Conjecturing and generalising

What is special about the difference between squares of numbers adjacent to multiples of three?

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

There are unexpected discoveries to be made about square numbers...

Can you see how to build a harmonic triangle? Can you work out the next two rows?

Can you find an efficent way to mix paints in any ratio?

The illustration shows the graphs of fifteen functions. Two of them have equations $y=x^2$ and $y=-(x-4)^2$. Find the equations of all the other graphs.

Starting with two basic vector steps, which destinations can you reach on a vector walk?

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

Can you work out which spinners were used to generate the frequency charts?

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?