One of my favorite ways that I like to enhance instruction in my math classroom, particularly in Geometry, is by using hands-on learning with my students. This has them in effect learn by discovery. Nothing beats watching my students as they actively engage in the learning process by exploring concepts, answering questions and discovering new relationships. As they work in cooperative groups I can see their confidence and self-esteem grow as they assume responsibilities within the team. In addition to this, I usually find that my students show higher comprehension of the concepts that they discovered on their own.
I introduced this activity to my students after we discussed the median and midpoint of a triangle. I then explained to them that the centroid of a triangle is the center of gravity for a triangle. The students were assigned a group where they constructed triangles, located the midpoints of each side of the triangle, drew in medians and then located the centroid which happens to be the intersection of the medians of the triangle. The students were able to prove that the centroid is the point of balance by threading a knotted string through the centroid and watching their triangle balance as they held up the string.
I then had each group measure and record the distances from the midpoint to the centroid and the centroid to the vertex of the triangle. The students were excited to see and discover a pattern! They came to realize through the hands-on lesson that the distance from the centroid to the vertex of a triangle will always be twice the distance from the midpoint to the centroid of a triangle.
As an extension to this activity, the students went through a process of locating the center of balance for an L-shaped figure. Students were quick to discover, as they all created L-shapes of different sizes, that while the centroid of a triangle must always lie inside the triangle, the centroid of an L-shaped figure will not always lie inside the shape.
It was a fun and educational activity for my 9th grade class right before Thanksgiving break. They really “learned by doing”!