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:
Is this an improvement on the student’s idea?
Relay race in Calc on Work. Their first relay race of the year. I like the activity, but these guys work hard enough on normal days that we don’t gain much from the frenetic activity. The winning group got TI Calculator skins. Sidenote: love the expression of the kid in the hall.
Short week. Here’s something that one of my students is working on. This is only 1/5th of the entire design. She’s making a big torus. I’m very excited.
I used Mega M&M’s to motivate rotational volumes in BC Calculus this week.
- Took a long time to gather data (found here) and get started (overall we spent ~an hour on the activity, data and initial setup was about 20 minutes).
- Great motivation to find the volumes of the actual chocolate to check Mars’ claim.
- Difficult, in the time allotted, to find (and eventually give in and explain) a method that we could easily and quickly use in class to measure the volumes.
- Desmos link was not as useful as hoped, students took it for granted that the ellipse was the way to go, and because the desmos pictures weren’t to scale, they weren’t useful when finding the equations. Need to use pixel measurements to find relational candy+chocolate to chocolate ratio.
- One major problem: I’m pretty sure they all used the same info, yet they all got (slightly) different answers. Uh oh.
I liked the activity, it was the first time I’ve used it in class, but it needs tweaking.
Extra action for this week: Can you arrange the numbers 1 through 36 in a ring so that consecutive numbers sum to perfect squares?
Precalc H predicting the temperature of a dead body (hot water in a coffee cup). For a prediction of 59 min in the future, the model predicts 32.5 degrees and the actual temperature?
Some really good questions:
What’s a temp that is too cold?
What’s a temp that is too hot?
Will k be positive or negative?
What are the units on k?
We calculated the Perimeter (infinite) and the area (finite) of the Koch snowflake in Precalc H near the end of the sequences and series chapter.