Category: Class Openers

David Letterman has his Stupid Pet (and human) Tricks…so today in class we started Stupid Student Tricks (please read that carefully —- stupid is describing the trick).  My classes understand I will begin each day a short opener, and I have now given them the opportunity to participate in the process.  On Edmodo, they can submit an idea for a class opener – it can be a video, a challenge, a picture, a story – to share with the class. Every Wednesday, one idea will be chosen to be the class opener. Chosen ideas will receive a bonus quiz grade during the semester. I’m looking forward to the ideas the kids choose to share!

RYAN’S CUBES

My first student “opener” volunteer is Ryan, who shared his skill of identifying perfect cubes.  Calling volunteers to the board, he asked them to think of a number from 1 to 100, and share it with the class (but not him).  Then, the volunteer cubed the number and the product was written on the board.  Within seconds, Ryan gave the original number.  It’s a pretty good trick, and one he has become quite quick with.  To show how the “trick” is done, Ryan shared a video from Scam School, a neat series of everyday tricks and scams.  Enjoy it here:

After last week’s experience with Sierpinski’s Triangle, I was eager to see other math landmarks my students had encountered. Knowing that our next unit will be on sequences and series, it seemed like a perfect time to share this:

“Von Koch curve” by António Miguel de Campos – self made based in own JAVA animation. Licensed under Public domain via Wikimedia Commons.

Many students identified “the Snowflake” immediately, and I filled in the “Koch Snowflake” gap.  Soon, our room was filled with ideas of fractals and self-similarity. We grabbed markers, and started drawing on our desks.

How many sides does this have?

What is its perimeter?

Tomorrow, we will look at patterns and develop explicit formulas for them. Today’s opener planted some seeds I hope to sow during tomorrow’s discussion.

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.

This 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!