Conjecturing and generalising

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

How many centimetres of rope will I need to make another mat just like the one I have here?

What do you notice about these squares of numbers? What is the same? What is different?

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal?

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

A red square and a blue square overlap. Is the area of the overlap always the same?