## Thursday, July 31, 2014

### Linear: The Seven Dwarves

Algebra with The Seven Dwarves

I find that even at the point when my 9th grade students reach High School, they still don't really "understand" even the basics of linear equations.   Sure, they can remember how to calculate slope once I remind them of the slope formula, but they don't know what it means.  Y-intercept.....forget it.  They just don't get it.

So....I usually throw in a little problem in the first week or so where we will construct two lines using all the stuff they probably covered in middle school.

This simple example hopefully is something I can reference throughout the year as an example.  The example works well for various topics, especially linear and linear systems.

These video examples are reduced in size to save space.  The versions I use inclass are much higher quality and size.

version 1:

version 2:

Here are some screenshots from the SMARTBoard presentation I use to build the problem and graph it step by step.

## Sunday, July 27, 2014

### TMC14 My Favorite "Moneyball Webquest"

Moneyball Webquest

http://rossettimath.weebly.com/webquest.html

### TMC My Favorite "Absolute Value Blackjack"

At TMC14, I presented three "My Favorites"  I have added a blog post for each.  If you have any questions about this activity, please tweet me at @aanthonya.

Absolute Value Blackjack

As a statistics teacher, I find it almost necessary to address gambling in my classes.  In fact, during my stats classes we sometimes have casino games!  Green felt tables, chips, everything except for real money.  This helps students to grasp the concept of probability.  All casino games are designed around probabilities.

I found that it generally accepted to do these events as part of statistical games with 12th graders since they are 17/18 years old.

Playing gambling games with younger students is a slippery slope so I decided to keep the rules of blackjack, but add in the idea that red cards are negative and black cards are positive.

General rules:
Play with standard blackjack rules with the added idea that reds are negative. Use the absolute value of ending hands for comparison.  A negative 18 beats a positive 17 because the absolute values of both hands are 18 and 17.  The dealer busts with a -22 or lower or a 22 or higher.  That simple.

You may add complexity by limiting the amount of cards to be drawn, or add in a twist like a "0" is as good as 21 or -21.

The problem with this game is the real probabilities go out the window, BUT it gets lower grade students to do mental math like maniacs!

## Sunday, June 8, 2014

### Wisdom of the crowd

As the year is ending, I realized i didn't do many of the things I had planned to do at the start of the year, so I needed to get in the things I felt most strongly about.

During TMC 2013 in Philadelphia some of the "Stats Mafia" took some time to watch a video demonstrating the wisdom of the crowd.  You can watch the clip here:

To make a long story short, in this video, 160 people guess how many jelly beans they think are in a container.  Almost everyone is pretty far off, but as a group they were ridiculously close!  I couldn't believe it!

I had to reproduce this activity and see if I could get similar results.  Guess what, I did!

To pull this off, I needed x-thousand "somethings" that were relatively small, inexpensive, consistent in shape and size, and light to carry in large quantities.  I decided to use those plastic beads that kids use to make necklaces, bracelets and other things.  They look something like this:

These are not the exact ones, but you get the idea.  I will post actual photos when I get some more free time.

I put 3,116 in a plastic container and hit the hallways.  I asked students, teachers, and staff to guess the quantity of beads.  I recorded a bunch of information about each guess so I could dig into the data afterwards and try to find interesting things.  For example, Social Studies teachers as a group guessed better than math teachers.  Juniors as a group were also closer than teachers.  In fact, they were the best group.  BUT individual math teachers had good guesses, closer than SS teachers and juniors.

Two freshmen guessed 3,100 which was the closest of all guesses, but i couldn't believe how bad people were guessing!  In fact, one student guessed 50,000 and another 250.  I was truly shocked and couldn't wait to tally the results and prove the video wrong. I spent about 5 days and got 142 people to guess.

Well boy was I wrong.  The average guess of the group was 3,098!  That's just 18 beads off!  Holy crap!  That's .59% off.  Only a couple of people guessed better than the crowd as a whole.