Saturday, September 30, 2017

Standard Deviation Boccie

I wanted to create some sort of mildly competitive a game that would convey the idea that standard deviation (or any measure of spread) does not depend on how high or low the average of a data set is, but on how much all of the data points vary from that average. Unfortunately, the objective of most games is to either get a high score (e.g. cup stacking challenge), or meet some other specific criteria (e.g. landing on red in roulette).

It turns out that boccie is one of the few games where the winner is not the person that throws toss their ball the farthest, but the person that can toss their ball closest to a designated ball, regardless of how close or far away it is. The real rules can be found here, but we needed to make a few modifications to make it work for us. There was no pallino, and the score wasn't calculated by counting how many balls were closest to the pallino. Here are some instructions:

(1) Put some sort of lines on the floor so students will be able to tell how far they've tossed the balls from where they are standing. I used chart paper, but you could easily just lay a measuring tape on the floor, or count floor tiles.

(2) Place the class into pairs - these pairs will be competing against each other. Each pair should take turns rolling 5 crumpled balls of paper onto the floor (we used ping pong balls originally, but they rolled too much). It helps if the two partners have two different colored balls.

(3) The objective is to get your balls as close as possible to each other, while making your opponent's balls more spread out. You are allowed to knock your opponent's balls away from the group as you toss.

(4) Once all 10 balls have been tossed, ask students to record the distance of their five balls from where they stood. If there is time, groups can play a second or third game.

(5) Once everyone in the class had played at least one game, ask students to find the standard deviation, range, and IQR of their 5 balls from one of their games. 

I asked students to determine which partner won, and why. This led to a really great discussion of how we calculate all three measures of spread, what the advantages and disadvantages of each measure is, and which measure was appropriate for this game. We didn't have enough time to delve too far into a discussion, but I could see this turning into a 5-practice routine where groups need to defend which measure of spread would be best for this game. I also think this is a great way to visually see the differences between standard deviation, range, and IQR for students that have trouble calculating each.

Who wins this game?

Saturday, September 16, 2017

Choose the Best Player: A 1-Variable Stats Anchor

I know that there are a lot of activities out there that you could use as an anchor for a 1-variable statistics unit, but they didn't quite fit my needs. So of course I made one...

I used this activity twice. I first gave it to students before we had started the unit on measures of center and spread. I told them that there were six high school seniors that had been identified by recruiters to play for the UCONN Basketball Team. Unfortunately, there were only scholarships for two players. They had to work with their group to pick the two players using the data I gave them, and create a poster defending their choice. We followed a 5-practice routine discussion structure, and I found that their responses gave me great insight into how to navigate the next two weeks of instruction.

I also gave this activity to students as an assessment when we were finishing up measures of center and spread. This time, I told them that none of the prospective players got recruited. They now had to play the role of angry parent and explain to me why their son should have made the team. I assigned each group a prospective player, read through the scoring rubric, and sent them on their way.

This time, I had the groups present out to the class. The class also had a chance to ask questions and respond. Here's the best line from that class:

Brendan is a great player, and you should choose him, because if you remove those two outliers his average increases. He just had a couple of bad days, and those days skew the data. 

What happened on those days?

His dog died. 

What about the other day?

His dog died... twice.