The Surprises Within a Triangle’s Angles
When I’m designing a lesson, one of my go-to tactics is to fight against my own “Curse of Knowledge.” The more familiar we become with a topic, the harder it gets to remember that there are lots of unexpected surprises. We take the content for granted and rob our own lessons of curiosity.
So, approach your lesson-planning with a beginner’s mind, wondering: if I knew nothing, what would be unexpected about this topic?
So What’s The Twist With Triangles?
What are the unexpected twists or interesting patterns of triangles?
- I’d always tell my students that a triangles’ angles must sum up to 180º. But, friends, imagine allowing students to play with triangles first. Build ten different shaped triangles, class. Finished? Now I’d like you to sum up the angles in each triangle. What do we notice?
- Imagine challenging students to create a triangle with a right angle. Then, challenge them to create a triangle with two right angles! As they realize it cannot be done, discuss!
- Pose the question: what’s the largest angle you can create inside of a triangle?
- What happens when we make one of the triangle’s angles very small? What happens to the other angles?
- What if we make one angle very very large? What happens to the other angles?
- You could also extend these wonderings to side lengths. When we make an angle big, what does it do to the triangles’ sides?
When we build our lesson around what’s actually interesting, all of the sudden a dull lesson becomes quite exciting (for them *and for me).
Build Around Unexpected Patterns
The angles inside of a triangle may not seem inherently interesting. The fact that the angles must sum up to 180º may seem like a dull fact we have to just tell kids. But, if we approach this topic purposefully looking for surprises or controveries, there are lots of interesting discoveries that we can purposefully set up for our students.
This tactic is the idea behind inductive learning: human brains are really good at pattern recognition. Lessons that build on patterns are naturally in line with the human brain, which means better learning and more dopamine! And I guarantee you that when students discover these properties, they’ll remember them far better than if you just told them.
All of this triangle thinking eventually turned into this lesson over at Byrdseed.TV.