Axes of Mathematical Doom
Just think… in a few weeks, you’ll have a new crop of brand-new Year 7 students. Shiny faces, uniforms without holes and a complete pencil case. For about a day.
So it’s nearly time to teach graphs.
You may have already seen the resources produced by the ASE on the Language of Maths in Science (LoMiS). If not, go download them for free and have a look. It’s worth it, really. For a quick taste, Richard Needham did a piece for the Royal Society of Chemistry a while back which is a great introduction to the aims of the project.
And here’s an approach I’ve come up with which you may find a useful beginning. It’s based on what I’ve done in lessons in the past with a final addition I’ve been discussing recently with delegates and colleagues at the SPN Oxford Summer School.
1 Number Lines
Putting numbers in sequence on a line is something students start to do at a young age, long before secondary school. To be honest, if kids can’t put whole numbers in the right order then graphs are going to be a distant dream. I agree that decimals make this harder at times, but I’m working on something about that too. Next week, maybe.
So give students a list of values and ask them to put them on a number line in order. Add challenge by having them convert values between units first, or have different numbers of significant figures. Top half of image:
2 Number Lines to Scale
They might do this automatically. If not, it shouldn’t be too hard to have them do so (image above). Once they have a scale sorted out for the line, placing laminated cards for your supplied values along it should be straightforward.
3 Number Line to Scale = Axis
If you now have your students put the two number lines (one from each set of values) at right angles, they should be able to see that they’ve defined each point.
4 Mathematical Axes Of Doom
Two wooden dowels from B&Q (other DIY stores are available), with insulation tape wrapped round at regular intervals. I deliberately chose different intervals. Next time, I’d probably use wooden dowels with rectangular cross-section, simply so they don’t roll. You could use metresticks but I wanted to avoid any numbers. The tape is all you need, really.
Put them at right angles and you have a set of axes, with the intervals clearly marked. Add the coordinate cards – because students have used the idea of a coordinate system for a lot longer than they’ve used graphs to tell a story – in the right places. They’re easy to adjust, so there’s less stress. (Low stakes, yes?) And if they look from above, any pattern is clear and anomalies can be considered. They can even see the best-fit line.
Extension ideas; use larger or smaller cards to get over the idea of precision in the readings. There is a link here to the idea of error bars, something we don’t usually cover but may find useful.
Thoughts, ideas, suggestions? Please let me know in the usual ways.
NB: you get funny looks if you carry the sticks on to a train.
Filed under: maths, planning, resource, teaching | 3 Comments