# Using Prime and Square Numbers - How Old Am I ?/Document

This could be a starter activity rather than a full lesson.

Introduction
On the board display the text:
“Last year I was square, but this year I am in my prime. How old am I?”
Ask the pupils to explain what this means. [My age last year was a square number, whereas this year, one year on, it is a prime number.]
Let them start to tackle the problem. This is a good task to begin with the pupils working individually, in silence. They can then, after a couple of minutes, share their ideas with three others and can work on it further. This allows them to have some ideas of their own but then to integrate them with other approaches and to change tack if necessary. They may discover that their initial approach was not the most efficient; explaining this is part of the learning process.

The most efficient procedure appears to be to list the square numbers and then to check whether the number one greater than these is prime or not. They should quickly realise that, apart from 1, it is not worth considering odd square numbers because the number one greater than these is even and the only even prime is 2.
1 -> 2
4 -> 5
16 -> 17
36 -> 37
64 -> 65 (which is clearly not prime)
100 -> 101
There are, therefore, five immediate possibilities (with more above 100 too) but of these the only credible one is that I am now 37 years old.