Introducing algebra

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

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

Can you find pairs of differently sized windows that cost the same?

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.

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.