Making Connections Matter

Year Level

Years 5 & 6

Duration

45 minutes

Unit Title

Mastering Multiples & Factors
Lesson 3 of 5

Lesson Title

Finding Common Multiples and Factors

Curriculum Links

Australian Curriculum – Mathematics (ACARA)
Number and Algebra – Number and Place Value

• ACMNA105 (Year 5): Identify and describe factors and multiples of whole numbers and use them to solve problems.
• ACMNA122 (Year 6): Investigate and apply digital technologies to represent and solve problems involving combinations of factors and multiples.

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WALT (We Are Learning To)

• Identify the common multiples of two or more numbers.
• Identify the common factors of two or more numbers.
• Explain the relationship between multiples and factors using correct mathematical language.

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Success Criteria

By the end of the lesson, students will be able to:

✅ Identify at least two common multiples of a given pair of numbers.
✅ Identify at least one common factor of a given pair of numbers.
✅ Accurately explain the difference between a factor and a multiple.
✅ Use mathematical reasoning to justify their answers.

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Resources

• Whiteboard and markers
• Student Table Worksheets
• ‘Factor Find’ activity cards (differentiated)
• Multiples & Factors Anchor Chart (displayed)
• Coloured counters or blocks
• Mini whiteboards and markers for each student
• Access to calculators (optional for differentiated needs)
• Timer

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Lesson Structure

❗Warm-Up (5 minutes) – Quick Fire Recall Game

Activity: True or False Wall Toss
Students take turns tossing a soft ball at the whiteboard where you’ve drawn “True” on one side and “False” on the other. You read a statement such as:

• “12 is a multiple of 3”
• “8 is a factor of 56”
• “15 is not a multiple of 7”
  They decide true or false and explain their reasoning.

🎯 Focus: Recall of vocabulary and fundamental understanding.
This rapid-fire activity gets brains buzzing!

Teacher Tip: For quieter students, allow them to confer with a partner before answering out loud.

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🧠 Explicit Teaching (5–7 minutes) – Short Burst Instruction

Key Visuals: Display a pre-prepared anchor chart:

• Multiples: Counting ON (e.g., 4, 8, 12...)
• Factors: Numbers that DIVIDE exactly into another (e.g., factors of 12 → 1, 2, 3, 4, 6, 12)

Model:
Use the example of 6 and 9.

• List first five multiples of each:
  6 → 6, 12, 18, 24, 30
  9 → 9, 18, 27, 36, 45
• Highlight common multiples → 18

List factors of each:
6 → 1, 2, 3, 6
9 → 1, 3, 9

• Highlight common factors → 1, 3

✅ Tip: Emphasise language.

• “Common means they share it.”
• “Multiples go UP. Factors go IN.”

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🤲 Guided Practice / Collaborative Exploration (15 minutes)

Paired Work:
Distribute worksheets with number pairs. Students must:

1. List at least the first 6 multiples of each number.
2. Circle the common multiples.
3. List all factors of each number.
4. Circle the common factors.
5. Use a sentence stem:
   "The common multiples of __ and __ are __. I know this because __."

✔ Students encouraged to use mini-whiteboards to try examples together.

🎯 Curriculum Alignment: Solving problems involving factors and multiples, and applying reasoning.

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🌟 Differentiation

Supportive Scaffolds:

• Use number grids or multiplication charts for students who struggle with recall.
• Offer counters and arrays for visual and hands-on learners.
• Provide calculators to assist students with computation fatigue.

Mid-Lesson Check-In:
Ask students: “Who has found multiples for both numbers? How do you know if they’re correct?”

🧑‍🏫 Small Group Support (as needed): Work with a small cluster of students who may need more guided modelling, using concrete materials.

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🎯 Extension for Fast Finishers

Factor Find Riddles:
Challenge cards where students must solve problems like:

• “I’m thinking of a number between 20 and 40. It is a multiple of 6 but not a multiple of 4. What could it be?”

Create Your Own Challenge:
Students create a multiple/factor riddle for peers to solve.

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🔁 Reflect and Share (10 minutes) – Student-Led Discussion

Activity: Peer Swap
Students pair up and swap completed tables. They double-check each other’s common multiples and factors, discussing any differences.

Prompt questions on board:

• “Was there more than one common multiple?”
• “What strategies helped you find the factors quickest?”

Student Voice Opportunity
Ask: “Who’d like to share a cool trick they discovered today?”

Encourage celebration of "aha!" moments.

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✅ Exit Ticket (Final 3 minutes)

Distribute small slips or mini-whiteboards and ask:

"List one common multiple and one common factor of 8 and 12."
Bonus: Add one thing you learnt or found interesting today.

Collect them or review immediately to assess understanding and prep for next lesson.

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Assessment (Formative)

• Observation during partner tasks.
• Responses during whole class discussion.
• Exit tickets to check understanding of key concepts.
• Participation in peer feedback and explanation.

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Looking Ahead

Next Lesson (Lesson 4):
Multiples & Factors in Word Problems
Applying understanding to real-world mathematical contexts (e.g., party bag grouping, arranging seats).

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Teacher Reflection Prompts

• Which students showed strong conceptual understanding through their explanations?
• Who could benefit from an anchor chart near their workspace?
• Did student-created problems reveal deeper understanding or misconceptions?

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Final Note

This lesson invites collaborative thinking, rich discussion, and shared ownership of learning—aligned with your teaching style. It allows students to explore, create, and make connections—because finding common ground, whether in maths or people, opens doors to deeper learning.

🧠💡 Let them lead, and they just might surprise you.