mathcoachblog

Here’s the picture which greeted students as they enetered today:

Those are all odd numbers.

Why are they purple?

What’s with the dollar signs?

They are prime numbers.

Are they all prime? How can we tell? Many students remembered the “trick” for determining if a number is a multiple of 3, but how do we check 8191?  Maybe 13 or 17 goes into it, or some other funky prime.

But once we establish they are prime, what’s special about THESE primes. I let this sequence marinate for a bit as I continued instruction, and eventually offered a hint.

Add 1 to each number in the sequence.

This led to a clear observation in one class, and one I didn’t expect in another:

They are powers of 2

They are numbers from the 2048 game

So true! But what is special about these powers of 2, and why did I exclude others?

The big reveal here is that the numbers shown at the start are Mersenne Primes: primes of the form shown on the right, where P is also prime.  And the Great Internet Mersenne Prime Search provides an opportunity for the amateur mathematician to participate in a quest to find bigger and bigger Mersenne Primes, and perhaps score a cash prize for your effort! Visit the GIMPS site for more information about the search, and the current status of the project, where the largest prime found boast over 17 million digits. While many in the class wondered why anyone would care about such primes (we will discuss codebreaking later our course when dealing with Matrices), others seemed intrigued by the pattern. And as we begin to discuss counting priniciples and large numbers tomorrow, this was a neat way to foreshadow.  Finally, I want to live someplace which values math so much that they put math on their postage, that would be cool….

After a probability quiz on Friday, students were given a problem to tackle and finish for homework. The problem, Come Fly With Me (shared below), features many overlapping events which students need to process. Ideally, the problem is best summarized using a Venn diagram, though certainly other methods can be used to reason it out.

While I find that 9th graders have generally been exposed to Venn diagrams, they also have little conceptual understanindg of how these diagrams are used to process overlapping events. To generate discussion, this photo appeared on the board as students entered:

If I buy a sandwich with bacon and sausage, where should I place my name? Should I place my name in the bacon only space, as I am getting bacon? How about sausage? And how do we feel about the placement of that mushroom circle?

Now it’s time to go over the “Come Fly With Me” problem, given below, and find out if the class absorbed anything from our brief Venn discussion.

So, did our opening discussion help students use Venn Diagrams more effectively? Results are mixed, as some groups altered their assignment based on the discussion, while others kept the numbers as they were. But hopefully a few students were reminded of the power of these organizational tools.

Isn’t it the best feeling in the world when a former student checks in to let you know about their expereinces, their adventures, and how much your class influenced their life?  Today’s opener is a Facebook post from my former AP Stats student Aneglo as he starts medical school. He shared this probability nugget from a course regarding risk calculation:

His observation regarding probability in the medical-world setting, and class advice for me,  is priceless:

Just tell them that pregnancy is basically like reaching into a bag of different colored marbles.

Message received and relayed. Thanks Angelo!