Year 9 Being curious

Where should you start, if you want to finish back where you started?

Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?

The farmers want to redraw their field boundary but keep the area the same. Can you advise them?

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

There are lots of different methods to find out what the shapes are worth - how many can you find?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

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

Can you make sense of these three proofs of Pythagoras' Theorem?

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?

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