Reviewing Inverses

The first few weeks of Pre-Calculus are always a little bit overwhelming for me. The course is designed to fill gaps of knowledge before students get in the ring with Calculus in an AP class or when they're off at college. Great, in theory. However, it means we need to make the gaps glaringly visible so we can address them. Before we tackle any of the really cool concepts, we have to tackle the misconceptions. One that I find the kiddos struggle with the most is inverses.

I've taught inverses so many different ways and always feel like I haven't quite hit the mark. I need a way to efficiently review the concept so we can get into some more skill based practice, but I don't want to do a full blown, hour long exploration. I also don't want to just lecture. I was playing around in Desmos and I decided I'd try a different approach this year. Spend less time trying to remind them of what they've learned in Algebra II myself and give them a little more time to think through it with a partner.  Here are my thoughts right now as to why I'm using Desmos instead of my beloved TI-84:

1) We can examine the concept of an inverse without worrying about the notation or the algebra just yet

The kids always are able to tell me "you just switch x and y," but they often have no idea what an inverse actually is or why switching x and y is important. I like we can build on what they do remember  (switch x and y) to tease out the actual concept. We don't need to get into messy algebra ("YOU EXPECT ME TO USE A LOGARITHM??") to illustrate it....yet. 

2)  The graphs are clear and the commands are user-friendly

We have block scheduling, so I have 2nd semester seniors who haven't seen a graphing calculator since they were first semester sophomores. It's definitely a challenge. Sometimes we spend so much time trying to reintroduce them to the steps ("Okay...2nd....calc....5.....enter....enter....enter") that our intentions get muddled. Yes, I know I need to reteach those, and we will get there. On a conceptual day, I'd rather not. 

We will definitely be examining the fact that the intersections all happen at a point where x=y.....why would that happen? What is demonstrated about the graphs here? This kind of conversations can lead to one to one functions, horizontal line tests, invertibility....all that good stuff. I'm hoping this gives us something concrete to refer back to throughout the year as we repeatedly see inverses in our curriculum. 

This is definitely simple and in the planning stages.  Here's what I have so far. Constructive feedback always welcome! 

A Day in the Life

So week one of the blogging initiative and I'm already behind (see my last post!).

4:30 am  The alarm goes off. I crankily roll over as I fall back to sleep to the sound of my saint of a husband piling on clothes to take the dog on a 25 degree walk. If he wasn't also a teacher I am pretty sure I'd be late to work every day. 

4:40 am Okay, okay....I get it, I have to get up. And shower. And decide what to wear. And think momentarily about putting on makeup before I say "nahhhhhh" and run out the door. It is the first day of classes....don't want to set the bar too high for the rest of the semester without makeup.

5:15 am Out the door dressed like as eskimo, scrape the car, and be thankful I'm not in my hometown buried under snow right now. I'll take 28 degrees at this point. 

5:35 am  Arrive at work and my competitive side is a LITTLE sad I'm not the first car in the lot. God bless the English teacher who, despite having 2 kids, beats my kid-less self to work every day. 

5:38 am  Quality time with the copier

5:51 am Track down a janitor to remind them that I still don't have enough chairs for my first period that starts in just over an hour. Try to hide my minor panic attack that my seating isn't done and ready yet.  

6:15 am Finally set up the 5 new seats that arrive in my classroom. Basically playing Tetris to fit 5 more 16 year olds into the room comfortably....a nice mathematical challenge for the morning.

7:15 am Homeroom starts. I see these kids maybe 5 days per year total. This will be the longest 10 minutes of my day....trying to keep calm 27 sophomore with whom I have no relationship other than I hand out their schedules and try to keep them quiet enough to hear the announcements a few days per quarter. Try to play off the fact that I've forgotten everyone's name since October, the last time we had homeroom. 

7:30 am - 10:35 am Pre-calc time!  I always start the first day with a fun game ( in this case, Math III Taboo - adapted from Pre-Calculus Taboo) to  pre-assess and get the kids talking and then I give them a sheet of skills they're expected to know from previous courses and give them some time to work collaboratively on them. I spend some time calming the panicking kids who haven't had math in over a year because of block scheduling. 

