In this Illustrative Mathematics task, students are asked to place a warehouse equidistant from three roads.

Students started on paper. Some used their ruler, some their compass, and some folded their paper. I was surprised how few thought to solve a simpler problem (equidistant from two roads), since we did that the lesson before with the fire hydrant. But I think I am beginning to recognize that problem solving itself is a practice – you have to practice it to get better at it, and you have to think about what you are doing and whether something you have done before might be helpful. I had a college professor who talked about a “bag of tools” – each time we would learn some new method, he would remind us to store that method in our bag of tools to consider using the next time we had to solve a problem.

Many students tried the centroid (point of concurrency for the medians).

Just for the record, I use the Reflector App through my computer & iPad to display student work on my Promethean Board so that everyone can see it and so that we can write on it as needed.

Some folded the roads on top of each other through each point of intersection to come up with the angle bisectors.

Some students tried the circumcenter again. So we showed that the circumcenter isn’t necessarily equidistant from each of the sides of the triangle.

We moved to TI-Nspire where students constructed the incenter of the triangle and then the inscribed angle. Students changed the triangle to observe the location of the incenter. Can the location of the incenter give us insight into the type of triangle like the location of the circumcenter?

We ended with the straightedge and compass construction for an angle bisector and paid attention to what is congruent in the result.

And so the journey continues…