Overview

This 45-minute lesson focuses on extending Year 4 pupils’ understanding of calculating fractions of a quantity, aligning with the National Curriculum for England, specifically:

• M4/4.3 Add and subtract fractions with the same denominator (to consolidate)
• M4/5.1 Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators
• M4/5.3 Calculate fractions of a quantity (primary focus)

This lesson builds on prior knowledge of fractions and links decimals and fractions to deepen conceptual understanding.

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Learning Objectives

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

• Calculate fractions of quantities through varied problem-solving contexts.
• Explain their reasoning when finding fractions of amounts.
• Understand the relationship between fractions and decimals in practical calculations.

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Success Criteria

• I can recall how to convert decimals to fractions and vice versa.
• I can calculate a fraction of a quantity accurately using division and multiplication.
• I can explain why my calculation for a fraction of a quantity is correct.
• I can identify and correct common misconceptions when finding fraction quantities.

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Resources

• Whiteboards and pens
• Printed task sheets with progressively challenging questions
• Visual fraction models (bars/pie charts)
• Mini-whiteboards for AFL
• Number cards (fractions and decimals) for retrieval practice
• Example notebook pages for modelling

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National Curriculum Links

• Number – fractions (Y4): Recognise and use fractions as numbers, calculate fractions of a quantity.
• Number – decimals (Y4): Round decimals with one decimal place to nearest whole number.
• Mathematical reasoning and fluency: Explain methods and justify answers (Mathematical talk).

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Lesson Breakdown

1. Introduction and Retrieval Practice (10 minutes)

Engaging Hook:
Display a large box of chocolates with a label: “If I eat 1/4, how many chocolates are left?”
Ask pupils to estimate then calculate. This hooks their natural curiosity and relates fractions practically.

Retrieval Practice:

• Flash rapid-fire questions converting whole numbers into decimals on mini-whiteboards for instant response. Sample questions:
  • What is 3 as a decimal?
  • Convert 7 into a decimal number (e.g., 7.0).
  • Write 0.5 as a fraction.
• Discuss answers briefly, reinforcing prior learning.

Targeted Questions:

• Why is 0.5 equivalent to ½?
• How can recognising decimals help with fractions of quantities?

AfL: Use mini-whiteboards for quick formative assessment. Teacher circulates to read answers, picks volunteers to explain their thinking aloud.

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2. Modelling and Teaching (15 minutes)

Step 1: Revisit basics

• Model calculating fraction of a quantity using simple example:
  Find 1/4 of 20.
  • Write step-by-step in the book: Divide 20 by 4 to find the value of 1 part = 5.
  • Multiply by numerator (if more than 1), e.g. 3/4 of 20: 20 ÷ 4 = 5 × 3 = 15.

Example Copied Into Books:

Example: Calculate 3/5 of 25  
Step 1: Divide 25 by 5 = 5  
Step 2: Multiply 5 by 3 = 15  
Answer: 15

Step 2: Address common misconception

• Problem: “Find 2/3 of 12.” Some pupils might multiply 2 × 12 = 24 or 12 ÷ 2 = 6 without considering fraction meaning.
• Explain why you must divide by denominator first then multiply by numerator.
• Use visual aid (fraction bars or circles).

Targeted Questions (Bloom’s Taxonomy - Applying, Analysing):

• Why do we divide by the denominator first and not multiply?
• Can you explain what would happen if you multiplied first?
• How does the visual model help you understand the method?

AfL:

• Use live questioning to assess understanding. Ask pupils to explain their reasoning orally or on mini-whiteboards.
• Observe common errors and address 1:1 if needed.

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3. Guided Practice with Increasing Complexity (12 minutes)

Task Design:
Start with straightforward calculations, then add complexity by:

• Using non-unit fractions (e.g. 3/4 of 32)
• Introducing word problems involving real-life contexts (e.g. 2/5 of 50 pencils)
• Present scenarios where quantities are not divisible cleanly, encouraging rounding or fractional answers (e.g. 2/3 of 14).

Sample Questions:

1. Find 4/5 of 20.
2. Sarah ate 3/8 of her pizza that was cut into 24 slices. How many slices did she eat?
3. Liam drank 2/3 of 15 litres of juice. How much did he drink?

AfL:
Circulate and ask pupils to explain their methods. Pick some to share and justify answers aloud:

• "Explain why you divided first and then multiplied."
• "What strategies did you use if the number wasn’t divisible evenly?"

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4. Plenary (8 minutes)

Problem with Misconception & Reflection:
Present this problem:
“Jenny said 2/3 of 18 is 12 because she multiplied 2 × 18. Is she correct? Why or why not?”

• Ask pupils to discuss in pairs, then share with the class their reasoning.
• Encourage explanations using visual models or stepwise calculations.

Deeper Thinking Questions:

• What is the mistake in Jenny’s approach?
• How can you prove that your method is correct?
• Could Jenny’s thinking work for any fractions? Why?

Wrap-Up:

• Summarise key steps to finding fractions of quantities.
• Revisit success criteria.
• Ask pupils to self-assess their confidence using criteria.

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Extension Idea (if time allows or for homework)

Create a ‘fraction of quantities’ challenge where pupils find fractions of quantities with more complicated numbers and explain their reasoning in writing. Encourage use of drawings or diagrams to support.

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Summary of AFL Points

• Retrieval practice: Mini-whiteboard answers for decimals and fractions.
• Modelling: Ask pupils to explain steps during live modelling; check understanding via Q&A.
• Guided Practice: Focused questioning to probe reasoning; live feedback and error correction.
• Plenary: Group discussion and justification of misconceptions to deepen conceptual understanding.

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Alignment with White Rose Maths Scheme

This lesson complements White Rose Maths Block 5: Fractions – Calculate fractions of amounts (Summer Term, Year 4). It mirrors the approach of concrete-pictorial-abstract learning, embedding reasoning skills and addressing known misconceptions.

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Summary

Phase	Timing	Key activities	AfL
Introduction	10 mins	Chocolate example + decimals-fractions retrieval practice	Mini-whiteboards, questioning
Modelling	15 mins	Stepwise fraction of quantity example; exploring misconceptions	Live questioning, oral explanations
Guided practice	12 mins	Graduated fraction tasks with real-life context	Circulate, targeted Q&A
Plenary	8 mins	Misconception problem; reflection and reasoning	Peer discussion, self-assessment

This structured lesson supports mastery of calculating fractions of quantities, promotes higher-order thinking via questioning, and uses formative assessment to ensure all pupils progress confidently.