National Curriculum Links

Mathematics Programme 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 100 and dividing tenths by 10.
  • Find equivalent fractions.
  • Add and subtract fractions with the same denominator.
  • 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. (Focus for this lesson)

• Number – Multiplication and Division:

  • Recall multiplication facts up to 12 × 12.
  • Use place value, known and derived facts to multiply and divide mentally, including multiplying by 0 and 1; dividing by 1; recognising and using factor pairs and commutativity in mental calculations. (Relevant for retrieval practice)

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Learning Objective

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

• Calculate fractions of a quantity using multiplication and division with both unit and non-unit fractions.
• Explain the process used to find fractions of quantities and justify their reasoning using fraction and multiplication vocabulary.

Success Criteria

I can:

• Identify the fraction and the whole quantity given.
• Divide the quantity by the denominator to find one part.
• Multiply the one part by the numerator to find the fraction of the quantity.
• Explain my method clearly and use correct mathematical language.
• Solve fraction of quantity problems with increasing difficulty.

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Lesson Duration: 45 minutes

Class size: 30 students

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Lesson Structure

1. Retrieval Practice (5 minutes): Multiplication Facts

Purpose: Refresh fluency in multiplication to support fraction calculation.

• Quick-fire oral quiz: Multiplication facts tables 1–12 (e.g. 7 × 8, 9 × 6, 12 × 4).
• Write three multiplication calculations in books and solve mentally.
• Challenge question: Explain how you can use factor pairs to find 9 × 6 quickly.

AfL: Use mini-whiteboards for pupils to write answers; monitor and address misconceptions in real-time.

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2. Engaging Introduction (5 minutes)

Scenario: "Imagine you have 24 sweets and your friend gives you 1/3 of them. How many sweets did you get?"

• Show a bag with 24 sweets (picture or physical objects).
• Ask: "How can we find 1/3 of 24?"
• Discuss different ideas from pupils, encouraging them to explain.
• Use visual models (drawing 24 sweets grouped into 3 equal piles).

High-Quality Questions:

• Why is it helpful to divide sweets into equal groups when finding a fraction?
• How does the denominator tell us what to do with the whole quantity?
• What would happen if we tried to multiply first? Would that make sense? Why?

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3. Modelling: Step-by-Step Method (10 minutes)

Example to copy into books:

Find 3/4 of 20

1. Identify the whole: 20 sweets (quantity)
2. Look at the denominator (4) – this tells us how many equal parts to divide the whole into.
3. Divide 20 by 4: 20 ÷ 4 = 5 (one part)
4. Look at the numerator (3) – how many parts we want.
5. Multiply one part by numerator: 5 × 3 = 15

So, 3/4 of 20 is 15.

Demonstrate visually with bar model or counters.

AfL 1: After step 3, ask pupils to use mini-whiteboards: “What is 1/4 of 20?”
AfL 2: After step 5, ask: “Explain why we multiply after dividing.”

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4. Whole Class Guided Practice with Bloom’s Questioning (10 minutes)

Work through these progressively with the class, challenging reasoning:

Fraction Problem	Question using Bloom’s Taxonomy
1/5 of 25	Remembering: What is the denominator and what does it mean here?
2/6 of 18	Understanding: Why do we divide 18 by 6 first?
3/8 of 32	Applying: Can you show me how to calculate this step by step?
5/10 of 40	Analysing: What patterns can you see between the denominator and the division?
3/4 of 28	Evaluating: If someone multiplies 3 by 28 directly, why would that be incorrect? What is wrong with that reasoning?
7/7 of 14	Creating: Can you make a word problem that uses 7/7 of a quantity and solve it?

Pupils explain their reasoning aloud; teacher records key approaches on the board.

AfL: Use targeted questioning and cold-calling to ensure all pupils are engaged and understanding their reasoning.

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5. Independent Task: Increasing Complexity (10 minutes)

Task progression:

• Level 1: Find fractions of quantities where answers are whole numbers (easy denominators). (e.g., 1/2 of 18; 3/4 of 16)
• Level 2: Introduce non-unit fractions and word problems requiring extra steps (e.g., share 36 pencils into 6 equal groups, then find 4/6 of them).
• Level 3: Apply fractions of quantities where answer is larger or more abstract, including where the whole number is multiple 100 (to link with hundredths). Include reasoning questions.

Example task for book copy:

1. Find 2/5 of 35.
2. Find 4/7 of 49.
3. Olivia has 48 marbles. She gives 3/8 of them to her brother. How many does she give him? Explain your steps.

Challenge:
Find 5/10 of a quantity without dividing first. Explain why dividing first may still be the best method.

AfL: Circulate, question pupils, and provide on-spot support for misconceptions such as trying to multiply numerator and denominator directly or misunderstanding the role of division.

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6. Common Misconceptions & Difficulties

• Misconception: Multiplying numerator directly by the whole quantity without dividing by the denominator first (e.g., thinking 3/4 of 20 = 3 × 20 = 60).
• Difficulty: Understanding the role of the denominator as “how many equal parts” and that division comes first.
• Confusion: Treating fractions as decimals; mixing up numerator and denominator roles.
• Error: Not identifying the whole quantity correctly, especially in word problems.

Address these by: Using visuals (bar models, counters), checking understanding with mini-whiteboards, and precise questioning.

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7. Plenary: Reflective Discussion (5 minutes)

• Ask pupils to explain, in their own words, the steps to find a fraction of a quantity.

• Pose reflective questions:

  • Which step do you find the easiest/difficult? Why?
  • Can you think of real-life examples where you need to find fractions of quantities?
  • How does understanding multiplication help you here?

• Share some answers aloud. Celebrate different approaches and emphasise correct mathematical reasoning.

AfL: Use exit tickets with one question: "Write one sentence explaining how to find 3/4 of a quantity." Use responses to inform next lesson planning.

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Resources Needed

• Mini-whiteboards and pens
• Counters or sweets (real or images)
• Visual fraction bars or drawings
• Worksheets with fraction quantity problems
• Interactive whiteboard for modelling

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Summary

This lesson is designed to build on prior multiplication knowledge and explicitly teach Year 4 pupils how to calculate fractions of a quantity accurately using the White Rose Maths approach and National Curriculum objectives. Through careful scaffolding, visual aids, formative assessment points, and challenging questioning, pupils develop sound conceptual and procedural understanding, including correcting common misconceptions.