## Sunday, September 21, 2014

### My Factor Captor Obsession

Last June I published post detailing my nearly year-long exploration of the game Factor Captor.  Up until the last week of school I had the fourth graders cutting apart the game board and playing around with the numbers:

 I was curious: How many multiplication sentences could be made using the 48 numbers on the board as both factors and products.  With three per sentence, could someone make 16?
 Close!!  But can you spot the mistake?
I didn't get any further than this; it was more of a test drive to see what would happen, and if the activity would be worthwhile for next year's class. But as fortune would have it, our grade 5 curriculum opens with a three-week unit on factors, primes, composites, squares, and divisibility rules.  So I knew I would have an opportunity to use the game to extend some learning.
First, Rich and I let them get reacquainted with the game.  We pulled out the boards they were familiar with.  I was pleased to see that the majority remembered how to play, and for the rest a quick review of the rules was sufficient to get them up and running.  I thought it might make things more meaningful if we explored the unit's vocabulary (prime, composite, even, odd, square), using the numbers from the board.  It seemed like the perfect opportunity to get out the scissors and glue again!
I thought they might find it helpful to use Venn diagrams.  Many of them chose prime and composite as their first sort.  Of course there was much debate about where to put the number 1.

 Some students used reference books.

Many students finished one sort, and we encouraged them to choose two new labels and try another. And since we're into noticing and wondering, we asked them to write one thing they noticed about their diagram.  These ran along the lines of statements like:

• Most of the even numbers between 1 and 37 are not square, except 4 and 16.
• There are no numbers that are both prime and composite.
• 2 is the only even prime number.
I liked that they were attempting to out into words what they were seeing in their Venns.

And since the obsession shows no signs of abating...

 We introduced the advanced grid with a noticing and wondering  "do now".
The kids had some interesting observations, including wondering if playing on the new grid made the game easier or more difficult, noticing that, except for 1, the single-digit numbers are repeated and wondering why that might be so, and wondering whether or not they would get a chance to play.  Well of course!
I knew that this question would come up, and I knew that, as comfortable as most of them were with the original Factor Captor game board, this one was going to be somewhat intimidating.  I mean, 51?  How would one go about finding its factors?  My hope was to build some intellectual need for divisibility.
My experience exploring the learning opportunities embedded in the game Factor Captor has me excited about the possibilities that lay hidden within other games, at other grade levels.  It has me thinking more about how we can put games to better use in math class.  In my experience, games such as Factor Captor are used as reinforcements for concepts and skills that have been previously taught. Teachers might provide their students with the opportunity to play them at centers, or when they are done with classwork.  But children who struggle often have limited opportunities to play; it may take them most of the class period to complete their assigned work.  For others, playing the same game in the same way over and over again can quickly become just as dull as another workbook page.  But what if we used the games, not as afterthoughts, or as ways to keep some kids busy while we work with others, but as the vehicles to deliver instruction? Turn them upside down and inside out, take them apart and put them back together?  Not every game lends itself to this kind of treatment, but there are many that will.  I have some in mind; feel free to comment with your thoughts and suggestions.

1. I like that, "Turn them upside down and inside out, take them apart and put them back together?"

One of my other - connected - obsessions is with the ancient Greek mathematician-philosophers and what they were up to. Playing games, it appears - my blog post:
http://seekecho.blogspot.fr/2007/04/pebbles.html
Every beach I go to, I collect pebbles of a certain shape for this.

Oh, and did you see Prime Climb?
http://mathforlove.com/games/
My digital copy has arrived, but I'm yet to explore it.

1. I did see Prime Climb! Bur totally forgot about it. Thanks so much for reminding me. I'm going to get on that right away. Do your kids get to play the pebble game? Love to see that. Wish we lived closer. I'd help you add to your collection.

2. I haven't yet. Need a lot more pebbles! But I think it could work well, and could have the rules changed lots, for instance to include rectangles. It would connect with factors nicely too!