List

Advanced Investigations

Fancy something very substantial? These challenging investigations will take time and you will need to pose your own questions in order to make your own mathematical discoveries.

The best square
problem

The best square

Age
16 to 18
Challenge level
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How would you judge a competition to draw a freehand square?
Trig-trig
problem

Trig-trig

Age
16 to 18
Challenge level
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Explore the properties of combinations of trig functions in this open investigation.
Chance of that
problem

Chance of that

Age
16 to 18
Challenge level
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What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?
Investigating Twilgo
problem

Investigating Twilgo

Age
16 to 18
Challenge level
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What can you create using 140 characters and our cool Twilgo environment?
Factors and multiples graphs
problem

Factors and multiples graphs

Age
16 to 18
Challenge level
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Explore creating 'factors and multiples' graphs such that no lines joining the numbers cross
Few and far between?
problem

Few and far between?

Age
16 to 18
Challenge level
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Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
A rational search
problem

A rational search

Age
16 to 18
Challenge level
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Investigate constructible images which contain rational areas.
Converging quadrilaterals
problem

Converging quadrilaterals

Age
16 to 18
Challenge level
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Explore the properties of this iterative geometrical procedure