Home›Lesson Plans›Mathematics›Functions · Grade 8

Functions: A Machine with One Output per Input

Students learn what makes a relationship a function — each input produces exactly one output — by feeding inputs into a “function machine” and watching the rule turn each one into a single result.

Grade 8Functions50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Define a function (one output per input).
  • ✓Use a rule to find outputs.
  • ✓Read a function from a table.
  • ✓Tell functions from non-functions.
Essential Question

Put a number into a rule and get exactly one number out, every time. What is a function, and how do you know a relationship is one?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

The Function Machine

Project this and choose a rule, then change the input. The machine applies the rule and gives exactly one output for each input.

⚙️ Feed in an input — get one outputTry it
2
→
y = 2x + 1
→
5
Input x: 2

The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — One In, One Out

5 min

A rule that turns each number into exactly one other — what is that?

👩‍🏫 Teacher Moves

  • Show an input-output machine.
  • Ask about the pattern.
  • Set the goal: functions.

🎒 Student Actions

  • Watch the machine.
  • Find the rule.
  • Predict the idea.
2

I Do — One Output Each

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Define a function.
  • Apply a rule to inputs.
  • Note: one output per input.

🎒 Student Actions

  • Learn the rule.
  • Find outputs.
  • See the one-output rule.
3

We Do — Machine Together

13 min

Class drives the Function Machine.

👩‍🏫 Teacher Moves

  • Pick a rule; change the input.
  • Read the output.
  • Build an input-output table.

🎒 Student Actions

  • Set the rule/input.
  • Read the output.
  • Make a table.
4

You Do — On Your Own

12 min

Students work with functions.

👩‍🏫 Teacher Moves

  • Assign function rules to apply.
  • Complete input-output tables.
  • Test if a relation is a function.

🎒 Student Actions

  • Apply rules.
  • Complete tables.
  • Test relations.
5

Close — Close

5 min

One function.

👩‍🏫 Teacher Moves

  • Give a rule and inputs.
  • Find the outputs.
  • Hand out the exit ticket.

🎒 Student Actions

  • Find outputs.
  • Explain “one output.”
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics, including the Standards for Mathematical Practice.

CCSS
8.F.1

Understand that a function assigns exactly one output to each input.

CCSS
8.F.2

Compare properties of two functions represented in different ways.

CCSS
8.F.3

Interpret y = mx + b as a linear function.

CCSS
8.F.4

Construct a function to model a relationship.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Use an input-output T-chart.
  • Sentence frame: “Input ___ gives output ___.”
  • Act out a function machine.

Support & Access

IEP / 504
  • Start with a simple rule (add 2).
  • Use a table to track outputs.
  • Focus on “one output each.”

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Compare two functions.
  • Find the rule from a table.
  • Explain why a relation is not a function.
Materials

What to gather

  • 📽️Projector / board
  • 📓Math notebooks
  • 💻The Function Machine
  • 📐Graph paper
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

functiona rule with one output per inputinputthe value you put in (x)outputthe value you get out (y)rulehow the function transforms inputdomainthe set of inputsrangethe set of outputstablea chart of inputs and outputslinear functiona function whose graph is a line
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
What makes a relationship a function?
Each input has exactly one output.
QUESTION 2
If the rule is y = 2x + 1 and x = 4, what is the output?
9.
QUESTION 3
A relation gives input 3 two different outputs (5 and 8). Is it a function? Why?
No — a function must have exactly one output per input, and this input has two.

Going deeper? Find the rule.

Have students look at an input-output table and figure out the function rule that produced it. A printable find-the-rule sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 FunctionsFlip
Card 1
Term
Tap to flip →
Meaning
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 FunctionsQuiz
Score: 0
1 / 6
Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ FunctionsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: domain, function, input, linear function, output, range, rule, table
  1. a function whose graph is a line
  2. a chart of inputs and outputs
  3. a rule with one output per input
  4. the value you put in (x)
  5. the set of outputs
  6. the set of inputs
  7. the value you get out (y)
  8. how the function transforms input

Part B · Show what you learned

  1. What makes a relationship a function?
  2. If the rule is y = 2x + 1 and x = 4, what is the output?
  3. A relation gives input 3 two different outputs (5 and 8). Is it a function? Why?
Answer key — Part A: 1) linear function · 2) table · 3) function · 4) input · 5) range · 6) domain · 7) output · 8) rule
Part B: 1) Each input has exactly one output. 2) 9. 3) No — a function must have exactly one output per input, and this input has two.