## Wednesday, 17 June 2015

### Hannah's Sweets - Combining topics

The recent question about Hannah's Sweets on the Edexcel GCSE maths paper caused much angst and discussion on Twitter. Those students taught to answer previous exam questions seem to have been those complaining the most. However, the future direction of maths GCSEs means that more questions like Hannah's Sweets will appear. Unfamiliar contexts requiring problems solving will become the norm.

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.