Working systematically

A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

What could the half time scores have been in these Olympic hockey matches?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

Nine squares are fitted together to form a rectangle. Can you find its dimensions?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

How many ways can you find to put in operation signs (+, −, ×, ÷) to make 100?