Exploring Factors

Australian Curriculum Alignment

Year Levels: Year 5 & 6
Learning Area: Mathematics
Strand: Number and Algebra
Sub-Strand: Number and place value

Relevant Content Descriptions:

• Year 5 (ACMNA098): Identify and describe factors and multiples of whole numbers and use them to solve problems.
• Year 6 (ACMNA123): Identify and describe properties of prime, composite, square and triangular numbers.

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Lesson Overview

Title: Exploring Factors
Lesson: 2 of 5 in "Mastering Multiples & Factors"
Duration: 45 minutes
Class Size: 16 students
Teaching Style: Conversational, student-led learning with differentiated tasks

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WALT & Success Criteria

WALT (We Are Learning To):

• Understand what a factor is and how it differs from a multiple.
• Identify all factor pairs for a given number.

Success Criteria:

• I can correctly define a factor and explain how it differs from a multiple.
• I can use materials or strategies to find all factor pairs for a number.
• I can work collaboratively to identify patterns in factors.
• I can reflect on my learning and explain different methods used to find factors.

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Materials Needed

• Mini whiteboards and markers (1 per student)
• Factor flashcards (numbers 1–100)
• Counters (multi-coloured, approx. 100 per group)
• Grid paper
• Maths notebooks
• Factor Trees printed templates (for anchor activity)
• A3 chart paper for group recording
• iPads/tablets (optional for early finishers)
• Sticky notes

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Lesson Breakdown

⏱️ 0–5 mins: Welcome & Warm-Up

• Greet students and gather as a group on the floor.
• Quick recap of previous lesson: Ask students to recall the definition of a multiple.
  • Ask: “Can a number have only one multiple? Why or why not?”
• Today’s WALT is shared and written on the board.
• Ask: “Who’s heard the word ‘factor’ before? What's your guess at what it means?”

⏱️ 5–15 mins: Explicit Teaching – What Is a Factor?

• Use whiteboard to model:
  “Let’s investigate the number 12. What are all the numbers that divide evenly into 12?”
  List on the board: 1, 2, 3, 4, 6, 12 ⟶ Then pair them: (1×12), (2×6), (3×4)
• Define:
  • A factor is a number that divides evenly into another number.
  • A factor pair is a set of two numbers that multiply to give the original number.
• Compare with a multiple: “Multiple of 4: 4, 8, 12, 16… goes up forever. Factor of 12: must divide 12 exactly. Goes downward.”
• Use manipulatives (counters): Demonstrate finding factor pairs of 12 by grouping counters.
• Ask class: “Does the order of the factor matter? Is (3×4) the same as (4×3)?”

⏱️ 15–30 mins: Group Activity – Factor Hunt with Counters

Group Work (in mixed-ability groups of 4):

• Each group is given:
  • A set of number flashcards (range of numbers from 18–50)
  • A tray of counters and A3 sheet with a table:
    • Number | Factor Pairs (with diagrams) | Total Number of Factors

Instructions:

• Each group selects 3 number cards.
• Using counters or grid paper, they must find as many different factor pairs as they can for each number.
• Use a “build and record” method: Make equal groups using counters. If it divides evenly, it’s a factor.
• Encourage use of arrays and repeated subtraction for visual learners.

Support for Diverse Learners:

• Some students can use scaffolding sheets listing steps to test divisibility.
• Provide calculators for students who have numeracy challenges to check their workings.
• Have a buddy system where stronger students help peers.

Extension for Advanced Learners:

• Challenge: Investigate which numbers in their set are prime or square numbers.
• Research question (using maths notebooks or iPads): “Can you find a number with exactly 3 factors? What kind of number is it?”
• Record and display work as a mini “Did You Know?” maths fact sheet.

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⏱️ 30–40 mins: Reflect & Share

• Regroup on floor.
• Each group briefly presents one of their numbers and shares their factor pairs.
• Use guiding questions:
  • “What strategies helped you find the factors?”
  • “Did you notice any patterns in factor pairs?”
• Teacher models a Factor Tree (e.g. for 36) on the board to connect factor work to future prime factorisation.

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⏱️ 40–45 mins: Exit Reflection

• Each student writes a reflection on a sticky note:
  • “Today I learnt…”
  • “A question I still have is…”
• Stick notes on the Factor Reflection Wall.

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Differentiation Strategies

Learner Type	Strategy
Visual learners	Use colour-coded counters & grids for factor identification
Hands-on/kinesthetic learners	Physical grouping, moving counters, manipulating objects to build understanding
Lower-ability students	Scaffolding mats/chart guides with step-by-step checks
Higher-ability students	Extension challenge - identify prime numbers, make connections to prime factors and square numbers
EAL/D students	Visual support with diagrams and sentence starters, peer modeling

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Optional Independent Practice (Early Finishers)

• Digital Challenge (optional use of iPads): Use virtual manipulatives to build arrays and model factor pairs.
• "Mystery Number" Card Game: Students write factor clues. Peers guess the number based on clue prompts.

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Teacher Reflection Prompts (Post-Lesson)

• Which students seemed confident identifying factors conceptually?
• How effectively did students work in groups, particularly mixed-ability pairs?
• Were students able to describe the difference between multiples and factors correctly in their own words?
• Which activities engaged students most deeply?

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Looking Ahead – Lesson 3 Preview

Next Lesson: "Prime Time!"
Students will learn to distinguish prime and composite numbers, build on their knowledge of factors, and use fun visual patterns to identify primes.

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This lesson is designed to spark both conversation and curiosity around factors — while giving students the tools and freedom to trust their own mathematical thinking. With deliberate space for hands-on exploration and accessible language around numeracy concepts, students are invited to take ownership of their learning and work toward achieving their very best.