No photo, forgot to take pictures. Here’s a fractal pancake that I made:

And here a spiral pancake:

This was a presentation for “my favorite”.

And my proof:

Here’s their outline.
Some book choices from the fantastic library…

Showed this video as a motivation for working on vectors:

Here’s a student mapping out his game in computer programming. He’s figuring out what level will warp to what other level. Paper is certainly better in this case.

Here’s the groups working in pairs on each others problems in the final projects. Sometimes it so helpful to get another perspective on a problem. Sometimes not.

## Introduction

Here’s some classroom action:

## Act 1

I presented the Money Duck to my PreCalculus H classes. We were in the midst of probability and we were moving towards probability distributions and expected value. This activity popped up at just the right time to (quickly) try it out. So without any lead in to the activity, I showed the picture of the money duck:

Then showed the video that Dan made:

After the video I overheard quotes like

Student Alpha: That’s really annoying that they didn’t show the price.

So the pump was nicely primed.

## Questions 1 and 2

I gave out Dan’s handout and each group of 2/3 worked through it independently and I went around and poked and prodded with questions.

Here are some quotes from the first two questions:

Question 2:

B can’t be possible because they add up to more than 100%.

(some groups got confused about the question… they were trying to figure out which distribution was the same as the ducks from the video)
Student Beta: C is the one from the video.
Student Gamma: D is also possible from the video.

## Question 3

Student Delta: I feel like A would be bad because no one would keep buying ducks.

Student Epsilon: But B would be bad because you’d be losing money.

## Question 4

The students had an easy time sorting out the most and least likely to buy for \$5 (by eyeing it), but a difficult time sorting out the two middle positions. I’d say the groups were evenly split at the guesstimate for sorting the middle two. I went around to each group and asked how they sorted, and mentioned that it’d be nice if there was some way to formalize the guesses.

## Questions 5 and 6

About half the groups got calculating right away without giving a gut guess (on question 5). I didn’t help out with question 6 unless asked, just put the expected value formula up on the board. Most groups figured it out on their own.

## Extension

When groups finished up, I put them in the position of the producers. Asked them to come up with:

• Group Name (this might have been a mistake, took many groups a LONG time to pick a clever name)
• A probability distribution
• A price for the soap

When they came up with those three things they either entered in the information at my teacher computer, or on my chromebook.

When they were finished with entering in the information I asked them to step away from their companies goal, and become individual buyers of the soap. Which would they buy… and why?
These students quickly found out that they had to do a bunch more calculations of expected value, and they were becoming bored with this calculation. Thankfully spreadsheets are both fast and accurate at calculations, so I put in the required formulas and calculated the expected values…

Interestingly a couple of groups either went down the route of a non-profit (but not really) corporation, or they didn’t understand how to properly set a price for their soap.
Nice activity, a nice extension might be to go from the theoretical to the empirical world by actually “making” the ducks, and seeing how the gambling buying of the soap actually turns out.

BTW, these students don’t watch Game of Thrones. Should have gone with Harry Potter.

We were calculating probabilities in precalculus and working with student birthday. Hidden assumption: all days are equally likely as a birthday.

Nope.

BC calculus practice in pairs.