Cycle Match Slides The Cycle Match
Mastering LCM with Mr. J
Warm Up
Let's break it down! In your notebook, define what each letter stands for:
L
C
M
Wait for your teacher before revealing the answers!
Watch & Learn
Embedded media
Least Common Multiple (LCM) | Math with Mr. J
Pause & Reflect
Where do things repeat?
Mr. J says LCM shows up in real-world situations.
Can you brainstorm 3 things that repeat at different times?
Ex: School bell schedule
Your idea here...
Your idea here...
Level Up
The Three-Number Challenge
Mr. J is about to find the LCM for 12, 4, and 8.
Prediction Time:
Does the listing strategy change when we have 3 numbers instead of 2? How long do you think we will have to extend our lists?
Sync Up Activity
Hot Dog Buns Dilemma
Hot dogs come in packs of 10.
The Goal:
Find the smallest number of each pack you need to have an equal amount of hot dogs and buns.
Use Mr. J's Listing Method:
Exit Ticket
Show what you know!
Find the LCM of 3 and 4
On your paper, explain what this number means in a real-world context (like bells, buses, or blinking lights).
Grocery Sync Cards Grocery Sync
Word Problem Challenge
Name:
Date:
Instructions: For each scenario, use Mr. J's listing method to find the Least Common Multiple (LCM). Show your skip counting clearly!
Problem 1: The BBQ Dilemma
Hot dogs come in packs of 10 . Hot dog buns come in packs of 8 . What is the smallest number of packs of each you need to buy to have an equal amount of hot dogs and buns?
Multiples of 10:
Multiples of 8:
LCM: ___________
Total items of each
Packs of Dogs
Packs of Buns
Problem 2: The Commuter Sync
The Blue Line bus stops at the station every 15 minutes . The Red Line bus stops every 20 minutes . If they both arrive at 8:00 AM, how many minutes until they arrive at the same time again?
Multiples of 15:
Multiples of 20:
LCM: ___________ minutes
Next Sync Time:
___________ AM
Grocery Sync Cont.
Problem 3: The Plant Care
Maya waters her Fern every 3 days and her Cactus every 5 days . If she waters both today, in how many days will she have to water both plants on the same day?
Multiples of 3:
Multiples of 5:
LCM: ___________ days
Problem 4: Neon Sync (Challenge)
A neon sign has three sections. The first flashes every 2 seconds , the second every 4 seconds , and the third every 6 seconds . When will all three flash at the exact same time?
Multiples of 2:
Multiples of 4:
Multiples of 6:
LCM: ___________ seconds
Perfect Timing Exit Ticket Exit Ticket
Perfect Timing
Demonstrate your LCM mastery
Name:
Date:
1 Find the Least Common Multiple (LCM) of 3 and 4 using the listing method.
Multiples of 3:
Multiples of 4:
LCM = ___________
2 What does this number mean in a real-world context?
Think about things that repeat (like school bells, blinking lights, or a bus schedule).
Exit Ticket
Perfect Timing
Demonstrate your LCM mastery
Name:
Date:
1 Find the Least Common Multiple (LCM) of 3 and 4 using the listing method.
Multiples of 3:
Multiples of 4:
LCM = ___________
2 What does this number mean in a real-world context?
Think about things that repeat (like school bells, blinking lights, or a bus schedule).
Cycle Match Teacher Guide Teacher Guide
Lesson: The Cycle Match (LCM)
Grade Level
5th Grade
Objective
Students will apply Least Common Multiple (LCM) strategies to solve real-world word problems involving cyclical events. They will master Mr. J's listing method to prove synchronization between repeating events.
Materials Included
Cycle Match Slides
Grocery Sync Cards
Exit Ticket
Video: Math with Mr. J
Pacing Guide
Warm-up 5 min
Video & Discussion 10 min
Hot Dog Dilemma Activity 25 min
Closure / Exit Ticket 5 min
Key Discussion Anchors
Pause at 2:20
Question: "Mr. J found 6 and 12 in both lists. Why isn't 12 the answer?" (Answer: We are looking for the LEAST common multiple—the first time they sync up.)
Pause at 4:30
Question: "Can we find the 'Greatest Common Multiple'?" (Answer: No, because multiples are infinite; they go on forever.)
Pause at 6:15
Question: "The list for 4 isn't long enough to reach 24 yet. What should we do?" (Answer: Extend the list further!)
Answer Key: Grocery Sync Cards
1. BBQ Dilemma (10 & 8)
10: 10, 20, 30, 40 , 50
8: 8, 16, 24, 32, 40
LCM: 40
4 packs of dogs, 5 packs of buns
2. Commuter Sync (15 & 20)
15: 15, 30, 45, 60 , 75
20: 20, 40, 60 , 80
LCM: 60 minutes
Next Sync: 9:00 AM
3. Plant Care (3 & 5)
3: 3, 6, 9, 12, 15
5: 5, 10, 15 , 20
LCM: 15 days
4. Neon Sync (2, 4, 6)
2: 2, 4, 6, 8, 10, 12
4: 4, 8, 12 , 16
6: 6, 12 , 18
LCM: 12 seconds
Answer Key: Exit Ticket
LCM of 3 and 4:
3: 3, 6, 9, 12 / 4: 4, 8, 12
Real World Meaning:
"If a light flashes every 3 seconds and another every 4 seconds, they will flash together at 12 seconds." (Accept any logical repeating context: bells, schedules, game loops, etc.)
