# Surprises you get watching kids do math

My older son is finishing up a chapter about right triangles in his Geometry book.  The last section in the chapter discusses how to construct perpendicular lines.  This topic has come up a few times previously, so I dedicated a bit more time to the previously section – Heron’s formula – before starting in with the new section this morning.  I also left one of the examples in the book for him to work through as part of his homework.

One of the other homework questions was to construct a segment with length $\sqrt{3}$ given a segment of length 1.  I thought this might be a little bit of a challenge and was pretty interested to see how he would approach it.

When I got home from work this afternoon I got a nice surprise:

Me: Were you able to construct the 30-60-90 triangle?

Him:  That wasn’t one of the homework questions.

Me:  Oh, I thought there was one about constructing a length equal to $\sqrt{3}.$

Him:  I made a 1 – $\sqrt{2}$$\sqrt{3}$ triangle for that one.

Funny how focused your mind gets when you “know” how to do something.  Wouldn’t have thought of this approach in a million years.  Nice little construction!