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.

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 .

Lesson Duration

60 minutes
Class size: 22 students

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

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?"

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.

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.

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.

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.