Friday, June 13, 2014

"The world would be a great place if we could play Factor Captor all day long."

     Factor Captor is an Everyday Math game designed to help students practice identifying factors and multiples, and explore prime and composite numbers.

The rules are not as complicated as they look.  

Here's a close-up of the board.   Jeff and I decided to use Grid 1 (Beginning Level).

   We introduced the game to the fourth graders in October, at the beginning of our first multiplication unit.  It took a few days, but eventually the kids got the hang of it.  We encouraged them to use multiplication tables to find factors, and made a solemn vow not to use the words prime or composite.  We just let them play and hoped that at some point they would come to the realization that some of the numbers had more factors than others.

      One day, about a week after we had introduced the game, I was walking around the room with my iPad  and decided to record some kids playing a round.  I got about 5 minutes of video, and later watched it during lunch.  Knowing how much they like to see themselves on TV, I played it for the class the next day.  As the kids watched the action, something occurred to me: why don't I use it like a coach would use game film?  So before the next move was made, I hit the "pause" button.
    "What do you think the next move will be?" I asked.  There were lots of opinions as to what the best next move was, and I made sure that each one was backed up by some type of explanation.  The idea that there was some strategy involved, which some kids had already begun to intuit, was brought out into open discussion.  And after everyone who wanted to had a chance to express their opinion, I just hit "play" and we saw what actually happened.  The kids loved it!  So we continued in this way for several turns, and came back to it the next day with more video.
    This is when I began to think that maybe we should push this game a bit more.  At the very least the kids were getting practice with some multiplication facts (3 x 9 = 27 was pretty much automatic by that point), they were also adding (as they kept score), and of course continuing to build some understanding about factors and multiples.  Besides, they were still having fun with it.
  A look at a random notebook page where two kids had kept score of a game they played gave me another idea:

How easy would it be to recreate a game based on a copy of the score sheet?  
     Jeff and I tried this ourselves one day at lunch.  It wasn't so easy.  Some of the numbers on the page represented a first number selected, others represented factors or factor totals selected in response, and others represented running cumulative score totals.  We weren't sure how the kids would respond, but we decided to give it a try.
     This got frustrating for some as there were often several false starts, and kids were confused as to what the numbers actually meant.  But the majority were able to piece together at least the beginning moves of the game.
    Of course next came the reverse: Given a picture of a board from a game that is already in progress...

...can you recreate the score sheet?

     By this time the unit was nearing its conclusion, the assessment was just days away, we still hadn't introduced the terms prime and composite, and Jeff was starting to panic.  So we decided to have another class discussion about Factor Captor strategies.  It was centered around numbers that were "good to pick".  By this time the kids knew that 11 and 13 were good because they had no other factors except 1 and themselves.  In fact, in most games, 11 and 13 were the first numbers selected.  This is how we organized the concept of a prime number.  Other numbers might be more or less "good to pick", but they had other factors besides 1 and themselves.  So that's how we organized the concept of a composite number.  Jeff was relieved.  And the unit drew to a close.
   At this point we would have put the game away.  The next unit dealt with fractions, and so did the one after that.  No need for factors and multiples, prime and composite numbers anymore.  But Jeff and I decided we wanted to continue to explore the game with the kids, and that these explorations could take place in and around other lessons and activities.
  Circling back to our conceptions of primes and composites in relation to the game, and the strategy involved in playing, I thought it would be interesting to see if the kids could classify the numbers on the board as "really good", "kind of good", or "not so good", and give a reason to back it up.  The fact that they would have to cut up a board appealed to my sense that if you want to understand something, it's a good idea to take it apart.

Jeff and I liked this explanation.
These kids understood that the classification would have something to do with the point differential.

Here's what we were driving at: what's the point differential?  These kids nailed it for 27.

   After spending several days working on this project, we decided to let them play the game again, this time using their charts.  We asked them to keep in mind whether or not their charts were helpful, and whether some numbers might be classified incorrectly.
     My supervisor came to observe me in December.  I wanted to use the observation as a chance to showcase some of the different projects and activities we had been exploring in grade 4.   We started with a homemade estimation 180 activity, and then divided the class in half.  Some were working on the highway sign project, and others playing factor captor and working on their strategy posters.  He liked the game, and noticed how engaged and excited the kids were.
  "The world would be a great place if we could play factor captor all day long!" he said wistfully.
  It's now June.  And Jeff and I have made it a point to integrate the game into our guided group routine at least twice a month. This has provided another opportunity for us to reteach, conduct formative assessments, and have the kids revisit the skills and concepts.

As they have played, their strategy posters have been amended, edited, and revised.

Some have needed more paper!
     Jeff and I agree that the strategic use of games like Factor Captor, and the Pie Eating Contest, must be an integral part of our program going forward.  These games have the potential to be repurposed, taken apart, and mined for their rich content.  They have too much going for them to be played just once or twice and then put away.


  1. Love this post Joe!

    What a brilliant idea! Videotaping student play, then revisiting later on is a great way for teachers to gain insight into students' thinking (SMP #2 & #3). I'm sure the conversations sparked from the review were extremely powerful. I am definitely stealing this along with playing the game backwards.
    Game play is such a vital part of math class because it gives students an opportunity to solidify their internal strategies and build fluency.

    1. Steal away Graham...I've stolen plenty from you!

  2. I'm going to snatch this one away too. Just googled and found a PDF of it. We've done a few lessons about factors and primes, so I'm hoping it will ring bells...

  3. What a fabulous way to wring every bit of goodness out of a game. Love this. As soon as I get outside of the school building I'm in which blocks twitter (sigh...) I'm tweeting this gem.

  4. Thanks so much! As always, your positive comments are inspiring.

  5. I think there is a lot of potential discussion just looking at the structure of the board. I notice that you did something like this with a teacher group recently when you wanted to introduce MTBoS ideas. I wonder what the teachers said and I wonder what ideas kids would identify.

    I'm planning to use this next week with some 2nd and 3rd grade students. I am tempted not to give them complete rules, for example, leave out:
    - restriction on choosing numbers less than 10 as the first number in a round
    - opportunity for opponent to capture points that are missed by the 2nd player in the round

    I expect these situations will come up and I'll ask the students what they think the rules should be.

  6. Many teachers (and kids) noticed that there were numbers missing (like 23), and others were there multiple times (like 2), and wondered why that was so. The more I think about it, the more I like introducing a game this way. I plan on doing it next week in grade 3 with the Marilyn Burns game "4 Strikes and You're Out". I like you're idea about leaving out certain rules or restrictions and seeing what the kids come up with.
    I've just discovered your blog, and plan to spend some time digging into your archives. Are you on twitter?