Year 10 Being resilient

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

Explore the effect of combining enlargements.

Explore the effect of combining enlargements.

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

It would be nice to have a strategy for disentangling any tangled ropes...

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Is it possible to find the angles in this rather special isosceles triangle?

Can you match these calculations in Standard Index Form with their answers?

A mother wants to share some money by giving each child in turn a lump sum plus a fraction of the remainder. How can she do this to share the money out equally?

The area of a square inscribed in a circle with a unit radius is 2. What is the area of these other regular polygons inscribed in a circle with a unit radius?

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

Which numbers can we write as a sum of square numbers?

Can you explain what is going on in these puzzling number tricks?

Can you create a Latin Square from multiples of a six digit number?