Fraction Fundamentals Slides Fraction Factory
Lesson 1: The Blueprint of Parts
Shift Objectives
Identify the Components
Define and label the numerator and denominator in any fraction blueprint.
Visualize Production
Represent fractions using models of whole shapes and groups of objects.
Definition
The Fraction Blueprint
A fraction represents a fair share or a part of a whole.
Engineering Note:
Every part must be exactly the same size for it to be a true fraction.
1 / 2
Anatomy of a Fraction
3
Numerator
"How many parts we have"
4
Denominator
"How many parts make a whole"
Models: Parts of a Whole
3/4 of a Circle
1/3 of a Bar
🍕
6 total slices
Parts of a Pizza
Models: Parts of a Set
What fraction of the factory parts are orange?
2 / 5
Factory Floor Challenge
An order came in for 5/8 of a shipment to be painted blue.
Think:
What is the denominator?
What is the numerator?
How many parts are in the whole shipment?
Prepare your blueprints (worksheets) now!
Blueprint Basics Worksheet Fraction Factory
Quality Control: Blueprint Basics
Inspector:
Shift Date:
Station 1: Component Labels
5
8
Label the Top Number:
________________
Label the Bottom Number:
________________
Station 2: Precision Painting
The factory needs these parts painted according to the blueprints. Shade the shapes below.
3 / 4
2 / 6
5 / 8
1 / 2
Station 3: Inventory Sorting
Fraction of parts that are BLACK:
/
Fraction of gears that are DARK:
/
F-FACTORY // UNIT 01 // SHEET 01
QC APPROVED
Production Schedule Unit Guide Production Schedule
Fraction Factory: 3-Week Unit Plan
Daily Shift Length:
45 Minutes
Week 1: Parts & Precision
Shift Operation / Objective Daily Routine (45m) 01 Fraction Fundamentals
Numerator/Denominator & Area/Set Models
|
• 10m: Intro Slides & Terms
• 20m: Guided Model Building
• 15m: Blueprint Basics Worksheet
|
| 02 |
Number Line Legends
Linear measurement & placement
|
• 10m: Number Line Logic Slides
• 20m: Human Number Line Activity
• 15m: Milestone Marker Worksheet
|
| 03 |
Equivalent Engines
The Multiplier Rule (Scaling Up)
|
• 10m: Visual Equivalence Slides
• 20m: Engine Match Activity
• 15m: Equivalent Engines Worksheet
|
| 04 |
Simplification Station
Simplest form & GCF protocol
|
• 10m: Consolidation Slides
• 20m: "Simplify" Card Sort
• 15m: Station Worksheet
|
| 05 |
Half-Mark Heroes
Benchmark comparison to 1/2
|
• 10m: Benchmark Estimation Slides
• 20m: Greater/Less than 1/2 Sort
• 15m: Hero Benchmark Worksheet
|
Week 2: Addition & Subtraction
<table class="w-full text-left border-collapse"><tbody class="divide-y divide-slate-100"><tr><td class="p-4 w-24 align-top font-bold text-slate-400">06</td><td class="p-4 align-top"><p class="font-bold text-lg">Comparison Combat</p><p class="text-sm text-slate-500">Unlike denominators & cross-products</p></td><td class="p-4 text-sm"><ul class="space-y-1 w-64"><li>• 10m: Battle Slides</li><li>• 20m: War Card Game</li><li>• 15m: Comparison Combat Sheet</li></ul></td></tr><tr><td class="p-4 w-24 align-top font-bold text-slate-400">07</td><td class="p-4 align-top"><p class="font-bold text-lg">Like Denominator Lab</p><p class="text-sm text-slate-500">Basic addition & subtraction</p></td><td class="p-4 text-sm"><ul class="space-y-1"><li>• 10m: Lab Slides (Joining parts)</li><li>• 20m: Pattern Block Sums</li><li>• 15m: Lab Reports Worksheet</li></ul></td></tr><tr><td class="p-4 w-24 align-top