## Tuesday, November 17, 2015

### 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!

1. Here's the decimal version: http://mathhombre.blogspot.com/2010/05/decimal-point-pickle.html.

My math club kids enjoy playing a variation with fraction strips: We mix the strips face down in a draw pile and then pull out five strips and arrange them in a row, still face down. Then we turn our strips up. (But you could start with a blank staircase, if you prefer.) Take turns drawing a strip, trade with a strip in your row, and mix the discard back into the pile. First to get a row that increases from left to right wins the game.

1. Thanks for the link Denise! Just what I was looking for, because I was stumped on how to have kids generate decimal combinations of tenths, hundredths, and thousandths. Will be perfect for our fifth graders.

2. I was thinking fractions also! What if you used playing cards and drew 2 cards for your fraction? You could limit what cards are in the deck to match students' ability. Going to go look at the fraction version now!

1. I like this idea, and limiting the denominators based on grade level and ability is a good way to differentiate. This would also build the intellectual need for an accurate way to compare fractions.What about running the stairs from 0-2 to allow for improper fractions?

3. HI Joe, The stairs are such a dynamic visual to go along with this concept! Here at home we play a game called RACKO http://goo.gl/vyI0iM that is based on a similar concept. At first it seemed all like luck, but when I started winning ALL the time my family caught on, and now I rarely win a game. I like the way that probability plays into the game, and how risk balances with number sense. bTW I am still thinking about your cereal box posts...

1. I remember RACKO! Old school. I used to play that when I was a kid but haven't thought about it since then. That would be a good game to have in classrooms for kids to play during free times like indoor recess.