Adding and Subtracting

National Curriculum Links

• Mathematics: Number – Addition and Subtraction
  Pupils should be taught to:
  • add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate
  • estimate and use inverse operations to check answers to a calculation
  • solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why

Learning Objectives

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

• Use the formal written methods of columnar addition and subtraction to add and subtract numbers with up to 4 digits, including missing number problems.
• Justify their reasoning by explaining the method they chose to find missing numbers in calculations.
• Estimate answers and use the inverse operation to check their work confidently.

Success Criteria

• I can set out addition and subtraction calculations correctly in columns.
• I can use number facts and place value to find missing numbers in column addition and subtraction calculations.
• I can explain my thinking and how I checked my answer using inverse operations.
• I can solve increasingly complex missing number problems involving addition and subtraction with 4-digit numbers.

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Lesson Overview (30 minutes)

Time	Activity
0-5	Introduction & Engagement
5-15	Modelling & Guided Practice
15-25	Independent/Paired Work (increasing complexity)
25-30	Plenary & AfL

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Introduction (0-5 minutes)

Engage pupils with a real-life scenario:

“Imagine we’re managing a museum’s ticket sales for a day. Yesterday, they started the day with 3,682 visitors recorded. They then sold 2,147 tickets in the morning. By lunchtime, we want to know how many visitors there are in total. How can we find this out?”

• Write this calculation on the board:

  3,682 + 2,147 = ?

• Quickly recap using informal methods, then introduce the formal written method with a clear step-by-step on how to set the numbers out in columns.

Questioning using Bloom's Taxonomy:

• Remembering: What are the place values of each digit in these numbers?
• Understanding: Why do we start adding from the ones column?
• Applying: Can you explain what happens when the sum of a column goes above 9?
• Analysing: How do you know where to put the carried number?
• Evaluating: Why is it helpful to check your answer using the inverse operation?
• Creating: How might you use this method to find a missing number?

Common misconceptions:

• Pupils confusing place value, especially when carrying over.
• Adding from left to right instead of right to left.
• Ignoring the carried numbers or subtracting incorrectly in the borrowed digits process.
• Misunderstanding how to set up missing number calculations (e.g., missing addend or subtrahend).

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Modelling and Guided Practice (5-15 minutes)

Step 1: Model the formal written method of addition and subtraction with 4-digit numbers including missing-number problems.

Example on board for column subtraction:

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

Ask pupils:

• What could the missing number be?
• How do we find the missing number? (Encourage reasoning)
• Can you explain your steps out loud?

Use sentence stems for reasoning:

• “I think the missing number is ___ because...”
• “When I check my answer using inverse operation, I...”

Set a timer for 1 minute for discussion and explanation before writing.

Assessment for Learning (AfL) points:

• Use thumbs up/down or mini whiteboards to check understanding during modelling.
• Ask pupils to explain the process verbally to a partner or the class (active reasoning).
• Spot misconceptions by listening carefully to explanations and address immediately.

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Task: Increasing Complexity (15-25 minutes)

Task 1: (Simple missing number addition)

  1 2 4 7  
+ ? 3 5 8  
---------
  2 6 0 5

Task 2: (More complex subtraction with borrowing and missing number)

  6 ? 2 5  
- 3 4 7 8  
----------
  2 8 5 7

Task 3: (Two-step problem with explanation)
Sara had a collection of 4,536 stamps. She gave some to her friend and then bought 1,247 more. Now she has 5,698 stamps. How many did she give away?

• Set out calculation as a missing number subtraction and explain how to find that number.

Layered questioning during tasks:

• How do you decide which digit to subtract first?
• How does borrowing work here?
• Can you estimate whether your answer is reasonable?
• How would you check your answer using addition?
• Why might using the inverse be a better way to check than re-working the subtraction?

AfL:

• Monitor pupils’ work and ask explaining questions individually.
• Use quick ‘show me’ signals for confidence before moving on.

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Plenary (25-30 minutes)

Use a proving/reasoning question for active discussion:

Question:

In this subtraction, why do you think the missing digit in the hundreds place is 4?

  7 1 4 3  
- 3 4 ? 8  
----------
  3 7 9 5

Ask pupils to discuss with a partner using sentence stems:

• “I think the missing digit is __ because…”
• “I know this because when I add ___ back, it equals…”
• “If the digit was different, the calculation would be…”

Set a 2-minute timer for verbal explanation before pupils write their response.

Final AfL:

• Collect written reasoning to assess understanding and plan next steps.
• Use pupils’ verbal feedback to clarify misconceptions or extend thinking in next lessons.

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Additional Teacher Notes

• Align resources with White Rose Maths Scheme terminology and progression (including columns, place value, carrying and borrowing).
• Reinforce vocabulary: sum, difference, digit, place value, carry, borrow, missing number, inverse operation.
• Use visual aids such as place value charts and counters for pupils needing more concrete understanding.
• Encourage peer explanation to consolidate learning and deepen reasoning skills.

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End of Lesson Plan.