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 coordinates


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:

Number lines

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.

2 axes

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.

3 plotted

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.


3 thoughts on “Axes of Mathematical Doom”

  1. I agree that the “low stakes” is v important for low achieving students in particular. I have used acetate sheets and dry wipe markers in the past for this, I like your way too (I guess you could also use art straws too)
    Human graphs can be good fun too put 2 large tapes/pieces of string/sellotaped metre rulers, get kids to mark up the axes and give each one a coordinate and they stand there. Teacher photographs (usually stood on a stool oops health and safety!) and project onto screen.

  2. I like the idea of writing the coordinates on different sized pieces of paper, to reflect uncertainty in the measurement, and how this can be used to indicate ‘error’.
    Do children find ‘axes’ off-putting when they first encounter creating their own graphs? It seems obvious to experienced graph drawers that the axes are always at right angles, and that they appear on the left and below the graph, at least when handling data with two variables. Making a grid with four axes may help children to understand the derivation of the two axis convention, and should make locating coordinates more straight forward. They will recognise that scales on the right and top axes are unnecessary once they have developed confidence in locating coordinates.
    So my suggestion is to get down to B&Q and buy some square section dowel, mark up four equal lengths with tape as suggested above, and see if children find this an easier way in to graph drawing.

  3. See ASE’s AKSIS publication on graphs for further suggestions on ‘human graphs’ and choice of scales (unfortunately out of print). The Language of Mathematics in Science also provides guidance on graph drawing and choice of scales.
    For some children – A4 perspex sheet drilled with 3mm holes in a grid, and black tape left and bottom sides to represent axes. Use match sticks/ cocktail sticks to mark coordinates by placing in relevant holes. Join sticks with a rubber band to indicate curve of best fit. Then transfer to paper by placing grid over graph paper and replacing each stick in turn with a pencil mark. Helps remove the ‘anxiety’ of putting incorrect marks on ‘special paper’.

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