Month: September 2014

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Class Openers Geometry

Class Opener – Day 19 – A Blast From Geometry Past

During yesterday’s group work, which included a discussion of Pascal’s Triangle, I overheard some groups mention Sierpinski’s Triangle, which they had seen some in Geometry last year. That led to today’s opener, an applet from the awesomely mathy site Cut The Knot:

sierpinski

In the “Chaos Game” a point be-bops about a triangle under specific rules:

  1. The red point starts one of 3 randomly selected vertices of the triangle.
  2. Next, one of the 3 vertices is randomly selected, and the red point moves half-towards this new point.
  3. The process is repeated over and over, and all landing points are marked.

At first, I have the applet run slowly, and students don’t quite absorb what is happening. But as we speed up the animation, something interesting develops….

sierpinski2

Our old friend, Sierpinski’s Triangle! Later in the period we saw this famous structure again when discussing Pascal’s Triangle and factors. Check out this cool coloring remainders applet and have fun!

465px-Animated_construction_of_Sierpinski_Triangle

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Class Openers

Class Opener – Day 18 – We’re Going Bowling!

A unique sculpture greeted students as they entered class today:

balls2

There’s a lot of math goodness happening in this picture, but I don’t want to steer conversation in any particular direction right off. Time for some Noticing and Wondering! Students shared their thoughts on the back board:

notice

Most of our class time today will be spent completing a jigsaw activity which guides students through many of the rich connections between Pascal’s Triangle, Combinations and the Binomial Theorem.  Knowing that I would eventually talk about Pascal’s Triangle (one of my favorite shares of the year!), I was hoping to see if we could generate ideas on triangular and tetrahedral numbers organically.  This visual opener did the trick. And while I ran out of time today for my Triangle chat, it’s in my pocket for tomorrow!

After sharing this experience on Twitter, Annie Fetter (the queen of noticing and wondering) chimed in with her ideas:

So many great ideas for packaging to be had here, but thinking I share it and leave it to my geometry colleagues to explore.

Categories
Class Openers

Class Opener – Day 17 – Time for a Card Trick

Today is the last day of school before a 4-day weekend. Since we have been talking a lot about cards and probability in class, it’s a great time for a card trick to maintain enthusiasm before a few days off. Enjoy a glimpse into the craziness which is my classroom…

A “how to” guide for this trick is given here by Mismag822 on YouTube:

In the instructional video, you find that the secret to this trick lies in the cards being face-up the first time around, which does transform the order of the cards during a “switch”. Later, when the cards are dealt face down, two single cards placed face down individually is equivalent two cards switched and placed faced down. For my geometry folks, there is a cool transformation introduction here.