Saturday, September 27, 2014

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.


  1. Wow...that Georgia education page is incredible! Thanks for sharing!

    1. I know. Let Graham know how great it is! And if you find any special treasures there let me know. There is so much to look at I'm afraid i'm going to miss something.

    2. I second this! I hope NJ takes a lesson. Wow.

  2. What a fun game! And neat Noticings and Wonderings.

    One thing I always like asking kids when playing games is whether the game relies on skill or luck. Top-It (pretty much all varieties) relies on luck, for example. Good for kids to realize, especially if they are losing, that it's not their fault! This is a bit of both, obviously, and I like hearing students talk about the differences.

    1. Thanks Annie. This is something important to talk to the kids about. But you've got me thinking...I'm visualizing a vertical bar and two colors, one for skill and one for luck. Kids would have to color in the bar based on how much of the game is based on one or the other, then explain their rationale. Something else to try next week!

  3. Thank you for being such a clear and thoughtful voice on elementary mathematics. I read so many math blogs written by middle and high school teachers and sometimes wonder if they don't steer me a bit off course. It is so helpful to see those same ideas in elementary classrooms. I teach second grade and agree that Fill the Stairs is perfect for this time of year. We have been using anchor numbers to help us place other numbers on an open number line. It has been really interesting to see how the students understand and represent the distance between numbers. This game is different way to get them thinking about the same ideas. Thanks!

    1. Thanks for stopping by and commenting. I think it's a great idea to use number lines whenever you can. I'm thinking it might be a good extension to have the kids take the numbers they wind up with on their staircase and transfer them to a number line, could be vertical and horizontal since the staircase suggests both. Another way to see how they understand and represent the distance between numbers.

  4. You nailed it again Joe! Your ability to change existing resources doesn't go unrecognized. One of the things that @turtletoms and the creators of this work wanted to do was make the units accessible to all stakeholders. Of course, almost ever state’s instructional framework is under lock-and-key or shared as a pdf which makes it difficult to modify, but all of the units can also be found here and they are shared AS A WORD DOC!

    Removing the rules and pre-writing before the game is brilliant. It’s like a sneak attack to journaling for the kids that hate writing! At this point no one is wrong because it all stems from student observation which is a phenomenal way to assess what students already know and understand. Stealing this right now! The pre-write is very similar to the way estimation is used to hook students into a 3-Acts.

    What I really like about this game is that the majority of mass produced hundred charts start with 0 or 1 at the top which aligns to reading but not how students recognize quantities in the primary grades. Next time you walk around the little people classrooms check and see how many hundreds charts have the tens at the bottom. Hmmm?

    Thinking purposefully here-We want kids increase a group of 10 but the hundreds chart makes them go down. I find this counter-intuitive as kids initially need structure to make sense of numbers. If we’re increasing by 10 should the number go up? I would suggest that most kids developing number sense would agree. A great example of this is found in the 1st grade frameworks unit 2 called Number Hotel. Some great questioning built into the opening. It’s a personal favorite but I know you’ll make it better!

    Shout out to my wife for writing that one! #mathcollaborationforpillowtalk

    1. Number Hotel has already been tagged! I'm playing around with a slight modification in the board (hope I don;t mess it up but I can't resist). Hope to have it ready soon and I'll let you know how it goes.

  5. Wow! Thanks for the sweetness, Joe. This is a lovely post, and exactly how I hoped our units would be used. Take them, make them yours, and in your case, make them way better! Graham, I'm thinking we need to somehow rope Joe in when/if we have another revision. He'd make a great team member!
    Interstate collaboration. What a concept. Thanks again, Joe. This is beautiful.

  6. Thanks Turtle. I would be honored to be a part that process. You are all making a tremendous contribution, and I hope that you receive the recognition you deserve.

  7. A bunch of possible variations to play:
    (1) each player has a different color to write their number and claim a stair. Player who claims more stairs is the winner.
    (2) players have hands with more than 2 cards (5 is often a good number, reasonable amount of choice, but not too much) and get to choose which cards they play on their turn. Could be played head-to-head as in (1) or parallel
    (3) different stairs have different point values and/or last stair claimed gets a bonus
    (4) different stairs have multipliers that multiply the value entered (for kids who are ready to do some 2 digit by 1 digit multiplication)
    (5) A 1-digit version with fewer than 10 steps with or without 0 and 9 already marked

  8. I love all these variations, scaling both up and down. I think when I introduce the game to the second graders this year I'm going to try numbers 1-3. How about a K/early grade 1 version where it's still 10 stairs but boundaries are 0 and 20 played with a set of cards 1-19?