Formal Written Addition

Overview

This 60-minute lesson supports Year 4 pupils in mastering the formal written method to add 4-digit numbers, aligned with the National Curriculum for England and White Rose Maths Scheme (Summer Term, Block 1: Addition and Subtraction).

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National Curriculum Links

Mathematics Programmes of Study (Year 4):

• Number – addition and subtraction
  • Pupils secure addition and subtraction facts to 1,000 and fluently add and subtract numbers with up to 4 digits using the formal written methods of columnar addition. (NC Statement)
• Use of place value and efficient written methods to solve problems.

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Learning Objectives

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

• Use the formal written column method to add two 4-digit numbers accurately.
• Understand and apply place value concepts to carry digits correctly.
• Explain their reasoning and justify their solution strategies using mathematical vocabulary.

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Success Criteria

• I can set out 4-digit numbers correctly in columns.
• I can add ones, tens, hundreds, and thousands columns in the right order.
• I know when and how to carry a digit to the next place value.
• I can check my work and explain my thinking clearly.

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Resources

• Whiteboard and markers
• Visual place value charts
• Individual mini-whiteboards and pens for pupils
• Example worksheet with 4-digit addition problems
• Place value counters (optional to support kinesthetic learners)
• Example for pupils to copy into books

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Lesson Structure

1. Introduction & Engagement (10 minutes)

Goal: Engage pupils and review prior knowledge of addition and place value.

• Start with a quick mental warm-up: "Let’s add 1,234 + 2,345 in our heads. How might we do that?" (Q encourages pupils to think about mental strategies.)
• Share a brief story context: “Imagine you have 1,234 LEGO bricks, and your friend gives you 2,345 more. How many bricks do you have now?”
• Use a place value chart on the board showing the digits lined up: Thousands | Hundreds | Tens | Ones.
• Highlight the value of each digit and emphasise neat, aligned column placement.

Key Questions (using Bloom’s Taxonomy):

• Remembering: What does each digit represent in this number?
• Understanding: Why is it important to line the numbers up correctly when adding?
• Applying: Can you explain what happens when the digits in one column add up to more than 9?
• Analysing: What strategies could we use to carry numbers to the next column?
• Evaluating: How would you check your answer is correct?
• Creating: Can you come up with your own 4-digit addition problem and explain the steps you would use?

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2. Modelling (15 minutes)

Goal: Demonstrate the formal written method and highlight common misconceptions.

• Present the example problem:
  4,278 + 3,657

• On the board, model the column addition step-by-step:

  	4	2	7	8
  +	3	6	5	7
  =	?	?	?	?

• Add the ones column: 8 + 7 = 15. Write 5, carry 1 to the tens.

• Tens column: 7 + 5 + 1 = 13; write 3, carry 1 to the hundreds.

• Hundreds column: 2 + 6 + 1 = 9; write 9.

• Thousands column: 4 + 3 = 7; write 7.

• Final answer: 7,935

Address Common Misconceptions:

• Pupils forgetting to carry over the extra digit.
• Misalignment leading to adding incorrect place values (e.g., tens with hundreds).
• Not adjusting the carry digit appropriately (e.g., carrying a 2 instead of 1).
• Adding digits incorrectly in their place values.

AfL Opportunities:

• After each column, ask targeted questions: "What did I do first here? Why did I write a 5 and carry 1?"
• Invite pupils to explain why we "carry" digits in column addition.
• Use mini-whiteboards for pupils to solve a similar column as a check-in – for example, add 6,789 + 4,328 (focus on the ones column first).

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3. Guided Practice (15 minutes)

Goal: Pupils practise the formal method with teacher guidance and peer discussion.

• Present 3 similar 4-digit addition problems on the board:
  1. 5,463 + 2,379
  2. 1,785 + 6,247
  3. 7,532 + 4,888
• Pupils work in pairs using whiteboards or books to set out and complete the calculations.
• Circulate, targeting support and scaffolding understanding, highlight any misalignment or incorrect carrying immediately.

Targeted Questions to Use:

• How do you know where to carry the digit?
• Can you explain why you added these two digits first?
• What would happen if you forgot to carry here? How would your answer change?
• Is there a way to check if your answer could be right without doing the calculation again?

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4. Independent Work (10 minutes)

• Pupils copy the example below into their books and complete 2 similar addition problems independently:

Example to copy:

  5  3  9  7  
+ 2  6  4  5  
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• Then solve:

1. 4,216 + 3,789
2. 7,345 + 1,456

• Pupils encouraged to write full sentences explaining their method and any challenges.

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5. Plenary & Review (10 minutes)

• Choose 3 pupils to explain their reasoning for the independent addition out loud.

• Use a few prepared higher-order questions:

  • How does knowing place value help you in adding large numbers?
  • Can you think of situations where adding 4-digit numbers might be useful in everyday life?
  • If you had to teach a friend how to add 4-digit numbers using this method, what key advice would you give them?
  • Why is it important to check your work and how could you do so quickly?

• Recap the success criteria by asking pupils to self-assess.

• Highlight the vocabulary: place value, column addition, carry, digits.

AfL:

• Use thumbs up/down to check confidence.
• Pinpoint common errors to address in future lessons.

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Additional Notes for Teachers

Differentiation:

• Provide number lines or place value cards for pupils needing extra support.
• Extension: Challenge confident pupils with 4-digit addition that requires multiple carryovers or adding three numbers.

Common Areas of Difficulty:

• Place value misunderstanding causing misalignment
• Forgetting to carry or incorrectly carrying digits
• Anxiety or low confidence with multi-step addition

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Summary

This lesson builds on Year 3 prior knowledge and carefully scaffolds pupils towards using the formal written method for 4-digit addition. Embedded questioning encourages mathematical reasoning beyond simple recall. Continuous AfL supports targeted feedback to enhance attainment aligned with both the National Curriculum and White Rose Maths progression.