A walk through a challenging probability problem

Saw a great problem from the 2009 AMC 10 last night:

Here’s the problem:

Problem 24 from the 2009 AMC 10a

3 verticies of a cube are chosen at random.  What is the probability that the plane formed by those three verticies contains points inside of the cube?

This is a great problem (and a challenging one, too).   My older son took a few missteps walking through it, but our whole conversation about the problem this morning was great.

here’s the first part:

 

In the second part he takes a little misstep, but hopefully the mistake turned into a good learning opportunity:

Now we back up to where the misstep happened and try to get to the end of the problem:

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Tracy Johnston Zager’s latest blog post makes me happy and sad

Tracy Johnston Zager has an excellent blog post summarizing her experience at a recent conference. The post is a must read:

Disrupting the Usual Rhythm

Her post made me happy because everyone should experience math the way Zager describes in her post. In fact, everyone should experience math in this way all time time!

Oddly, though, the post left me a little sad, and I couldn’t really put my finger on why. One reason came to mind as I was thinking about it tonight, though.

I remember this post from David Coffey last year:

Whose Fault is it that you aren’t good at math?

One line, in particular, came to mind tonight (and I’d encourage you to read the original blog post to understand the full context):

“I’ll grant you that it might take a gift to be great at math, but if you’re not good at math, it’s no because of your genes. It’s because of your experiences.”

So, I guess I’m a little sad because the great time that Tracy wrote about in her blog seems to be quite the exception rather than the rule when it comes to experiencing math.

My response to Coffey’s post is here (and seems to have acquired a little formatting problem that I’ll try to fix tomorrow):

Responding to David Coffey’s Challenge

Zager’s post is probably a better response, though, because it directly shows the power of that great experiences in math can have. It certainly gave me a goal to have everyone walking away from my math projects at least as excited as Zager was after this conference!