Low threshold – High ceiling (open ceiling investigations)

							   ‘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?