Fishtank Learning

8th Grade Math
Unit 4: Functions
Lesson 1

Objective

Define and identify functions.

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?

no siblings
1 sibling
2 siblings
3 or more siblings

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

fewer than 15 minutes
15 minutes or more

Question 3: What grade are you in?

6th grade
7th grade
8th grade
any other grade

Question 4: What color clothing are you wearing?

blue
white
red
brown

Question 5: In what month were you born?

January
February
March
April

Guiding Questions

Discuss any challenges that came up in responding to the questions, particularly with questions 4 and 5.
Are there any questions that are different from the others? How so?
Did you have a place to go to answer each question? Were you torn between any places to go for any questions?
Questions 1–3 are considered functions, while questions 4 and 5 are not functions. What do you think is a characteristic of a function?

Notes

This Anchor Problem introduces the concept of a function by juxtaposing the clarity of a function next to the confusion of a non-function. Questions 1–3 have clear, precise answers that students can identify based on their experiences; every student has a discrete number of siblings that cannot be more than one value at a time. Questions 4–5, however, could be answered in more than one way or not at all; a student may be wearing both blue and white, or a student might not have been born in any of the four months mentioned.
Use this problem to define a function as a relationship between two sets in which every input has exactly one output. Discuss this definition as it relates to the questions asked. What are the inputs in this activity? What are the outputs?
Also consider cases that may seem like they are not functions, but do follow the definition. For example, examining question 3, most likely several, if not all, students stood under C. This is still a function because each student had one place to go to, even if every or multiple students went to the same place.
One analogy that is sometimes used with functions is a soda vending machine. Each button will release a specific drink (each input has exactly one output), even though some buttons may be the same (such as two Coke buttons). A vending machine that gave either Coke or Diet Coke when you pushed the Coke button would be considered non-functioning.
As an alternative to moving around the room, students may use white boards and dry-erase markers to record a single letter response to each question.

Anchor Problems - 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

What challenges came up in filling in these tables?
Explain your strategy or what you did to address these challenges.
For each chart, what represents the input values? What represents the output values?
How does changing the input and output sets change the way you look at the relationship?

Notes

Be watchful for students who incorrectly enter a value of 0 for the values in part b that do not have any associated data. Ask them, “If the value was a 0, would it be represented by a data point, and is that the case? What can be used instead of 0?”
An extension or preview of this Anchor Problem could be creating input/output tables as a class, where students are the input. Outputs could be age, height, birthday month, # of languages spoken, countries visited, pet names, etc.

Anchor Problems - 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.

Problem Set

View Problem Set

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.