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.

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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)

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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.

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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

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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.

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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.

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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.

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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.

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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.