One of the hardest, yet easiest, concepts for students in my class is the Pythagorean Theorem. It is one of the easiest because if students memorize the formula, they can just plug and chug all they want. But, what is difficult is the reasoning behind WHY it works. Students start to understand that the hypotenuse is the largest side, but this visual is always best to show so students really see it. This is also a great way to introduce students to the many ways that you can prove something in math....it doesn’t always have to be boring and/or difficult! Sometimes a simple picture is all you need!
I also sometimes do this by having students actually create the sides of a right triangle out of graph paper. This here is a site that explains how this can be done: http://www.regentsprep.org/regents/math/algebra/at1/TActive.htm Students have to think about what it means to be “Squared”, and what it means that all sides are squared. This really helps my students understand the Pythagorean Theorem, but perhaps more importantly, my students really grasp the understanding of something “squared”.
