Fractions, Decimals & Shapes

Overview

This 60-minute lesson engages Year 6 students in deepening their understanding of fractions, decimals, percentages, and basic geometry, in line with the National Curriculum (England). The lesson focuses on consolidating equivalences between fractions, decimals, and percentages and revisiting properties and classification of 2D and 3D shapes. It integrates practical, collaborative, and problem-solving activities to ensure conceptual fluency and reasoning skills.

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National Curriculum Links

Mathematics Programmes of Study: Years 5 and 6, Number and Geometry

• Fractions (Number - Number and Place Value & Number - Fractions/Decimals/Percentages)

  • Recognise the percent symbol (%) and understand that percent relates to "number of parts per hundred," and write percentages as a fraction with denominator 100, and as a decimal (Y6).
  • Use common factors to simplify fractions; use common multiples to express fractions in the same denomination (Y6).
  • Recall and use equivalences between simple fractions, decimals, and percentages, including in different contexts (Y6).

• Geometry (Properties of Shape)

  • Draw 2-D shapes using given dimensions and angles (Y6).
  • Recognise, describe, and build simple 3-D shapes, including making nets (Y6).
  • Identify 3-D shapes, including cubes and other cuboids, from 2-D representations (Y6).

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Learning Objectives

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

• Convert between fractions, decimals, and percentages confidently.
• Simplify fractions using common factors and express fractions with a common denominator.
• Identify and classify 2D shapes based on their properties, including angle measures.
• Recognise and build nets of 3D shapes and visualise 3D shapes from 2D representations.
• Explain the relationships between fractions, decimals, percentages, and geometry using mathematical language.

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Resources Needed

• Whiteboard and markers
• Printed fraction, decimal, and percentage cards for matching games (per group)
• Set of 2D shape cutouts with dimensions marked (e.g., triangles, squares, rectangles, pentagons)
• Nets of 3D shapes printed on card (cube, cuboid, pyramid)
• Mini whiteboards and pens for each pupil
• Rulers and protractors
• Interactive visualiser/document camera (optional)
• Worksheets with problems and reasoning questions

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Lesson Breakdown (60 minutes)

1. Starter Activity: Fraction-Decimal-Percentage Matching (10 minutes)

• Pupils work in pairs.
• Each pair receives shuffled cards with fractions (e.g. ½, 0.75), decimals (e.g. 0.5, ¾), and percentages (e.g. 50%, 75%).
• Task: Match fraction cards to their equivalent decimal and percentage cards.
• Teacher circulates, checking understanding and prompting with questions (“How do you know ¾ equals 75%?”).
• This activity recalls prior knowledge and sets the foundation for deeper exploration.

2. Guided Teaching: Fraction Simplification and Common Denominators (15 minutes)

• Using the whiteboard:
  • Demonstrate simplifying fractions using common factors.
  • Show how to find a common denominator to express fractions equivalently.
• Mini plenary:
  • Pupils use mini whiteboards to simplify fractions or convert them to equivalent fractions with a given denominator.
• Discuss real-life examples where simplification helps (recipes, measuring).

3. Practical Geometry: Identifying and Drawing Shapes (15 minutes)

• Distribute 2D shape cutouts and rulers/protractors.
• Pupils, in small groups, measure angles and sides, then classify shapes (triangle type, quadrilateral, other polygons).
• Challenge: Draw a shape with given dimensions and angles.
• Discuss key properties and reinforce terminology — vertices, edges, angles.

4. Exploring 3D Shapes and Nets (10 minutes)

• Provide nets of cubes, cuboids, and pyramids.
• Pupils fold nets into 3D shapes individually or in pairs.
• Use real objects or visualiser to compare and match nets to solids.
• Discuss properties such as faces, edges, and vertices.
• Pose the challenge: “Can you visualise a cube from this 2D drawing? What clues help you?”

5. Plenary & Assessment: Reasoning Questions and Peer Explanation (10 minutes)

• Use structured reasoning questions on mini whiteboards:
  • "Convert ⅗ to a decimal and percentage. Explain your steps."
  • "Which 2D shape has all equal sides and angles?"
  • "If this net folds into a cuboid, how many faces will it have?"
• Pupils explain their answers to a partner or the class, encouraging mathematical vocabulary.
• Teacher uses observational notes and mini whiteboard responses to assess understanding and identify pupils needing support or challenge.

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Assessment Ideas

• Formative assessment through observation during activities and mini whiteboard tasks.
• Peer explanations during plenary to assess verbal mathematical reasoning.
• Collection of worksheets with fraction simplification and shape classification for marking.
• Use a short exit ticket: a quick question converting fractions to decimals or identifying shape properties before leaving class.

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Extension (for faster learners or homework)

• Problem-solving task: Given a real-world scenario, such as shopping discounts, calculate percentage savings using fractions and decimals.
• Design and draw a net for a less common 3D shape (e.g., triangular prism) and explain its properties.

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Differentiation

• Support: Paired work with prompts, use of visual aids, scaffolded worksheets.
• Challenge: Extension tasks with higher-order reasoning, creating shape nets, and converting complex fractions.

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This lesson strategically reinforces core number concepts and geometric understanding, developing both procedural fluency and reasoning in line with the Year 6 National Curriculum. The varied activities aim to engage different learning styles and promote deeper mathematical thinking.