What is a Function?

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Objective

SWBAT identify functions from ordered pairs, a table, a graph, and a mapping diagram.

Big Idea

Students will identify whether a relation is a function by examining its inputs and outputs or with the vertical line test.

Do-Now

5 minutes

Students will complete today's Do Now in about 4 minutes.

Afterward, I will call the problems out aloud, and students will respond back with the answer.

Next a student volunteer will read today's lesson objective, "SWBAT identify whether a relation is a function".

Introduction + Guided Practice

30 minutes

To introduce the idea of a function I will act out the following narrative while Slide 3 of Functions is showing:

One day I was walking down the street and I decided that I was really thirsty. I saw a soda machine and pulled out a dollar to get something to drink.

At this point I will tap on the board to simulate getting a soda out of the machine, and I will ask students to make and fill in the blank input/output table at the top of their notes. The input will be the button that I push, and the output is the corresponding table:

      Input                        Output

Coke Button      -->         Coke Can

Coke Button     -->          Coke Can

Sprite Button    -->         Sprite Can

Coke Button     -->          Coke Can 

I will ask students to to turn-and-talk to their neighbor for about 30 seconds about what happened in my simulation. I will ask students if anything strange happened, and to decide if the machine is functioning.

Next, I will proceed to the soda machine on Slide 4. I will also tell students a similar narrative about wanting a beverage to drink, and I will ask students to fill in the second input/output table for this new machine:

     Input                        Output

Coke Button      -->         Coke Can

Coke Button     -->          Sprite Can

Sprite Button    -->         Root Beer Can

Coke Button     -->          Water Bottle

Again, I will ask students to turn-and-talk to their neighbor about what happened in this simulation. I will ask students if anything strange happened, and to decide if this machine is functioning. I will also ask students to describe the relationship between the inputs and outputs in both machines, and how the the presence of a repeating input or output affected whether or not the machine functioned correctly.

Finally, I will show students the tables on next slide, and invite students to create their own definition of the word function. After a brief discussion and examination of about functions and non-functions, I will introduce the vertical line test as a way to classify functions on a graph. I will ask students to use what they know about functions to explain why the vertical line test works. 

Students will follow along with this lesson using Guided Notes.

Partner Practice: Card Sort

30 minutes

Students will work in pairs to complete the Function Card Sort Activity. Pairs will first cut up the cards. Next, students will sort the cards into two groups (Function/Not a Function) and glue the card onto the corresponding side. Lastly, students will write a sentence on page two justifying their response using math terminology.

After about 20 minutes, we will reconvene as a whole group and compare our responses. I will ask students to share their examples of functions that they created on their own.

Closing

10 minutes

I will ask a few students to summarize what we learned today, and to give a definition of a function in their own words. Students will then complete an Exit Card.