# Low threshold – High ceiling (open ceiling investigations)

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Low threshold – High ceiling (open ceiling investigations)

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2/23/2010
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```							   ‘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?

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