Mastering Compact Multiplication

National Curriculum Links

• Mathematics - Year 4 - Number - Multiplication and Division
  • Use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; multiplying together three numbers.
  • Multiply two-digit and three-digit numbers by a one-digit number using formal written layout.

Learning Objectives

• LO1: Understand and accurately use the compact method for multiplication involving two-digit and three-digit numbers multiplied by one-digit numbers.
• LO2: Develop reasoning skills to explain the steps and place value significance in the compact method.
• LO3: Apply the compact method confidently to increasingly complex multiplication problems.

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Success Criteria

I will be successful if I can:

• Use the compact method to multiply two and three-digit numbers by a one-digit number correctly.
• Show clear organisation of digits according to place value in my calculations.
• Explain why the compact method works using place value language.
• Solve multiplication problems that require carrying digits to the next column.
• Check my answers using inverse operations or estimation to confirm accuracy.

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Lesson Outline (45 minutes)

1. Introduction & Engagement (10 minutes)

Hook:
Show a short scenario with a supermarket checkout where a customer buys multiple packs of sweets with 123 pieces each, multiplied by 4. Ask, “How many sweets in total?” Start with asking if anyone has a quick method for multiplying large numbers by one digit, then introduce the compact method.

Discussion & Targeted Questions:

• What happens to the value of digits when we multiply? (Remembering)
• Why do we write digits “carrying over” to the next column? Explain that step. (Understanding)
• How does place value help us manage larger numbers in multiplication? (Applying)
• Imagine you multiply 124 by 3; how would you check your answer? (Evaluating)
• If you made a mistake adding the carried digits, what difference would that make? (Analysing)

Use this to scaffold thinking and activate prior knowledge.

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2. Modelling & AFL (15 minutes)

Use the whiteboard/document camera to model:

Example to copy into books:

Multiply 243 × 7 using the compact method.

Step	Explanation	Calculation
1	Multiply 3 (ones) × 7 = 21	Write 1 in ones, carry 2
2	Multiply 4 (tens) × 7 = 28 + 2 (carry) = 30	Write 0 in tens, carry 3
3	Multiply 2 (hundreds) × 7 = 14 + 3 (carry) =17	Write 17 in hundreds and thousands
Final	Answer = 1701

AFL Point 1 (After Step 1): Ask a volunteer, Why do we only write the 1 and carry the 2? (Checks place value understanding)

AFL Point 2 (After Step 2): Ask, How did adding the carried number affect the digit in the tens column? What would have happened if we forgot to add it?

AFL Point 3 (After Step 3): Explain why the final answer has four digits even though we are multiplying by one digit.

Highlight the importance of lining digits correctly and carrying number values.

Common Misconceptions to Highlight:

• Confusing place values when carrying numbers.
• Forgetting to add the carried number to the next multiplication.
• Misaligning digits during addition in the compact method.
• Mistaking the multiplication of digits independently without carrying.

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3. Guided Practice - Scaffolded Tasks (15 minutes)

Organise students into pairs. Task progressively increases in difficulty:

Task Level	Question	Focus
Level 1	36 × 4	Introduce simple two-digit × one-digit multiplication
Level 2	147 × 6	Three-digit number multiplied by one-digit, including carrying
Level 3	325 × 9	Larger digits requiring multiple carry steps
Level 4	486 × 7 AND estimate answer	Application plus estimation to judge if answers are reasonable

Throughout the task:
Teachers circulate, posing higher-order questions:

• Explain why you wrote the digits where you did. (Understanding)
• Can you identify which step is the trickiest and why? (Analysing)
• How do you know your answer is reasonable? (Evaluating)
• Could there be a quicker way to check your answer? (Creating)

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4. Plenary (5 minutes)

• Invite pupils to share their answers on the board.
• Use targeted questions to recap learning:
  • What is the purpose of carrying in the compact method?
  • How did your understanding of place value help?
  • If you multiplied a 3-digit number by 2 digits, would the method change? How?
• Quick peer assessment: pupils give thumbs up/down if they feel confident, then pair-share a tip they learned.
• Exit ticket question (on mini whiteboards): Solve 152 × 8 using the compact method and explain one step in your own words.

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Additional Teacher Notes

• White Rose Maths Alignment: This lesson corresponds to the White Rose Year 4 block on multiplication, specifically building on formal written methods introduced in earlier weeks.
• Encourage fluency and reasoning alongside procedural skill.
• Use careful language to reinforce place value and the logic behind carrying digits.
• Use manipulatives or place value counters for concrete learners requiring visualisation aids.

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This structured approach builds confidence in using the compact multiplication method while ensuring deep conceptual understanding, aligned with the National Curriculum's expectations for Year 4 mathematics.