Merry-Go-Round Project Revisited

Last March, I did this project for the first time and blogged about it here.  I really liked how it went and decided I would do it again, but this time I got my superintendent to stop by a couple of weeks ago, interrupt my class, and pose the question of refurbishing the hexagonal merry-go-round question to us.

I asked the students if they were willing to take this on.  I told them that we would have to fit it in along with our other work, but that I thought they could do it.  In fact, I was sure they could.  They told him they would and then they peppered him with questions:

• Was it a regular hexagon?
• How big was it?
• How much was the paint?
• How many coats?
• What was the area of the merry-go-round?
• Was it wooden or metal?
• Did the hand railings need painting too?

And on and on.  It was great.  He said he would have to ask the person who had emailed him and he would get back to us.

I let them work on it one day that cycle (we were doing polygons.....what a COINCIDENCE!).  One cherub asked me if this was a real project.

I gave him a deer in the headlights look.....and then said, "oh, Jake.  You know, Mr. H and I have been friends for a really long time.... I am assuming this is real. I don't know that he would take time out of his busy schedule, but you could be right!  Maybe he is pranking me!!"

Today we finally got back to this.  I started by sharing Jake's pondering about the reality of this project.  "But tell you what.  I have arranged for Mr. H to come and listen to us present this.  IF this is a prank, let's prank him back!  Can we find at least 3 different ways to find the area of this hexagon?  That way he will have to sit through THREE presentations!!  Here is the info he sent us."   I had them work in pairs, and conferenced with each pair.  As I found pairs that used a common method, I grouped them into larger groups until we had exhausted methods.

My students found FOUR unique ways to find the area:  Trigonometry, special right triangles, Pythagorean Theorem, and (my personal favorite) Heron's Formula!  I did not let them assume the hexagon was made up of 6 equilateral triangles.  They had to prove it, and they did:  using 2 different methods.

I am really proud of these kiddos.  They really got excited when they found yet another way for solving the area of the small triangles.  The great thing is that not all kids saw 6 triangles:  some kids saw 2 trapezoids, and another saw 3 parallelograms.  In the end, they all had to calculate a height.  Whoot!  Tomorrow we present and I will add pictures.