National Curriculum Links

Mathematics - Year 4: Number - Multiplication and Division

• Recognise and use factor pairs and commutativity in mental calculations
• Recall multiplication and division facts for multiplication tables up to 12 × 12

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Learning Objectives

By the end of this lesson, pupils will:

• Understand what factor pairs are and how to identify them for a given number.
• Use factor pairs to solve multiplication and division problems.
• Explain their reasoning when identifying factor pairs and calculating products.

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Success Criteria

• I can identify all factor pairs of a given number.
• I can explain why two numbers make a factor pair.
• I can use factor pairs to solve problems involving multiplication and division.
• I can justify my answers using clear mathematical reasoning.

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Resources Needed

• Whiteboard and markers
• Individual mini whiteboards and pens
• Printed ‘Factor Pair’ grids for activities
• Number cards (1-20)
• Worksheets for independent practice
• Visual aids (arrays, factor trees)

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Lesson Structure (45 minutes)

1. Introduction (10 minutes)

Engagement Hook:
Display a large rectangle on the board made up of 24 dots arranged in rows and columns (e.g., 4 rows × 6 columns). Ask:

• How many dots are there in total? (Recall of multiplication)
• Can you find different ways to arrange these dots into equal rows and columns without leftovers?

Explain:

• These different arrangements show factor pairs of 24.
• Define factor pairs: pairs of numbers that multiply together to make the original number.

Targeted Questions (Whole Class):

• Why do you think 4 and 6 are called factor pairs of 24?
• Can there be more than one factor pair for a number? Can you justify your answer?
• If 3 is a factor of 24, what does this tell us about 24?
• How could knowing factor pairs help you solve other maths problems?

Encourage pupils to explain their thinking, promoting reasoning skills aligned to Bloom’s levels: Understanding, Applying, and Analyzing.

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2. Modelling (10 minutes)

Display the number 36 on the board. Model the identification of factor pairs step-by-step:

• Start with 1 × 36 = 36
• 2 × 18 = 36
• 3 × 12 = 36
• 4 × 9 = 36
• 6 × 6 = 36

Highlight that after 6 × 6, factor pairs start repeating in reverse, so we can stop here.

Model the explanation of why these are factor pairs, e.g.:

• Because 2 multiplied by 18 equals 36, 2 and 18 are factor pairs.
• 6 multiplied by 6 equals 36, so 6 and 6 is a factor pair where both factors are the same.

AfL Checkpoints:

• Ask pupils to write on mini whiteboards whether 8 is a factor of 36 and to explain their reasoning.
• Invite 2-3 pupils to share their responses and justify answers verbally.

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3. Guided Practice (10 minutes)

Task: Identify factor pairs of given numbers gradually increasing in complexity:

• Begin with 12 and 24 (familiar numbers).
• Progress to 48 (larger number).
• Challenge: find factor pairs of 50 and explain if 7 is a factor of 50.

Use number cards and ‘Factor Pair’ grids where pupils place pairs into arrays or fill factor pair tables.

Whole Class Questioning:

• Why did you decide to try 2 as a factor for 48?
• If you find a factor that is greater than the square root of a number, what does that tell you in relation to factor pairs?
• How can you check that your factor pairs are correct?
• Can a negative number be a factor pair here? Why or why not?

Encourage pupils to explain their thinking in complete sentences and use mathematical vocabulary.

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4. Independent Task (10 minutes)

Pupils complete a worksheet requiring:

• Listing all factor pairs for 36, 40, and 56.
• Explaining why certain numbers are or are not factors.
• Applying factor pair knowledge to solve a word problem, e.g., arranging items evenly into boxes.

Example to Copy into Books:

Number	Factor Pairs
36	1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6

• Explanation: I know 3 × 12 = 36, so 3 and 12 are factor pairs. Since 6 × 6 = 36, 6 is a factor repeated in the pair.

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5. Plenary (5 minutes)

Reflective Questions:

• Can someone explain what a factor pair is in their own words?
• How did you decide which numbers to test as factors?
• Was there anything tricky about today’s work? What did you do to solve it?
• How might understanding factor pairs help in other areas of maths?

Exit Ticket: Ask pupils to write on a mini whiteboard one factor pair for 30 and explain why these numbers work together.

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Common Misconceptions & Difficulties

• Pupils may confuse factors with multiples; clarify that factors divide a number exactly with no remainder.
• Difficulty identifying when to stop searching for factor pairs (stop at the square root). Emphasise this modelling step clearly.
• Misunderstanding commutativity and listing repeated pairs (e.g., counting 2 × 6 and 6 × 2 as distinct pairs).
• Challenges explaining reasoning; support with sentence stems like "I know... because..."

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Differentiation

For less confident pupils:

• Provide smaller numbers and visual aids (arrays) to support understanding.
• Use practical objects like counters to physically build factor pairs.

For more confident pupils:

• Challenge with larger numbers and investigate factor pairs of prime, composite, and square numbers.
• Ask to explore factor pairs in context of division word problems and explain their steps.

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Alignment to White Rose Maths Scheme

This lesson aligns with White Rose Maths Year 4 Block 1 (Number – Multiplication and Division), specifically supporting pupils to develop fluency and reasoning about factors and multiplication facts. It builds mental calculation strategies through understanding the concept of factor pairs, laying foundations for efficient calculation methods and problem solving.

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Summary

This lesson plan combines visual engagement, strategic questioning using Bloom’s Taxonomy, opportunities for reasoning, stepwise modelling and differentiation that match the National Curriculum in England. It builds both procedural skill and conceptual understanding of factor pairs suitable for Year 4 pupils.