# Probability Ponderings

It’s been a great week in my probability and statistics classes.  I’m not sure why I’m pleasantly surprised.  This time of year it’s absolutely essential that we engage kids in meaningful mathematics and when we do, they respond well.

Monday, we did expected value and Dan Meyer’s Money Duck.  See Monday’s blog post for details.  Extra Credit if you can find my duck pun in there.

Tuesday, after assessing expected value, we moved to tree diagrams and conditional probability.

Wednesday, I used Nrich’s In a Box problem to create some discussion about dependent and independent events.

I started with a bag with unifix cubes and had them do some experimenting to see if the game was fair.  What I love about this problem is that the initial answers that the kids come up with are usually completely wrong.  It really allows the teacher to identify the misconceptions.  Additionally, this problem is so easy to extend.  Simply have the students come up with a scenario of ribbons that creates a fair game.  Most will come up with something like 2 red and 2 blue. Have them test their theory, find out it’s wrong and then test another.  Even when they find the magic combination that creates a fair game, there is still the task of generalizing the results that’s challenging.

Thursday, I totally stole Andrew Stadel’s 4! lesson.  What a great intro to the idea of factorial.  Last trimester I used IMP’s ice cream bowls and cones, which I still might refer to.  I felt like having a few students up in front at the beginning got everyone on the same page at the same time.  It was completely awesome to see the different methods for solving this.  I love the repeated reasoning here:

Plus, opportunities to use animal counters in HS math are scarce.

What’s the most pleasing about this week is that I think that this group’s conceptual foundation of these concepts is more solid than it has been in any previous year.  We still have practice to do, but I feel like they have made a good connection to what their answers represent.  In the past, my formula driven instruction didn’t bode well for retention of the concepts. I’m more hopeful this time around.

# Alright, Mr. Stadel. We’ve Got Some Bacon Questions

Greetings, Mr. Stadel.  We know that you are very busy.  We appreciate your brief attention.  Rather than bombard you with tweets, we decided to bloggly address our questions and comments about your Bacon Estimates.

First of all, bravo.  You dedicated an entire section of your estimation180 blog to a culinary wonder some refer to as “meat candy.”  Even our vegan teacher felt compelled to engage us with these estimates.  (She says it is for the sake of the learning.)

Second, the time lapse videos of the cooking are pretty sweet.  Too bad the school internet wouldn’t stop buffering.  But nice touch, Mr. Stadel.  Nice touch.

A question:  Did you know that the percent decrease in length of bacon is 38% after cooking, but the percent decrease in width is only 23%?  We figured that out adapting your “percent error” formula to the uncooked/cooked bacon.  Do you have any initial thoughts about that discrepancy?  Is it bacon’s “fibrous” fat/meat striped makeup that allows it to shrink more in length than width, inch for inch?

Also, did you know that the percent decrease in time from the cold skillet to the pre-heated skillet is 29%?  That one was a little harder for us to calculate, because we figured out that we needed to convert the cooking times to seconds rather than minutes and seconds.

To summarize, we wanted to thank you, Mr. Stadel.  Our teacher tells us that you dedicate your time and energy to the estimation180 site so that WE don’t have to learn math out of a textbook.  We wanted to tell you that we appreciate it.  And the bacon.  We appreciate the homage paid to bacon.

Sincerely,

Mrs. Schmidt’s Math Class

St. Francis, MN