National Curriculum Links

• Mathematics Programmes of Study (Year 4):
  • Number – Addition and Subtraction:
    • “Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate.”
    • “Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.”
• White Rose Maths Scheme Reference:
  • Year 4 – Block 1: Number – Addition and Subtraction (Weeks 1-2)

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Learning Objectives

By the end of this lesson, pupils will:

• Understand how to solve one-step mixed addition and subtraction problems involving 4-digit numbers requiring regrouping (exchanging).
• Accurately use the formal written methods (column addition and subtraction) to solve these problems.
• Explain their reasoning and justify their choice of operation and method when solving problems.

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Success Criteria

• I can confidently use column addition and subtraction for 4-digit numbers.
• I know when I need to exchange (regroup) and can explain how I do it.
• I can solve one-step word problems involving addition or subtraction with 4-digit numbers.
• I can explain my reasoning clearly when solving a problem.

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Resources

• Whiteboards and pens for whole class activities
• Printed worksheets with progressive difficulty one-step mixed addition and subtraction problems
• Visual place value charts and counters for regrouping demonstration
• Example problem printed and projected on the board
• PowerPoint with question slides
• Books and writing materials for pupils

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Lesson Structure

1. Introduction (10 minutes)

• Begin with a quick interactive quiz to recap place value and regrouping with 3-digit numbers. Write a few 3-digit addition and subtraction problems on the board and ask pupils to solve quickly on mini whiteboards.
• Engage pupils by showing a puzzle scenario: “Imagine you have 3,458 stickers and you buy 1,274 more. How many stickers do you have now? What if you give away 678 stickers?”
• Ask: “What operation will we do first, and why? Can you explain your thinking?”
• Use a place value chart to visually represent numbers and point out where exchanging (regrouping) might be needed.

Targeted Questions (Bloom’s Taxonomy)

• Remembering: What is the value of the digit 7 in 1,274?
• Understanding: Why do we sometimes need to exchange when subtracting?
• Applying: How would you set the numbers up to add 3,458 and 1,274? Which digits do you add first?
• Analysing: If the ones column can’t add without regrouping, what do you do next?
• Evaluating: Which method helps you check your answer, and why?
• Creating: Can you think of a real-life example where you might need to add or subtract big numbers like this?

Assessment for Learning (AfL)

• Collect quick whiteboard answers to assess baseline understanding.
• Listen to explanations and reasoning during questioning to identify misconceptions early.

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2. Modelling & Guided Practice (15 minutes)

Step 1: Addition with regrouping

• Project this example and copy it together into books:

  3  4  5  8  
+ 1  2  7  4  
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• Walk through each column right to left:
  • Units: 8 + 4 = 12 → Write 2, carry over 1 to the tens.
  • Tens: 5 + 7 + carried 1 = 13 → Write 3, carry over 1 to hundreds.
  • Hundreds: 4 + 2 + carried 1 = 7 → Write 7 in hundreds.
  • Thousands: 3 + 1 = 4 → Write 4 in thousands.
• Result: 4,732
• Explain every step aloud, emphasising why we carry digits.

Targeted Question:

• Why do we carry over the 1 at the tens column? What would happen if we forgot?

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Step 2: Subtraction with regrouping (exchanging)

• Now solve:

  5  1  0  2  
- 2  4  7  9  
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• Model the exchange process:
  • Units: 2 - 9 (Not possible, so regroup)
  • Borrow 1 ten → units become 12; tens reduce by 1
  • Now 12 - 9 = 3 in units.
  • Tens: 0 - 7 (Not possible again) → Borrow 1 hundred → 10 - 7 = 3
  • Hundreds: 1 - 4 (Not possible) → Borrow 1 thousand → 11 - 4 = 7
  • Thousands: 4 - 2 = 2
• Result: 2,323

Targeted Questions:

• What does ‘regrouping’ mean in this subtraction?
• How did borrowing from the thousands help solve the problem?
• Is there another way you might tackle this subtraction?

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3. Independent/Paired Practice (20 minutes)

• Task: Pupils complete a worksheet with 10 one-step problems (5 addition, 5 subtraction), all 4-digit numbers requiring regrouping.
• Earlier problems have no regrouping or simple regrouping, progressing to problems with multiple regrouping steps (e.g., borrowing multiple times in subtraction).
• Pupils write out their working using column methods in their books and explain their reasoning in a short sentence for each problem.

AfL:

• Teacher circulates, asking pupils to explain how they decided to carry or borrow.
• Identify pupils struggling and prompt with visual aids or stepwise questions.

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4. Targeted Whole Class Questioning (10 minutes)

• Select a few pupil answers to discuss. Using Bloom's Taxonomy, ask:
  • “Explain why you carried a 1 in problem 4?”
  • “How did you confirm your subtraction answer was correct?”
  • “If you found two different answers, how would you decide which one is right?”
  • “Could you make a real-life story problem for this calculation and explain how you’d solve it?”
• Encourage pupils to listen to peers’ reasoning and ask clarifying questions.

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5. Plenary (5 minutes)

• Play a quick ‘Maths Mixer’: Pupils stand and pair up to explain one addition and one subtraction problem they completed, including how they used regrouping.
• Finish by asking: “What is one tip you would give to someone finding regrouping tricky?”
• Summarise key points on board: Always check place value, don’t forget to carry or borrow, explain your thinking.

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Common Misconceptions & Difficulties

• Forgetting to carry over when the column sum is 10 or more in addition.
• Not borrowing correctly, especially when multiple regrouping is required in subtraction (e.g., borrowing across zero).
• Confusing when to add or subtract in mixed problems.
• Writing numbers in the wrong columns or dropping digits.
• Giving the final answer without showing working, making it hard to check errors.
• Difficulty explaining reasoning beyond just calculating an answer.

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Summary

This lesson plan offers a scaffolded, inquiry-based approach aligned with the National Curriculum (England) and White Rose Maths. It combines direct instruction, visual modelling, progressive challenge, peer discussion, and plenty of opportunities for formative assessment and metacognition to deepen understanding of mixed addition and subtraction involving regrouping with 4-digit numbers.