The idea of truth, including notions of 'true', 'not true' and 'sometimes true', underpins other ideas, such as:
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equality and equivalence
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deduction and proof
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chance and probability.
There are many opportunities for teachers of mathematics to ask questions:
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Is (this proposition) true?
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Is it just sometimes true, or is it always true?
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When is it true?
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How do you know?
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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.