National Curriculum Links

• Mathematics - Key Stage 2 (Year 4)
  • Number - Addition and Subtraction:
    “Add and subtract numbers with up to 4 digits using formal written methods of columnar addition and subtraction where appropriate.”
  • Programme of Study:
    Pupils should be taught to:
    • “Subtract numbers mentally with increasingly large numbers.”
    • “Use formal written methods of columnar addition and subtraction.”

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Learning Objectives

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

• Subtract 4-digit numbers involving one exchange using formal written methods confidently.
• Explain and justify their reasoning during subtraction, articulating when and why exchanges are necessary.
• Identify when exchange is required in column subtraction and apply it accurately.

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Success Criteria

I can:

• Set out a subtraction sum using the formal written method correctly.
• Identify when I need to exchange in a subtraction sum.
• Carry out one exchange accurately when subtracting four-digit numbers.
• Explain why I made an exchange using clear mathematical language.
• Check my answers by estimating or using inverse operations.

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Resources Needed

• Whiteboard and markers
• Visual place value charts with 4-digit numbers
• Individual mini whiteboards for pupils
• Printed worksheet with subtraction problems of increasing complexity
• Base-10 manipulatives or place value counters (optional)

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Lesson Structure (30 minutes)

1. Introduction (7 minutes)

Engagement:

• Begin by showing a 4-digit number on the board and asking:
  “What happens if we subtract a smaller number that has a bigger digit in the units column? What do we do if 2 − 5 is impossible without borrowing?”
• Display the example: 3241 − 1987 (or a simpler example for introduction, e.g., 4235 − 2786) and ask pupils to discuss briefly with their partner what would happen if we just subtract each column straight away.

Targeted Questions:

• “Why might it be tricky to subtract the units column here?” (Understand problem)
• “Can you explain what ‘exchange’ means in subtraction and why it helps?” (Apply knowledge)
• “How do you think exchange relates to place value?” (Analyse)

Assessment for Learning (AfL):

• Use mini whiteboards to have all pupils attempt 5 − 8 mentally and then vote thumbs up/down for understanding.
• Listen to answers in paired talk to ascertain conceptual understanding of ‘exchange’.

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2. Modelling (10 minutes)

Step-by-step demonstration:

• Model the subtraction 4235 − 2786 on the board, talking aloud:
  • Start from the units column: 5 − 6 can’t be done, so exchange 1 ten for 10 ones (cross out 3 tens and change to 2 tens, add 10 to 5 ones to make 15).
  • Subtract units: 15 − 6 = 9
  • Move to tens: after exchange we have 2 tens − 8 tens, cannot subtract, so exchange 1 hundred for 10 tens (cross out 2 hundreds to 1 hundred, add 10 tens to 2 tens making 12 tens).
  • Continue subtracting each column while explaining the logic behind each step.

Example to copy into books:

   4  2  3  5
 - 2  7  8  6
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   1  4  4  9

(With marks to show crossing out and exchanging)

Targeted Questions (whole class):

• “Why did I need to exchange from the tens to the units, and then from the hundreds to the tens?” (Understand and apply)
• “How would the answer change if I forgot to exchange?” (Analyse consequences)
• “Can someone explain how this connects to place value understanding?” (Analyse and evaluate)

AfL:

• After modelling, ask pupils on mini whiteboards to solve 4352 − 2697 application problem by showing their workings.
• Identify common mistakes such as subtracting without exchanging or exchanging incorrectly.

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3. Guided Practice (8 minutes)

Task structure:

Stage	Task Description	Complexity Level
1	Subtract 4-digit numbers with one exchange in units only (e.g., 5341 − 2876)	Basic exchange in units
2	Subtract 4-digit numbers needing one exchange in tens (e.g., 6352 − 2784)	Exchange moves to tens
3	Subtract where exchange moves through hundreds but only one total exchange (e.g., 7431 − 3675)	More complex borrowing

• Pupils complete the problems individually with base-10 counters available for support.
• Circulate the room, asking specific pupils to explain their thinking:
  • “Tell me where you exchanged and why you did that there.”
  • “What would happen if you skipped the exchange? How do you know?”
• Encourage pupils to verbalise their methods with their partner before writing answers.

Common Misconceptions to address:

• Subtracting smaller digits from larger without exchanging and getting negative digits.
• Exchanging from the wrong column.
• Forgetting to reduce the number in the column from which the ten/hundred was exchanged.
• Exchanging multiple times unnecessarily.

AfL:

• Observe work, listen to reasoning, and note misunderstanding for immediate feedback.
• Use a traffic-light card system for pupils to self-assess confidence on the tasks.

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4. Plenary (5 minutes)

Class discussion:

• Select 2-3 pupils to explain their subtraction process and reasoning aloud.
• Pose these questions:
  • “How does exchanging help us subtract numbers more accurately?”
  • “Can you think of real-life situations where you might need to subtract large numbers and exchange?”
  • “What tips would you give a friend who is stuck on subtraction with exchanging?”

AfL:

• Use exit tickets: pupils answer a quick question on a post-it, e.g.
  “What is one important step to remember when subtracting with one exchange?” or “Show on my number line where the exchange happened.”
• Collect and quickly scan to guide next lesson planning.

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Bloom’s Taxonomy Question Examples

Cognitive Level	Question Examples
Remembering	“What does ‘exchange’ mean in subtraction?”
Understanding	“Explain why you can’t subtract 8 from 3 in the tens column.”
Applying	“Show how you would subtract these digits using column subtraction.”
Analysing	“Why do we cross out a digit when exchanging? What does this represent?”
Evaluating	“Is it always better to exchange from the next column? Why or why not?”
Creating	“Can you create your own subtraction problem with one exchange to challenge a classmate?”

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Summary

This lesson aligns with the Year 4 National Curriculum and White Rose Maths schemes by focusing on formal written methods for subtraction of four-digit numbers with one exchange. It incorporates clear success criteria, targeted higher-order questioning, AfL checkpoints throughout teaching, and gradually increasing task complexity to scaffold learning. Common misconceptions are identified and addressed explicitly through modelling and guided practice. This lesson also builds pupils' reasoning and metacognition skills through oral explanation and peer discussion.

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If needed, I can also generate a detailed printable worksheet and teacher’s notes for this lesson!