National Curriculum Links

• Mathematics Programmes of Study: Year 4 (Number - Fractions):
  "Recognise and show, using diagrams, families of common equivalent fractions."
  "Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten."
  "Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number."
• Aligned with White Rose Maths Scheme: Block 4 - Fractions (Week 3-4 focus on calculating fractions of a quantity).

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Learning Objectives

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

• Understand how to calculate fractions of a given quantity confidently (e.g., find 3/4 of 20).
• Apply multiplication and division strategies to solve fraction of quantity problems.
• Justify their mathematical thinking using precise vocabulary and reasoning.

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Success Criteria

I can:

• Identify the numerator and denominator in a fraction.
• Divide the quantity by the denominator and multiply by the numerator to find the fraction.
• Explain and justify my method and answer using the correct mathematical language.
• Solve increasingly complex problems involving fractions of quantities.

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Resources Required

• Whiteboard and markers
• Mini whiteboards and pens for students
• Printed question cards or slides
• Visual fraction bars or fraction circles
• Exercise books

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Lesson Structure

1. Introduction (10 minutes)

Engaging Starter - Retrieval Practice on Rounding (5 mins)

Pose 3 quick questions on Year 4 rounding skills to activate prior knowledge and mental agility. Write on board or say aloud:

• Round 246 to the nearest 10. Explain why.
• Round 18.76 to the nearest whole number. How do you decide?
• Round 5,682 to the nearest 1000 and justify your choice.

Ask: "Why is rounding helpful when solving problems?"

AfL: Use mini whiteboards here to check for understanding quickly. Pupils write answers simultaneously showing reasoning.

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Introduction to Fractions of a Quantity (5 mins)

• Show a visual example: "Imagine I have 20 chocolates."
• Write a fraction question: “What is 1/4 of 20?”
• Use fraction bars or draw the chocolates divided into 4 equal groups.

Questioning:

• "What does the denominator tell us to do with the chocolates?" (Bloom's Remembering/Understanding)
• "How would you divide 20 into 4 groups equally?" (Understanding)
• "If one group has some chocolates, how can we find the amount in 1/4?"
• "What would happen if I wanted 3/4 of the chocolates?" (Applying)

AfL: Verbal questioning to assess pupils’ conceptual understanding and use of correct terminology.

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2. Modelling (10 minutes)

Step-by-step example for children to copy into books:

Calculate 3/5 of 25.

1. Divide the total quantity by the denominator: 25 ÷ 5 = 5
2. Multiply the result by the numerator: 5 × 3 = 15
3. Therefore, 3/5 of 25 = 15

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Explicit teaching points:

• Always start by dividing by the denominator to split the whole into equal parts.
• Then multiply the number of parts needed (numerator).
• Write key vocabulary on the board: numerator, denominator, quantity.

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Scaffolded example for pupils:

Find 2/7 of 35.

• What operation will you do first?
• Why do we divide by 7?
• After dividing, how will you find 2 parts?

AfL: Ask pupils to write down the steps in their books and explain aloud to partner. Teacher circulates, offering immediate feedback.

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3. Guided Practice (15 minutes)

Gradual Complexity Task (grouped by difficulty):

Task Level	Question Examples	Focus
Level 1 (Basic)	Find 1/4 of 16; Find 3/10 of 50	Single step, whole number answers
Level 2 (Medium)	Find 3/8 of 64; Find 5/6 of 36	Larger quantities, tricky division but answers are whole numbers
Level 3 (Challenge)	Find 7/10 of 90; Find 9/12 of 96; Find 4/5 of 75	Apply multiple steps, encourage reasoning about divisibility

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Questioning for deeper thinking (whole class):

• "Why is dividing by the denominator important before multiplying?" (Understanding)
• "Can you explain why 3/5 of 25 is not the same as 5/3 of 25?" (Analysing)
• "How might you check that your answer is reasonable?" (Evaluating)
• "If I increased the quantity from 25 to 50, how would the answer change? Why?" (Creating)

AfL: During practice, use mini whiteboards or exit cards for pupils to write answers and explanations. This gives immediate insight into misconceptions.

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4. Common Misconceptions & Difficulties (5 minutes)

• Misconception: Pupils multiply numerator by the quantity directly without dividing first.
  Clarify by revisiting the meaning of denominator: split into equal parts first.
• Difficulty: Understanding why division comes before multiplication in this context.
  Use visual aids and concrete examples.
• Misconception: Confusing numerator and denominator order or meaning.
  Reinforce vocabulary with flashcards or visuals.
• Over-generalising fraction rules: Applying fraction calculations to non-whole number results without checking context.

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5. Plenary (5 minutes)

Reflective questioning and consolidation:

• "Explain to me in your own words how to find 2/3 of 18."
• "Why is it important to divide before multiplying when working with fractions of quantities?"
• "Can you find 4/5 of 25? Tell us how you did this and why your method works."
• "Imagine you get stuck on a problem involving fractions of a quantity. What strategy would you use to break it down?"

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Quick self-assessment

On mini whiteboards, pupils rate their confidence:

• Green: I understand and can calculate fractions of quantities confidently.
• Yellow: I need some more practice but I understand the method.
• Red: I’m confused and need help.

Collect these to help plan next steps.

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Summary of AfL Opportunities

Stage	AfL Strategy	Purpose
Retrieval Practice	Mini whiteboards	Check prior knowledge and reasoning
Introduction	Verbal questioning	Assess conceptual understanding
Modelling	Partner explanations, questioning	Consolidate steps and vocabulary use
Guided Practice	Mini whiteboards & exit cards	Monitor progress & identify misconceptions
Plenary	Confidence self-rating, oral sharing	Reflect and plan next steps

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This detailed, engaging lesson plan builds upon Year 4 National Curriculum objectives and White Rose guidance to enable pupils to master fractions of quantities, promoting reasoning and mathematical communication throughout.