Centroid of a Triangle

Yesterday, my grade 10 classes learned about triangle centres. They each had a triangle awaiting them on their desk as they walked in (I copy them onto thicker-than-normal paper). 

I gave instructions along these lines:
- cut out the triangle
- figure out how to balance it on your pencil
- make note of the balance point
- figure out how the balance point relates to the coordinates of the vertices of the triangle
- when you think you know, create your own coordinates for a triangle ABC, write them on the board along with their balance point

That last part was new. Its inspiration is Joel Bezaire's Variable Analysis Game which you can learn more about here. It helped some students see the pattern (especially the last line that I added to make it a little more obvious) and kept those who had found it early engaged as they were checking that other student's coordinates and balance points worked.

It was a fun way to start the class so I thought I would share... Thanks, Joel!