Overview

Duration: 60 minutes
Class Size: 30 pupils
Year Group: 4
National Curriculum Reference:

• Mathematics – Number – Addition and Subtraction
• Pupils should be taught to:
  • Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why (NC Year 4 Programme of Study)

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Learning Objectives

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

• Solve two-step addition and subtraction problems involving 4-digit numbers.
• Choose the correct operation (addition or subtraction) for each step in a problem.
• Explain and justify their choice of operations and methods.
• Work systematically through problems to find solutions.

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Success Criteria

I can:

• Read and understand two-step word problems involving 4-digit numbers.
• Decide whether to add or subtract in each step.
• Solve the problem accurately using column addition and subtraction methods.
• Check my answers and explain my reasoning clearly.

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Resources Needed

• Whiteboards and pens
• Student books
• Printed question cards for group tasks
• Place value charts for 4-digit numbers
• Visual aids showing column addition and subtraction methods
• Number line (optional)

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Introduction (10 minutes)

Engagement Strategy:
Begin with an exciting scenario: “Imagine you’re a town planner and need to solve problems about the number of people entering and leaving a large event.” Display the problem:

"At a music festival, 3,476 people arrived in the morning. Later, 1,289 more came. After lunch, 2,178 people left. How many people are there now at the festival?"

Use a clear visual (e.g., counters or a pictorial representation) to represent numbers.

Whole-Class Questions (encouraging reasoning):

1. What information are we given? (Understanding)
2. What is the first step we should do? Why? (Applying)
3. Which operation will you use first? Add or subtract? Explain your thinking. (Analysing)
4. After you solve step one, what will you do next? (Sequencing)
5. How can you check your answer is correct? (Evaluating)

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Modelling (15 minutes)

Step 1: Understanding the problem

• Read the problem aloud together.
• Underline keywords (arrived, more came, left) and link them to addition or subtraction.

Step 2: Set out the first calculation

• Model column addition for 3,476 + 1,289:
  • Show carrying/ regrouping explicitly.
  • Emphasise place value.

Step 3: Set out the second calculation

• Model column subtraction for the total - 2,178:
  • Show borrowing/regrouping explicitly.
  • Explain how to check subtraction by addition.

AfL Points:

• Ask pupils to explain why we add first and subtract second.
• Pause and ask: “What might happen if we subtract first? Why is order important here?”
• Ask pupils to identify where they “carry” or “borrow” in the method.

Example to copy into books:

Step	Calculation	Explanation
1	3476 + 1289 = 4765	Add people who arrived in morning + more came. Column addition, regrouping/carry tens.
2	4765 – 2178 = 2587	Subtract those who left. Column subtraction, borrowing. Check by adding result + number left to get total.

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Guided Practice (20 minutes)

Task: Pupils work on two-step word problems with 4-digit numbers. Start with simpler numbers, then progressively increase difficulty by:

• Including larger numbers that require multiple regrouping steps.
• Varying context (e.g., money, distances, populations).
• Mixing problems where the two steps are addition then subtraction, or subtraction then addition.

Examples:

1. “A library had 4,823 books. They bought 1,256 more and then lent out 2,143 books. How many books are left in the library?”
2. “There were 9,564 visitors at a zoo. 3,417 left in the afternoon, and 1,829 arrived later. How many visitors are there now?”

Targeted questions during work:

• Why did you choose to add/subtract first? Please explain your reasoning. (Explain)
• How did you carry/ borrow in your calculation? (Understanding)
• What strategy did you use to check your answer? (Evaluating)
• Could there be a different order of operations? What would happen then? (Analysing)

Physical Activity Variation (Optional): Pupils pair up and explain their method and answer to each other orally before writing. This builds confidence and reasoning.

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Addressing Common Misconceptions and Areas of Difficulty

Misconception / Difficulty	Strategy to Address
Confusing when to add or subtract	Use vocabulary focus on keywords; underline in problems. Use ‘increase’ vs. ‘decrease’ visuals.
Forgetting the order of operations	Emphasise sequencing; use arrows to show problem steps.
Errors in regrouping (carrying or borrowing)	Highlight place value with place value charts. Model carefully with varied numbers. Use counters or base-ten blocks as aids.
Not checking answers or just guessing	Model checking methods (inverse operations). Encourage peer checking.
Writing disconnected numbers, not aligning columns properly	Explicitly model careful setting out in columns with place value headings.

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Plenary (10 minutes)

Activity: 'Explain to the Expert'
Select 3 pupils (or groups) to explain one of the two-step problems and their reasoning to the whole class with visual aids.

Whole-class reflection questions:

• What was the most helpful strategy you used today? (Reflecting)
• Why is it important to solve problems step-by-step? (Understanding)
• Can you think of real-life situations where this might be useful? (Applying)
• How would you help a friend who found regrouping tricky? (Creating a strategy)

Quick AfL: Use thumbs up/down or mini whiteboards to answer:

• Do you feel confident solving two-step problems now?
• What is one thing you found tricky and how did you overcome it?

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Extension Activity (for early finishers or homework)

Create your own two-step word problem involving 4-digit numbers related to something you like (e.g., sports scores, money, books) and solve it. Then exchange problems with a partner and check each other’s reasoning.

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Alignment with White Rose Maths Scheme

• This lesson corresponds with the Year 4 Block 1: Number – Place Value & Addition and Subtraction units from White Rose, with focus on applying addition and subtraction strategies to increasingly complex, multistep problems involving larger numbers.
• Pupils use formal written methods (column addition and subtraction) as recommended.
• Emphasis on solving word problems and reasoning corresponds closely with White Rose's emphasis on problem-solving and reasoning fluency.

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Summary

This lesson plan ensures Year 4 pupils develop strong, confident skills in solving two-step addition and subtraction problems involving four-digit numbers, with a clear structure to help pupils reason and articulate their methods. It blends explicit modelling, scaffolded practice, deep questioning, and targeted assessment for learning, adhering strictly to the National Curriculum and the White Rose Maths philosophy.