A fun way to transition from lines to triangles is this activity from Mr. Stadel. I retyped it to get the instructions and diagram on one page, it's exactly the same as his though.

With just a single extra line, you can prove that the angles of a triangle add up to 180:

http://en.wikibooks.org/wiki/Trigonometry/Proof:_Angles_sum_to_180 |

Now we've mentioned the word triangle, time to explore sides and angles! This sheet is adapted from one in my textbook. I edited it with my colleagues. It was awesome. Kids sat quietly cutting out their side lengths, trying triangles and figuring out what worked. They weren't just quiet because they were cutting and tracing, there was thinking involved in the process. They were noticing and wondering, because, as one student declared, "You

**always**ask us that!" She was complaining that I asked her to write something down when she finished, but what a great complaint 'You always want to know what we think!' I smiled, I have no idea what thoughts ran through her head, but then she commenced recording her ideas.

I'd have a picture of graph paper rulers, but I forgot to take one. Might remember tomorrow. Idea: cut out rectangles 1 box wide in the length needed. Compasses, wooden rulers and plastic rulers all work as well, but compasses are tough to hold steady and most rulers are long and thus unwieldy. We used graph paper just a bit larger than the standard size. Give kids one full sheet to draw on and a quarter sheet to cut from and they're good to go.

Goals of this activity: figure out what side lengths make a triangle (triangle inequality) and discover the angle-side relationship. Having the side lengths in decreasing order would make the second discovery more obvious. I chose to have kids work for it a bit, but am open to change. This page was typeset in LaTeX, if you want the original file so you can edit it please let me know.

My next step would have been to define all the words that we use to classify triangles, but since I already did that it will be to have kids work through stations practicing and applying the rules they discovered. I'm unreasonably excited about the coupon holder I got at Staples for keeping all of my station activities in order. Organizers are such fun!

Great post!! I like the measuring activity to prove what is a triangle or not. I did Stadel's activity with my previous unit on Triangles and the students loved it. Thank you for blogging about this and helping me plan my unit!!

ReplyDeleteThanks for pushing me to post, I've been meaning to!

ReplyDeleteFun activities. Makes me wish I was teaching geometry this year! The second document in particular makes me think about how to use Sketchpad or some such techno-savvy tool to accomplish the same goal. Not sure if it would be worth it in the end, except that we would be asking students to use the same tools later on in the unit...

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