Function Factory Slides
5th Grade Math
FUNCTION
MACHINE
FACTORY
Analyzing Patterns & Relationships
Input/Output
Rules
WARM-UP: The Mystery Box
What happened inside?
Input
5
Output
10
Input: 8 Output: 13
Input: 12 Output: 17
Class Discussion
- • What did the box do to every number?
- • How can we write this as a rule?
- • If the input is 20, what is the output?
KEY VOCABULARY
Terms
The individual numbers that make up a pattern or sequence.
5, 10, 15, 20...
Corresponding Terms
Numbers that are in the same position in two different patterns.
A: 10
B: 12
WATCH & LEARN
Patterns & Relationships
Embedded media
Pause at [3:00] for Verification Check
Pause at [5:50] for Troubleshooting
RECAP: Example 1
| Pattern A | Pattern B | Relationship |
|---|
| 0 | 2 | 0 + 2 = 2 |
| 5 | 7 | 5 + 2 = 7 |
| 10 | 12 | 10 + 2 = 12 |
Rule: A + 2 = B
Inverse: B - 2 = A
THE FACTORY FLOOR
Main Activity: Your Turn
1
IDENTIFY
Look at the patterns provided. What operation is changing A into B?
2
BUILD
"Draw" your machine. Label it with the correct rule and operation.
3
TEST
Choose 3 NEW inputs. Use your machine to find the outputs!
Extension: Mega Machine
X
Input
MACHINE 1
+ 2
MACHINE 2
× 3
Y
Output
The Challenge:
If you put in 4, what comes out the other side?
Can you write a single rule for this "Stacked Machine"?
Function Factory Worksheet
Function Machine Factory
Quality Control Lab: Grade 5 Math
Operator:
Shift Date:
Part 1: Video Briefing
Term
Corresponding Terms
PROBLEM #1 ADDITION
Pattern A
Pattern B
0, 5, 10...
2, 7, 12...
RULE:
PROBLEM #2 MULTIPLICATION
Pattern X
Pattern Y
4, 5, 6...
12, 15, 18...
RULE:
PROBLEM #3 DIVISION
Pattern C
Pattern D
30, 25...
6, 5...
RULE:
PROBLEM #4 SUBTRACTION
Pattern M
Pattern N
42, 36...
38, 32...
RULE:
Part 2: The Factory Floor
BUILD A MACHINE
Input Table
10
25
40
Internal Processing Rule
÷ 5
Draw your gears or labels inside the machine!
Output Results
Production Analysis:
What is the rule in words?
Write the equation:
Part 3: The Mega-Machine Extension
Stack two machines together! The output of the first machine becomes the input of the second.
INPUT: 4
+ 2
× 3
FINAL OUTPUT: _______
Can you find a single rule that does both jobs at once?
Function Factory Exit Ticket
Factory Exit Pass
Shift Completion Check
Operator:
Date:
Analyze the following production tables. Identify the rule and write the equation for each machine.
MACHINE #101
| Input (A) | Output (B) |
|---|
| 7 | 15 |
| 12 | 20 |
| 20 | 28 |
| 45 | 53 |
Describe the Rule:
Write the Equation:
A [ op ] [ num ] = B
MACHINE #204
| Input (X) | Output (Y) |
|---|
| 3 | 12 |
| 6 | 24 |
| 10 | 40 |
| 2 | 8 |
Describe the Rule:
Write the Equation:
Quality Control Test
A machine uses the rule M ÷ 4 = N. If the input (M) is 48, what is the output (N)?
Inspection Complete
Function Factory Teacher Guide
Teacher Facilitation Guide
Lesson: Function Machine Factory | Grade 5 Math
Duration: 55-60 Minutes
Learning Objective
Students will analyze numerical patterns, identify rules between corresponding terms, and represent these relationships using input/output tables and algebraic equations (e.g., \(A + 2 = B\)).
Standards Alignment
CCSS.MATH.CONTENT.5.OA.B.3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms.
Materials Needed
- Function Factory Slides
- Student Worksheets
- Exit Tickets
- Colored pencils/markers
Lesson Execution
0-5 MIN
Warm-up: The Mystery Box
Use Slide 2. Present the box. Ask: "If 5 goes in and 10 comes out, and 8 goes in and 13 comes out, what is the 'secret sauce' happening inside?" Elicit the rule (+5).
5-15 MIN
Video Analysis
Watch Mr. J's video. Students fill out the Part 1 grid on their worksheet. Key Pauses:
- [3:00] Verification: Ask: "Why did Mr. J check the rule for EVERY term? What happens if it only works for the first one?"
- [5:50] Troubleshooting: Ask: "Addition didn't work for Example 2. What's our next mathematical tool?" (Multiplication).
15-35 MIN
Main Activity: Factory Floor
Students build their own machine on the worksheet. They must apply the rule \( \div 5 \) to the input table and generate the final output. Encourage them to draw "gears" or "levers" inside the machine area to reinforce the concept of a process.
35-45 MIN
Mega-Machine Extension
Challenge students to stack machines. Discuss how composite rules work (e.g., \( (4 + 2) \times 3 = 18 \)). Discuss if the order matters (Does \( \times 3 \) then \( + 2 \) give the same answer?).
45-55 MIN
Closure & Exit Ticket
Distribute Exit Pass. This is independent work to assess mastery of identifying rules from tables.
Support (Scaffolding)
Provide students with a "Rule Menu" (+, -, ×, ÷). For the Factory Floor, have them write the calculation next to each input (e.g., \( 10 \div 5 = 2 \)) before filling the output table.
Enrichment (Challenge)
Challenge students to create a "Broken Machine" table where one output is intentionally wrong. A partner must find and fix the "mechanical error."