font-bold text-slate-400">08</td><td class="p-4 align-top"><p class="font-bold text-lg">Common Ground</p><p class="text-sm text-slate-500">Unlike addition/subtraction (LCM)</p></td><td class="p-4 text-sm"><ul class="space-y-1"><li>• 15m: LCD Slides & Modeling</li><li>• 15m: Common Ground Puzzles</li><li>• 15m: Common Ground Sheet</li></ul></td></tr><tr><td class="p-4 w-24 align-top font-bold text-slate-400">09</td><td class="p-4 align-top"><p class="font-bold text-lg">Mixed Number Mechanics</p><p class="text-sm text-slate-500">Improper ↔ Mixed conversions</p></td><td class="p-4 text-sm"><ul class="space-y-1"><li>• 10m: Mechanics Slides</li><li>• 20m: Mixed Number Construction</li><li>• 15m: Conversion Worksheet</li></ul></td></tr><tr class="bg-blue-50/30"><td class="p-4 w-24 align-top font-bold text-slate-400">10</td><td class="p-4 align-top"><p class="font-bold text-lg">Word Problem Warehouse</p><p class="text-sm text-slate-500">Real-world factory applications</p></td><td class="p-4 text-sm"><ul class="space-y-1"><li>• 5m: Problem Solving Protocol</li><li>• 30m: Collaborative Problem Hunt</li><li>• 10m: Exit Ticket Challenge</li></ul></td></tr></tbody></table>
Week 3: Multiplication & Division
<table class="w-full text-left border-collapse"><tbody class="divide-y divide-slate-100"><tr><td class="p-4 w-24 align-top font-bold text-slate-400">11</td><td class="p-4 align-top"><p class="font-bold text-lg">Multiplication Mills</p><p class="text-sm text-slate-500">Fraction of a whole number</p></td><td class="p-4 text-sm"><ul class="space-y-1 w-64"><li>• 10m: Mills Slides (Counters)</li><li>• 20m: Inventory Multiplier Activity</li><li>• 15m: Mill Output Worksheet</li></ul></td></tr><tr><td class="p-4 w-24 align-top font-bold text-slate-400">12</td><td class="p-4 align-top"><p class="font-bold text-lg">Cross-Section Crafts</p><p class="text-sm text-slate-500">Fraction × Fraction (Area Models)</p></td><td class="p-4 text-sm"><ul class="space-y-1"><li>• 15m: Layered Area Slides</li><li>• 15m: Transparent Overlay Models</li><li>• 15m: Craft Blueprint Worksheet</li></ul></td></tr><tr><td class="p-4 w-24 align-top font-bold text-slate-400">13</td><td class="p-4 align-top"><p class="font-bold text-lg">Division Diversion</p><p class="text-sm text-slate-500">Whole number ÷ Unit fraction</p></td><td class="p-4 text-sm"><ul class="space-y-1"><li>• 15m: Division Visual Slides</li><li>• 15m: "Sharing" Model Activity</li><li>• 15m: Division Logic Sheet</li></ul></td></tr><tr><td class="p-4 w-24 align-top font-bold text-slate-400">14</td><td class="p-4 align-top"><p class="font-bold text-lg">Reciprocal Rangers</p><p class="text-sm text-slate-500">Inverse operations & review</p></td><td class="p-4 text-sm"><ul class="space-y-1"><li>• 10m: Reciprocal Logic Slides</li><li>• 20m: Keep-Change-Flip Game</li><li>• 15m: Ranger Review Packet</li></ul></td></tr><tr class="bg-indigo-50/30 font-black"><td class="p-4 w-24 align-top font-bold text-slate-400">15</td><td class="p-4 align-top"><p class="font-bold text-lg">Quality Control Finale</p><p class="text-sm text-slate-500">Unit Assessment & Celebration</p></td><td class="p-4 text-sm"><ul class="space-y-1"><li>• 40m: Final Certification Test</li><li>• 5m: Graduation / Reward</li></ul></td></tr></tbody></table>
Primary Goal
Master all 4 operations using visual and numerical protocols.
