Developing an Intuitive Understanding of Triangles

Lots of students think they understand triangles ~ three sides? three corners? What else?

Well, you don’t have to know trigonometry to realize that there’s so much more to learn about triangles. How can we teachers create lessons that get students engaged with exploring and making sense of triangles?

What do we want students to be able to do with triangles?

• Use academic vocabulary when reading, writing, or speaking about triangles.
• Given the size of two angles in a triangle, find the third.
• Find the area of triangles.
• Be able to identify the side opposite the largest angle.
• Identify when a specific triangle has mirror symmetry.

Without an automatic understanding of the above list, students will struggle later on, when they are asked to:

• Identify congruent triangles.
• Identify similar triangles.
• Find the orthocenter, centroid, circumcenter, or incenter of a triangle.
• Draw altitudes, medians, perpendicular bisector, or angle bisector.

What is Meaningful Messing About?

Meaningful messing about gives students time to explore, ask their own questions, state their own findings and compare their observations and discoveries with those of their peers.

hands on – purposeful, but low-risk,