Exploring Triangles

As promised here is how our triangle exploration activity went. The activity we developed used Geogebra to have students create three different types of triangles and then measure the angles. Click here to see the handout we worked from. We started out the lesson by having students recap the different triangle classifications. After we got Geogebra up and running on the laptops each pair of students took off making triangles. My CT and I talked about how surprised we were that they were picking up how to use the program so quickly. Especially when we compared it to when we used it for the first time (let’s just say it was more confusing for us then it was for them). As they made their triangles, their goal was to make three different triangles of different types (scalene, equilateral, etc.), then measure all the interior angles of the triangle, and then find the sum of the measures of the interior angles. Our hope was that they would see that it appeared likely that the sum of the measures of the interior angles for any triangle would be 180o.

We finished up this exploration the next day by first having groups of students report out what they found out about the different types of triangles. From this we had our hypothesis that the angle sum of a triangle is 180o. But now we still couldn’t just accept this we had to prove this. We did a “proof” where our students made and cut out any triangle they could draw on a piece of paper and then label the angles A, B, and C.

Part 1.

Part 1 of the Proof.

 Next we cut the triangle into three pieces making sure each piece contained an angle.

Part 2 of our Proof.

Part 2 of the Proof.

Our students then tried to prove the angle sum of any triangle by using the three pieces. We told our students to try and think about if there was anything they had learned about previously that had an angle measure of 180o. It took us around 5-10 minutes for all the students to get the proof. The main problem that we seemed to run into was students were trying to include angles that were not part of their original triangle in their proof.

In the end though all of our students were able to use the three angles to show that the sum of the angles is 180o by showing they could be lined up in a straight line.

Part 3 of the Proof.

Part 3 of the Proof.

After thinking about how this went I was really glad that we were able to do this. First off it went a lot better than expected our students worked hard throughout the entire process. Some were trying to get the greatest obtuse triangle or working really hard to get a right triangle a different way than was stated in the directions. When we started the proof some of students were already seeing it and there were others who needed some directed questions. In the end all of our students were able to figure the proof out, which was really rewarding to see. I think it also helped them to see that doing math is more than a teacher telling them something and expecting them to remember it. We hope to be able to incorporate more Geogebra activities in our class time as we work through our geometry unit. We also have more discovery based learning ahead! This week our students are going to be working in groups to find properties of different quadrilaterals and then sharing with the whole class what they found in order to work toward creating the quadrilateral hierarchy. It’s great to see how engaged our students are when we do these types of activities rather than notes everyday!

“Give the pupils something to do, not something to learn; and the doing is of such a nature as to demand thinking; learning naturally results.”

John Dewey

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