Fractions: Adding & Subtracting

National Curriculum Links

Mathematics – Year 4, Number - Fractions

• Pupils should be taught to:
  • Add and subtract fractions with the same denominator (NC Programmes of Study, 2014)
  • Recognise and show, using diagrams, families of common equivalent fractions (context for understanding addition and subtraction of fractions)

White Rose Maths Scheme – Year 4, Block 4, Fractions – Add and subtract fractions

• Add fractions with the same denominator
• Add two fractions
• Subtract fractions with the same denominator

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Learning Objectives

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

• Add fractions with the same denominator accurately
• Subtract fractions with the same denominator accurately
• Explain and justify their method of solving addition and subtraction of fractions problems

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Success Criteria

I can:

• Identify fractions with the same denominator
• Add fractions by adding the numerators only
• Subtract fractions by subtracting the numerators only
• Write my answers in simplest form if possible
• Explain why fractions can only be added or subtracted if they have the same denominator
• Justify my answers using examples and clear reasoning

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Resources

• Whiteboards and pens
• Fraction strips or fraction circles (manipulatives)
• Worksheets with progressive activities
• Interactive visualiser or board for modelling work
• Pupil lined books

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Lesson Structure (30 minutes)

1. Introduction & Engagement (5 minutes)

Hook:

• Show a visual fraction strip or circle split into equal parts (e.g., 1/4).
• Ask: “If I have 1/4 of this pizza and I get another 1/4, how much pizza do I have now?”
• Use a real-life scenario: “Imagine you have 1/4 of a cake, and your friend gives you 1/4 more. How do you find the total amount you have together?”

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

• What does the denominator tell us in a fraction?
• Why do you think these fractions are easy to add?
• Can you explain why we don’t add denominators when adding fractions?
• What do you notice about the pieces we are adding?

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2. Teaching & Modelling (12 minutes)

Step 1: Modelling adding fractions with the same denominator

• Write example on board:
  [ \frac{2}{7} + \frac{3}{7} = ? ]
• Step through the process: numerator + numerator, denominator stays the same:
  [ \frac{2 + 3}{7} = \frac{5}{7} ]
• Explain using fraction strips, physically showing two 2/7 strips and three 3/7 strips combining.

AfL Point:

• “Show me on your whiteboards how you think you could add these fractions.”
• Ask a volunteer to explain their steps aloud. “Why do you think the denominator stays the same?”

Step 2: Modelling subtracting fractions with the same denominator

• Example:
  [ \frac{6}{9} - \frac{2}{9} = ? ]
• Demonstrate subtracting numerators:
  [ \frac{6 - 2}{9} = \frac{4}{9} ]
• Use manipulatives to represent subtraction physically.

AfL Point:

• “Who can explain what happens to the denominators and why?”
• Pose: “How would the answer change if the denominators were different?” (Link to future learning and conceptual understanding)

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3. Guided Practice (10 minutes)

Worksheet Task:
Pupils complete the following progressively harder tasks in pairs or individually:

1. Simple addition with same denominators:
   [ \frac{1}{5} + \frac{3}{5} = ? ]
2. Simple subtraction with same denominators:
   [ \frac{7}{8} - \frac{5}{8} = ? ]
3. Addition of two fractions where numerators require careful adding:
   [ \frac{4}{9} + \frac{2}{9} = ? ]
4. Subtraction resulting in zero numerator:
   [ \frac{5}{6} - \frac{5}{6} = ? ]
5. Writing answers in simplest form (if applicable):
   [ \frac{6}{12} + \frac{3}{12} = ? ]

Challenge:

• Pose an open-ended question: “If you add (\frac{3}{7} + \frac{2}{7}), how can you check if your answer is correct without using a calculator?”

Targeted Whole Class Questions (Analysis & Evaluation):

• “Can someone explain what the numerator and denominator represent after adding?”
• “Why does simplifying fractions make your answer clearer?”
• “Is it ever possible to add fractions with different denominators? Why or why not?”

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4. Plenary (3 minutes)

• Bring the class together and ask:

  • “How do you add fractions quickly?”
  • “Why is it important that denominators are the same?”
  • “Can someone explain to the class how you subtract fractions in your own words?”

• Use an exit ticket:

  • Write down:
    [ \frac{3}{10} + \frac{4}{10} = ? ]
  • And explain your answer in one sentence.

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Example to Copy into Books

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Adding Fractions with the Same Denominator
[ \frac{3}{8} + \frac{2}{8} = \frac{3+2}{8} = \frac{5}{8} ]

Subtracting Fractions with the Same Denominator
[ \frac{7}{9} - \frac{4}{9} = \frac{7-4}{9} = \frac{3}{9} \text{ (can be simplified to } \frac{1}{3}) ]

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Differentiation

• Support: Use fraction strips and visual aids; guided support during worksheet activities.
• Challenge: Extend to adding/subtracting mixed numbers with like denominators or exploring fractions with denominators as multiples (preparing for future lessons).

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Final Notes

This lesson aligns fully with the National Curriculum for England and the White Rose Maths scheme for Year 4. This lesson builds fluency and conceptual understanding through concrete, pictorial and abstract methods. The questioning strategy ensures higher-order thinking engagement throughout the lesson, encouraging pupils to reason and justify their answers with confidence.