Discovering the triangle inequality theorem
About the Activity: This hands-on activity is designed for a 7th grade mathematics course in which students discover the Triangle Inequality Theorem themselves (which states the sum of any two sides of a triangle must be larger than the third side) using string. Students will be given various lengths and told to create triangles with them, then record which combination of lengths actually form a proper triangle and which do not (meaning each end of the string connects without bending or overlapping). Variations of this lesson can utilize pipe cleaners, straw, strips of paper, etc. Students must investigate patterns found in their data collection to create their own conjectures and discuss findings with peers, and then test their conjectures to find out what the Triangle Inequality Theorem truly states. When making a conjecture, students may incorrectly state something like, "The lengths that form a proper triangle are the ones that go in numerical order, such as 3, 4, 5 and 6, 7, 8." As the teacher, it is your job to guide the conversation so that students do not construct the incorrect knowledge. You can assist students by pointing out a counter example, such as demonstrating that the lengths 3, 5 and 7 form a triangle, which disproves that each of the lengths must only be an inch apart. During this lesson, it is important for the instructor to see how much knowledge they can pull out of their students before feeding them any information.
Reflection: When students discover relationships on their own, they better retain the information as opposed to simply copying it down on the board and being told to memorize it. Math also becomes a lot more fun when it is hands-on and collaborative! This activity touches upon higher levels of Bloom's Taxonomy. As opposed to remembering and recalling, (the bottom/most basic layer of Bloom's), students understand and analyze by examining their data and explaining their findings. After students have a solid understanding of the Triangle Inequality Theorem, they can practice with the given examples on the worksheet, but this knowledge can also be extended to other areas. For example, the final example on the worksheet incorporates algebra concepts. The sky is the limit in mathematics!