Introducing algebra

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

There are lots of different methods to find out what the shapes are worth - how many can you find?

Can you find a way of counting the spheres in these arrangements?

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

The Number Jumbler can always work out your chosen symbol. Can you work out how?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

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