## Tuesday, February 1, 2011

### Decimal Race

 by easylocum @ Flickr
This is a game that I got to play with the fifth graders, and it was pretty fun.  The game is nothing revolutionary, just moving along in 5 hundredths increments.  What made it more interesting is the kids designed their own spinners.  It actually raises some really nice probability questions.  While the expected value is made manageable for 5th graders by being done as a sum, with higher grades you could do a first day on expected value, which raises good decimal multiplication questions.  I also let them have the option of designing their own board, but all but one just used my sample.  If you want to force board design, don't let them have it!  Their boards didn't have to be with a money context, but did have to increment by .05 to 2.00.

There was quite a bit of content value to students adding their move to their position, and a few that struggle with decimal operations really took to the idea of nickels, dimes and quarters.  When demonstrating or playing with students, I encourage you to show different ways to figure out how far your move takes you.

DecimalRace-MakeSpinners

I modeled for them a couple ways to design.  Put in 9 values, then figure out the last to make 2.00; adjusting from a previous spinner design by moving around tenths or 5 hundredths; or thinking of having $2, and spreading it out among the slots. Many students were enthralled by the 9 zeroes spinner, but no one chose the 10 times .2 spinner. One team asked if it was okay to design multiple spinners and switch during the game. I said if it was okay with their opponents, since it was mathematically okay, if they were all fair spinners. DecimalRace-BlankSpinners If you don't have clear overlay spinners, you can get by just as easily with a bobby pin. Hold the pin at the center with a pen or pencil and spin away. (The fifth graders found bobby pins to be an interesting subject... go figure.) The squares along the bottom are for making game pieces to move around the board. Some students really got into it because they could decorate their spinner and game piece. That makes me think of the whole player psychographic thing that game designers think of, and wonder why I have never applied it to teaching before. (First guess: many unengaged students are Vorthos, and many teachers design lessons for Melvins.) Decimal Race Board It does occur to me that different spinners are better or worse depending on the game's special squares or conditions. Of course, if students are thinking about this, more power to them. They deserve to get to Candyland. Feedback always appreciated! (Seldom received. Sigh.) #### 5 comments: 1. Thanks for sharing the activity. I was surprised no one chose the 10 times the .2 spinner. It requires the least amount of work, and pieces can be moved without waiting for the spinner to stop. Possible way to add to the excitement is alternate between high and low values. You can win big or lose big, and you won't know until the spinner stops completely. One thing that might help is adding color. While spinner is going around, it'll be difficult to see the numbers well. Colors will make them stand out. Adding color to the high and low values, at least, could do the trick. 2. Thanks, Mr. H! I think you're exactly right. One of the groups decorated their spinner, and after they played with another pair, the new pair almost always decorated their spinner afterwards. Alternating colors were key in their designs. I like the idea of alternating values... guess I was being mathematician-like by organizing them. 3. This comment has been removed by the author. 4. "I was surprised no one chose the 10 times the .2 spinner." In addition, you win in 9 moves due to the bonus on 0.2. Expectation is a weird measurement here, because presumably the game ends when one player wins, so what we really care about is how often one strategy (aka a spinner) wins in comparison to another one. In this case, I played around with a couple variations before settling on [0.85, 0.85, 0.1, 0.1, 0.1, 0, 0, 0, 0, 0] because it gives fairly good chances of hitting either of the bonuses on 0.2 or 0.85, while making it very hard to hit the penalties on 1.5 and 1.75. This strategy wins in 9 turns or less with probability ~ 0.509, which means you expect to win or tie the "all 0.2" strategy more than half the time. Expected number of turns is at least 10.7, but if we only care about how often we lose (as opposed to by how much we lose), it's ok. Alternatively, a spinner that is [2 0 0 0 0 0 0 0 0 0] will finish in the first 9 turns with probability ~0.613, so it's even better (esp. if you like high variance). The MTG references were great, as I did a double-take when I first saw Vorthos. Also, what happened to 1.7 on the board? 5.$1.70! None of the kids caught that. Just my mistake.

Excellent work on the probability, Hao!

And I'm glad to know there's an MtG reader of the blog. Did you see http://mathhombre.blogspot.com/2010/05/this-and-that.html? It's the only other time I've tried to connect magic and teaching.