Functions

Lesson 1

Math

Unit 4

8th Grade

Lesson 1 of 12

Objective


Define and identify functions.

Common Core Standards


Core Standards

  • 8.F.A.1 — Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Function notation is not required in Grade 8.

Criteria for Success


  1. Define a function as a relationship between two sets in which every input has exactly one output. 
  2. Create input/output tables to represent relationships. 
  3. Determine if input/output tables and relationships are examples of functions.
  4. Identify examples of non-functions in which either an input does not have an output or an input has more than one output. 

Tips for Teachers


This lesson introduces students to the concept of a function to describe a relationship. Though they have worked with functions prior to eighth grade with equations and proportional relationships, this is the first time they will formally define it. Through this unit and the next unit, students will explore functions in-depth; this lesson provides the basic definition of a function as a relationship of inputs and outputs where every input has exactly one output.

Lesson Materials

  • Optional: Dry erase marker (1 per student)
  • Optional: White board (1 per student)
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Anchor Problems


Problem 1

Put the letters A, B, C, and D around your classroom. Tell students that they should respond to each question you ask by standing under the letter that represents their answer.

Question 1: How many siblings do you have?

  1. no siblings
  2. 1 sibling
  3. 2 siblings
  4. 3 or more siblings

Question 2: How long did it take you to get to school today?

  1. fewer than 15 minutes
  2. 15 minutes or more 

     

Question 3: What grade are you in?

  1. 6th grade
  2. 7th grade
  3. 8th grade
  4. any other grade

Question 4: What color clothing are you wearing?

  1. blue
  2. white
  3. red
  4. brown

Question 5: In what month were you born?

  1. January
  2. February
  3. March
  4. April
 

Guiding Questions

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References

Dan Meyer If Functions Are Aspirin, Then How Do You Create The Headache?

If Functions Are Aspirin, Then How Do You Create The Headache? by Dan Meyer is made available at dy/dan under the CC BY 4.0 license. Accessed Oct. 26, 2017, 7:55 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

For each situation below, fill in the missing information in the tables. Then determine if each chart represents a function.

a.   A parking meter takes only dimes, and each dime is worth 6 minutes on the meter.

Number of Dimes Minutes of Parking
2  
3  
7  
Minutes of Parking Number of Dimes
0  
12  
54  

b.   Each point on the graph below shows how many shots a player on a basketball team took and made in the first half of a game.

            

Shots Attempted Shots Made
2  
4  
7  
Shots Made Shots Attempted
1  
4  
6  

Guiding Questions

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References

Illustrative Mathematics Introducing FunctionsPart a.i and a.ii

Introducing Functions, accessed on Oct. 26, 2017, 7:57 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 3

Create an input/output table for each rule below.

a.   Input any number. Add 2, then square the number.

b.   Input any number. If it is greater than or equal to 6, then record a 0; if it less than or equal to 6, then record a 1. 

Guiding Questions

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Problem Set

Fishtank Plus Content

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task


In each example below, an arrow is used to show an input mapping to an output. Determine which relationships are functions. For each relationship that is not a function, explain why.

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.

  • Problems similar to the Target Task, where students are given tables or input/output maps and determine if they are functions
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Lesson 2

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

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