Math = Love: Conic Sections Flow Chart

## Sunday, February 16, 2014

### Conic Sections Flow Chart

It's crazy to think about how much things can change over the course of a year.  Last year, I was dreading teaching conic sections to my Algebra 2 students.  When I took Algebra 2 in high school, there were really only two topics that gave me grief: matrices and conic sections.  And, by grief, I just mean that I had to really, really, really work at them.  Math has always came easily for me.  Though, I did have a really terrible time learning to tell time in the first grade.  I still remember getting clock worksheets returned, covered in red ink.

 Conic Cards In Action
Through the amazing community that is the #MTBoS, I was introduced to Cindy Johnson's conic cards.  At first, my students were really frustrated with the process of trying to match up verbal descriptions, equations, and graphs.  But, the more they talked through the matching process with their partner and the more we practiced, the more my students (and I) started to fall in love with conic sections.  As I helped my students look for and identify patterns, I started to see things I had never noticed as a high school student.

 Conic Cards In Action

I've been eagerly anticipating starting conic sections!  This year, I've made some changes to how I'm teaching conic sections.  Oh, we're still using the conic cards.  I can't imagine teaching without them!  But, instead of having the students use the reference cards in the deck, I have created interactive notebook pages for my students to use.  It's a beautiful, beautiful thing to watch my students use their notebooks.

 Sorting Conic Cards - My student insisted on her hand being in this picture so the entire world could see her beautiful nails!

This unit has been one where I've had to employ a lot of tough love.  As much as possible, I want students to discover the patterns and relationships for themselves.  So, the very first day with the conic cards, I refused to give my students any help.  Instead, I directed them to page 63 in their notebooks.  When they protested, I told them that I had faith in them and their ability to figure this out for themselves.  I had some very angry students that day.  But, almost all of them have eventually came around.

Even though I'm trying to be less helpful, I've put no restrictions on letting students help other students.  I love watching these mini-tutoring sessions.  Usually the conversations go a lot like this:

Student 1: I'm never going to be able to figure these out.
Student 2: Have you asked Ms. Hagan for help?
Student 1: No, she's just going to tell me to look in my notebook for help.
Student 2: Well, where is your notebook?  Why don't you at least open it up?

Student 2 usually goes on to walk Student 1 through the process of matching up a couple of cards.  They reference the notebook page and explain every step of their thought process.  I've learned so much more about how much my students understand by listening to these tutoring sessions than if I had explicitly explained my solving process to the class.  How many other times have I cheated my students out of the opportunity to discover things for themselves?

Another change I have made this year is using Rebecka Peterson's Conic Sections Flow Chart.  I downloaded it from her blog, and I was pleased to discover it was already perfectly formatted to fit right in our interactive notebooks!  This photograph isn't the best, but this has been an amazing resource for my students.

Whenever someone holds up a card and asks, "Is this a circle?", I immediately ask them if they have checked their flow chart.  We go through the questions.  Are both variables squared?  Are the squared ters subtracted?  Do the squared terms have different denominators?

 Conic Sections Flow Chart
Later this week (hopefully), I will be posting the individual pages I created for each different conic section.