Recently I have been teaching angle properties and calculations to Year 7 and Year 9. Particularly in Year 9 we have been exploring problems that require multiple properties and steps to arrive at a solution such as the problem below:
rather than trying to find h and then trying to find i, we instead just went through the different angle properties we knew and found angles that fit, including completely useless facts like 46 +90 + 44 = 180. Altogether we wrote down:
h + 46 + 90 + 44 + 61 + i = 360 (full turn)
h + 46 + 90 = 180
46 + 90 + 44 = 180
44 + 61 + i = 180
61 + i + h = 180 (all straight lines)
h = 44
i + 61 = 46 + 90 (both vertically opposite).
Only when we had written all of this down did we talk about and look at which bits of information may be useful in helping find h and i (quickly identifying multiple ways of finding both h and i) and eventually writing down the values of both angles.
This approach is definitely having an impact in terms of pupils working through these sorts of problems as they are less hung up on the fact that they can't immediately find values of an angle and are correspondingly (nice use of terminology!) more ready to make an attempt at these problems. This, coupled with a visualisation of walking down the paths that the diagram shows (more on this in a blog to come) seems to be a real support to pupils in working with these sorts of diagrams.