You're having a graph
A creative combination of equations and ellipses might get your pupils to see the bigger picture. Colin Foster shows how
It can be hard enough at the best of times to get software to do what you want. But it's even more of a challenge when you're deliberately trying to use it for something it wasn't designed for.
Children naturally push equipment to its limits to find the biggest product their calculators will work out or how far they can zoom in when using graph-drawing software.
There is a long tradition of using maths equipment for purposes for which it was never intended. In the old days, you used to be able to make up calculations with answers that would read as words when the display was turned upside down. For example, 07734 reads as HELLO and 77345993 as EGGSHELL.
But most up-to-date calculators print the numbers too precisely for this to work well any more, and many allow you to type in letters anyway.
So how about using graph-drawing software such as Omnigraph or Autograph to draw pictures?
One option is for pupils just to experiment however they like and see what they can create.
Alternatively, you can make it more structured by indicating the kinds of mathematical graphs that you wish them to use.
For instance, just using equations of circles and ellipses, Year 10 pupils can make some quite impressive drawings, such as the snowman (above).
A lot of good mathematical thinking is necessary to achieve a picture like this. Typically, your curve doesn't appear quite where you want it or is the wrong size.
If something goes wrong, you ask: "Why did it do that? What do I need to change to get it the way I want it?"
The beauty of a computer-based approach is that pupils can quickly and easily modify their equations, experiment and get instant feedback, and there is no visible record of the "mistake".
Even when a drawing is "finished", you can always pose subsequent challenges: "How can you give him a bigger smile? A smaller head? A taller hat? Bigger eyes? Fingers?"
Pupils have a lot of fun being creative and some of their drawings can be quite stunning. Even just using straight-line graphs, there is a lot that can be done.
Here are more challenges:
- Can you write your initials or design your logo?
- Can you draw a flower or a butterfly?
- Research what superellipses are and see what drawings you can make from them.
- What other animalsaliensmonstersobjects can you draw?
This activity has the potential to be memorable, with pupils some time later recalling what the graphs of certain equations look like because they stumbled over them in the computer room.
This can also develop a subconscious sense about how a graph can be altered by changing its component parts, which can last longer and be more meaningful than a more traditional, rule-based approach.
Colin Foster teaches mathematics at King Henry VIII School in Coventry.