Lesson Plan
Function Machines: Inputs & Outputs
Students will define a function and identify its input and output from given tables, rules, or scenarios, understanding how these components interact within a function.
Understanding functions is crucial as it forms the basis for higher-level mathematics, helping students analyze relationships and make predictions in various real-world contexts.
Audience
9th Grade Students
Time
65 minutes
Approach
Through direct instruction, guided practice, and hands-on activity.
Materials
Smartboard or Projector, Markers or Whiteboard Pens, Slide Deck, Build a Function Machine Activity, Input-Output Tables Worksheet, and Exit Ticket
Prep
Teacher Preparation
20 minutes
- Review the Lesson Plan and all generated materials.
- Prepare the projector/smartboard for the Slide Deck.
- Print copies of the Build a Function Machine Activity (one per small group).
- Print copies of the Input-Output Tables Worksheet (one per student).
- Print copies of the Exit Ticket (one per student).
- Gather markers or whiteboard pens if using a physical whiteboard.
Step 1
Introduction & Hook: What's a Machine?
10 minutes
- Engage (5 minutes): Begin by asking students what a machine is and what it does. Guide them to think about input, process, and output (e.g., a vending machine: input = money + selection, process = internal mechanism, output = snack).
2. Introduce Functions (5 minutes): Explain that in math, we have 'function machines' that take an input, apply a rule, and produce an output. Introduce the Slide Deck to show the 'What's a Machine?' slide.
Step 2
Direct Instruction: Defining Functions, Inputs, and Outputs
15 minutes
- Slide Presentation (10 minutes): Use the Slide Deck to present the definition of a function, emphasizing that each input has exactly one output. Explain input (domain), output (range), and how they relate. Show examples of functions represented by rules, tables, and graphs.
2. Key Vocabulary (5 minutes): Define 'function,' 'input,' 'output,' 'domain,' and 'range.' Encourage students to write down these definitions.
Step 3
Guided Practice: Function Machine Explorations
20 minutes
- Activity Introduction (5 minutes): Explain the Build a Function Machine Activity. Divide students into small groups.
2. Group Work (15 minutes): Each group will work through the Build a Function Machine Activity, creating their own function rule and demonstrating inputs and outputs. Circulate to provide support and answer questions. Encourage groups to present a simple example to the class.
Step 4
Independent Practice: Applying Knowledge
15 minutes
- Worksheet Distribution (2 minutes): Hand out the Input-Output Tables Worksheet.
2. Individual Work (13 minutes): Students complete the worksheet independently. This allows them to apply their understanding of inputs and outputs in various table formats. Circulate to offer individual help as needed.
Step 5
Wrap-up & Assessment: Exit Ticket
5 minutes
- Review (2 minutes): Briefly recap the main concepts of functions, inputs, and outputs.
2. Exit Ticket (3 minutes): Distribute the Exit Ticket for students to complete individually. Collect it as they leave to assess their understanding of the lesson objectives.
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Slide Deck
Function Machines: Inputs & Outputs
Understanding How Things Work
Welcome to the world of Function Machines! Today, we'll explore how these machines take something in and give something out, just like in real life.
Let's get ready to build our own understanding of functions!
Welcome students and introduce the day's topic. Get them thinking about how things work.
What's a Machine?
Think about machines you use every day...
- A vending machine
- A toaster
- A calculator
What do these machines have in common?
They take something in...
They do something to it...
They give something out!
Start with a relatable example. Ask students to share examples of machines they use every day and what they do. Guide them to think about what goes into the machine and what comes out.
What is a Function?
A Function is a special kind of machine!
- It takes an INPUT (something you put in).
- It applies a RULE (a special operation).
- It produces exactly one OUTPUT (what comes out).
The Golden Rule of Functions: For every input, there is ONLY ONE output!
Introduce the formal definition of a function. Emphasize the 'one output for every input' rule. Provide a simple mathematical example if appropriate, like y = x + 2.
Input, Output, Domain, & Range
- Input: The values that go into the function. (Think of it as the 'ingredients'.)
- Also known as the Domain.
- Output: The values that come out of the function. (Think of it as the 'finished product'.)
- Also known as the Range.
- Function Rule: The operation or process that transforms the input into the output.
Clearly define input, output, domain, and range. Use a visual example or a simple table to illustrate these concepts.
