Equivalent Fractions Mastery

National Curriculum Links

• Mathematics Programme of Study (Years 3-6):
  • Section: Number – Fractions (Year 5)
  • Objective: Recognise and use equivalent fractions.
  • Focus: Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred equal parts and dividing tenths by ten.
  • Outcome: Use common factors to simplify fractions; use common multiples to express fractions in the same denomination.

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Learning Objectives

By the end of this 30-minute session, students will be able to:

• Identify and explain equivalent fractions using visual fraction models (pizza slices) and numerical representations.
• Use key vocabulary correctly: numerator, denominator, equal value, same whole.
• Demonstrate understanding that two fractions can have different denominators yet be equivalent.
• Solve an age-appropriate problem that challenges their reasoning on equivalent fractions ("Can two equivalent fractions have different denominators? Convince me.").

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Key Vocabulary

• Numerator
• Denominator
• Equivalent fractions
• Equal value
• Same whole

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Resources

• 32 individual paper pizza cut-outs divided into fractions (varied denominators: halves, quarters, eighths, tenths)
• Whiteboard and marker
• Fraction cards with numerator and denominator written clearly
• Visual aids: fraction bars/strips
• Challenge cards for extension tasks
• Concrete manipulatives (optional: fraction cubes or counters)

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Lesson Structure

Introduction (5 minutes)

• Engage: Begin by displaying a whole pizza image and ask, "If I cut this pizza into 4 equal slices and eat 1, how many slices have I eaten?" Lead students to identify numerator and denominator.
• Vocabulary focus: Introduce and clarify numerator (top number; number of parts taken) and denominator (bottom number; total equal parts).
• Whole concept recap: Re-emphasise “same whole” to avoid misconception that fractions being compared are parts of different wholes.

Main Activity (15 minutes)

• Guided exploration:

  1. Distribute various individual paper pizza slices representing different fractions (e.g., 1/2, 2/4, 3/6, 5/10).
  2. Ask students to work in pairs (TA to support SEND and EHCP pupils) to arrange their pizza slices on the desk to visually compare sizes.
  3. Encourage them to find pairs of slices that look equal in size but have different denominators. Facilitate by prompting: “Can 2 slices be the same size even if the number of slices the pizza is divided into is different?”
  4. Use the whiteboard to list these fractions, highlight numerators and denominators, and show how you multiply numerator and denominator by the same number to generate equivalent fractions. Example: 1/2 = 2/4 = 4/8.

• Support strategies:

  • Break down instructions clearly; use visual aids continuously.
  • TA to work alongside dyslexic students and EHCP pupil, using manipulation of physical pizza slices for kinaesthetic learning.
  • Use coloured fraction strips for SEND pupils who find number notation challenging.

Challenge / Going Deeper (7 minutes)

• Pose the open-ended question to the class:
  “Can two equivalent fractions have different denominators? Convince me.”
• Invite several students to present their physical pizza slice comparisons and justify their reasoning using the key vocabulary.
• Encourage both visual and numerical explanations.
• Write down their arguments and ensure reasoning references "same whole” and the concept of equal value despite different denominators.
• Optional: quick peer discussion to support learners in constructing reasoning.

Plenary (3 minutes)

• Quick-fire quiz: Flash fraction pairs (e.g., 2/6 & 1/3) and ask thumbs up/down whether they are equivalent.
• Recap vocabulary orally.
• End by reminding the class why understanding equivalence is important for simplifying fractions and solving real problems.

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Assessment

• Formative: Observe pairs during the pizza slice sorting and listen for correct use of vocabulary and reasoning.
• Summative: Evaluate verbal reasoning during the challenge question to check deeper conceptual understanding.
• TA to support those with SEND/EHCP by noting engagement and conceptual grasp.
• Optional exit card (for confident students): Write one pair of equivalent fractions with different denominators and explain why.

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Differentiation

• Support:
  • Concrete materials for those struggling with abstract fraction concepts.
  • Simplified language and one-step tasks for the EHCP pupil and SEND learners.
  • Use of sentence starters for written or spoken explanations (e.g., "These fractions are equivalent because...").
• Extension:
  • Challenge more able children to write equivalent fractions by finding multiples or simplifying fractions.
  • Investigate equivalences beyond the denominators used (e.g., 3/9 equivalent to 1/3).

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Reflection and Teacher Notes

• Ensure the TA is clear on their role to support SEND pupils and monitor peer discussions to maintain focus.
• Look for misconceptions around "same whole" and denominators—reinforce these during next lesson as required.
• Note responses to the challenge question as indicator of higher-order thinking for groupings in future lessons.

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This lesson aligns tightly with the National Curriculum for England’s expectations in year 5 and uses a highly engaging, concrete pizza-based resource to embed conceptual understanding of equivalent fractions, vocabulary development, and mathematical reasoning.