In my Advanced Geometry class we had been learning about triangle centers. If you had ever taught triangle centers, you probably know that students are confused pretty much the entire time since there are so many different things to remember. I found this beauty on Teachers Pay Teachers from All Things Algebra (she is wonderful!) to help students organize their information and see the four different centers in one location. It has been a lifesaver and has helped the students out a lot.
Once we wrapped up triangle centers, we started the Triangle Inequality Theorem. For my advanced students, this would have been a pretty easy concept to say, "here it is, this is how it works, do it." At this point, however, we are tired of doing worksheets and taking notes. So I was searching Pinterest for some ideas on how students can discover the theorem, not just have it given to them. I came across several different posts that I liked and combined them a little. One post that I liked in particular was called Spaghetti Triangles (and I'm sorry that I didn't credit that person, but I can't really find the pin). In this activity, students are given 10 pieces of spaghetti noodles (I actually gave mine linguini because it's just a little bit thicker). They had to break one noodle into three different pieces, measure those pieces in centimeters, and try to make a triangle. They did this 10 times, all the while figuring out what they needed to do to break their noodle to make a triangle. They then had 3 questions they had to answer regarding their results and what conclusions they could make. They LOVED it! It's hard to get some advanced students into simple tasks like this, but this was one that everyone participated and was engaged in the entire time. Once we finished the activity, we came together as a class and talked about some examples of measurements that did and did not make triangles. This helped lead up to talking about the triangle inequality theorem and how it works with triangles. This is probably one of the most fun activities that I had ever done in a class. It was simple, yet very effective. Here is the paper I gave my students. Feel free to download it and use it for use in your own classroom.
Here are some pics of my students doing this activity.
If you use this, you won't be disappointed. I'm sure your kids will love it. Enjoy!