Visual Fraction Representation

National Curriculum Links

• Mathematics Key Stage 2
• Year 4 Number – Fractions
• Pupils should be taught to:
• 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
• 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
• Use diagrams and models (e.g. part-whole models, bar models, number lines) to represent fractions

Learning Objectives

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

• Represent fractions visually using diagrams such as shaded shapes, bar models, and number lines
• Explain how fractions correspond to parts of a whole in different visual models
• Justify their reasoning about equivalent fractions and fraction placement on number lines
• Use models to compare fractions and understand fraction equivalence and ordering

Success Criteria

Pupils will:

• Draw and label accurate diagrams (shapes divided into equal parts, bar models) to represent given fractions
• Accurately mark fractions on number lines and explain their reasoning aloud and in writing
• Use sentence stems to explain their answers and justify fraction equivalence or inequalities
• Respond to reasoning and “prove it” style questions confidently, supporting explanations with their own diagrams or models

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Lesson Overview (35 Minutes)

1. Introduction and Hook (5 minutes)

Engage and activate prior learning:

• Start by showing a large visual of a pizza divided into 4 equal slices with 1 slice shaded. Ask:
• “What fraction of the pizza is shaded? How do you know?”
• “Can we represent this fraction in other ways? Draw it with shapes or on a number line.”
• Use this familiar context to introduce the concept of representing fractions visually through diagrams and models.
• Explain how different models help us understand fractions better.

Use targeted whole-class questioning with Bloom’s Taxonomy:

• Remembering: “What is a fraction?”
• Understanding: “Why do the parts have to be equal?”
• Applying: “Can someone draw a different shape to represent 1/4?”
• Analyzing: “What fraction is larger, 1/4 or 1/3? How do you know using your diagrams?”
• Evaluating: “If I shaded 2 parts of 6 equal shapes, can I show this fraction on a number line too?”
• Creating: “Can you create your own fraction model showing 3/8 and explain it?”

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2. Modelling and Explanation (10 minutes)

Teacher Models Drawing & Reasoning

• Using a whiteboard/projector, model how to represent fractions using:
• Shapes (circle divided into equal parts, shading a number of parts)
• Bar models (rectangles divided into equal segments)
• Number lines (dividing a line from 0 to 1 into equal intervals)

Example for pupils to copy into books:

• “Draw a rectangle divided into 5 equal parts. Shade 2 parts. Label it 2/5.”
• “Mark 2/5 on the number line between 0 and 1 by dividing it into 5 equal parts.”

Prove It / Reasoning Question (with timer):

• “Is 2/5 larger or smaller than 1/3? Look at the diagrams and number lines you have created. Use the sentence stems...”
• "I think 2/5 is ___ than 1/3 because..."
• "In my diagram/model, I can see that..."
• Provide 1-2 minutes for pupils to verbalise answers with a partner before writing.

AfL (Assessment for Learning) checkpoints:

• Observe pupils’ diagrams during modelling; ask “Why did you draw the parts this way?”
• Use mini whiteboards for quick visual checks on pupils’ drawing of fractions
• Listen to explanations during the “prove it” talk partner activity

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3. Guided Practice Task (10 minutes)

Gradually Increasing Complexity

• Part 1: Draw simple fractions on shapes (circles, rectangles). Shade fractions like 1/3, 3/4.
• Part 2: Represent same fractions on number lines, label fractions correctly.
• Part 3: Draw two fractions and compare them on models and number lines. Explain which is larger and why.
• Part 4 (Challenge): Draw a shape split unevenly, identify why this is incorrect to represent a fraction. Then correct it.

Examples:

• Draw a circle split into 6 equal parts, shade 4 parts, label 4/6. Draw a number line and mark 4/6.
• Compare 4/6 and 2/3 using diagrams. Explain if these fractions are equivalent and why.

Teacher circulates providing feedback and challenges pupils who need extension tasks (e.g., representing fractions greater than 1 using mixed numbers and diagrams).

AfL Points:

• Use questioning during task: “Can you show me how you knew the parts had to be equal?”
• Ask pupils to explain their reasoning aloud when stuck and adapt support accordingly.

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4. Common Misconceptions and Difficulties

• Confusing numerator and denominator — pupils may shade the wrong number of parts or divide unevenly
• Thinking that parts don’t need to be equal size to represent fractions correctly
• Placing fractions incorrectly on number lines (e.g., confusing 1/4 and 1/5 positions)
• Difficulty comparing fractions with different denominators without visual support

Strategies to address:

• Emphasise equal partitioning in diagrams
• Use step-by-step drawing guides
• Reinforce concepts with physical models or manipulatives (optional)
• Use layered questioning: “How does the size of the parts affect your fraction?” “Why does 1/4 come before 1/3 on a number line?”

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5. Plenary (5 minutes)

Active Reasoning and Reflection

• Bring class together and pose a final “prove it” question:
• “Here are two fractions: 3/8 and 5/12. Using your models, explain which is larger and why. Use the stems…”
• After verbal explanations, invite 3-4 pupils to share their reasoning aloud.
• Recap the success criteria, asking pupils to self-assess by ticking which criteria they met today.
• Affirm the value of using diagrams and models to help understand fractions deeply, encouraging pupils to use these tools whenever working with fractions.

AfL:

• Verbal responses indicate depth of understanding and reasoning
• Teacher notes misconceptions and plans next steps in learning for individual/group support

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Additional Notes

• This lesson aligns closely with the Year 4 White Rose Maths scheme, focusing on fractions represented visually and increasing problem complexity.
• Visual models and number lines form a core approach in White Rose’s mastery approach, supporting deep conceptual understanding.
• Sentence stems and paired reasoning discussions tie directly to developing mathematical vocabulary and explanation skills as promoted by the National Curriculum.

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Sentence Stems for Reasoning

• "I know this fraction is ___ because the shape is divided into ___ equal parts and ___ parts are shaded."
• "On the number line, ___ is placed to the left of ___, so it is smaller because..."
• "These fractions are equivalent because..."
• "I can compare these fractions by..."

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This lesson plan encourages engagement through visual representation and active reasoning, developing strong foundational skills in fraction understanding for Year 4 pupils while meeting National Curriculum requirements.