Factors Introduction

WALT (We Are Learning To)

• Explore the concept of factors by identifying pairs of whole numbers that multiply to form a given product.
• Use manipulatives to visualise and understand factors.
• Complete factor trees for numbers up to 50.

Success Criteria

• I can explain what a factor is.
• I can find pairs of factors for numbers up to 50.
• I can use manipulatives to show how factors multiply to a product.
• I can complete a factor tree for numbers up to 50.

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Curriculum Links

This lesson aligns with the Western Australian Curriculum AC9M5N010 (Year 5 Mathematics):

• Create and use algorithms involving sequences of steps and decisions and digital tools to experiment with factors, multiples and divisibility; identify, interpret and describe emerging patterns .
• Supports understanding of multiplication and division facts as per AC9M5A01 and AC9M5A02 to deepen factor knowledge .

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Lesson Duration

60 minutes
Class size: 22 students

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Resources Needed

• Counters or coloured blocks (manipulatives)
• Whiteboard and markers
• Large paper for factor trees (one per student or pair)
• Printed worksheets with numbers up to 50 for factor tree activity
• Dyslexia-friendly printed resources with clear font, spacing, and colour coding

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Lesson Sequence

1. Introduction (10 mins)

• Begin with a brief discussion: Ask, "What do you think a factor is?" Collect ideas.
• Introduce the definition of a factor: "A factor of a number is a whole number that divides it exactly, leaving no remainder."
• Use a simple example on the board: 12
  Ask students to think about numbers that multiply to make 12 (e.g., 1 × 12, 2 × 6, 3 × 4).
• Demonstrate with counters how 3 groups of 4 make 12.

2. Hands-on Exploration Activity (20 mins)

• Distribute counters to pairs of students.
• Provide each pair with a range of numbers (e.g., 24, 30, 36, 40, 48) and ask them to use the counters to visualize all the factor pairs of their assigned number.
• Encourage students to write down the factor pairs they discover.
• Encourage communication: pairs explain their findings to another pair.

3. Guided Factor Tree Activity (15 mins)

• Introduce factor trees: a way to break down numbers step-by-step into their factors.
• Model completing a factor tree for number 36 on the whiteboard, showing the breakdown into factors and prime factors.
• Give each student (or pair) a worksheet with numbers up to 50 and ask them to complete a factor tree.
• Circulate, providing support and using questioning strategies to deepen understanding (“Why did you choose that factor?”, “Are these factors prime?”).

4. Reflection and Sharing (10 mins)

• Invite some students to share their factor trees and explain their thought process.
• Review the definition of factors, reinforcing what was learned.
• Use questioning to consolidate concepts: "Can 1 and the number itself always be factors?" "What about prime numbers?"

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Differentiation Strategies

• For diverse learners:

  • Use manipulatives and visual aids liberally to support conceptual understanding.
  • Provide dyslexia-friendly print materials with a clear, sans-serif font, larger text size, and soft colour backgrounds for reading ease.
  • Use step-by-step instructions and scaffolded worksheets.
  • Pair students strategically for peer support.

• For advanced learners:

  • Challenge with factor trees for numbers beyond 50.
  • Investigate prime factorisation and discuss prime vs composite numbers.
  • Introduce simple programming/algorithmic thinking by designing step sequences for factorisation.

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Extension Activities

• Introduce the concept of multiples and how factors relate to multiples.
• Explore identifying common factors of two numbers.
• Use digital tools or apps where students can experiment with factors interactively.

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Assessment (Ongoing Formative)

• Observation during hands-on activities – check students’ ability to find factor pairs.
• Review students’ completed factor trees for accuracy and understanding.
• Questioning and student explanations during reflection to assess conceptual grasp.

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This lesson builds a solid foundation in factors aligned with the Western Australian Curriculum, preparing students for more complex factor and multiple concepts in upcoming lessons. It uses hands-on activities and visual tools well-suited to Year 5 students’ cognitive and developmental level, ensuring engagement and understanding across diverse learners.

If you would like, I can also prepare lesson plans for the subsequent five lessons in the "Factors and Multiples Mastery" unit following a similar format.