A Tale of Three Classrooms

      If there is a better state curriculum document than the Common Core Georgia Performance Standards, I challenge you to send it to me right now.  I was made aware of it reading a post from one of its developers, Graham Fletcher.  Starting in kindergarten, it includes 3-act tasks, estimation180 challenges, problems with "open middles", and all the goodies an MTBoS groupie could desire.  As my focus turns more towards the primary grades, it has become a go-to source for ideas and activities, and I have barely scratched its surface.
  Looking through the grade 1 frameworks, I was stopped in my tracks by a game called Fill the Stairs.

The premise is simple.  Students take turns rolling  two 10-sided dice and creating a two digit number.  For each turn, the player writes the number created on any stair.  The object of the game is to keep the numbers in order between 10 and 100.  If there is no space to write the number, that player loses their turn.  First to fill in all the stairs wins.

    I felt that the game was better suited, at least at this point in the year, for our second graders.  I made a slight modification to the game board, adding two small spaces at the bottom for place value purposes.  In the first classroom I visited, I explained the rules and started playing a demonstration game against the classroom teacher, with the students acting as "advisers".  After we were confident the kids understood the premise, we set them off to play, first asking them to turn in a sheet recorded in pencil, then asking them to play on blank ones in their SmartPals. 

It was interesting to see their strategies develop as they became more experienced playing the game.  We allowed them to decide which die they wanted to use to represent the tens and which to represent the ones.  So if you rolled a 4 and an 8, you could choose 48 or 84, whichever worked best for you.

   The kids loved it, and as the period came to a close we debriefed with some strategy talk.  I left the game with their teacher to use in a center, or with a guided group of students still shaky with their number sense, but as I reflected on the experience I decided to make some changes as I brought it into second grade class #2.  I replaced the dice with number cards, and further modified the game board.

I removed the rules.  I left a larger space for the cards.  Another modification I wanted to try was to not allow the kids to manipulate the place value of the number.  The first card pulled would always be the tens digit, the second card the ones.  Why?  I was curious to see what would happen.

    I gathered the class in the front of the room and showed them the page on the Smart Board.
    "Today I'm going to teach you a game," I told them.  "But before I do, I'd like you to do something for me."
    Although they had never done it before, I asked them to respond to the following prompts:
   "What do you notice?  What do you wonder?" 
   There was quite a bit of buzzing as they shared their observations with each other.  They noticed stairs, the 10 and the 100, the lines at the bottom of the page, the big space in between the two.  They wondered what the rules of the game might be, if they were going to be asked to count by 10s, why there was a space for tens and ones. 
   Being prohibited from changing the place values of the digits changed the nature of the game.  It took longer to fill the stairs because there were fewer options, but I felt it removed a layer of complexity and reduced the game's potential to build both number sense and understanding of place value.

Many students adopted the strategy of using the second step for the 20s, the third for the 30s, and so on.   What happens now?

   So it was on to classroom #3.  I followed the same procedure, but this time made no mention of the fact that it was a game.  And I asked the kids to write down their "noticings and wonderings" in their notebooks.  Many children wrote that they noticed stairs and numbers, others wondered if they were going to be asked to count by 10s, and whether or not they would be playing a game.
     I need to thank our three amazing second grade teachers for allowing me to turn their classrooms into laboratories.  I am excited to work with them this year, together exploring some different practices and new principles in the attempt to build number sense and make math more meaningful for our second graders.