Teaching Plan
Centroid of a Triangle
Title: Centroid of a triangle ( Center of gravity in a triangle)
Grade : 9th
Lesson Summary:
    This lesson plan is to introduce the concepts about the centroid in a triangle. This plan not only has students know the definition,  but also has students be able to determine and analyze the properties through Sketchpad.

Lesson Standards Link

NCTM     NCTM Standards-1989
                 Geometry 5-8     9-12
Illinois State Board Education
Mathematics Standards - Geometry
Lesson Objective:
1. Understand the meanings of centroid in a triangle and identify the relationship among segments and areas
2. Know how to determine the center of gravity in triangle or other polygons
3. Connect and compare with other similar triangle geometric concepts

Computers, Geometer's Sketchpad software,  GSP files

Lesson Plan (One Day)
           Step 1- Introduction and class discussion
           Step 2- Group Activity
           Step 3- Group Discussion, Sharing, and Conclusion


Step 1: Introduction and class discussion
    At first, the instructor introduces the definition of centroid (the center of gravity in a triangle) to whole class. Review basic concepts such as midpoint of a segment, triangle. Ask some questions to warm up the class and clarify the definition for students. Such as: Can you find other method to find the centroid in a triangle? How many centroid points are there in a triangle? What is the difference with incenter of a triangle to renew related old triangle concepts.

Step 2:
a) Group Activity to understand the center of gravity in a triangle
    Have 4-5 students form a group.  Use computers to observe the possible properties and record them in order to discuss in next step. GSP file.
How can you find another centroid in the same triangle?
Can you find different methods to find the centroid in a triangle?
Can  you find some common rules of the centroid in a triangle?
Which of these small triangles appear to have equal areas?
What can you say about the areas and perimeters of  small triangles?
Are these small triangles congruent?
Can you use mathematics geometric proof to prove these properties?
Change the shape or size of  the triangle to observe the outcomes and explain them.

Step 3 : Group Discussion, Sharing, and Summary.
    Lead students to discuss their findings and make connection with the properties with other similar triangle concepts (e.g., incenter in a triangle)

In a right triangle ABC, angel ACB= 90 degree, CB=6cm, CA=8cm, G is the centroid of triangle ABC.
(1) What is the DISTANCE from point G to segment AB? [hint: Pythagoras theorem]
(2) What is the sum of  segment AG+BG+CG?

gsp file.

Any Comment: Yi-wen Chen  ychen17@uiuc.edu