Representing Functions
Functions can be represented in different ways:
- Rules: Like an instruction manual (e.g., "add 3 to the input")
- Tables: Organize inputs and their corresponding outputs.
- Scenarios: Real-world situations that show an input-output relationship.
- Graphs: A visual picture of the input-output pairs.
Show examples of how functions can be represented. Use a simple rule, a corresponding table, and briefly mention how a graph would look.
Time to Build! Your Function Machine
Now that we know the basics, let's get hands-on!
In your groups, you will:
- Create your own Function Rule.
- Identify Inputs.
- Calculate the Outputs.
- Be ready to share your amazing function machine with the class!
Transition to the activity. Explain that students will now get to build and demonstrate their own function machines.
Independent Practice
Now it's your turn to practice individually!
You will receive a worksheet with various input-output tables.
Your task is to:
- Identify the Input and Output values.
- Determine the Function Rule for each table.
Work quietly and do your best!
Explain that students will now apply what they've learned independently with a worksheet.
Reflect & Assess
Great work today, everyone!
- What is a function?
- What's the difference between an input and an output?
- Why are functions important in math and real life?
Now, for a quick Exit Ticket to see what you've learned!
Wrap up the lesson by reviewing key concepts and preparing for the exit ticket. Emphasize the importance of functions.
Activity
Build a Function Machine!
Objective: To understand how functions work by creating your own function machine, identifying inputs, rules, and outputs.
Materials: Pen/pencil, paper, your amazing brain!
Instructions:
-
Form Your Group: Work with your assigned small group.
-
Design Your Machine: As a group, come up with a creative name for your function machine.
-
Create Your Rule: Decide on a simple mathematical rule for your function machine. It could be:
- "Add 5 to the input"
- "Multiply the input by 2, then subtract 1"
- "Divide the input by 3"
- Be creative, but keep it clear!
-
Identify Inputs: Choose at least three different numbers (inputs) that you will put into your machine.
-
Calculate Outputs: For each input, apply your rule to find the exact output.
-
Record Your Findings: Create a small table like the one below to show your function machine in action:
Input (x) Function Rule Output (y) -
Be Ready to Share! Your group will present your function machine to the class. Be prepared to:
- Tell us the name of your machine.
- State your function rule.
- Show one of your inputs and its corresponding output.
Example (Don't copy!):
Machine Name: The Doubler-Minus-One Machine
Function Rule: Multiply the input by 2, then subtract 1
| Input (x) | Function Rule | Output (y) |
|---|---|---|
| 3 | (3 * 2) - 1 = 6 - 1 | 5 |
| 0 | (0 * 2) - 1 = 0 - 1 | -1 |
| 10 | (10 * 2) - 1 = 20 - 1 | 19 |
Good luck, future function experts!
Worksheet
Input-Output Tables Worksheet
Name: ____________________________
Date: _____________________________
Objective: Complete the tables and determine the function rule for each function machine.
Part 1: Find the Output
For each table, apply the given function rule to find the missing outputs.
1. Function Rule: Add 7 to the Input
| Input (x) | Output (y) |
|---|---|
| 1 | |
| 5 | |
| 10 | |
| -2 |
2. Function Rule: Multiply the Input by 3
| Input (x) | Output (y) |
|---|---|
| 2 | |
| 0 | |
| 7 | |
| -4 |
3. Function Rule: Subtract 4 from the Input, then Multiply by 2
| Input (x) | Output (y) |
|---|---|
| 5 | |
| 2 | |
| 10 | |
| 0 |
Part 2: Find the Function Rule
For each table, determine the function rule that describes the relationship between the input and the output.
4.
| Input (x) | Output (y) |
|---|---|
| 1 | 3 |
| 2 | 4 |
| 5 | 7 |
| 8 | 10 |
Function Rule: _________________________________________
5.
| Input (x) | Output (y) |
|---|---|
| 1 | 5 |
| 2 | 10 |
| 3 | 15 |
| 4 | 20 |
Function Rule: _________________________________________
6.
| Input (x) | Output (y) |
|---|---|
| 0 | -1 |
| 1 | 1 |
| 2 | 3 |
| 5 | 9 |
Function Rule: _________________________________________
Quiz
Function Machine Exit Ticket