Hands-On Protocol
Daily use of pattern blocks, number lines, or counters.
Standards Alignment
Full coverage of fractional equivalence and base operations.
Fraction Factory Hands-On Guide Hands-On Manual
Fraction Factory: Lab Activities
Activity 01: Human Production Line
Lesson 02
Resources
• 15ft Masking Tape
• Index Cards (0, 1, fractions)
• Bean Bags
Shift Time
20 Minutes
Protocol:
Lay tape across the floor. Mark 0 and 1 at ends.
Assign 2 students to be "Denominator Drillers" — they must place tape ticks to divide the line into equal spaces.
Give other students "Coordinate Cards" (e.g., 3/4).
Students must physically stand at their coordinate on the line.
Challenge: Have students toss a bean bag to a target coordinate called out by the Foreman (Teacher).
Activity 02: Pattern Block Assembly
Lesson 07
Resources
• Pattern Block Sets
• Yellow Hexagon = 1 Whole
• Red Trapezoid = 1/2
• Blue Rhombus = 1/3
• Green Triangle = 1/6
Protocol:
Model addition by placing triangles (1/6) on a hexagon until full.
Joining Parts: "Assembly Part A is 2/6 (2 triangles). Part B is 3/6 (3 triangles). Join them. What is the total?"
Simplifying: Can the combined triangles be replaced by a different block? (e.g., 3/6 → 1/2 trapezoid).
Subtraction: Remove pieces from a full assembly to see the remainder.
Activity 03: Overlay Crafting
Lesson 12
Resources
• Transparent Sheet Overlays
• Dry Erase Markers
• 4x4 Grid Prints
Protocol:
Take two clear squares. Divide one vertically into halves. Divide the other horizontally into thirds.
Shade 1 part of each (1/2 and 1/3).
The Cross-Section: Overlay the two squares.
The area where the shading overlaps is the product (1/6).
Count the total new squares created by the overlap grid (denominator) and the overlap color (numerator).
TEACHER RESOURCE // LAB MANUAL
HANDS-ON APPROVED
Number Line Legends Slides Number Line Legends
Lesson 2: Measuring the Production Path
The Linear Factory
In our factory, parts move along a Production Line.
Quality Check:
The distance from start to finish is 1 whole unit.
Start (0)
End (1)
The package is at 3/4 of the line.
Process
Building the Scale
1
Identify the Denominator. This tells you how many equal spaces to make between 0 and 1.
2
Count the Numerator. This tells you how many spaces to jump from zero.
0
1/3
2/3
1 (3/3)
Target: 2/3
Precision Measurement
Where is the part?
0
1
Answer: 3/4
Pro-Tip
We count the SPACES, not the tick marks.
Space 1
Space 2
The Milestone Mission
A robotic arm needs to be calibrated at 5/6 of the way across the track.
Calibrating...
0
1
Open your Milestone Marker worksheets and let's calibrate!
Milestone Marker Worksheet Fraction Factory
Calibration: Milestone Markers
Technician:
Shift Date:
Mission Briefing
All robotic arms and conveyor belts must be calibrated to exact fractional coordinates along the production line. Use the number lines below to complete the calibration process.
Station 1: Reading the Line
1. Identify the location of the package marked with the star:
0
1
Coordinate:
/
2. Identify the location of the gear marked with the star:
0
1
Coordinate:
/
Station 2: Manual Calibration
Draw tick marks to divide the production line and place an X at the target coordinate.
3. Target Coordinate: 3/4
0
1
4. Target Coordinate: 2/5
0
1
5. Target Coordinate: 5/6
0
1
F-FACTORY // UNIT 01 // SHEET 02
LINE CALIBRATED
Equivalent Engines Slides Equivalent Engines
Lesson 3: Redesigning for Performance
The Redesign Challenge
Sometimes, a factory part needs to be divided into smaller sections without changing the total amount of material.
