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Class Openers

Class Opener – Day 23 – Galton Boards and Plinko

Today’s opening video was intended to spiral back to Pascal’s Triangle, and generate discussion surrounding the behavior of outcomes in binomial experiments.

In particular, do objects dropped from the center tend to gravitate towards the middle bottom slots? What needs to occur for marbles to reach the end slots?  This led to one of my favorite activities of the year: playing Plinko!

You can find more details about the Plinko lesson in this previous Plinko post. In my Prob/Stat classes, we connect these probabilities to binomial theorem expansions, which we just studied.

pingpongThis fun applet, from mathisfun.com, has adjustable probabilities and rows and was then used to demonstrate the behavior of binomial experiments over many trials. This was especially helpful when we started talking about binomial settings where the results are not equally likely.

So, let’s get ready to play Plinko!

plinko

 

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Class Openers

Class Opener – Day 22 – Mickey D’s contest

The McDonalds Monopoly game is back! Time to fatten up on crappy burgers, cold french fries, and …… look at probability distributions?

McD

Not much time to chat today, as we have a quiz during class. But many students picked up on the fact that McDonalds probably prints a small number of certain, coveted, properties and large numbers of the rest.  This is confirmed by an article on the math behind the McDonalds promotion.

You’ll find many folks online offering to trade game pieces, hoping to locate folks who have the pieces they covet, or to sell their pieces to the highest bidder.  This led to an interesting debate:

If I have Park Place, and you have Boardwalk, should we combine our pieces and split the million dollars?

In my morning class, the vibe was largely pro-sharing, until a few vocal students argued that having Boardwalk was such a huge advantage, we could just go out and buy french fries until Park Place was found. In the end, the class understood the value of these rare pieces, though the discussions and debates were rich.

Now turn your desks and get ready for the quiz!

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Class Openers

Class Opener – Day 21 – 3D Graphs

Today’s opener turned into much, much more than I originally expected – and a truly powerful share at the end.

binomialsFor the last few days, my students have been working through the binomial theorem, expanding and finding specific terms. There has been much movement around class, with students at the board, working together, sharing ideas. I provide problems off the top of my head, giving more difficult ones if the students seem ready, and peeling back if we need more practice.  To provide solutions, I use WolframAlpha to expand the binomial and project solutions from my iPad. This has worked well, but students have also taken note of the deeper info Wolfram provides in these calculations.  In today’s opener, one of these interesting graphs appeared on screen as students enetered:

wolfram

The Wolfram player allowed students to move around this strange object and explore it from all angles. One of my classes impressed me by relating what they related the picture to the Continental Shelf, which they were exploring in science. I provided a 2-minute intro to the (x,y,z) plane – always a fun time.

It was then that one of my students who participates in robotics shared his experience with a 3D printer this summer. I was surprised that few students had heard of these devices, and they seemed intrigued by the idea.  I was reminded of a powerful video involving a student their age, whose father “printed” a prosthetic hand for his son. The end of class then featured two videos I dug up and shared in the last few minutes of class to make students aware of the engineering possibilities.

3D Yoda:

Inspiring story of 3D printing in action:

When the kids leave with a “wow” moment, something has gone right!