Subtracting 4-Digit Numbers

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Overview

Duration: 60 minutes
Class size: 30 pupils
Year group: Year 4
Focus: Understanding and applying the formal written method for subtraction of 4-digit numbers
Curriculum links:

• National Curriculum for England (Mathematics, Year 4)
• White Rose Maths Scheme – Block 2, Week 4 (Formal Written Subtraction)

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National Curriculum Objectives

Mathematics Programmes of Study, Number – Subtraction:

• Pupils should be taught to:
  • "Subtract numbers with up to 4 digits using the formal written methods of columnar subtraction where appropriate"
  • "Estimate and use inverse operations to check answers to a calculation."

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Learning Intentions

• I can subtract 4-digit numbers using the formal written method (column subtraction).
• I can explain my subtraction process using correct mathematical language.
• I can check my subtraction answers using inverse operations.

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Success Criteria

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

• Set out column subtraction correctly with place value aligned.
• Accurately subtract 4-digit numbers using the formal written method, including regrouping (borrowing).
• Explain each step of the subtraction method and justify why regrouping is needed.
• Use inverse addition to check the subtraction result.
• Identify and correct common errors such as subtracting in the wrong order or misunderstanding regrouping.

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Resources Needed

• Whiteboard and pens
• Place value charts (optional)
• Student exercise books
• Number cards for interactive questions
• Mini-whiteboards for quick AFL responses
• Subtraction word problems for higher order thinking

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Lesson Structure

1. Introduction - 10 minutes

Engage pupils:

• Begin with an attention-grabbing story/problem:

"Imagine you have 3,742 bricks, and you use some to build a wall. You need to figure out how many are left. How could you work this out carefully when the numbers are so big?"

Key questions:

• What methods do we know for subtracting numbers?
• Why might subtracting 4-digit numbers be tricky?
• How can we be sure our answer is correct?

Targeted whole-class questioning (using Bloom’s taxonomy):

• Remembering: What is subtraction used for in real life?
• Understanding: Why do we need to line numbers up by place value when subtracting?
• Applying: How would the subtraction of two 4-digit numbers look different from smaller numbers?
• Analysing: What happens if you subtract a bigger digit from a smaller one in a column?
• Evaluating: Can you explain why it is important to check your subtraction answer?
• Creating: Can you think of another way to check subtraction answers besides inverse operations?

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2. Teaching & Modelling - 20 minutes

Step 1: Review column subtraction without borrowing (simple example)
Example: 4321 – 1234

• Write numbers vertically, align by place value.
• Subtract each column starting from ones place.

Discuss use of place value and column alignment.
AFL: Use mini-whiteboards to try a simple column subtraction (e.g., 3251 – 1242).

Step 2: Introduce regrouping (borrowing) method
E.g. 7423 – 2587

• Model step-by-step: when a digit in the top number is smaller than the digit below, regroup from the next column.
• Show how “borrowing” works practically with place value.
• Emphasise crossing out and updating digits carefully.

Guided questions during modelling:

• Why do we need to borrow in this column?
• How does borrowing affect the digit we borrowed from?
• What happens if we forget to borrow properly?
• Can you explain each step of the method in your own words?

Increasing complexity in examples:

• 6500 – 2894 (borrowing zeros)
• 1000 – 675 (borrowing across multiple zeros)

AFL checkpoints:

• After each example, ask pupils to write down the next step or explain aloud what to do next (live modelling feedback).
• Use targeted questions to check understanding, e.g., “Why can’t we subtract 7 from 0 here? What do we do?”

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3. Guided Practice Tasks - 20 minutes

Task 1: Low ability (Focus on subtracting 4-digit numbers without multiple regrouping)

• 4327 – 2158
• 5612 – 3125
• 7310 – 4219

Task 2: Middle ability (Includes regrouping from one column, including borrowing across zero)

• 6035 – 2784
• 4702 – 3615
• 5000 – 2864

Task 3: High ability (Multiple regrouping layers, including using inverse addition to check answers)

• 7001 – 2857
• 10000 – 6474
• Word problem: "A library had 8432 books. They removed 3765 books for repair and then lent out another 2356 books. How many books are left?"

Instructions:

• Pupils will work independently in their books.
• Emphasise showing working clearly and using place value layouts.
• High ability pupils should also write out inverse sums to check their answers.

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4. Plenary - 10 minutes

Whole Class Discussion:

• Invite volunteers to show one of their working out on the board.
• Focus on explanations: "Tell us how you borrowed and why."
• Pose reflection questions:
  • How do you know when to borrow?
  • What did you find tricky?
  • How does inverse addition help check your answer?

Common misconceptions to address:

• Subtracting the smaller digit from the larger but reversing when columns are mixed up.
• Forgetting to subtract the borrowed 1 from the next column digit.
• Not lining digits up by place value.
• Borrowing from a zero without continuing to move left to find a non-zero digit.

Success Criteria Recap:

• Check off the success criteria as an exit ticket: pupils confirm which targets they have met and explain one aspect they feel confident with.

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AFL & Assessment

• Regular use of mini-whiteboards for quick individual response.
• Questioning that requires explanation (not just answers) checks deeper understanding.
• Modelling with visible thinking aloud gives immediate feedback.
• Written work from differentiated tasks provides evidence of progress.
• Use of inverse operation to self-assess answers encourages independent checking skills.

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Example for Pupil Book (Copy and Annotate)

  7 4 2 3
- 2 5 8 7
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Start with ones:
3 - 7 (cannot do! Borrow 1 ten)
Borrow 1 ten from 2 (tens column becomes 1), ones column becomes 13
13 - 7 = 6

Tens:
1 - 8 (cannot do! Borrow 1 hundred)
Borrow 1 hundred from 4 (hundreds column becomes 3), tens column becomes 11
11 - 8 = 3

Hundreds:
3 - 5 (cannot do! Borrow 1 thousand)
Borrow 1 thousand from 7 (thousands column becomes 6), hundreds becomes 13
13 - 5 = 8

Thousands:
6 - 2 = 4

Answer: 4836

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Extensions / Home Learning Ideas

• Create your own subtraction word problems with 4-digit numbers needing borrowing, and swap with a partner to solve.
• Explore multi-step subtraction with money involving borrowing to build real life relevance.
• Use inverse addition in a quiz format for self-checking subtraction answers.

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This detailed and differentiated lesson plan ensures pupils develop confidence and competency with the formal column subtraction method for 4-digit numbers, building on prior place value and subtraction knowledge inline with the Year 4 National Curriculum and White Rose Maths guidance.