Calculating Fractions Quantities

National Curriculum Links

• Mathematics – Year 4 (Number - Fractions)

  • Use common factors to simplify fractions; use common multiples to express fractions in the same denomination.
  • 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.
  • Recognise and write decimal equivalents of any number of tenths or hundredths.
  • 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.

• White Rose Maths Scheme Reference: Year 4 – Summer Term – Block 5: Fractions

  • Week 5: Calculate fractions of quantities

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Learning Objectives

By the end of this lesson, pupils will:

• Understand how to calculate fractions of a given quantity confidently.
• Use multiplication and division to find fractions of amounts.
• Explain their reasoning clearly when solving fraction problems involving quantities.
• Apply their understanding to progressively more complex word problems involving fractions.

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Success Criteria

I can:

• Identify the numerator and denominator in a fraction.
• Use division to find 1 part of the quantity (1 ÷ denominator).
• Multiply the 1 part amount by the numerator to find a fraction of the whole.
• Show my working clearly using diagrams or bar models.
• Explain how I found a fraction of a quantity in my own words.
• Solve problems where the fractions are non-unit and the answer is a whole number.

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Resources

• Whiteboard and markers
• Counters or small cubes for demonstration
• Visual bar models and fraction circles
• Printed task sheets with increasing difficulty
• Maths notebooks and pencils

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Lesson Structure

1. Introduction (10 minutes)

Engagement Hook:
Begin with a real-life scenario: “Imagine you have 24 chocolates to share with your friends. If you want to give 3/4 of the chocolates to your friends, how many chocolates is that?”

Questions to pose:

• What does 3/4 mean in this question? (Remember to ask pupils to explain their thinking)
• How could we find 1/4 of 24? Why might that be helpful?
• How can we use that to find 3/4 of 24?

Whole class discussion and demonstration:

• Use counters or cubes to demonstrate physically dividing 24 into 4 equal parts.
• Show that 1/4 of 24 is 6 (model 24 ÷ 4 = 6).
• Then model multiplying 6 × 3 = 18 to find 3/4.

Targeted questioning (Bloom’s Taxonomy – Understanding & Applying):

• Can someone explain why we divide by the denominator first?
• How do we know that multiplying the result by the numerator gives us the correct answer?
• Is there another way we could find the solution without using cubes?
• How could we check our answer?

AFL Checkpoint:
Use mini whiteboards to ask pupils to show 1/3 of 21, and explain their steps verbally for formative assessment.

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2. Modelling: Calculating Fractions of Quantities (10 minutes)

Modelling example for pupils to copy:

Example: Find 2/5 of 35.

Step 1: Find 1 part (35 ÷ 5) = 7
Step 2: Multiply by numerator (7 × 2) = 14
So, 2/5 of 35 is 14.

Visual model: Draw a bar divided into 5 equal parts with 7 units shaded in each part, then highlight 2 parts.

Common Misconceptions to address:

• Pupils multiply the quantity directly by the numerator without dividing first (e.g., 2 × 35 = 70).
• Confusion between numerator and denominator roles.
• Thinking that the denominator always divides the whole quantity evenly (e.g., difficulty with numbers not divisible evenly).
• Forgetting to multiply at the end after division.

Targeted Questions (Bloom’s Taxonomy – Analyzing & Evaluating):

• Why don’t we multiply the whole quantity by the numerator straight away?
• What would happen if the number wasn’t divisible by the denominator? How could we approach the problem then?
• How could drawing the bar model help avoid mistakes?
• Can you explain why multiplication comes after division?

AFL Checkpoint:
Ask pupils to explain the steps out loud to a partner and observe explanations to catch misunderstandings. Provide immediate corrective feedback.

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3. Guided Practice: Increasing Complexity Tasks (15 minutes)

Task progression:

• Level 1: Find simple fractions of quantities where the denominator divides the quantity exactly, e.g., 3/4 of 32, 1/5 of 25.
• Level 2: Fractions involving larger numerators and denominators, e.g., 5/6 of 48, 4/7 of 56 (using rounding or approximations).
• Level 3: Word problems requiring reasoning, e.g., “A baker made 60 cupcakes. She sold 3/5 of them in the morning and the rest in the afternoon. How many cupcakes did she sell in the morning?”

Visual support and scaffold: Encourage drawing bar models or using counters for visualisation.

Targeted questions for group work (Bloom’s Taxonomy – Applying & Creating):

• How did you find the fraction of the number? Can you justify your method?
• Can you represent your calculation visually? Does your answer make sense in this context?
• What strategies did you use if the number wasn’t easily divided?
• How could you check your answer without a calculator?

AFL: Circulate during task - pose probing questions and listen to pupil reasoning. Encourage self and peer-assessment by asking pupils to check each other’s calculations and explanations.

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4. Plenary (10 minutes)

Activity: Fraction Reasoning Quiz (Whole class review)
Display four worked examples with mistakes (some misconceptions included):

Example 1: 3/4 of 20 = 15 (Correct)
Example 2: 2/3 of 18 = 12 (Correct)
Example 3: 4/5 of 30 = 24 (Incorrect, pupil multiplied numerator by quantity only)
Example 4: 5/8 of 40 = 10 (Incorrect, pupil divided quantity by numerator instead of denominator)

Questions for pupils:

• Which answers are correct and why? Explain your reasoning.
• What mistakes can you spot in the wrong answers?
• How could those errors be avoided?
• Can you write the correct working to replace the errors?

Final AFL: Use a quick thumbs-up/down or mini whiteboards for pupils to indicate confidence or ask questions on remaining difficulties.

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Differentiation

• Lower ability: Use smaller numbers and more practical resources (counters) to visualise fractions before moving to abstract methods.
• Higher ability: Challenge pupils to find fractions of quantities that do not divide evenly and explain how to round or approximate answers.
• Extension: Explore non-unit fractions greater than one (e.g., 7/4) applied to quantities.

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Assessment for Learning (AfL) Summary

• Introduction: Use mini whiteboards for 1/3 of 21. Observe and question reasoning.
• Modelling: Partner explanations provide insights into conceptual understanding. Correct misconceptions on the spot.
• Guided Practice: Circulate and ask probing questions, encourage peer explanations. Note misunderstandings or conceptual gaps.
• Plenary: Analyse incorrect examples as a whole class to reinforce learning and reveal remaining confusions.

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Final Teacher Notes

This lesson combines the White Rose Maths approach of concrete → pictorial → abstract, fostering deep understanding through visual models and collaborative reasoning. The carefully scaffolded questioning ensures pupils are not only performing calculations but justifying and explaining their thinking, embedding a mastery mindset aligned to Bloom’s higher-order cognitive objectives.

By explicitly addressing common misconceptions and integrating assessment throughout, this lesson supports personalised learning and gradual release of responsibility to pupils — essential for long-term mastery of fractions of quantities at Year 4 level.