One of the issues with Hannah's Sweets is that it combined probability with quadratic equations, two topics not usually seen together. I wondered what might happen if two topics from other areas of maths were taken together at random and a question generated from it.

I created a grid of topics and considered the intersections:

Percentages | Sequences | Angles | Pythagoras | Ratio | Averages | |

Percentages | ||||||

Sequences | ||||||

Angles | ||||||

Pythagoras | ||||||

Ratio | ||||||

Fractions | ||||||

Averages |

So what might these questions look like?

__Angles & Ratio__

A triangle's angles are in the ratio 1:3:6. How big are the angles?

__Angles & Sequences__

A triangle's angles are in an arithmetic sequence with common difference 20. How big are the angles?

__Angles & Averages__

In a right angled triangle, the median average of the angles is 54.How big are the angles?

__Ratio & Average__

Three numbers are in the ratio 1:4:5. Their mean average is 40. Find the numbers.

__Sequences & Average__

Four numbers form an arithmetic sequence with common difference 2. If their mean average is 40, what are the numbers?

The potential for this type of question generation is huge. If you create any questions using this system, I would love to see what you come up with.

ps I had great fun considering right angled triangles where the sides formed an arithmetic sequence.