## Constructing Triangles

“Constructing Triangles” is not one of my favourite topics to teach. There is the niggling fear that one of the boys may stab another (this has never happened while I’ve been teaching, but I remember it happening on more than one occasion way back in the 90’s during my own schooling!) and there is the fact that pupils seem to think that using mathematical instruments is licence to chatter more. Neither of these, however, is the reason I dislike it. I enjoy teaching some construction, I like having lessons on using compasses, giving pupils licence to create patterns with them. I like getting the class to draw scale drawings involving construction. I like teaching Loci and other applications of it. It’s specifically the triangles.

The reasons why are numerous, but they boil down to two things: “I can’t see why it is important,” and “I can’t see any creative way to hook pupils in.”

**I can’t see why it is important: **

I understand the technical skills involved are important for many jobs, such as architecture and others in the design and building industries, but the explicit construction of triangles isn’t. Pupils need to be able to draw and measure angles using a protractor, pupils need to be able to use a pair of compasses correctly and pupils need to be able to draw and measure straight lines accurately, but never, past their GCSEs will they be asked to construct a specific triangle.

**I can’t see any creative way to hook pupils in:**

I taught this yesterday to Y8 and I taught it in a similar fashion to the way I had done before, we practiced drawing angles, I gave them an ASA triangle and asked them to have a go. The more able worked it out and so I had them talk me through how to do it on the board for the rest of the class to do it then we worked a few out. I then repeated this for SAS and SSS.

The class already had the technical skills needed (i.e. to use a ruler, a protractor and a pair of compasses) and so it was about how to apply these to a triangle construction. I don’t think the lesson went brilliantly well, to be honest. By the end of it all pupils could construct all types of triangles and most of the class managed to figure out the challenge of “construct and angle of 60o” when I took away the protractors, so they all made the progress I wanted, but the lesson was a little messier than I would have liked.

I think that next time I will try to incorporate these constructions into a wider skills lesson. I find that for boys, getting them to construct a scale football pitch can be a good hook for constructions, so I need something similar that will work to hook the wider demographic. Any ideas/resources would be very much welcomed!

Now they make “safety” compasses which barely have a point.

Perhaps start by asking students to make a triangle with sides 3, 4 and 8 and see who “gets” it first.

Here are 2 tasks that use constructions in solving problems:

http://fivetriangles.blogspot.com/2012/12/41-constructing-circle.html

http://fivetriangles.blogspot.com/2013/06/80-equidistance.html

Cheers for these links, they are cool!

I already use the question you mention, although I use 9cm 3cm and 3cm! Its a good one because it gets them thinking about why. I find the brightest ones can see without trying that it won’t work (only two or three kids have done this in my lessons). There are always some who lack confidence who assume they’re wrong, and the majority figure it out given a bit of time.