Equivalent Fractions
Different numbers, same value.
1/2
=
2/4
Rule Book
The Multiplier Rule
To make an equivalent fraction, multiply the top and bottom by the same number.
1
3
×
2
2
=
2
6
This is like multiplying by 1. It doesn't change the size, just the number of pieces!
Engine Consolidation
We can also divide the top and bottom to consolidate parts.
Inventory Check:
4
12
÷
4
4
=
1
3
4/12
is the same as
1/3
Workshop Task: Part Matching
Engine Part A-101 requires a fuel mix of 2/5.
Available Mixes:
Surprise!
They are all the same. Your job is to prove it using the multiplier rule!
Start Engine Matching Worksheet
Equivalent Engines Worksheet Fraction Factory
Maintenance: Equivalent Engines
Lead Engineer:
Shift Date:
Engineering Protocol
To keep our engines running, we must create parts with the exact same value using the Multiplier Rule. Multiply the numerator and denominator by the same factor to create equivalent designs.
Station 1: Scaling Up
1
4
×
2
2
=
2
3
×
3
3
=
3
5
×
4
4
=
1
8
×
5
5
=
Station 2: Discovery Portals
Find the missing factor that was used to create the equivalent part.
2 / 3
×
?
?
=
10 / 15
3 / 8
×
?
?
=
9 / 24
Station 3: Quality Matching
Color the second part to make it equivalent to the first. Then write the fraction.
1 / 2
=
Design:
/
1 / 3
=
Design:
/
F-FACTORY // UNIT 01 // SHEET 03
ENGINES SYNCHRONIZED
Simplification Station Slides Simplification Station
Lesson 4: Consolidating for Efficiency
The Efficiency Audit
In our factory, we want the cleanest possible parts.
Simplest Form
When the numerator and denominator share no common factors except 1.
4
8
1
2
"Consolidated!"
Protocol
The GCF Protocol
01
List Factors
List all factors for both the top and bottom numbers.
02
Find GCF
Find the Greatest Common Factor they share.
03
Divide Both
Divide both numbers by that GCF to get the simplest form.
6
10
÷ 2
=
3
5
Quality Control Audit
3 / 7
Simplest Form
Only factor in common is 1.
4 / 12
Needs Work
Common factor found: 4
Consolidation Challenge
A shipment of 12/18 heavy-duty gears is taking up too much storage space.
Can you simplify this inventory record?
12 / 18
→
? / ?
Open your Simplification Station worksheets!
Simplification Station Worksheet Fraction Factory
Maintenance: Simplification Station
Chief Inspector:
Shift Date:
Station 1: GCF Audit
List the factors for both numbers, circle the Greatest Common Factor (GCF), and then divide to simplify the fraction.
6
10
Factors of 6:
Factors of 10:
GCF
?
→
Simplest Form
/
4
12
Factors of 4:
Factors of 12:
GCF
?
→
Simplest Form
/
9
15
Factors of 9:
Factors of 15:
GCF
?
→
Simplest Form
/
Station 2: Precision Sorting
Circle the parts that are already in Simplest Form. Cross out the parts that need consolidation.
2 / 5
4 / 10
3 / 8
6 / 9
5 / 7
8 / 16
1 / 4
10 / 25
F-FACTORY // UNIT 01 // SHEET 04
EFFICIENCY VERIFIED
Half Mark Heroes Slides Half-Mark Heroes
Lesson 5: The Power of the Benchmark
The Benchmark Secret
Experienced factory inspectors can estimate a part's value just by looking at it. They use the 1/2 Benchmark.
The 1/2 Rule
If the numerator is exactly half of the denominator, the value is 1/2.
4
8
4 is half of 8!
Training
Classifying Parts
Small
Numerator is less than half of the denominator.
2 / 10
Target
Numerator is exactly half of the denominator.
5 / 10
Large
Numerator is greater than half of the denominator.
8 / 10
Quick-Scan Audit
Is this engine part More, Less, or Equal to 1/2?
