# Sequences, Subscripts, and Being a Newbie

Welcome back to high school!  School started this past Monday for me and after four years teaching middle school I am back in high school!  Although I do miss my sweet middle school kids and my colleagues at my last school,  I must admit that I love teaching high school students again.  And I LOVE THE MATH.  I’m not sure if it’s so great for me because it is high school math, or if it is just nice to change things up after a while.  Whatever the reason, I am extremely happy right now.  I love my new school and everyone in it.  I love my students already, and I love the subjects that I am teaching.  Life is crazy busy, but good.  Please don’t pinch me, because I don’t want to wake up from all of this amazingness.

Not that everything is smooth sailing, of course, because I am a NEWBIE.  I get still get confused (or physically lost) almost everyday.  I don’t know everyone’s names or what school seminars I’m supposed to go to (or again, WHERE), or how I’m supposed to do things, or where I’m supposed to get things.  I can’t wait until I just know things!

As exciting as it is to teach a new level, and new subjects, there are some unavoidable pitfalls as well.  Enter Algebra 2.  My first unit is recursively defined sequences.  I knew (and had even been forewarned) that subscripts would be difficult for them.  But, before I actually taught it I didn’t know know how difficult or how to do it better.  Experience really is the best teacher.  So, day one was rather rough, but I adjusted and (hopefully) day two was much better for them.  Next year I will know that this topic will take two days, and I will be able to structure it so that they do not go home freaked out the first day.  Yes, I feel bad about that.

Next year, I think I will not even introduce subscripts until day two.  I may just write sequence = previous term + common difference or x common ratio.  Tables and graphs have really been our friends.  I will need to create a homework that has patterns, tables, graphs, and then just ask them to write in words how to find the subsequent terms.  Then, day two I will let them help me develop the notation so that the sequence definition will be more efficient to write (and subsequently put into the graphing calculators).  Also, the graphs of sequences on the TI-84 are just treacherous.  The zooms are nuts and the window option is so complicated.  Eli promised me that they were working on recursively defined sequences in Desmos.  I am just praying it is finished before next August so we won’t all have to suffer the TI graphing torture again next year.  (Side note:  I also didn’t know that Alg2 students weren’t proficient at the graphing calculator.  I’m not either, and I was hoping that they could teach me.  It may be good that we will all learn together though!)  This year, I taught them how to enter the sequences in the TI-84 and we leaned on the tables, but the graphs were a mess.  I made all of my graphs in Google Spreadsheets so I could show them what was happening in the long run.  Thank goodness for spreadsheets!

I created an activity using Skittles for recursively defined sequences that decay.  It went pretty well and I hope to blog about it in the next couple of days.

Thanks again to Sam for his AMAZING sequence and series packet!  I leaned on it heavily during these two days and plan on using parts of it to make this new day one homework assignment that I am dreaming up in my head.  As I have said many times before, I love this village.