Something kinda cool happened yesterday

Yesterday was the first day back from break.  You know that type of day...everyone is still on break schedule and anything that was taught before break might as well have been taught last year.  In my current position, I pull struggling students out of their math classes to work with them in smaller groups on the same content.  Yesterday, we started our study of quadratics.  Our classes are pretty traditional in terms of flipping.  Kids watch videos at night and then come in and do problem sets during the day, though many of my students often watch the videos in class. 

Since the students were not assigned a video over break, I decided to introduce quadratics in a different way.  The Common Core is big on the idea of comparing and contrasting different function families.  So, we reviewed linear and exponential growth/decay functions.  Then, I put y=x^2 on the board and asked them to graph it on their graphing calculators (we use the desmos app).  Then I put y=5x^2 and asked them to graph that simultaneously.   Then, something a little crazy happened.  My students (even my first block sleepies!) were super curious.  "What if it was 100x^2?"  "What if it was -5x^2?"  And one of my favorites, "what if it was y=x^3?"  I allowed them to play for a while and within minutes, students were sharing patterns they had discovered.  "So, if it is an even exponent, it looks like a U or upside down U."  "If it is odd, it is kinda like an S."

This led into an interesting conversation about how quadratics are different than linear functions and even how solving them is different. 

Many people think the idea of the Common Core or even problem/project based learning has to be complicated and time-consuming for the teacher.  However, my experiences yesterday show just to the contrary.  Sometimes if you just start students down a path of exploration, they will take off and discover thing that are well beyond Algebra 1 material!  I had never seen this group of students so engaged and excited about math before.  I hope to continue this momentum through our next 9 weeks of quadratics study!