MathsConf24 – Teaching Compound Measures with Ratio and Proportion

Today saw me do my first ever MATHS related presentation at a MathsConf. I was pretty worried about talking about this – because the closer it got to the day, the more I thought this session was really simple. I felt like it was common sense…. then I remembered that 3 years ago, it wasn’t common sense to me, so I went ahead and shared.

Anyway, technology got the better of me today and I ended up with a slightly blurry presentation. So as promised, here are my slides, so if you need to have them alongside my speaking on any replays!

I haven’t included any more annotations to go with them, but will provide a link to the recording of the live session if I am able to in the coming days.

To summarise:

  • Formula Triangles are a no-no. I said ‘hate’ a few times. And I meant it. They do not promote an understanding of the underlying concept, and do not aid with algebraic manipulation either.
  • Bar Models are a useful place to start – but where we, as teachers, can efficiently see how to break these down to reach ‘1 hour’, many students can’t see them as easily. There are too many potential factors/multiples of 1 hour/60 minutes to potentially work with, and picking the ‘split’ adds to the cognitive load for many!
  • Multiplicative reasoning seems much more straighforward for some pupils – they only need to think about the multiplication and division, not ‘splitting a bar’.
  • The key is that a compound measure is a UNIT RATIO. You just need to identify the unit. E.g. Speed is a ratio of distance to time, with time as the unit.
  • “Playing” with these to find related facts, including unit changes, cements the concept even further.
  • Ratio tables and notation expose the multiplicative links clearly – students tend to use them intuitively in this notation.
  • Changing within the unit requires a change on ‘both sides’. Change to the unit i.e. m to km, can be done on one side.
  • Speed examples are used predominantly here, but there are applications in density and pressure.. and MANY other topics!

Please feel free to get in touch with me by email or on Twitter to discuss more if you would like to!

If you would like to access the video on the 5th slide you can find it here.

Thank you so much to LaSalle for hosting again – it was a brilliant day – and thanks so much for allowing me to speak! Thank you to anyone who came to the session, and for all the kind comments and questions. You’re all helping to make me better too!

One thought on “MathsConf24 – Teaching Compound Measures with Ratio and Proportion

  1. Thanks for the slides. I discovered this after listening to Craig Barton’s podcast with Jo Morgan. As a physics (and occasional maths) teacher, I spend a lot of time teaching compound measures. I love to use ratio and proportion to develop understanding of these ideas and to set the scene for more complex algebraic reasoning in year 12. I’ve never used the boxes structure though and particularly like the idea shown in slide 11. I usually talk about “per” meaning “divided by” and will look at how to pull these ideas together.


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