Balancing Triangles: Finding the Centroid is a hands-on geometry activity in which students discover that the centroid of a triangle is its balancing point, or center of mass.

Students begin by learning about medians and the centroid, then use the 2:1 ratio to solve practice problems and check their understanding. Next, students cut out a triangle from a sturdy material such as cardstock, cardboard, a cereal box, or poster board. They find the midpoint of each side, draw the three medians, locate the centroid, and test whether their triangle balances on the tip of a cone, pencil, or other narrow point.

This resource helps students move beyond memorizing a definition and actually see why the centroid works. Because students may use different types of triangles and different materials, the activity naturally leads to rich discussion and deeper understanding.

This resource includes:

• Teacher guide with preparation steps, lesson flow, tips, and safety notes
• 2-page student activity
• Optional reflection and extension page
• Answer key
• Open-ended writing questions
• A measurement table to help students verify the 2:1 ratio

This activity is especially helpful for educators because it:

• gives students a concrete, memorable experience with medians and centroids
• works well for Geometry, Honors Geometry, and advanced middle school math
• encourages student choice and creativity
• supports mathematical reasoning, measurement, and written explanation
• can be completed in class, assigned as a project, or used as enrichment
• requires only simple, inexpensive materials