10:40 am - 12:40 pm AP Calculus Time. I gave back midterms and gave kids time to correct them, identifying and explaining their mistakes. Was going to jump into a new topic today, but first day back from a 5 day weekend and jumping into  a new topic without addressing their mistakes seemed crazy. Take an awkward 25 minute lunch break 30 minutes into class because of our strange 4 lunch schedule. 

12:40- 2:15 pm Planning! I've never had 4th period planning before and I'm not sure how I feel about it yet. It's a good opportunity to reflect on the day and make tweaks, but also to get ready for tomorrow. It also includes all the chores of the day....check mailbox, file papers, walk to office to pick up package with turns out to be the greatest thing a parent could ever drop off...a bulk store's biggest pack of Kleenex! 

Got copies ready for tomorrow, sent lesson plans for Friday and Monday to have them brailled, nursed my Diet Coke to help try to stay focused, set up my new Canvas courses for the semester, sent some parent emails, etc. 

I think it also goes without saying that I refresh the weather report about 35 times during this person too, as some reports are saying we'll get a dusting and some are saying we're going to get 15 inches. 

2:15 pm The last bell rings. New people are starting their afternoon duties and I somehow didn't get parking lot duty. Needless to say, I'm feeling like...

2:40 pm The time I mean to leave school to let me poor puppy out after being home alone since 5:15 am. 

3:10 pm The time I actually manage to sneak out the door. 

3:30 pm Arrive home, long dog walk as an excuse to play in the flurries we are getting right now, settle in for some serious lesson planning to make sure I have time later to relax a little. 

7:00 pm  Realize I've been snacking for 5 hours and actually eat dinner, torture my husband through an episode of Vanderpump Rules, and get ready for bed.

8:45 pm In bed. I realize this is embarrassing, but it's #teacherlife. Alarm is set for 4:30 am...it's coming fast. 

Balancing Act

Saying I've had a trying last 5 months would be putting it nicely...an understatement equivalent to saying that you should probably not put the buffalo chicken dip near me at a party if you want anyone else to get some of it (I'm good at sharing with others until it involves cheese and buffalo-y goodness).   It's been unbelievably challenging personally and the thing that's hit me the hardest is the way it has made me feel as a professional. We go into this profession because we love to help. If you're teaching and you don't love kids and seeing them light up, you need to find another line of work. We work 60....70....80 hour weeks for the first few years of our career to try to prove ourselves. We do all those things you see teachers do in the movies- bring kids things from your own home to make sure they don't go without, commiserate with kids who are struggling with situations that are more than just academic, and get truly invested in a group of munchkins who you will have to say goodbye to in just a few short weeks.

When life happens, it's hard to strike a balance between that "movie" teacher we want to be and the reality of what we can handle. I had to spend a few weeks working to my contract hours only and it's almost unimaginable the amount of things that couldn't get done- the grading, the tutoring, the formative assessment and feedback, the parent emails, the committee meetings, the re-writing of lessons to help them to meet the needs of different kids, the club meetings that had to be cancelled, the bathroom breaks (yes, those and lunch go right out the window first). I don't think in my years of trying to prove myself I realized just how much of my own time I was giving up to be the type of teacher I wanted to be. And I didn't realize the guilt I'd feel when I needed to invest my own time in myself and not in my kids. 

I'm still working on getting back in balance....on being able to take some time out of my own personal life to let myself heal without feeling like I'm letting kids down. On being able to be okay with working only 50 hours a week. If anyone has found a magic pill to cure this, let me know. Until then, I'm taking it one day at a time and knowing that I'm doing the best I can. I'm also saluting everyone who gets up every morning and smiles at kids as they walk into homeroom while putting aside their concerns about their own children, their own family, a chronic illness,  a whole history of personal tragedies and fears. This career is not for the faint of heart and the only way to sustain it is to find a way to be both a teacher and a person.