Geometry: Properties of Shapes — Year 5 Lesson Plan
National Curriculum: Mathematics KS2 (Year 5) — Pupils should be taught to identify 3D shapes from 2D representations; to know angles are measured in degrees; to estimate and compare acute, obtuse and reflex angles; to draw given angles and measure them in degrees; to identify regular and irregular polygons.
Overview
This lesson extends pupils knowledge of 2D shapes to include regular and irregular polygons, reflex angles and the properties of circles. Pupils use the properties of shapes to reason and solve problems, building on their knowledge of angle measurement and classification. The lesson emphasises mathematical reasoning: pupils are expected to justify their classifications, identify what must be true about a shape and explain their thinking using precise geometric vocabulary.
Learning Objectives
- Know the properties of regular and irregular polygons and explain the difference
- Identify reflex angles and estimate, compare and classify angles up to 360 degrees
- Use the properties of 2D shapes to reason and solve geometric problems
- Draw 2D shapes accurately using a ruler and protractor with given dimensions and angles
Key Vocabulary
Suggested Lesson Structure
Display a set of polygons on the board including both regular and irregular examples of triangles, quadrilaterals, pentagons, hexagons and octagons. Ask pupils to sort them into two groups. After allowing thinking time, take feedback. Establish the definition of regular: all sides equal and all angles equal. Test this understanding with one or two tricky examples (e.g. a rhombus has equal sides but is it regular? No — the angles are not equal). Ask: What other properties could we use to sort these shapes?
Recap the angle types pupils already know: acute, right angle and obtuse. Introduce reflex angles: angles greater than 180 degrees. Show how to identify and estimate reflex angles using a full turn as a reference. Demonstrate measuring a reflex angle using a protractor: measure the non-reflex angle and subtract from 360 degrees. Then focus on the interior angles of regular polygons: demonstrate that the interior angles of a triangle sum to 180 degrees using torn-corner demonstration. Introduce the idea that regular polygons have interior angles that can be calculated.
Pupils work in pairs on a set of reasoning cards. Each card shows a polygon with some information given and asks pupils to find missing information or justify a statement (e.g. A regular hexagon has interior angles of 120 degrees. How do you know? or Is this shape regular? Explain your reasoning.). Pairs discuss and record their thinking. Circulate and prompt with questions: How do you know? Can you prove it? Can you find a counter-example?
Pupils complete two tasks. Task 1: Use a ruler and protractor to draw three shapes accurately from given specifications (e.g. a regular hexagon with sides of 4 cm; a triangle with angles 60, 70 and 50 degrees; a quadrilateral with given side lengths). Task 2: A problem-solving question — identify the odd one out from a set of shapes and justify the choice using geometric vocabulary. Extension: explore how many lines of symmetry a regular polygon has compared to its number of sides and write a generalisation.
Display a shape on the board and give pupils 30 seconds to write down everything they know about it using precise mathematical vocabulary. Take feedback and build a class description. Award a point for each new property correctly identified. Use this as a vocabulary check and as a model of mathematical communication. Set a challenge question to think about for next lesson: Can a quadrilateral have exactly one reflex angle?
Common Misconceptions
- Pupils sometimes think a square and a rhombus are the same shape because both have four equal sides; clarify that a square is a special rhombus in which all four angles are right angles
- Pupils sometimes measure the wrong angle when asked for a reflex angle; emphasise that a reflex angle is always greater than 180 degrees and model the technique of measuring the acute or obtuse angle and subtracting from 360
Prior Knowledge
Pupils should already be able to:
- Ability to measure and draw angles up to 180 degrees using a protractor
- Knowledge of the properties of common 2D shapes including triangles and quadrilaterals
- Understanding of acute, right angle and obtuse angles
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