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MP8: The Centroid of a Triangle

17 Aug

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”?

SMP8 #LL2LU Gough-Wilson

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.

1 Screen Shot 2015-03-03 at 9.43.12 AM.png

What is significant about the coordinates of the centroid?

2 Screen Shot 2015-03-03 at 9.43.24 AM.png

Students then interacted with dynamic geometry software.

Centroid_1.gif

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.

Centroid_2.gif

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

4 Screen Shot 2015-03-03 at 9.54.50 AM.png

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 …

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2 responses to “MP8: The Centroid of a Triangle

  1. LeeanneBranham (@LeeanneBranham)

    August 19, 2016 at 12:49 pm

    really enjoying this series – thanks!

     

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