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Algebra Class Openers

Class Opener – Day 20 – Infinite Chocolate

How is that possible? Tell me the answer?

Some of my students haven’t picked up on my sneaky side yet. There are no free answers in my class, including this visual which greeted them today:

choc

Some students had seen this before, but few could figure out the mystery of the infinite chocolate. In my afternoon class, one student took charge, showing the subtle differences in the sizes of the pieces as they are reconnect…a future math teacher in the making. Today’s opener wasn’t intended to connect to anything course-related; it’s just a fascinating geometric mind trick, and great for generating math conversation right away. You can Google this problem and find a number of versions, many which explain the illusion, but we ended this opener with a video which shows some potential geometric shenannigans.

Today I desired a short and snappy opening hook, as my goal was to get students to the boards right away to work on binomial theorem problems. This was the second day students viewed videos and took notes for homework, and the response has been outstanding. Classes the last two days have been energetic, as the group doesn’t need to hear me drone on….they heard that at home. The focus today was terms in a binomial sequence – enjoy the video notes here.  Also, pay attention for the rough edit at the end due to my mistake….was more fun to leave that in than to edit it out.

Categories
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

Categories
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.