Exploring Factor Pairs

Overview

This 60-minute lesson is designed for Year 4 students (ages 8-9) to develop a solid understanding of factor pairs, aligned with the National Curriculum for England’s Mathematics Programme of Study. The lesson incorporates hands-on manipulatives, visual aids, and well-structured practice tasks to deepen conceptual understanding of factors, multiplication, and division relationships.

Curriculum Links

Mathematics – Number: Multiplication and division

Pupils should be taught to:
- Recall multiplication and division facts for multiplication tables up to 12 × 12
- Recognise and use factor pairs and commutativity in mental calculations (NC ref: Programmes of Study, Key Stage 2)

Mathematics – Number: Properties of numbers

Identify factors, including common factors and factor pairs of numbers (NC ref: Yr4 Number – multiplication and division)

Learning Objectives

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

Define what factors and factor pairs are in relation to a given number.
Identify all factor pairs of numbers up to 100.
Understand the relationship between multiplication and division through factor pairs.
Apply knowledge of factor pairs to solve reasoning and problem-solving questions.

Resources

Arrays mats or grid papers (30)
Counters or square tiles (approx. 300)
Whiteboards and markers (30)
Factor pair challenge cards (prepared sets with numbers 1-100)
Large poster/interactive whiteboard with factor pairs grid for group demonstration
Worksheet with factor pairs exercises

Lesson Structure

1. Starter (10 minutes)

Objective: Activate prior knowledge about multiplication and factors.

Begin with a quick oral quiz reviewing multiplication facts (focus on 1 to 12).
Display the number 24 on the board.
Ask students to shout out all the pairs of numbers that can multiply to make 24 (e.g., 1 and 24, 2 and 12, etc.).
Introduce the term “factor pairs”: explain that they are pairs of numbers multiplied together to get a specific product.
Use a visual aid (array formed with counters on a grid) to show factor pairs of 24 physically.

2. Main Activity 1: Manipulatives Exploration (15 minutes)

Objective: Explore factor pairs practically using manipulatives.

Give each student an array mat and 24 counters to form arrays representing factor pairs of 24.
Allow students to arrange counters in rows and columns to show factor pairs (e.g., 1x24, 2x12, 3x8, 4x6).
Circulate and ask guiding questions: “How many rows? How many columns? Is this a factor pair?”
Show how factor pairs come in switched forms but represent the same product (commutativity).

3. Main Activity 2: Visual Sorting and Challenges (15 minutes)

Objective: Apply factor pairs understanding to different numbers and reinforce recognition.

Use factor pair challenge cards. Students work in pairs to identify all factor pairs for different numbers (e.g. 18, 30, 36, 40).
Provide large charts where pairs can be physically placed under correct numbers (using velcro or sticky notes), creating a whole-class factor pair wall.
Discuss results as a class; highlight common factors and the importance of knowing multiplication tables.

4. Independent Practice (10 minutes)

Objective: Consolidate learning with written exercises.

Distribute worksheets where pupils:
- List factor pairs for given numbers up to 100.
- Identify missing factors given one factor and the product.
- Answer reasoning questions such as: “Which number has the most factor pairs and why?”

5. Assessment and Plenary (10 minutes)

Objective: Check understanding and address misconceptions.

Quick oral questions on factor pairs to the whole class.
Use mini whiteboards for pupils to write factor pairs of a given number (e.g., 36).
Ask pupils to explain in pairs why some numbers have more factor pairs than others (introducing the concept of prime numbers gently).
Wrap up with a real-life link discussion: "Why are factor pairs important? Where might you see them outside maths?" e.g., arranging seats, packaging.

Differentiation

Support: Provide extra manipulatives and one-to-one guidance for pupils struggling with arrays.
Challenge: Extension activity to explore factor pairs of larger numbers or to identify if a number is prime based on factor pairs.

Assessment for Learning

Formative questioning during activities to check conceptual understanding.
Observation during practical array work to assess ability to form factor pairs.
Review of worksheet answers for accuracy and reasoning.
Plenary mini whiteboard activity to identify quick gaps.

Reflection Notes for Teachers

Encourage ready use of multiplication facts to increase fluency in identifying factors.
Strong emphasis on visual aids helps solidify the abstract concept of factors.
Make explicit links between multiplication, division, and factors to support conceptual connections.
Consider using technology (interactive screens) for factor pair grids in future lessons if available.

This lesson plan is designed to engage Year 4 learners actively and give them confidence with factor pairs as a key foundation for future number work.