## Thursday, February 27, 2014

### Itty-Bitty Update!

Ok, quickie update. If you want more info about anything, you can dig through my current lesson plans here.

1. Life is still busy, but I am finally feeling myself again at work. Despite some rough times behind me, I am feeling pretty good about where my kids stand in terms of their understanding, and that feels motivating. My advisees are also quite successful this year, and even though their teachers' expectations have gone up and up during this year, their grades have still improved steadily. Way to go! I am feeling great about all of this.

2. After a very successful group quiz experience, we are finally doing our first big Calculus project. For some reason, in my head, I had pictured this to be much easier to have the kids create a rollercoaster that is smooth and continuous in all sections and contains a variety of functions. Not so. When I was going through an intermediate example on the board, it was either too easy or too complicated for most kids, and I have had to go around and conference with each group individually to help them achieve their very elaborate plans. After giving them five 45-minute periods and they were still not done, I was feeling quite discouraged. I had to tell them that we were going to stop for a little bit, switch gears to work on integral Calculus, and to come back to the project so that they're not just spinning in place. Fortunately, last time they worked in class (Class meeting #6 on this project, which is just a lot of time), I saw the light at the end of the tunnel. I think after one more class, they'll be able to polish off the rest on their own. Whew. And then we'll be able to move on to our Integral Calculus art project, which is more current and practicing our current algebra skills.

3. In Precalculus, we have been doing lots of trig and it has been just lovely.

a.) The kids had done a Logger Pro exploration of rotating bicycle wheels and a pendulum, and what was even more lovely was the discussion that we were able to have about amplitude, period, and midline based on these real-world examples.

b.) Following that, I got two free cardboard pizza boxes from Domino's and made four circular wheels. The kids played around with showing me places on the unit circle that have the same height ("Estimate where on the unit circle there is a height of 0.7? Where else?") and the same horizontal location ("Estimate where on the unit circle there is a horizontal coordinate of -0.4? Where else?") The tactile display really helped them reinforce their understanding of signs.

c.) They really explored the idea that the graph changes shape (wave vs. circle), when you are graphing time versus X(t), time versus Y(t), or X(t) versus Y(t). Another colleague came to observe this class, and remarked afterwards that the whole time, I never had to write anything on the board! The kids made their own explorations on their worksheets, which is the way things typically go for them.

d.) Without dipping into radians yet, they explored all kinds of transformations to the circle and how that impacts the equation and the shape of its parametric equations.

e.) We played review games with wave equations in degree mode! It was so fun. I let the kids wager points, even though the points didn't count in the end for anything. They - went - nuts.

f.) For learning about radians, I brought in strings for them to estimate how many times the radius fits into a circumference. We talked about what a radian is, and why it's related intimately to the word radius. They then converted degree-mode equations into radian-mode equations simply by using the idea of analyzing units. X(t) = 2cos(20t) + 1 in degree mode means that the point on the circle is traveling 20 degrees/time unit, which means that it is obtained by simplifying (360 degrees)/(length of period). In radian mode, we'll need that number to have the units "radians per time unit", which represents the total circle in radians divided by the length of the period, or (2pi)/(length of period). Easy breezy. Kids understood the reasoning immediately.

4. In Algebra 2, we've finally finished quadratics. Some kids are just breezing through everything, which is just a joy to watch. The others who struggle, boy, do they work hard for me. They're doing okay, earning their way from an F to a B every marking period through sheer valiance and persistence. It keeps me on the edge of my seat to still have them be teeter-tottering through the term, but I love that feeling in the end when they've truly earned their way to a B or even (most recently, two of them got) an A- through endless requizzes and incredible hard work!! So, I feel really good about that!! I love my struggling 10th-graders, and I can only hope that every bit of extra work they do this year is an extra assurance that they'll be able to handle the transition to Precalc next year.

Our next topic is exponential functions. We've already dipped our toes in, and I was pleased to see that they felt comfortable writing linear and exponential equations manually and finding quadratic equations via regression. This is in addition to being able to sketch quadratic systems and analyzing number of expected function intersections via (their joint) discriminant! Hurray to my little algebra troopers!!

That's it for my quick check-in. Hope you guys are doing well and enjoying the SPRING!!!!! OMG, what's this warm golden thing on my skin? I thought that winter would never end this year. Time for weekend bike rides!!!!!