Solve Number Problems

Overview

Age group: Year 4 (8–9 years old)
Duration: 60 minutes
Class size: 30 students
Curriculum link:

• Mathematics Programme of Study – Number: Number and place value and addition and subtraction
• Key Objective: Solve number and practical problems involving positive numbers, including large numbers within 10,000 and context-based problem solving (National Curriculum for England, Year 4)
• White Rose Maths Scheme alignment: Block 1 – Number: Place Value & Block 2 – Number: Addition and Subtraction (Problem solving focus)

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Learning Objectives

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

• Solve practical problems involving addition and subtraction of positive whole numbers (up to 10,000) using efficient written methods.
• Interpret and solve multi-step word problems involving positive numbers.
• Develop reasoning skills by selecting appropriate operations and explaining their problem-solving process.

National Curriculum refs:

• Solve number and practical problems that involve more than one step (Year 4 Mathematics Programme of Study)
• Add and subtract numbers with up to 4 digits using formal written methods of columnar addition and subtraction.

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Resources

• Whiteboards & pens
• Place value counters and digit cards (0–9 digits)
• Problem-solving worksheets adapted from White Rose schemes
• Visual aids (place value charts, number lines)
• Timer/stopwatch for activities
• Mini whiteboards for AFL

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Lesson Outline

1. Engaging Introduction (10 minutes)

Objective: Activate prior knowledge, stimulate curiosity, contextualise problem-solving

• Begin with a real-life story context:
  "Imagine you are planning a school's charity fair. You have £3,587 raised so far and expect to raise another £1,236 on the day of the fair. How much will you have in total?"

• Show the problem visually on the board.

• Ask rapid-fire ‘Think-Pair-Share’:

  • What operation do you think we need to use here? (Addition)
  • Why do you think that?
  • Can we use mental methods here, or do we need a formal method?

AfL: Use mini-whiteboards for quick mental sums (e.g., 587 + 236) – show me your answers! Check for understanding and discuss misconceptions.

• Connect problem to place value knowledge by showing the numbers partitioned into thousands, hundreds, tens and ones.

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2. Modelling with Increasing Complexity (20 minutes)

Step 1: Simple Addition Using Formal Written Methods (5 minutes)

• Model adding two 4-digit numbers using columnar addition without regrouping (e.g., 2,435 + 1,204).
• Think aloud each step: adding ones, tens, hundreds, thousands.
• Show the place value chart to reinforce understanding.
  AfL: Ask individual students to come up and explain each step as you proceed.

Step 2: Addition with Regrouping / Carrying (7 minutes)

• Model a problem where regrouping is needed (e.g., 3,789 + 2,476).
• Highlight the carrying process, explain why it is necessary.
• Pause and ask: What happens if the sum of the tens is greater than 9? Why do we move a digit over?
• Model writing the carried digit on the top of the next column.

AfL: Use mini-whiteboards for students to attempt a similar sum and hold up answers.

Step 3: Multi-step Word Problem involving Addition and Subtraction (8 minutes)

• Present a problem: "At the charity fair, £3,245 was collected on Saturday and £2,917 on Sunday. £1,200 was spent on decorations. How much money is left?"
• Model identifying operations (add money collected, then subtract expenses).
• Solve step-by-step using formal addition and subtraction, explaining decisions aloud.
• Show checking strategies (e.g., estimation).

AfL: Pose reasoning question: Could you solve this problem in another way? Why or why not? Collect verbal answers.

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3. Independent / Paired Practice (20 minutes)

• Hand out problem-solving worksheets with a range of problems escalating in difficulty and real-life context:

  • Simple addition and subtraction within 10,000 (using formal written methods).
  • Two-step word problems involving positive numbers.
  • A reasoning challenge: Explain how they solved a given problem.

• Circulate to provide scaffolded support, prompting key questions:

  • Have you lined up your numbers correctly?
  • Can you explain your method?

AfL: Use exit tickets at 5-minute intervals: select 3–4 students to write a quick sentence explaining their method/answer to a chosen problem. Review these to assess understanding and adjust future lessons.

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4. Plenary (10 minutes)

• Conduct a quiz-style recap with 5 quickfire questions moving from simple to complex, e.g.:

  1. Add 2,540 + 1,330 (no regrouping)
  2. Add 4,765 + 3,728 (with regrouping)
  3. Solve: £1,234 + £2,345 - £1,500 = ?
  4. Which is bigger: 5,632 + 2,198 or 6,500 + 1,200? Explain.
  5. Explain in your own words why it is important to align numbers by place value when adding.

• Encourage students to explain their answers orally or write on mini-whiteboards.

AfL: Use ‘traffic light’ cards for students to self-assess their confidence with today’s learning: Green = confident, Amber = some help needed, Red = need more support.

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Differentiation

• Support: Use digit cards & place value charts to scaffold modelling and independent tasks. Encourage peer support.
• Challenge: Include problems with larger numbers, comparisons, and multiple steps involving estimated checks and explanations.

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Assessment Opportunities & Use of AfL

• Throughout mini-whiteboard tasks for live feedback.
• Use of exit tickets during independent work to assess understanding.
• Oral questioning during plenary to assess reasoning and confidence.
• Teacher marking of reasoning explanations for insight into conceptual grasp.

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Reflection / Next Steps

• Record common misconceptions (e.g., errors in carrying, misunderstanding when to add or subtract).
• Plan targeted intervention or extension based on exit ticket responses.

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This detailed, engaging lesson plan leverages storytelling and context to engage Year 4 learners, follows the National Curriculum expectations, and aligns with the White Rose Maths scheme to progressively build problem-solving confidence with positive numbers. The use of varied AfL strategies ensure ongoing assessment and adjustment to meet learners’ needs.