Gave the precalc classes a fun problem. Find the distance from the origin to a point in 3D. As you’d imagine, the toughest part is the visualization. Here’s some of the student work:

Showed this video to the computer programming class:

Some fantastic math(s) and computer programming topics related:

• Traveling Salesman Problem
• Quintic easing
• Rates
• Parametric Equations
• Random Physics Awesomeness
• etc

So cool, not alone the fantastic power of the kids seeing some code in the video and thinking… hey I could do that:

Tis the time of year when the IB students learn some different stuff than the AP BC kids.

## AP Calc BC

Cross-sectional volumes. This quick demo worked just fine. Also had a bunch of 3D printed models to show, but the paper on board technique worked nicely.

## IB Math HL

We also did this exact same example in PreCalc H that day (who is also doing prob/stats). A great motivator for why just about everyone in the room should know how this stuff works. I’d bet everyone in the room has a family member who has already been, or will be affected by cancer.

Here’s the setup:

A blood test has been developed to detect cancer. The probability that the test correctly detects someone with cancer is 0.97. The probability that the test correctly identifies someone without cancer is 0.93. Approximately 0.1% of the population has this cancer.
Question: You walk in to the doctors and take this test. It comes up positive. What is the probability that you have cancer?

What a great lead-in to Bayes Theorem. Give it a second, what would you guess the answer is?

Here’s the Bayes method of solving the problem. A bit strange and abstract. Hard to handle.

Still, an amazing result. Only 1.4% of the people who test positive actually cancer???????

Lets make this more concrete: Take a population of 1,000,000 and walk through the actual amount of people who have cancer etc…

I like that so much better. Same math, but so much easier (for at least me) to understand.

Gave this task to a student who had already seen the BEAM problems. Can you come up with a strategy for reflecting a point over a circle (inversion through a circle)? Each point outside the circle has to map to one and only one point inside, and vice versa.
Here’s his thinking on a whiteboard:

He is using the angle between the two tangents to uniquely map the image inside (and outside if necessary) the circle.

Here’s his desmos sketch. Really cool.

Had a little of extra time with the precalc students so the worked on the BEAM entrance problems. Really great, love it. Do it with your students (they’re designed for 7th graders). Love how students used problem solving techniques on problem number 3: They were making the problem smaller so that it was easier to understand.

Gathered Shomomi numbers that we can do some stats calculations with real data. After they calculated it, we had them “calculate” what would happen if they ate an Alice in Wonderland mushroom and their shoe size went up by 5.

So many definitions and they can use clues to get the rest. Lots of vocab, and this worked out nicely as an intro.

I’ve found it useful to give junior PreCalc H students time to work together on take home “exams” in class because it builds some fantastic community and teamwork skills. I instituted new rules to their work: Non-permanent work only. If they work on paper, it has to be tossed. No pictures either.

My thought process is that when they go away to write up the problems that they worked on together, there will be some good things going on in their brains to try and rethink the (upwards of) 20 moves that had to be made to solve these problems (IB questions). What do you think? Does this idea have any basis?

This activity also stands in nicely for a trig review thing that I used to do quite differently.

This post is mostly for myself, but maybe there is some value for you too (isn’t this the case for all blogging)?

I gave out this 2nd quarter feedback form to my Precalc honors and AP Calculus BC classes:

My comments will be in italics. The rest will be verbatim or summarized.

### Similarities for Q1: What activities/methods/strategies have we done in class that have worked well for you?

• Standing Groupwork on Whiteboards (HUGE positive response here. Loud and clear, at least for those who like it.)
• (PreCalc H) Take Homes (they enjoy working together on tough problems. The students actively liking this is a new one for me, I think it’s because I’ve given more classtime for these takehomes).
• Marbleslides (A set of Desmos activities) (We didn’t do many other Desmos activities this quarter, the topics didn’t warrant the need.)
• Writing down examples in notebooks and having the classnotes in a shared google drive. (There is a significant group of students who would rather work on paper than whiteboards, I’d put it at 1 in 5 students. They find some solace in printing out my written notes from the tablet, or at least having those notes available, but I think they’d rather do everything on paper.)

### Similarities for Q2: What activities/methods/strategies have we done in class that have NOT worked well for you?

• Writing more things down in notebook (This is nicely paired from the last bullet in Q1)
• Seated Whiteboards (They really do like the standing aspect!!)
• Desmos Activities (This was a small amount of feedback, but they had some great points. A lot of their feedback is talking about my custom activities, so this is not a shot across the bow for Desmos, only for my custom activities. Quick take: I think I make them too dense for some students. There is a high load that they’re being asked to lift on some of these, and there are students who don’t thrive in that environment, depending on the timing of the activity and their (random) partner).
• Not going over homework consistently (Yep. Not too much volume on it, but it’s dead on. I think their volume was turned down because I figured it out in December and have been improving on it in January).

### Similarities for Q3: What can we do to help you learn better in this class?

• Scattershot mostly, but hand back work quicker. (Yep.)
• Some requests to slow down. (This is a hard one. I know where we need to be to put the majority of students in a good spot for May of their senior year when they’ll take the IB or AP exam. I don’t have a great response for this. Do you?)

### Excerpts from Q4: Anything else you want to say about class to me? Suggestions?

• I enjoy the music keep that up.
• I love whiteboards and take homes!!
• It would be nice if reassessments could be done on other days than just Thursday or during school study halls.
• I really like this class. It is fun and interactive. Cool music btw.
• I enjoy doing whiteboard work and take home work in class.
• Nothing additional other than stand is great.
• Love the background music when we work.
• Great learning efficiency, but sometimes comes with dreadfulness from repetition or notes.
• Its actually quite enjoyable
• Are there any good videos to explain some of the methods? Even if they were just linked to classroom that’d be good.

Hey teachers, if you don’t do some sort of feedback form, consider it. Some fantastic feedback, a nice mix of stuff for me to chew on, and some nice motivational stuff from what is working well too.

I often like to wing it when coming up with examples. I like the messiness that occasionally happens. We had 3 different answers for the length of the missing side. Their homework? Find out which one was correct (spoiler alert: none!). What a great accidental lesson.

We tried something different today in Precalc H. I gave the students 8 minutes to work by themselves on the feedback quiz by themselves, and then 4(ish) minutes to work together. These are difficult topics, so I wanted them to know where they stand (the 8 minutes should give them a pretty good idea), and then I wanted supports built in (the 4 minutes of partner time). We went over questions and the key after these two sessions. Worked well, would do again. Two thumbs up.