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Truth of propositions

The idea of truth, including notions of 'true', 'not true' and 'sometimes true', underpins other ideas, such as:

  • equality and equivalence
  • deduction and proof
  • chance and probability.

There are many opportunities for teachers of mathematics to ask questions:

  • Is (this proposition) true?
  • Is it just sometimes true, or is it always true?
  • When is it true?
  • How do you know?
  • How could you demonstrate or show or prove that it is true?

A year 8 scenario about the tessellation of quadrilaterals is useful for illustrating a 'truth' activity.

Do quadrilaterals tessellate?

A teacher asked students to consider the statement "Any quadrilateral will tessellate" and whether this is true some of the time, all of the time or never true.