Subtracting Fractions Mastery

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Overview

Duration: 45 minutes
Class: Year 4 (age 8-9)
Class size: 30 pupils
National Curriculum Reference:

• Mathematics Programme of Study (Key Stage 2 - Year 4)
• Number - Fractions: "Add and subtract fractions with the same denominator within one whole" (NC Maths PoS)
• Link to White Rose Hub Block 3: Fractions – Week 3 (Subtracting fractions with the same denominator)

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Learning Objectives

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

• Understand and apply subtraction of fractions with the same denominator within one whole.
• Represent subtraction of fractions visually and numerically.
• Explain their reasoning about subtracting fractions, using correct mathematical vocabulary.

This supports the NC:
“add and subtract fractions with the same denominator within one whole” (Year 4 Number Fractions).

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Success Criteria

Pupils will be successful when they can:

• Correctly subtract fractions with the same denominator.
• Use pictorial models (fraction bars or circles) to represent subtraction.
• Explain why the denominators remain the same and the numerators are subtracted.
• Solve increasingly complex subtraction of fractions problems, including word problems.
• Justify their answers using mathematical language and reasoning.

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Resources Needed

• Whiteboard and visualiser
• Fraction bars or fraction circles (1 whole divided into equal parts)
• Individual whiteboards and pens for pupils
• Printed subtraction of fractions problems sheets - differentiated (basic, intermediate, challenge)
• Worksheets for independent task
• LARGE fraction wall poster for reference
• Stopwatch/timer

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Lesson Structure

1. Engaging Introduction (8 minutes)

• Hook (3 mins):
  Show a big cake (real or image) divided into 8 equal slices. "Imagine we have 8 friends sharing this cake, and 3 slices have been eaten. How much cake is left?"
  Write the fraction: 8/8 - 3/8 = ?
  Pupils respond on whiteboards.

• Show fraction bars representing 8/8 and subtract 3/8 visually.

• Introduce focus: “Today, we are going to learn how to subtract fractions with the same denominator just like our cake slices, making sure we understand how and why this works.”

• Questioning: Use targeted questions to promote thinking:

  • “Why do you think the denominator stays the same when we subtract fractions?” (Understanding the whole and equal parts)
  • “Can we subtract numerators and denominators both? Why or why not?” (Conceptual understanding)
  • "If I have 5/8 and I take away 2/8, what does the result tell me about the size of the part left?"

Prompt pupils to explain their ideas, not just give answers.

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2. Teaching & Modelling (15 minutes)

• Write example on board for pupils to copy:

  [ \frac{7}{10} - \frac{4}{10} = ? ]

• Draw 7/10 on fraction bars (or circles), then cross off 4/10.

• Count remaining parts to get the answer: (\frac{3}{10}).

• Explain reasoning:

  • The denominator represents how many equal parts make the whole—this doesn’t change because the whole stays the same.
  • Subtract numerators because we are subtracting parts of the same size.

• Use targeted AFL questions:

  • “What does the denominator tell us about the fractions we are subtracting?”
  • “Why can’t we subtract denominators here?”
  • “What would happen if the denominators were different?” (Deeper thinking, linking to future learning)
  • “How does representing the fractions visually help us understand the subtraction?”

• Display an incorrect subtraction example for discussion (e.g., ( \frac{5}{8} - \frac{2}{8} = \frac{3}{6} )) and ask:

  • “Is this answer correct? Why or why not?”
  • “What mistake was made?”

• Checkpoint (AFL):
  Ask pupils to explain the subtraction process to a partner and listen to reasoning. Circulate and listen, noting misconceptions.

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3. Guided Practice with Increasing Complexity (12 minutes)

Set differentiated tasks. Begin with straightforward subtraction and progress to word problems and mixed operation tasks.

• Task 1: Subtract fractions with denominators of 4 and 10 (simple numerators).
  E.g., 3/4 - 1/4 = ?

• Task 2: Subtract fractions with larger numerators.
  E.g., 9/12 - 5/12 = ?

• Task 3: Word problem applying subtraction of fractions.
  “Jamal had 7/8 of a litre of juice. He drank 3/8 litre. How much juice is left?”

Pupils work individually; teacher uses quick AFL during activity:

• Ask pupils to explain their answers in full sentences, e.g., "I subtracted the numerators because the size of the parts (denominator) stayed the same."
• Circulate to ask:
  • “Can you describe the steps you took to solve this?”
  • “Why did you choose to subtract the numerators?”
  • “Could this be solved in any other way?”

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4. Plenary (10 minutes)

• Quickfire Whole Class Quiz: Use mini whiteboards and rapid questioning. Example questions using Bloom’s taxonomy:

  • Remembering: “What do the numerator and denominator represent in a fraction?”
  • Understanding: “Explain why you subtract only the numerators when subtracting these fractions?”
  • Applying: “If I have 6/9 and subtract 4/9, what real-world example could this represent?”
  • Analysing: “Look at these fractions: 5/7 - 3/7 and 5/7 - 3/8. Which can you subtract directly and why?”
  • Evaluating: “If someone said ‘You add denominators to subtract fractions,’ is that correct? Why or why not?”
  • Creating: “Can you create a subtraction problem involving fractions with the same denominator and solve it?”

• Reflection:
  Each pupil writes one sentence about what helped them understand subtracting fractions today and one question they still have.

• Teacher gathers a few reflections to address in next session or quickly clarify.

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Additional Notes

• Clear use of ABCD (Audience, Behaviour, Condition, Degree) objectives:

  • Audience: Year 4 pupils
  • Behaviour: Subtract fractions with same denominator
  • Condition: Using pictorial and numeric methods
  • Degree: With 80% accuracy and correct verbal explanation

• Use of visual models aligns with White Rose recommended concrete-pictorial-abstract (CPA) approach.

• Encourage use of correct vocabulary: numerator, denominator, whole, parts, subtract, difference.

• AFL sprinkled throughout lesson ensures misconceptions caught early.

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This detailed, engaging lesson plan is designed to build deep conceptual and procedural understanding of subtracting fractions with the same denominator, fully aligned with the National Curriculum for Year 4.