What is on Your High School Math “Mount Rushmore”?

Today was math club day.

Math club is a strange creature, where the content is always dependent on the interests and audience of kids who show up.  Some days, we will work through interesting past contest problems.  Other days, we will discuss “not taught in class topics” like Mersenne Primes or Cryptography.  One day last year, we watched and enjoyed the “Pi vs e Debate“, which is fun viewing, but will produce odd looks from those who aren’t in on the joke.

Today, I challenged students to think of the “3 most important math equations” they had encountered in their high school career.  This opener caused some discussion of what should be considered “important” as opposed to memorable.  A few students shared their responses on the board:

This led to my presenting a  video I came across recently, “10 Mathematical Equations that Changed the World”.  The ranking is by no means scientific, and a few of the equations are well-above high school math.

This also produced discussion of the blurred line between physics and math, especially as students begin to take more challenging courses.  Ask your students tomorrow “What are the 3 most important math ideas you have learned in your life”?  Can our students summarize and prioritize their math experiences and reflect upon their learning?

As a teacher, which concepts belong on your high school math “Mount Rushmore”?  Shrink down the high school math experience to the 4 most central ideas.  Here’s mine:

• Quadratic Formula.  Is this one a gimme?  One of the first times our students consider a general case and the gatekeeper to algebra 2.
• A proof of the Pythagorean Theorem.  I’m going back and forth on this one, thinking perhaps law of  sines / cosines would be better.  Pythagorean Theorem alone seems too middle-school, but being able to develop and defend a proof then moves it to a summary of geometry.
• The Central Limit Theorem.  The backbone of confidence intervals and hypothesis tests.  If you don’t teach stats, this might be out of your wheelhouse.  If you do, I think you are with me.
• The fundamental theorem of calculus.  Ties together all of our algebraic and abstract-thinking skills in a nice tight package before we send the kids off to college.

Would love to hear your “Mount Rushmore”!