Mastering Written Subtraction

Overview

A 60-minute lesson for Year 4 pupils to develop a thorough understanding of the formal written method for subtraction, aligning with the National Curriculum for England (Maths Key Stage 2).

---

National Curriculum Links

• Mathematics Programme of Study (Year 4):
  • Number – Addition and Subtraction:
    • “Subtract numbers with up to 4 digits using the formal written method of column subtraction where appropriate.”
  • Working mathematically:
    • Solve problems involving subtraction, including with larger numbers and different steps of calculation.
  • Understanding place value in subtraction calculations.

---

Learning Objectives

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

• Use the formal written method of column subtraction for numbers up to 4 digits confidently.
• Explain the steps and reasoning behind the borrowing (exchanging) process in column subtraction.
• Identify errors and correct misconceptions related to the formal subtraction method.
• Solve subtraction problems involving regrouping with increasing complexity.

---

Success Criteria

Pupils will:

• Set out subtraction calculations in columns correctly (digits aligned by place value).
• Use exchanging (borrowing) where appropriate to subtract digits from a smaller number.
• Explain why exchanging is necessary in specific cases.
• Check their answers for accuracy and reasonableness.
• Apply the method to solve subtraction problems with different contexts.

---

Resources

• Whiteboards and pens (for AFL)
• Notebooks or exercise books
• Example subtraction worksheet with scaffolded steps and varied difficulty
• Place value counters or dienes (optional, for visualisation)
• Visualiser/document camera (if available)
• White Rose Maths scheme materials as reference

---

Lesson Structure

1. Introduction (10 minutes)

Engagement & Contextualisation:

• Begin with a quick mental warm-up: "If I have 4321 cakes and I eat 1589, how many do I have left?"
• Elicit different mental strategies pupils might use and note limitations for larger numbers, introducing the need for a formal written method.
• Show a written subtraction problem on the board:

  4321  
  

• 1589

• Ask learners:
  • “Why can’t we just subtract one column at a time without thinking about the size of the digits?”
  • “What problems might occur if the digit on top is smaller than the one below?”
• Questioning:
  • Remembering: “What is subtraction?”
  • Understanding: “What happens when you subtract a larger digit from a smaller one?”
  • Applying: “How could we ‘borrow’ from another column to help us?”
  • Analysing: “What does borrowing do to the digits involved?”
• Set the context: Formal written subtraction helps us subtract large numbers efficiently and correctly.

AFL: Use mini whiteboards for pupils to write down what they think is “borrowing” or “exchanging” in subtraction in their own words.

---

2. Modelling & Teaching (20 minutes)

Step-by-Step Modelling:

• Use a problem on the board:

  7032  
  

• 4785

• Model first without exchanging to expose why it won’t work.
• Then demonstrate the formal written method with exchanging across columns:
  • Explain how you ‘borrow’ 1 ten from the hundreds place, turning 3 into 2 hundreds and adding 10 to the tens column.
  • Follow the process carefully, emphasizing place value and what happens when you exchange.
• Write an example in books:

    6  9  12  12  
   7  0   3   2  
  

• 4 7 8 5

---

2 2 4 7

- **Explain each step aloud,** modelling clear reasoning:  
- “Here I cannot subtract 5 from 2, so I borrow 1 ten...”  
- “Now, this 10 reduces the next column from 3 to 2…”  

**Common misconceptions & difficulties:**  
- Thinking you subtract from bottom to top instead of top to bottom.  
- Forgetting to decrease the column from which you are borrowing.  
- Not aligning digits correctly by place value.  
- Confusing when to borrow (e.g., borrowing when no need).  
- Mixing up borrowing in tens, hundreds, thousands place.  

---

### 3. Guided Practice (15 minutes)  

**Task:** Pupils complete three subtraction problems of increasing complexity in their books:  

1. *No exchanging required:*  

5243

• 3212

2. One exchange required:

   6421  
   

• 3587

3. Multiple exchanges required:

   7002  
   

• 4839

Targeted whole-class questions:

• “Why did you choose to exchange in this column?”
• “What happens if you don’t exchange here?”
• “How do you check if your answer is reasonable?”
• “Can you explain the effect of borrowing on the different place values?”
• “How do you know when to stop exchanging across columns?”

Encourage answers that justify the process, not just the result.

AFL: Circulate, observe pupils, ask individuals to explain their process aloud or on mini-whiteboards.

---

4. Independent Task (10 minutes)

Application & Problem-Solving:

• Provide word problems involving subtraction requiring formal written methods including exchanging. Examples:
  • “A shop had 7,230 pencils. It sold 3,785 pencils today. How many pencils are left?”
  • “Sarah read 7,002 pages in her book and then read 4,839 more. How many pages did she read in total?” (Change to subtraction scenario)
• Encourage pupils to set out their working neatly and explain their steps in a sentence or two after solving.

---

5. Plenary (5 minutes)

• Use a few examples from the independent task to review common errors and successes.

• Ask reflective questions:

  • “What was the hardest part of the subtraction method today?”
  • “How does borrowing help you subtract bigger numbers?”
  • “If a friend forgot to borrow, how would you explain why their answer might be wrong?”

• Recap success criteria and celebrate pupils meeting these.

---

Assessment for Learning (AfL) Points Throughout

• Introduction: Check understanding of vocabulary using mini whiteboards.
• Modelling: Ask pupils to predict the next step before you write it down.
• Guided Practice: Use questioning to assess reasoning, not just answers.
• Independent Task: Collect books to assess correct method and explanation.
• Plenary: Use pupil feedback to adjust follow-up teaching or to identify specific misconceptions to revisit.

---

Reflection & Next Steps

• Use misconceptions observed to plan targeted small group support.
• Link subtraction written methods to formal addition to build fluency.
• Introduce problem-solving with subtraction and mixed operations next lesson.

---

WOW Factor Idea

Borrowing Role-Play: Use place value counters and pupils as digits in different columns to physically illustrate borrowing — for example, a pupil holding 10 ten counters “gives” 1 ten to the next place. This tangible manipulation deepens conceptual understanding beyond abstract numbers.

---

By following this plan, Year 4 pupils will confidently use the formal written subtraction method with understanding, reflecting the National Curriculum and supported by White Rose Maths standard progression.