To solve this question for student aged 8 to 13 might be quite tricky, especially if you do not know them yet and if you have to get a very good notion of their skills and knowledge in only few hours. You need to „assess“ their skills without stress and tests, but in a way that makes them feel more interested in mathematics (and some of them got in their old schools already disinterested). Mathematics includes many disciplines that are quite different – arithmetic, algebra, geometry, general logic and more. On the other side we do live in an interconnected world and these disciplines are also very well connected. The basics are the same and have the same beginning. And this is also the very natural beginning – the numbers.
So, a possible approach is the start with the numbers. The first task that we can state to the kids is to write the number 1 in as many different ways as they can. This gives almost unending possibilities which are only restricted by the children’s creativity! But it is endless, by fact!
Then we keep going with the numbers 2, 3 and so on up to 10. It is important that the teacher can lead the kids to recognise that we can observe the numbers as quantities, but behind them there is also a specific quality. What is the meaning of 1? It is the unity! Where can we find this number in the world around us? And so on for the other numbers. On the other side, 1 remains in some way unique, because we can write every other number in terms of 1! We can even write whole words with this single number! We only need to use the different mathematical operations and some basic logic.
We can also go from 1, from the unity, down to its parts – 1/2, 1/3, 1/4, which we can represent in many different ways – 0,5; 0,(3); 0,25 or 50%; 33,(3)%; 25% and so on. In this process we get not only an overview of the numbers, but also of the operations of numbers. But we can also ask the students (if they do not come alone to that idea) to represent the numbers with some drawings or even with some geometrical figures.
We use this kind of introduction also in order to define the different subareas of mathematics, that we are going to explore in details in the future. And to show how the different cultures handle mathematics. Every culture shows similarities with its fellow cultures, but is also unique and that can be seen in the way how people think and how they handle mathematics.