It’s the way they write the questions: a case study

The great @mathjem recently took advantage of snowy weather to post this question:

On the one hand, it’s quite nice: using the weather and a popular culture reference to set a question on a semi-realistic topic. On the other, I have problems with it.

Let’s brush aside ‘percentage rate’ – it’s not a term I recognise, but I can work out from the context that the same percentage of snowman melts in every time period, so it’ll be a compound interest/geometric series problem. In an ideal world, that wording would be a little clearer.

The real problem is, percentage of what? According to @mathsjem, it’s the height – but that’s certainly not the way I’d interpret it. If we’re talking about the percentage of snowman melting, you would need the volume (I’d measure melting in $\text{cm}^3\text{h}^{-1}$, myself, not centimetres per hour.) If you’re talking about physical reality, I’d expect the melting rate to vary with the surface area rather than either height or volume.

I’m assured that none of these issues have ever come up in class, but I’m not especially reassured to hear that: I think students should be questioning ambiguous questions, or else they’re likely to end up averaging goats1.

Don’t get me wrong, though, there are times for ambiguous questions, and the discussion thereof can be extremely useful – if only as a riposte to the endless complaints of “I don’t like the way they write the questions.”


Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.

  1. I don’t have the reference to hand, but the experiment asked students something like “You have 128 goats in four pens — how old is the goatherd?”; many students diligently worked out $128÷4=32$ and confidently asserted that was the goatherd’s age. []


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