Imagine you are entering a classroom and the teacher has placed 3 chocolate bars on one table, 2 on another, and 1 on a third. There are 4 of you waiting to be seated, and you are the first in the room. The chocolate will have to be shared by whoever sits at a table. Given that you all love chocolate (who doesn't?), and that you can sit wherever you like, but must stay there once sat down, where do you sit to get the most chocolate?

Let's see. If you sit at the table with the most chocolate (3 bars), you've got the most, haven't you? Well: the next child will see that sitting with you will mean 1 and a half bars each, so they sit at the table with 2 bars. OK so far. Now the THIRD child will see a table with one bar, sharing two bars with another child or sharing three with you. So they sit with you. The fourth? Ah, they can get a table and a bar to themselves, or sit with a classmate and get just one bar. So it depends on whether they want company, or whether they like their classmate enough to let them have the two to themselves. Either way, your best bet is to sit at the table with two bars and scowl at the fourth child! Only joking; but this problem has many different variables - numbers of children, numbers of tables, numbers of chocolate bars. If there are 5 children, you are definitely in a better place sitting at the 2 bar table. Can you see why? What if there were 6?

Part of the way I teach is to show people relatable problems and how to work methodically through them to find a solution. And to show how to adjust that solution for different scenarios.

In your head, think of a cube and imagine touching all of its corners and faces. Now, imagine that you are a wizard, and can turn the faces into corners, and the corners into faces. Pull out the faces into corners, and flatten each of the corners (not the new ones). Drawing this new shape might help you. How many corners does it have now? How many faces? What shape will the faces be?

Why is 1 plus 1 2, when 1 times 1 is 1? Does that make sense? What actually IS multiplication? Can you write down in words what you do to a number when you times it by 6?

Imagine there are an infinite number of seats on a bus (an infinitely-long bus). Imagine there are an infinite number of people on that bus. Is it full? What if another infinite number of people joined the queue to get on. Could they be accommodated by everyone in the bus moving back to the row number they're in times 2? Why can't they just move one row back?

Let's figure it all out together!