Polygons and Merry-Go-Rounds

I love the Mathematics Assessment Project and all the wonderful ideas and tasks they provide.  My geometry class just did the polygon lesson.  It gave them great opportunities to think, share, revise, ponder, etc.  One thing I especially loved about this unit, was the part where they show how different fictional students solved the problem, and my kids had to explain what the fictional student was doing.

But I wanted something that would pull together everything we have been doing: polygons, triangles of all sorts, Pythagorean theorem, special right triangles, trig, and areas.  So I put this up on the SmartBoard and asked them to do a notice and wonder,

One student wondered why I was showing them the picture. Yippee!  I made up a scenario:  One of our sending towns (we are a regional high school) has a similar merry-go-round that they would like repainted purple.  They asked our Superintendent if one of our classes could figure out the cost of doing this using a special (and expensive) type of paint.  I told him the Superintendent assigned the task to our class because he found out we were studying polygons.

I was VERY impressed by the number of ways that the students worked at finding the area of a single triangle.  Most tried to tell me that these were equilateral triangles, but when I said they were breaking the Don't Make Assumptions rule, they worked at proving to me that they were correct.

From there, some used Pythagoras to assist in finding the height.  Some used special right triangles, and others used trig.  There were all sorts of methods used to get an angle measure.  I do believe they are beginning to hear: there is NO RIGHT WAY.  Again and again I ask students to share:  How did YOU look at this problem?  

We will finish this up next time I see them, but they made some great progress today and I am proud of them.  Here is a link to the SmartBoard Notebook I made to go with the student pages.

I want to thank members of the MTBoS who continue to challenge and inspire me.  My goal is to create a nation of thinkers (or "noodlers" as we call them in my classroom): one student at a time!!