I was team teaching with a trainee today and she asked a question similar to the bottom middle question. The students found the unknown angle to be 70° and she asked ‘how did you know you could halve 140° to get the unknown angle?’ Students gave the answer ‘you take 70° from 180° and then you always halve whats left’ The trainee questioned that ‘do you always halve? What was it you saw in this question that let you know you could do this?’
So It made me think about questions that could have answer of 70° sometimes, always or never.
After a post on Twitter by @mathsjem https://twitter.com/mathsjem/status/1381970532912885764
I started thinking about angles in triangles and how its used in other areas of geometry. I had already looked at angles around a point https://mathshko.com/2020/08/09/angles-in-a-full-turn/ and angles on a straight line https://mathshko.com/2020/10/26/angles-on-a-straight-line/ in this way. I had taken some time to link angles in straight lines and round a point with pie charts, clocks, bearings and angles in polygons but hadn’t looked at angles in a triangle in the same way. Jo shared some exercises from an SMP book and commented on its being “a nice idea” and that she currently (typically) covers a huge chunk of circle theorems content in one go, often in Year 11″ and “why not introduce one or two earlier? Particularly isosceles triangles in circles” So I looked at questions where you could use the angles in and isosceles triangle but also discuss other ideas from the solutions.
I’m not going to discuss circle theorems with year 8 when I use this but just let them use angle in a triangle/isosceles triangle to work out the angles – we can discuss what we notice after