Explaining, convincing and proving

problem
Tetra inequalities

Age

16 to 18

Challenge level

Can you prove that in every tetrahedron there is a vertex where the three edges meeting at that vertex have lengths which could be the sides of a triangle?
problem
Look before you leap

Age

16 to 18

Challenge level

Relate these algebraic expressions to geometrical diagrams.
problem
Parabella

Age

16 to 18

Challenge level

This is a beautiful result involving a parabola and parallels.
problem
Sixty-seven squared

Age

16 to 18

Challenge level

Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?
problem
Three by one

Age

16 to 18

Challenge level

There are many different methods to solve this geometrical problem - how many can you find?
problem
T for tan

Age

16 to 18

Challenge level

Can you find a way to prove the trig identities using a diagram?
problem
Big and small numbers in physics - group task

Age

16 to 18

Challenge level

Work in groups to try to create the best approximations to these physical quantities.
problem
Stats statements

Age

16 to 18

Challenge level

Are these statistical statements sometimes, always or never true? Or it is impossible to say?
problem
Contrary logic

Age

16 to 18

Challenge level

Can you invert the logic to prove these statements?
problem
Direct logic

Age

16 to 18

Challenge level

Can you work through these direct proofs, using our interactive proof sorters?