Triangles I

I really do not like the progression of topics in the geometry text we are using, so I've cobbled together a mix of triangle topics that the students explore through a variety of mediums. Students began with a GeoGebra investigation to explore the Triangle Sum Theorem and the Triangle Exterior Angle Theorems. Students are still learning GeoGebra, but they really helped each other out locating tools in the menu and surprisingly the laptop cart was cooperative. I'd say this approach, while dynamic, was only so-so in terms of its value.

The next day, we talked about what it takes to make a triangle. As students came in to class, I gave each student a sticky note and had them write three numbers from 1 - 20 then they stuck the note on the board. Each student then took 2 pieces of spaghetti, 3 mini-marshmallows and a random sticky and set about constructing the triangle with the given side lengths.

We ended up with a nice assortment of triangles and non-triangles. Students added their results to a table on the board (next time I'll use a Google Spreadsheet). Some students were surprised that there were combinations of numbers that did not produce triangles, and some of those of students were initially concerned that they had done something wrong.

After compiling a list of what worked and what did not, the students conjectured about what they could conclude about the side length relationships needed to form a triangle. We finished with a summary of the Triangle Inequality Theorem. They caught on quickly with the visuals provided by the spaghetti and were quick to describe the collapsing triangle or the one with sides that just couldn't stretch far enough. All of them correctly completed the exit ticket problems related to this topic, but only time will tell if these relationships stick.

And yes, 9th grade boys will eat raw spaghetti or pretend to be smoking a cigar or pretend to be chewing on hay.