##
* *Reflection: Real World Applications
What is a Function? - Section 2: Introduction + Guided Practice

Multiple examples: Today's topic can feel very abstract for some students, especially for those who have never been introduced to the idea of a "function" in math. The more real world examples I am able to use in my explanantion of a function, the better students are able to conceptualize what is going on.

I stray far away from the explanation "it's not a function if the first number repeats". This brief "shortcut" allows students to answer numerical questions, but fails to help them understand the significance of functions in mathematics. It also hinders their success for future lessons that need students to think critically about domain, range, and algebraic relationships.

Additional examples that I have used to describe a function:

-number of cats vs. number of legs --> which relation is the most resonable? {(1,4) (2,8) (2,8) (3,12)} or {(1,4) (2,8) (2,9) (3,12)} Which relation is a function and why? Are you able to predict the output for each input?

-day of the week vs. temperature

-y = x + 3. when x is 4 the output is usually 6, but sometimes the output is 7. Is this a reliable situation? Will you always know what the output will be when "4" is inputted?

-Draw two "function machines" on the board: Examples

*Multiple Examples*

*Real World Applications: Multiple Examples*

# What is a Function?

Lesson 1 of 10

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

#### Resources

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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.

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#### Partner Practice: Card Sort

*30 min*

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.

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#### Resources

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I love the idea of using the soda machine. Asking is it functioning? If you press the Sprite button and a Coke comes out the machine could be functioning just someone stocked it wrong. However, if you press the Sprite button again and then a Root Beer comes out. Something is wrong with the machine. Smart!

| 5 months ago | Reply

Where do you get you Do It Now problems? Are you using this similar to Automaticity?

Nice job by the way!

| 7 months ago | Reply

Love this!!! I was looking for a sorting activity and when I saw this lesson, I was amazed at how we think alike. Thank you.

| 10 months ago | Reply

This is exactly what I needed to teach next week. Thank you so much for the resource I can't wait to use it!

| one year ago | Reply

I love your lesson! Lots of interaction and very specific. Did you use the slides as the cards for card sort or make up new examples? Sorry to be so picky but I

m a Sped teacher teaching Algebra in a self contained class and this is NOT my major!! Thanks again.

| one year ago | Reply*expand comments*

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- UNIT 1: Welcome Back! - The First Week of School
- UNIT 2: Linear & Absolute Value Functions
- UNIT 3: Numeracy
- UNIT 4: Linear Equations
- UNIT 5: Graphing Linear Functions
- UNIT 6: Systems of Linear Equations
- UNIT 7: Linear Inequalities
- UNIT 8: Polynomials
- UNIT 9: Quadratics
- UNIT 10: Bridge to 10th Grade

- LESSON 1: What is a Function?
- LESSON 2: Domain and Range
- LESSON 3: Function Notation
- LESSON 4: Writing Linear Equations (Day 1 of 2)
- LESSON 5: Writing Linear Functions (Day 2 of 2)
- LESSON 6: Slope & Rate of Change
- LESSON 7: Graphing Linear Functions (Day 1 of 2)
- LESSON 8: Graphing Linear Functions (Day 2 of 2)
- LESSON 9: Graphing Absolute Value Functions (Day 1 of 2)
- LESSON 10: Graphing Absolute Value Functions (Day 2 of 2)