Out of the Box

    One of the first things I did when I took over the position of math specialist at my school was take inventory of what had been left in my new room.  There was quite a collection gathering dust in the closets, cabinets and drawers, most of it dating back many years: office supplies, manipulatives, old textbooks and workbooks, files, games, flashcards, and measurement tools.  Some of it I tossed.  Some of it I distributed to teachers and classrooms.  The rest I kept.

A battered survivor of the purge.

     One day, looking for something to fill a few extra minutes with one of my basic skills students, I grabbed the game, opened the box, and gave it a try.

Roll 3 dice, two 1-6 number cubes and another with addition and subtraction symbols.  The die with the operations was missing, so I made a replacement.  Use them to create an addition or subtraction number model.   Find the sum or difference...

...and move a token (snail, frog, turtle, or snake)  around the game board from the start, through the swamp, to the lily pad at the finish.

     Simple.  I grew to love the game, and it soon became a stand-by.  It has many benefits:

• Basic addition and subtraction fact practice
• Counting with one-to-one correspondence
• Identifying numbers as odd or even (If you land on a square that says "even" you roll a number cube.  If the result is an even number you move forward that many spaces; same for an odd number.)
• Social aspects of a good, old-fashioned board game, including learning how to take turns, handle adversity, and be a gracious winner... or loser.  Because I don't let kids win.  Well, hardly ever.

 The game has one insidious aspect, the dreaded "Endless Loop":

Once you enter the loop, you need to keep going around and around until you land exactly on the exit.  Only then can you dash to the lily pad.  It can get very frustrating.

  Last week, I was playing the game with one of my grade 2 basic skills students.  She had traveled around the endless loop a few times, and her frog sat one square before the exit.  She picked up the dice, but before she rolled I stopped her, and asked a question it had never occurred to me to ask before:

   Me: What will you have to roll to land exactly on the exit?
   Her: A one.
   Me: Yes, a one.  How can that happen?  (I knew that a roll of 11 would also work, but that's not where I wanted to go.)
   Her: (silence)
   Me: Show me what the roll would have to look like for you to get a one.

It was fascinating  to watch her think through this task, turning the dice and working with her fingers until she found a combination that worked.

   Her (putting up two fingers and taking one down): 2 minus 1 equals one!
   Me (realizing I might be on to something): What else could you roll?

She continued  manipulating the dice and using her fingers to calculate.  I pulled out a whiteboard and started writing down what she told me.  I was hoping she would see a pattern, and use it to generate the rest of the combinations, but no go.  She got stuck with one more left to find.

She needed a lot of prompting to come up with the final combination...

...but then she saw it, and continued to generate more subtraction number sentences equal to one.

    The period was coming to a close, and we finished the game.  I put the whiteboard aside, with the intention of taking it out again at our next meeting and using it to help her dig through what she had discovered about differences equal to one.   And I understood that there were more benefits embedded in the seemingly simple game than I had realized.  I had been focused on content standards, and had overlooked the opportunities to engage students in practice standards; in this case, a nice combination of SMPs 1 and 7.
     I've written about games before; how they can be used and repurposed.  I'm glad my predecessor left Sum Swamp behind.  More importantly, I'm glad I held on to it.  I never could have imagined what would come out of that box.