Introducing algebra

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

Amy's mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?

In 1871 a mathematician called Augustus De Morgan died. De Morgan made a puzzling statement about his age. Can you discover which year De Morgan was born in?

Can you substitute numbers for the letters in these sums?

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

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