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?

I had a great discussion on twitter about how to properly close a class with a reflection.

Thank you to @TracyZager @ekazemi @bkdidact @kassiaowedekind and @MathMinds for the discussion.
Here’s some questions and information that I gathered with a reflection question at the end of a lesson. Keep up with this Dan.

Needed some 1D statistics to calculate population standard deviation from mean (by hand). Values had a high variance, 7 to 562.

Exploding Dots with James Tanton in computer programming. Awesome, fun, engaging, powerful lesson. Not often that I can use those descriptors all together.
I (loosely) used this worksheet to get them going, but the class was small enough so that I could think on my feet.

Sidenote: What base is deadmau5 using?

(note: week 20 was midterm / Regents week so no post)

This was the last week of classes before midterms and finals, and I got distracted by a couple of projects. The first is a plastic 3d printed form, and the second is a chocolate and cardboard 3d structure (although the chocolate:cardboard ratio is shrinking quickly).

To fight the winter sleepiness, I try to get the students up and on their feet as much as possible. It’s an interesting twist to how they work. If on paper, they default to working quietly by themselves; if in groups on desk whiteboards, they default to working together on one problem; and if standing at whiteboard, they default to individual work but lots of help from the people to the left and right. Here’s two different days of pre-calc being forced to support their bodies with their legs:

PreCalc H was working on proving trig identities. They were asked to come up with their own trig identity by starting with a previous identity and modifying it. They checked their result in desmos (were the graphs of each side of the equation the same?), and I collected their identity and swapped it with another student and they had to prove each other’s equation.

But they were getting confused with when they could work across the equal sign, and when they couldn’t (the difference between the create and proof steps). Sam Shah had a great setup for working with trig identities. He gave an equation, and they had to check to see if it was true first, and then if so, prove it true. I really liked this approach.

In PreCalc H we started off this last day before break with PolyGraph Hexagons (as a warmup) and then progressed to PolyGraph Rational Functions.

The kids had a good time, and there was a lot of great discussion that followed. Here a small subset of the questions being asked by the students, as seen on the teacher dashboard:

In calculus we first had a My Favorite. This student has been working on this origami project for 2 or 3 months now. ~555 postits! She discussed how the different polygons (pentagons -> heptagons) provide different curvature for the shape. how their arrangement changes the 3D structure.

We did some quick practice and then they chose to look into the Sierpinski gasket, so I helped them get started and then they came up with the following:

Finally, they were itching to do some Calculus Caroling, so they went over to the AB class and entertained them. Tons of singers, so they sounded great too!

I’m struggling with notation in Calculus. We’re talking about derivatives of inverses and how they are related to the original function.

I really dislike this:

So we replaced it with this:

Still awful. So after I complained for a couple of blocks, a student came up with this:

Much better.

Is this an improvement on the student’s idea?