functions are shown below.

Function 1:  $${y={2\over3}x +1}$$

Function 2:  

$$x$$ $$y$$
4 3
6 4.5
8 6
10 7.5

 

Ella thinks that Function 2 has a greater initial value because $$3>1$$.
Tommy thinks that Function 2 has a greater rate of change because $$1\frac{1}{2} > \frac{2}{3}$$.

Both Ella and Tommy made a mistake in their thinking. Help each of them understand their mistake and make a new comparison. 

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

Cora and Daniel are both saving money each month. The total amount in their savings accounts is a function of the number of months they have been saving. Each account is represented below.

Cora: $${y=65x+100}$$, where $$y$$ represents the total amount and $$x$$ represents number of months 

Daniel:

a.   Who started with more money in their savings account? 

b.   Who is saving at a faster rate? By how much?

c.   After 6 months, who will have more money in their savings account? 

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.

Next

Compare functions represented in different ways (Part 2).

Lesson 10
icon/arrow/right/large

Lesson Map

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

Topic A: Defining Functions

Topic B: Representing and Interpreting Functions

Topic C: Comparing Functions

Topic D: Describing and Drawing Graphs of Functions

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