Find the size of each of the angles in the pattern blocks shown. Protractors are not allowed!
When the students began the task proper (and after they asked me a dozen times if I really meant they couldn't use their protractors!) it was interesting to see their strategies.
Some just estimated angles (below). It was a quick fix to show these students that some of their answers were contradictory and that they needed exact answers instead.
Some recalled that there are 180° in a triangle so this meant that each angle in the equilateral triangle was 60° and progressed from there. Others put compared three equilateral triangles to two right angles (or squares) as shown:
As much as possible, I am learning to hang back and not jump in and show students what to do: when I do this, I realise that it is me doing the maths, not them; it is me reasoning and proving, not them. There certainly are some awkward pauses when I do this but this is most likely because the students are mulling over what they could do.
And sure enough, they could solve the problem without my help:
And for fun, they could verify their solutions in more than one way:
So when it comes to problem solving, I really like the philosophy from Singapore's Ministry of Education:
Teach less, learn more.