Week 12 – Mega M&Ms and 1 through 36 puzzle

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.

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Extra action for this week: Can you arrange the numbers 1 through 36 in a ring so that consecutive numbers sum to perfect squares?





Week 11 – Newton’s Law of Cooling

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?


33 degrees!

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?


Week 10 – Koch Snowflake P and A

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.



Week 9 – Field trip to Vicarious Visions and “Super” Ball

(I didn’t take a picture, so here’s a picture that I borrowed):
The two Introduction to Programming classes took a field trip to Vicarious Visions, a computer game development studio just north of Albany. This was the fourth trip to VV over the years, a real treat to be able to visit such an amazing company. The students had a tour of the entire studio (sorry no pictures, they’re locked down because future games are in development), and then we had a presentation on the jobs involved and a quick Q and A with one of their engineers.
Here are some student responses to trip:

I was really interested in learning about the narrative aspect of video game creation. I love writing, and I never thought of taking that route until I heard about game storytelling in the presentation. I also really loved seeing the building, and the employees at work. They look like they really enjoy being there!

I loved how being an artist goes a long way in the video game industry! Since I doodle a lot, I love the thought of one day having doodles that can potentially count towards something in the future where someday I can say, “”I made that :)”” and feel proud about a design. I thought it was cool to have the ability to take something you drew and put it on the computer where you can color it in just by touching the screen.

Future classes should go on this trip because they would learn a lot about designers,artists, etc, and it would be helpful for them if they are interested in this field

Future classes should definitely go back to VV. The trip was very good, and helped me see what I want to be when I choose my career path.

Part two for this week, geometric sequences and Super balls. We took slow motion video and predicted the height of successive bounces using geometric series. Fun!



Week 8 – Skype with Dark Sky

The Introduction to Computer Programming Class had a Skype Q and A with Jason from Dark Sky (Dark Sky is an iOS weather app, check it out, it’s fantastic. They also make the great weather site forecast.io.) Super nice guy, I just emailed and asked, and it was scheduled a day later. Great experience for these kids.

Here’s some student responses to the prompt: “What blew your socks off? What’d advice/stories/information was surprising?

  • When how he told that if you really want to learn something. you need to be able to do it on your own time
  • I think it is motivational that someone who is successful had a hard time and still does sometimes and still does what he wants to do.
  • I thought it was really interesting when he talked about “reverse engineering” video games, and that was how he learned trigonometry. But now that I think about it, it isn’t surprising that it was easier for him to learn something difficult while immersing in something he was passionate about.
  • The most surprising fact was that he wrote 45,000 lines of code to make the app originally, and then he modified it to do more, but only required 8,000 lines of code. I also really liked how he encouraged people to go on their own and explore other programs by themselves.
  • What I guess what surprised me the most was how he compared computer programming to dance or singing or art. Going into this class I perceived computer programming as a very technical and systematic subject…that everything is by the book. While this may be true… talking to the developer brought to my attention that computer programming can be largely reliant on self discovery and self error.
  • I was shocked when Jay told us how long it took to create his app and how many lines of code it required (45,000).

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Week 7 – Mandelbrot

Here’s the PreCalculus H classes playing with the Mandelbrot code to create their own variants of the Mandelbrot/Julia/Experimental fractals. More to come on this lesson, I’m presenting on it at the NYS Math conference in November and at NCTM in Boston in April.

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Week 6 – Max Min Word Problems and Economic Analysis

With about 10 minutes after a Calculus BC test, I quickly did an introduction to Max Min word problems. Instructions: Pick an x value and find the volume of the (open) box (I gave the diagram, but didn’t have the 11-2x and 8.5-2x, those came after the class came up with them).


They entered in their x and their volume on a google spreadsheet at a couple of computers and built the following chart.



Also fun economic analysis – piecewise function maximization:








Week 5 – Groupwork

(Re)Inspired by a tweet from Alex Overwijk,


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I used my “Vertical Non-Permanent Writing Surfaces” and “Visibly Random Grouping” in two classes today:

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and BC Calculus




The goofy outfits are to be blamed on Spirit week.


Week 4 – Graphing f'(x) and Peardeck

Peardeck is a neat program. Students given f(x) and had to graph f'(x). Next time they’ll be given f'(x) and will have to graph f(x). Here’s what the teacher sees:

And here’s the classroom action:


Week 3 – Distance Formula, Desmos, and Calculus Groupwork

Here’s some students using paper, pencil, and calculator to check their Scratch program output (they needed to calculate the distance between two points).
Desmos and transformations, a match made in (precalc) heaven.

Lastly here’s calc doing what we do nearly every day, group work.