Solving Mixed Money Problems

National Curriculum Links

• Mathematics – Year 4
  • Number – money: Solve problems involving money, including giving change (NC Programme of Study)
  • Mathematics – Year 4:
    • Use all four operations to solve problems involving measure [money], including simple fractions and decimals to two decimal places (NC)

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Learning Objectives

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

• Understand and interpret mixed money word problems involving addition, subtraction, and giving change.
• Choose appropriate operations and reason through multi-step problems involving pounds (£) and pence (p).
• Explain and justify their problem-solving strategies clearly using mathematical vocabulary.

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Success Criteria

I can:

• Identify the key information and amount(s) in a money word problem.
• Decide which calculation(s) to use to solve the problem involving pounds and pence.
• Show my working method clearly using column addition and subtraction with money.
• Explain my reasoning when solving money problems.
• Check my answer makes sense in the context of the question.

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Lesson Structure (30 minutes)

1. Introduction (6 minutes)

Engagement Hook:

• Start with a quick interactive story: “Imagine you have £5.00 to spend at a school fair. You want to buy a drink for £1.45, some crisps for 85p, and a toy for £2.35. How much money will you have left?”

Ask:

• "What information are we given?"
• "What do we need to find out?"

Use a visual place-value chart with pounds and pence displayed to help visualise the amounts.

Purpose:
To activate prior knowledge on addition and subtraction with money and set the context for multi-step problem solving.

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2. Teaching and Modelling (12 minutes)

Step 1: Analysing the Problem

• Write an example problem clearly on the board (see below).
• Underline key information and identify necessary steps.
• Model how to represent the first calculation using column addition/subtraction.
• Show how to convert pence to pounds (£1.45 = 1p + 45p) for clarity and consistency.

Example for pupils to copy:

At a toy shop, Tom has £10. He buys a game costing £3.75 and a book costing £4.60. How much money does he have left?

Step 1: Add the cost of both items: £3.75 + £4.60
Step 2: Subtract the total from £10

Progressive Modelling:

• Model clear column addition of £3.75 + £4.60 = £8.35
• Model subtraction £10.00 − £8.35 = £1.65

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3. Targeted Questioning (Whole Class Discussion)

Use Bloom’s Taxonomy for questioning, continually encouraging explanation and justification:

• Remembering:
  What is the total cost of the game and book?
• Understanding:
  Why do we add the prices first, rather than subtract?
• Applying:
  If Tom had £12 instead of £10, would the remaining money be more or less? Why?
• Analysing:
  What would happen if we subtracted first and then added? Would the answer be right? Explain your reasoning.
• Evaluating:
  How can we check if our answer makes sense?
• Creating:
  Can you write your own money problem involving two items and solve it?

AfL (Assessment for Learning) points:

• After modelling, ask a pupil to explain the steps aloud to check understanding.
• Use mini-whiteboards: pose a quick question for pupils to work out £5.20 − £2.45; check responses.
• Use thumbs up/down after explanation questions to quickly assess confidence.

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4. Independent Practice Activity (8 minutes)

Task with Increasing Complexity:

• Level 1: Simple two-step problems (addition then subtraction with money).
• Level 2: Problems that require finding total cost, then calculating change.
• Level 3: Multi-step word problems with an extra twist (e.g., discounts, multiple items, or differing currencies like pounds and pence).

Example problems to try:

1. Sarah has £8. She buys a sandwich for £2.50 and a drink for £1.75. How much money does she have left?
2. A pack of pencils costs £1.25. Joel buys 3 packs. How much does he spend? He pays with £5. How much change does he get?
3. Mia has £10 and buys 2 toys costing £3.45 and £4.90. She finds some coins on the floor worth 85p. How much money does she have now?

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5. Plenary (4 minutes)

• Ask 2-3 pupils to explain their solving method for a money problem they completed. Focus on clarity of explanation and justification.
• Revisit learning objectives and success criteria.
• Quick-fire quiz: Pupils write one thing they found easy and one thing they found tricky about money problems. Discuss common tricky points.

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Common Misconceptions and Difficulties

• Confusing addition and subtraction steps or the order in which they need to be applied.
• Difficulty aligning decimal points or understanding that 100p = £1 (leading to errors during column calculations).
• Forgetting to convert pence or mixing pounds and pence incorrectly in calculations.
• Misunderstanding ‘change’ as subtraction from the cost instead of from the money given.
• Skipping reading the full problem, leading to incomplete or incorrect solutions.

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Additional Notes

• Aligns with White Rose Year 4 Block on Money and Problem-Solving.
• Encourage use of concrete resources (coins, notes) if possible for kinaesthetic learners.
• Encourage clear written methods, and work towards mental methods for familiar amounts over time.

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End of Lesson Plan