Cuisenaire Rods

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

Making Boxes

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

A Right Charlie

Can you use this information to work out Charlie's house number?

Augustus' Age

Augustus' Age

In 1871 a mathematician called Augustus De Morgan died.
De Morgan made this puzzling statement about his age: he said that he was $x$ years old in the year $x^2$.

Can you discover which year De Morgan was born in?

Do you think anyone living at this time can say the same thing about their age and the year they were born? (That doesn't mean that they have to have been born the same year as De Morgan!)

This is a cartoon of De Morgan drawn by one of his students.

Why do this problem?

This problem is good for children who have just begun to work with algebra. It lends itself to a trial and improvement approach.

Key questions

How old do you think he could be?
Why not list some square numbers that could be appropriate dates?

Possible extension

The last part of the question offers plenty of scope for extending.

Possible support

A calculator will be necessary.