Decision Making With Right-Angled Triangles

Tl:dr – Pythagoras Trigonometry Angles Interleaved Practice resource

Teachers have always ‘atomised’ content. Breaking down big ideas and concepts into manageable steps is the bread of butter of good teaching (it’s even the bread and butter of naff teaching).

Every teacher knows when you mark mocks, the isolated nature of each of the questions means that if students see a right-angled triangle, often they try and do the last bit of maths that involved right-angled triangles explicitly. (I’m still haunted by the memory of a pupil find the third angle in a right-angled triangle, but then multiplying them together and dividing by two). It’s difficult. Making decisions about what maths to do isn’t something to be left to chance, and is actually teachable (or rather; practicable)

The first task in the sequence of lessons around trigonometry involved just identifying from a load of triangles which ones you’d need to use trig for and which ones you’d need to use Pythagoras for. I was very smug about how I’d made the implicit explicit for my kids and how gloriously set up they’d be for the future.


I had severely underestimated how much of that decision-making process they could undertake alongside all the other decisions needed to answer a fairly basic AO1 trigonometry out of context.

I couldn’t find anything that matched what I wanted (procedural fluency with decision-making with as little distraction from this as possible – sorry ladders against walls… not today) so made something myself.

The resource can be used as retrieval practice, interleaving mixed content areas or as a starting point for decision-making and is linked as a powerpoint at the top of this post.

Yes, it’s a boring pair of worksheets – until you give them to children!


Description and rationale


Sheet 1


Sheet 2

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