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Teaching notes
Key question/task Here are several shapes which have had lines of symmetry marked in. However, only on some of these are all the lines of symmetry marked correctly. Circle the ones that are correct. For the ones that are incorrect, explain what is wrong, and try to show the correct solutions. Supplementary questions:
- Have you checked whether there are enough lines of symmetry indicated on each shape?
- Have you checked whether there are too many lines of symmetry marked on each shape?
- Are there any shapes that have no lines of symmetry? Resources: - Resource sheet ‘Symmetry Properties’; - Plain paper, pencils, rulers. Commentary/notes: These activities will require reasoning about symmetry: reasoning about links between reflection and rotation symmetries, about how lines of symmetry are oriented within a shape, and why the number of lines of symmetry that a shape can have is always a factor of the number of sides. This reasoning is not often tackled in regular exercises. The content is suitable for all tiers. Solutions: The 3 correct answers are: Stimulus question 71
Symmetry Properties
The lines of symmetry on the other shapes should look like this: A common error is to place lines of symmetry along the diagonals of a rectangle. The triangle is equilateral, hence three lines of symmetry. A parallelogram has no lines of symmetry.
GCSE Subject Content Foundation Intermediate Higher Simple description of symmetry in terms of reflection in a line/plane. Regular and irregular polygons. Vocabulary of triangles, quadrilaterals and circles: isosceles, equilateral, scalene, exterior/interior angle, diagonal, square, rectangle, parallelogram, rhombus, kite, trapezium, polygon, pentagon, hexagon. Bisecting a given line, bisecting a given angle. Essential properties of special types of quadrilateral, including square, rectangle, parallelogram, trapezium, kite and rhombus; classify quadrilaterals by their geometric properties. Learner Outcomes and Assessment ( to aid comment-‐only marking ) Reasoning strand – Learners are able to: Assessment Guidance: Can learners:
- Identify, measure or obtain required information to complete the task;
- Identify what further information might be required and select what information is most appropriate;
- Select appropriate mathematics and techniques to use;
- Explain results and procedures precisely using appropriate mathematical language;
- Interpret mathematical information; draw inferences from diagrams;
- Explain and justify strategies, methods, reasoning and conclusions in a variety of different ways, including orally, graphically, writing (both with mathematical notation and without), using appropriate digital literacy equipment;
- Appreciate the difference between mathematical explanation and experimental evidence. - Support their arguments with convincing reasons? - Identify appropriate properties of shapes to support their arguments? - Create a chain of reasoning? - Use the correct mathematical vocabulary in their descriptions and explanations? - Draw diagrams accurately? - Recognise that simply by producing several examples of where a shape situation works, it does not mean that that it is always true? Some situations require deeper reasoning.
