Seeing and Working with Triangles in a New Way

Sometimes you just need a new way to “see” the math.

On Monday, I observed what was to be an 8th grade math lesson on solving for angles of triangles. I watched Mr. K’s 50-minute class period go by with homework being corrected and recorded, a few problems from the homework reviewed, and a start at classifying triangles.

In the middle of explaining the relevant terms (scalene, isosceles, acute, obtuse, etc.) Mr. K stopped, as there appeared to be some confusion about the relationship between the interior angles of a triangle. So, he had the students cut out a triangle and complete the following:

• Label each angle as 1, 2, and 3.
• Cut off the corners of the triangle, making sure you can still read the numbers.
• Arrange the cut corners by matching angles 2 and 3; and then angle 1 to 2.

After this, students were asked to observe the arrangement. The conclusion was that the sum of the angle measurements in the triangle totals 180 degrees, and that was true for all triangles. This can be observed, because the straight edges of the triangle all match up and form one edge, or a straight angle.

Triangle Angle Sum

The triangle activity Mr. K had the students complete was a good way to review previous learning. It was hands-on and focused on conceptualization. In fact, it was already used in the direct instruction of the lesson the previous week. But, the lesson just didn’t seem to go the way Mr. K wanted. Maybe it was because Monday was the first day back after the Thanksgiving break, or maybe it was that these 8th grade students just weren’t interested in math on a Monday morning. Or maybe, they just needed to “see” the math in a different way.

I talked to Mr. K after the lesson about the overall engagement of the students and the activity they worked on, and I asked him to stop by my office after school as I had a resource to show him that I thought would help him in his next lessons.

We looked at Adaptive Curriculum’s “Type of Triangles” in which dynamic modeling is used to create different triangles so that students can observe the changes in angle and side measurements as it relates to classification.

I chose this Activity Object not just because it focuses on the content being addressed in Mr. K’s lesson, but it allows for excellent use of Mr. K’s Smart Board, which would allow the students to get more engaged and involved in the lesson about the relevant vocabulary.

The plan was that we would use this Tuesday with his two classes.

This morning, we played around with “Types of Triangles” a little bit more and also looked at “Interior and Exterior Angles of Triangles.” Mr. K was excited about both of these Activity Objects and we played and discussed them for about 40 minutes. Mr. K decided that he wanted to spend some more time with these Activity Objects before using them with the class, and we made a new plan to use them on Friday.

I’m excited that Mr. K is excited! And I’m looking forward to spending more time in his classroom on Friday.

I’ll let you know how it goes with the students on Friday and how Adaptive Curriculum’s Activity Objects allowed students to “see” math in a new way.