4 / 7
Scan...
vs.
Inspector's Logic:
Half of 7 is 3.5.
The Benchmark Sort
Incoming Shipment: 3/8, 7/12, 1/5, 9/10, 4/8
We need to categorize these before they hit the assembly line.
Less than 1/2
Exactly 1/2
More than 1/2
Start Hero Benchmark Worksheet!
Half Mark Heroes Worksheet Fraction Factory
Field Test: Half-Mark Heroes
Chief Inspector:
Shift Date:
Station 1: Halfway Calibration
For each engine part below, identify what exactly 1/2 would be. Then decide if the actual part is greater or less than 1/2.
3 / 8
Actual Part
Target 1/2:
/ 8
Verdict:
? 1/2
5 / 6
Actual Part
Target 1/2:
/ 6
Verdict:
? 1/2
4 / 10
Actual Part
Target 1/2:
/ 10
Verdict:
? 1/2
9 / 12
Actual Part
Target 1/2:
/ 12
Verdict:
? 1/2
Station 2: Benchmark Logistics
Sort the following shipment parts into their correct storage containers. Write the fraction in the correct box.
2/5 • 7/10 • 1/8 • 4/8 • 5/9 • 3/10 • 11/12 • 6/12
Less Than 1/2
Exactly 1/2
Greater Than 1/2
F-FACTORY // UNIT 01 // SHEET 05
BENCHMARKS COMPLETED
Comparison Combat Slides Comparison Combat
Lesson 6: The Great Power Match-Up
The Battle of Unlikes
When parts have different denominators, we can't just look at the numerators.
The Warning
A bigger denominator means smaller pieces!
1/2
vs
1/3
Protocol
The Butterfly Strike
Use Cross-Multiplication to find the winner quickly!
2
3
?
3
4
2 × 4 = 8
3 × 3 = 9
8 < 9
Common Denominator Strategy
The Engineered Way: Transform them until the pieces are the same size.
1
Find a Common Denominator (like 12 for 3 and 4).
2
Use the Multiplier Rule on both.
3
Compare the new numerators.
8/12
vs
9/12
"The pieces are now equal!"
The Combat Challenge
A hydraulic press needs 3/4 gallons of oil, but your reserve only has 5/8.
3 / 4
?
5 / 8
Is there enough oil?
Engaging Comparison Combat Worksheet...
Like Denominator Lab Slides Like Denominator Lab
Lesson 7: Joining and Removing Components
The Assembly Protocol
When parts have the same size pieces (same denominator), we just join the counts!
The Lab Rule
Add or subtract the numerators only. The denominator never changes.
1 / 4
2 / 4
=
3 / 4
"The denominator stays 4 because the piece size didn't change!"
Component Removal
Total Inventory: 5/6. Ship out 2/6.
5
-
2
=
3
6
5 - 2 = 3
Lab Safety Protocol
Danger!
NEVER add the denominators.
1/4 + 1/4 = 2/8
Safe!
Keep the size the same.
1/4 + 1/4 = 2/4
The Lab Report
"Assembly Line 4 needs a combined power charge of 3/5 plus 1/5."
? / ?
Open your Lab Reports Worksheet!
Multiplication Mills Slides Multiplication Mills
Lesson 11: Scaling and Repetition
Parts of a Whole Number
When we multiply a fraction by a whole number, we are asking:
Inventory Request:
"I need 1/3 of these 12 gears."
Answer: 4 gears
The Calculation Protocol
1
3
×
12
1
=
12
3
→
4
Step 1
Turn the whole number into a fraction by putting it over 1.
Step 2
Multiply across (top × top, bottom × bottom).
Mill Inventory Check
"One vat of sealant covers 2/5 of a shipment. We have 20 shipments today."
2 / 5
×
20
=
8
"We need 8 vats of sealant to finish the shift."
The Multiplier Mission
Order #404
Find 3/4 of a set of 16 robotic arms.
Show your work on the Mill Output Worksheet.
