Reflection: Advanced Students Partitioning Segments in the Coordinate Plane - Section 6: Extension Task: Centroid as Partitioner

 

Knowing that the centroid is located 2/3 of the way along the median from a vertex to the midpoint of the opposite side is a very useful fact when solving problems involving points of concurrency (particularly in equilateral triangles when all centroid, orthocenter, circumcenter and incenter coincide). For this reason, I share this useful fact with my students.

Most students are happy just to know the fact and to be able to use it to make problems easier to solve. In fact they would prefer not to know the why and how of it. But I had one student, in particular, this year who would always stay after class and ask "But why is that true?" I designed this extension task for this student and students like him all over the world.

Seriously, though, in retrospect, how nice it would have been to be able to respond to this student's query with a prepared task such as this that would capitalize on his curiosity and challenge him in a way that would spur his growth. Well, next time this scenario occurs, I'll be prepared.

  Being ready when students ask 'Why?'
  Advanced Students: Being ready when students ask 'Why?'
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Partitioning Segments in the Coordinate Plane

Unit 9: Analytic Geometry
Lesson 6 of 7

Objective: SWBAT determine the coordinates of a point that partitions a line segment into segments of a given ratio.

Big Idea: 'Howdy Partishner'...In this lesson, students will use analytic geometry to define the coordinates of partitioning points.

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Saratoga Springs, NY
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Stephanie Conklin
 
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