Year 9 Exploring and noticing

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Can you do a little mathematical detective work to figure out which number has been wiped out?

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

Can you prove the angle properties described by some of the circle theorems?

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

Can you make sense of information about trees in order to maximise the profits of a forestry company?

Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?