When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Can you find a rule which connects consecutive triangular numbers?

Can you find a rule which relates triangular numbers to square numbers?

Show that all pentagonal numbers are one third of a triangular number.

This function involves absolute values. To find the slope on the slide use different equations to define the function in different parts of its domain.

Draw graphs of the sine and modulus functions and explain the humps.

The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?

When we add, subtract, multiply or divide we draw numbers from infinite sets. Here we see that sometimes we are working with an infinite group and sometimes not.

Infinity is not a number, and trying to treat it as one tends to be a pretty bad idea. At best you're likely to come away with a headache, at worse the firm belief that 1 = 0. This article discusses the different types of infinity.

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.