Factor Factory Slides Factor Factory
Multiplication by Deconstruction
Today's Mission
I can multiply three fractions by identifying and cancelling common factors before I compute.
Deconstruct
Cancel
Compute
Factor Blast
When a number appears, write two factors of that number on your whiteboard as fast as you can!
12
Example: 3 & 4 or 2 & 6
15
Ready?
24
Set?
Expert Training
Watch: 0:00 — 2:12
Embedded media
Pause to discuss key moments
Quality Control
"Why did he change the 8 into 4 × 2?"
"What happens to the top of the fraction if everything is crossed out?"
Misconception Alert: Does everything crossing out mean the answer is zero? Why or why not?
Factory Blueprints
The Method
1 Identify large numbers that can be factored.
2 Rewrite them underneath as multiplication (Deconstruct).
3 Slash matching pairs on top and bottom (Cancel).
4 Multiply the leftovers!
Worksheet Alert
Get ready to deconstruct complex fractions on your worksheet!
Factory Blueprint Worksheet Factory Blueprint
Multiplying Three Fractions • Deconstruction Unit
Operator:
Date:
Standard Operating Procedure
Don't multiply those big numbers yet! First, Deconstruct composite numbers into their factors. Cancel identical factors that appear on both the top (numerator) and bottom (denominator). Then, multiply the leftovers for a perfectly simplified product.
Testing Line A: The Basics LOG #001
\[ \frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} = \]
Deconstruction Zone
Show your cancellation and final multiplication here.
Testing Line B: Factor Hunt LOG #002
\[ \frac{3}{5} \times \frac{10}{12} \times \frac{4}{9} = \]
Deconstruction Zone
Testing Line C: Heavy Duty LOG #003
\[ \frac{4}{7} \times \frac{14}{15} \times \frac{25}{32} = \]
Deconstruction Zone
Hint: Look for factors of 14, 15, 25, and 32.
Testing Line D: Production Master LOG #004
\[ \frac{8}{9} \times \frac{3}{4} \times \frac{15}{16} = \]
Deconstruction Zone
System Check
Why is it safer to "deconstruct" the numbers before multiplying across?
Production Line Exit Ticket Production Line
Exit Ticket • Final Quality Inspection
Operator:
Shift:
Final Inspection Task
Solve the following multiplication problem using the Cancellation Method. Show your deconstruction (factoring) and clear slashes through cancelled pairs.
\[ \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} = \]
Workspace: Factor & Cancel
Shift Summary
Explain what happens to the numerator (top number) of your answer if every number on the top is cancelled out. Why?
Factor Factory Systems
CODE: CANCEL-05-EXIT
Factory Manager Guide Factory Manager Guide
Teacher Resource • Factor Factory Lesson
Lesson Briefing
This lesson shifts students from brute-force multiplication (multiplying large numerators and denominators) to a more efficient algebraic approach: factoring before computing. By the end of the session, students should see "large numbers" as opportunities for deconstruction rather than obstacles.
Key Vocabulary
Deconstruction
Cancellation
Composite Factors
Identity Element (1)
Shift Schedule (50 min)
05 min
Factor Blast Warm-up
Call out numbers: 12, 15, 24, 18, 20. Students write factor pairs. Speed is the goal.
10 min
Video Viewing & Pause Points
0:38: Ask: "How big would 3 x 5 x 12 be? Is there a better way?"1:50: Ask: "If everything crosses out, is it 0? No, it's 1 because we are dividing!"2:30: Stop for whiteboard practice of Problems A & B.
25 min
Worksheet: Factory Blueprint
Circulate and ensure students are writing the factors *underneath* or *beside* before crossing out.
10 min
Final Quality Inspection (Exit Ticket)
Problem: 2/3 x 3/4 x 4/5. Reflection on the "cancelled to one" property.
Quality Control: Answer Keys
Worksheet Key
Line A: 1/4 (2s cancel, 3s cancel)
Line B: 2/9 (10=5x2, 12=4x3. 5s, 4s, 3s cancel)
Line C: 5/12 (Video Example A)
Line D: 5/8 (Video Example B)
Exit Ticket Key
Math: 2/5 (3s cancel, 4s cancel)
Reflection: When everything cancels, we are left with 1. Because cancellation is division (e.g., 3/3 = 1), not subtraction.
Common Misconceptions
"I have to multiply across first." — Emphasize that while true, it makes the numbers much harder to simplify later. Breaking them down early is a 'cheat code' for easier math.
