‘Low threshold – High ceiling’ (open ceiling) investigations. Shape and space – symmetry. Objectives Year 6: Solving problems – Reasoning and generalising about numbers or shapes. 76-7 Explain methods and reasoning, orally and in writing. 78-9 Solve mathematical problems or puzzles, recognise and explain patterns and relationships, generalise and predict. Suggest extensions by asking ‘What if….?’ 80-1 Make and investigate a general statement about familiar numbers or shapes by finding examples that satisfy it. Develop from explaining a generalised relationship in words to expressing it in a formula using letters as symbols. Year 7: Begin to identify and use angle side and symmetry properties of triangles and quadrilaterals; solve geometric problems involving these properties, using step-by-step deduction and explaining reasoning with diagrams and text. Year 8 (level 5 – constructions) Use straight edge and compasses to construct: the mid-point and perpendicular bisector of a line segment; the bisector of an angle; the perpendicular from a point to a line; the perpendicular from a point on a line. Initial Questions How many lines of symmetry are possible in a quadrilateral? In any shape? Resources needed Dotty paper (isometric and squared), plain paper; pencils, rulers, protractors, (compasses) Further questions Analysis: (Higher order What do you notice about the three symmetry lines? questions, using What do you notice about two / four symmetry lines? Bloom’s taxonomy) What do you notice about the lines of symmetry through shapes with an odd number of sides? How is this different from the shapes with an even number of sides? Are any features of even-numbered sided shapes with 3 lines of symmetry are the same / different? (Any different from Odd-numbered sides). Synthesis: (What) If I pulled this point along this line of symmetry, what would happen to the shape? What would I have to do to keep three lines of symmetry? What other features could you explore? Evaluation: How would you prove that no quadrilateral could have three lines of symmetry? Explain why you think two lines of symmetry cross at 90°. Could two lines of symmetry cross at any other angle? Why not? If a triangle had two lines of symmetry, why must it have a third? Why can’t we use either dotty papers for regular pentagons?
"Low threshold – High ceiling (open ceiling investigations)"