In the number pyramid below, the number in the bottom left hand corner determines all the other numbers.

In a number pyramid, the numbers on the lower layers determine the numbers above them.

One day our teacher asked us a puzzling question.

Think of a number and follow the machine’s instructions… I know what your number is! Can you explain how I know?

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

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens…

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

25 of the storeys of a 50 storey building are painted gold, and the rest are painted black…

The sum of five consecutive integers is equal to the sum of the next three consecutive integers. Can you find the largest of these integers?

How old will Julie be when her age is equal to the sum of her daughters’ ages?

Surprising numerical patterns can be explained using algebra and diagrams…