**Title: **Lesson 1 – What is a function?

**Lesson Overview:**This lesson provides an introduction of what a function is addressing 9th grade algebra standards, while introducing students to the concepts of domain and range, at an entry level.

**Resources or Materials Needed:**Smartboard with projector, PowerPoint presentation with embedded YouTube video, required worksheets and exit slip.

**Lesson Objective:**Given a graph, Algebra 1 students at will be able to describe a function in terms of its name, domain and range, with 80% accuracy.

**Time:**(2) 50-minute class periods

**Step 1: Pre-Instructional Activity**

- Group students in pairs, then pose the following question:
*In your experience does age matter when people are dating? What is the youngest and oldest person that they are willing to date?*

- Give students a few minutes to share their opinions. Pick one group to state their answer to the above question and write it on the board in table format as below:

**Name Name**

**Your Age Your Age**

**Age of youngest person you should date Age of oldest person you should da**

- Tell them that this is Name of Student’s rule for dating and it is an example of a function.
- Write the word
**in**above the student’s age in both tables and write the word**out**above the age of the person whom they would date. - Have students represent this as an equation example: Student’s age is 16, age of oldest person they would date is 18. A way to represent this is y = (x – 7) * 2
- Introduce the function rule and write it on the board:
**When we are working with functions, for each input we can have only one output.** - Handout worksheet
*Maxine’s Rules for Love*. Allow students to work on this for 10 minutes, then discuss answers as a group. (See Appendix A)

**Step 2: Content Presentation**

- Show introduction to function machine video – YouTube link: https://m.youtube.com/watch?v=TqDybXFn_ww
- After video have a few minutes to field student questions

**Step 3: Learner Participation Day 1**

- Have students break into group of 3 to 4 students. Make sure each group has several sheets of notebook paper and pencils.
- Give each group a worksheet
*One Rule to Bind Them*(See Appendix B) - Explain that the purpose of this activity is that they are given the inputs and outputs of the function machine and they must determine what rule is used.
- Walk around the room to measure understanding of groups. If they are struggling give the students suggests as follows:
*Is the output a larger number? Should we add or multiply to the input?**Can you get from the input to the output in one step?**Pick a number and multiply by the input, then add to that number to get to the output. Can this rule be applied to the next input and output?*

**End of Day One**

**Step 4: Learner Participation – Day 2**

- Distribute
*Function Machine 1 and 2*handouts (See Appendix C) (Brant, Leece, Trushkowsky, & Appleton, 2015) - Instruct students that they are given various pieces of information about each function, their task is to figure out what is missing. They are either given the rule and must find the input/output or vice versa.
- Give students 15 minutes to work on this task.
- Walk around room to gage understanding/participation. Use prompts from above as suggestions for students who are struggling.
- Go over answers as class discussion.

**Step 5: Assessment**

- Give students
*Function Game*handouts. (See Appendix D) - Students will come up with a one step rule and a two-step rule. They will write this down on a piece of paper that they will hand in on the following day.
- They will then complete the handout filling in the inputs and outputs to turn in as their assessment. As the instructor you will try to figure out their rules and write it on the top of their papers. You will then hand these back to the students and they will see if the rule they wrote and the one you wrote match.
- Assessment will be graded based on the Function Rubric (See Appendix E), students will score with 80% accuracy based on the rubric.

**Step 6: Follow-Through Activities**

- Function Machine practice Internet resource:

**www.mathplayground.com/functionmachine.html**

**Step 7: Exit Ticket**

- Ask students to remember the activities from the two-day lesson. Pose the following 2 questions for their written response:
*What have you learned about functions?**What is one question you have about functions?*