MP8: The Centroid of a Triangle

We had been working on a unit on Coordinate Geometry.

How do you give students the opportunity to practice “I can look for and express regularity in repeated reasoning”?

When we have a new type of problem to think about, I am learning to have students estimate the answer first.

I asked them to “drop a point” at the centroid of the triangle. We looked at the responses on the graph first and then as a list of ordered pairs.

What is significant about the coordinates of the centroid?

Students then interacted with dynamic geometry software.

What changes? What stays the same?

Do you see a pattern?
What conjecture can you make about the relationship between the coordinates of the vertices of a triangle and the coordinates of its centroid?

Some students needed to interact on a different grid setup to see a relationship.

After a few minutes, I sent another poll to find out what they figured out.

And then we confirmed student conjectures as a whole class.

And so the journey to make the Math Practices our habitual practice in learning mathematics continues …