Being resourceful

A napkin is folded so that a corner coincides with the midpoint of an opposite edge. Investigate the three triangles formed.

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Can you see how to build a harmonic triangle? Can you work out the next two rows?

Can you find an efficent way to mix paints in any ratio?

If a sum invested gains 10% each year how long before it has doubled its value?

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

What is the same and what is different about these circle questions? What connections can you make?

Explore the relationships between different paper sizes.