## Reflection: Grappling with Complexity Proving the Medians in a Triangle Meet at a Point - Section 1: Activating Prior Knowledge

When I originally designed this lesson, in the next section I had students determining the location of the centroid starting with the coordinates of the three vertices. This was a very complex problem to tackle all at once. Students had to find the midpoint of each side. They had to find the slopes and the equations of the three medians. They had to set up and solve a system of equations. And they had to verify that the point of intersection was on the third median. Not to mention the fact that they needed to have the knowledge of geometry and algebra required to pull all of that off. For many students, this was a lot to be doing at once.

This happened to be a lesson for which I had a math coach observing me. Her feedback to me was, "Since you already have students practicing writing equations early in the lesson, possibly you might design the lesson so that students use the equations they write in the first part of the lesson in the second part of the lesson."

So this is how the idea came about to use the same triangle for this activating prior knowledge section and the next section. With this revised design, students already have the equations of the medians before they are asked to find the location of the centroid. In this way, they can focus more on the meaning of the centroid and the algebra required to locate it given the equations of the medians.

This seemingly small tweak significantly reduced the cognitive load on students and allowed them to access the lesson a lot better.

Jigsawing problem components to reduce cognitive load
Grappling with Complexity: Jigsawing problem components to reduce cognitive load

# Proving the Medians in a Triangle Meet at a Point

Unit 9: Analytic Geometry
Lesson 5 of 7

## Big Idea: Alphabet soup anyone? Students will really need to master the abc's of algebra and be on their p's and q's to digest what's on the menu in this lesson.

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120 minutes

### Anthony Carruthers

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