The Calculus class worked on their projects for the first half of class and then I totally nerdsniped them with this question. “How many odd numbers in row 2015 of Pascal’s Triangle?”
They didn’t want hints or answers at the end of the class (not that I would have given the answer anyway, I’d rather ruin their concentration for physics class haha!), so we’ll talk about it tomorrow to see if anyone found the connection….
Since we’re in the thick of derivatives in PreCalc (ironic isn’t it?), we’ve been working on particle motion. Recorded this video and took two data points and tried to figure out when the dice would hit the ground. Interestingly the refresh rate projector wasn’t fast enough, so our answers were a little off, but still a nice, quick application of particle motion. An now maybe the kids can also answer the question of why the “1/2″ in the following physics formula:
Because it’s the two weeks of AP testing, these PreCalc juniors are quite busy. To accommodate the desire for less work outside of the classroom, I’m giving them two 30 minute sections of free time in class to work on a take home exam. Pretty good work for the last 30 min of a Wednesday in May with beautiful weather outside.
Sidenote: At the end of every year I ask the students what worked and what didn’t on their end of the year evaluation of the class. And every year the students cite take homes as something that worked well. They get a ton out of the collaborative work with others. They traditionally have a test on the day that the take home is due as well, so it’s can be the best studying possible.
Make sure you take your time with the take homes!!!!!!! they make a huge difference.
Take home tests and class-work are filled with collaboration, find the smart kid or Anderson and see how they do the problem if you’re lost. In calculus we continue to use maths we learned on day 1 for the rest of the year, so it’s integral that you fix you’re mistakes as the year goes on as it will affect how you do on the next day.
When you allow students (these are PreCalculus Honors students) to choose how and where to do their work, you get many different results. Some students worked primarily by themselves and checked in with others at times, some worked in tight pairs, some worked in loose groups of three checking in with each other’s work after every step and asking questions, and some worked completely by themselves. They worked on paper, on horizontal whiteboards, and on vertical whiteboards. On a sunny spring day. Love it. I had to step back and get a panorama.
Because we’re now teaching IB PreCalculus and Calculus, we’ve moved our extra lab block down to the junior year. This means that the pre-calculus honors classes have started derivatives. If you teach derivatives, you need to do this before even mentioning the power rule. Each student gets a unique function that they need to find the derivative using the difference quotient and then post their result on the board. Their task is to find out the rule (but no helping others!). I let them burn on it overnight.
My first NCTM! Here are the notes from my favorite session by Michael Pershan and Max Ray about exploring Contexts for Complex Numbers. Not as pretty as Ashli Black’s notes, but they’ll have to do.
I also presented at NCTM this year; using the Mandelbrot Set in PreCalculus. More information on that here.
I use smiley faces to explain the chain rule, etc. It must have stuck with this student.
More on how I start class. Here’s the kind of impromptu conversations that happen without my intervention between students (very accomplished BC Calculus students) in the beginning of class. I was just creeping and took a picture when I saw what they were working on. The student on the left is explaining how to find the error of an alternating infinite series and those are his drawings.
We’re at the tail end of the BC curriculum. Worked on Vectors and Parametric equations, both topics that they’ve seen last year and this year in physics. They haven’t played with the calculus yet, but I wanted to see where they could get without any intro. Gave out a worksheet and had them work on it for the block in groups with me being a rover. At the end, I asked them to write a note to their past self for the things they wished they knew at the beginning of the lesson. Tricky.
I gave the PreCalc H kids three lines in vector form and asked what kind of triangle they formed. Here’s a student’s work.
It’s cool to see how proud they are to finish such an involved problem. How many pre-calculus standards are addressed by this one problem? I took a picture and printed out the picture for this student’s notes. Can you follow his strings of logic?