Relations that Function (Part 1)

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SWBAT understand the correspondence between input and output of a function. SWBAT determine when an input-output relation, given different forms, represents a function.

Big Idea

This laboratory apparatus is called a Cool Converter. Students will figure how it works when they see what goes in and what comes out. Functions work in much the same way.


20 minutes

Before showing the video, hand each student a COOL CONVERTER SLIP. The slip is a three column table labeled Input /  What’s happening? /  output.

I then present the video and ask the students to fill out their tables as we move along. Since something different is happening in each section {(1-3), (4-5), (6-7), (8-10), and (11-13)}, I would pause after each section so as to allow students to think about what to write in the "what's happening" column. (Note that these sections are divided by bold lines in the Cool Converter Slip)

Allow students to discuss their observations with an elbow partner. 

Cool Converter Machine Video


Call on students to share what they wrote in the “what’s happening” column. You may have to write the input-output data on the board if there is debate about an entry, and discuss the matter.

Next, ask students to come up something in the real world, something that they may even use regularly, where there’s an output for every input of information or data. (give clues like computers, phones, bills, video games)

Good answers would be:


Phone number-person

Minutes spoken-phone bill

Control buttons-action on game

Control button- TV channel

Formula or equation

If someone does not mention ‘formula or equation’, I would throw it in and ask,  "How is a formula, like the Celsius to Fahrenheit formula,  similar to the ‘cool converter” examples."

(The answer I want to hear, is that there’s an input, the C temperature, then a formula which is like the CC machine, and an output, the F temperature.)

End by stating that all these input-output relations function in real life circumstances. In mathematics, there are relations that work the same way, yet in order for these to be functions, these relations must meet a particular condition.


25 minutes

I begin this section by projecting each of 3 Scenarios.pdf to the class. Students should read and analyze each scenario, discuss the case with an elbow partner, indicating anything in the scenario which they find incorrect. I call on volunteers to express their ideas to the entire class.

Scenario 1: Students should see that at 150 pounds there are two dosages of medication, meaning there is one input value that corresponds to two output values. I say; This doesn't seem to "function"

Scenario 2: This situation is familiar to students and they should quickly determine that there is nothing incorrect in the scenario. I like to refer to the familiar "username-password" for email, or facebook accounts and ask students; Is it possible that two persons have the same password? (Students may take a few seconds to answer "yes" to this question)

Then I ask; Is it possible for two persons to have the same username? (They quickly respond that it is not possible)  I then ask: What happens when you open an account and the username you choose is taken? (The program suggests other usernames for you to choose from) So scenario 2 seems like it "functions"

Scenario 3: Students should not find anything wrong with Andres' input values representing the side lengths of a square. I keep this image up and ask: Could Andres have chosen values like 0.5, 0.01, or large numbers like 500? (Students should answer affirmatively)   Scenario 3 "functions" as well.

At this point I ask students to take a couple of minutes to speak with a partner and come up with their own definition of a relation that is a function. After a few minutes I call for responses.

Possible answers are: 

-A situation with input and output values but an imput cannot match with two outputs. (I ask this student to change the word "situation" for "relation", and the word "match" for "corresponds")

-When each input value has one output value.

-When the input values are not repeated.

I write the responses on the board and accept them, not without tweeking them a bit using appropriate vocabulary when necessary. 

I end this part of the lesson by asking the class if Andres in Scenario 3 could have used 0, -1, or -2 for input values in table, according to their own definition of a function. This question baffles some students because they realize that these values cannot be sides of a square, yet according to their definition of a function, the values could be used.  I state that in some cases, the set of input values have restrictions. In this case all input values must be greater than zero. 



5 minutes

To close part 1 of the lesson, I hand a One to One Exit Slip to each student, although they are still paired up and allowed to discuss their ideas. The language of functions is new, so I find it very important to know what it is they have learned and feel certain about, and what they may feel confused about. Like with all closures, this exit pass gives me an opportuntity for formative assessment and helps me decide whether I can move on to part 2, or provide additional practice and/or explanation. 

The "one to one" Exit slip asks students to write down one clear idea that they understood well, and one idea they are uncertain or confused about. I make sure I read each of these before continuing to part 2 of the lesson.