Fill the Stairs, Redux

     Last year we had an adventure in second grade with the game Fill the Stairs.

I stole it from the Georgia Frameworks.  It became one of the most popular games in the grade level.

   So when I saw that the second grade teachers had brought it back this year, I was delighted.  Turns out there are students who can compare numbers in traditional tasks like this:

...and correctly answer questions like this:

...who aren't always successful applying the skill in a different context:

Same student as above.  The game is another way to assess number sense.

     I knew the second grade teachers were working on having their students get better at constructing viable arguments and justifying their thinking, and had an idea about how to use the game to further that goal.  I ran the idea by Kristin, one of our second grade teachers, and she helped me come up with the following task:

We wondered if any students would choose to use 42.  None did.

Most kids had variations on similar answers.

Even our "strugglers" managed to get something down.

       My next thought was to have them actually play out a game, starting with the number 24 on the stair they selected, and then evaluate their choice.

We asked them to trace over their 24 with a marker to ensure it would not be moved before they completed the game...

...and write their reflection on the back of the paper.

 
   Next, a comment on the original post left by Joshua Greene inspired me to experiment with our first graders, some of whom are still working on counting and ordering numbers between 0 and 20:

I modified the staircase to run from 1 to 20, and decided to use an icosahedral die.

I tested it out with one of my basic skills students:

I gave her no hints or help of any kind.  I filled in my staircase first because she had limited her chances by placing 10 on the stair just below 20.

I was curious to know if she would learn from this experience, so I suggested we play another round:

This time I provided her with a number tape that ran from 0 to 20.  The first number she rolled was a 1, which she placed on the stair directly above 0.

     

She next rolled a 7, and then a 17.  Based on where she placed the numbers, I felt that she had learned from the previous game.

Next came 6, followed by 10.  And she had a nice spot between 1 and 6 to place the 4.  After the experience, I knew the game was ready to be rolled out to the grade level.

  Here are Joshua Greene's ideas:

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


And I'll add to his list: (6) a decimal version for the fourth and fifth graders.  Feel free to continue the list in the comments!