Fostering “Mathusiasm” with Jo Boaler’s Task “How Close to a 100?”

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Good to have you back math nerds!  And if you’re just checking in for the first time, welcome!

I had the opportunity to spend a day working with 10 elementary instructional coaches and reflecting on our work this year in the math classroom.  At one point, a colleague called another colleague a “rat bastard!”

Now that’s a successful PD, am I right?

Let me back up a step.  I’m a strong believer that all professional development workshops for math educators need to foster their “mathusiasm” (math + enthusiasm).  We all need opportunities to do math, to explore and play with content in an effort to develop a fuller, deeper, more flexible understanding of concepts.  We must be enthusiastic as we think more deeply about simple ideas and practice engaging in thoughtful mathematical discourse.  If we want to foster math nerds in our classrooms, we must practice being them ourselves outside of the classroom.

So when I came across Jo Boaler’s wonderful game “How close to 100?” in her book Mathematical Mindsets, I was very eager to try it out with this group of coaches to see what “mathusiasm” could be generated.  What transpired was one of the mathusiastic dialogues I’ve had in a PD, and I’d like to tell you about it.

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You can read the rules at the link above.  Here’s a brief explanation using language from Boaler’s site:

  • This game is played in partners. Two players share a blank 100 grid.
  • The first partner rolls two number dice.
  • The numbers that come up are the numbers the player uses to make an array on the 100 grid.
  • They can put the array anywhere on the grid, but the goal is to fill up the grid to get it as full as possible.
  • After the player draws the array on the grid, she writes in the number sentence that describes the grid.
  • The second player then rolls the dice, draws the number grid and records their number sentence.
  • The game ends when both players have rolled the dice and cannot put any more arrays on the grid.
  • How close to 100 can you get?

We played this version of the game once before playing a variation (also on Boaler’s site) where each player has their own blank 100 grid.   This creates the opportunity for the players to choose to be collaborative (help each other) or competitive (beat each other).

It was during this moment that a player called her opponent a “rat bastard!” for rolling the perfect roll to win the game.  I chalk that up to evidence of vested engagement and mathusism!  After playing several rounds, the coaches started to think of variations that would add nuances to both the game play and the mathematical thinking.

Here are some things that I heard/recorded while they played:

  • Laughter.
  • What makes a roll good?  bad?
  • I’m wondering if there’s a time limit.
  • How do we decide where to put shapes?
  • Probability…
  • Twenty four!  Sh*t!
  • Are bigger numbers better at the beginning?
  • Where should I put squares?  Where’s the worst place to put them?
  • How that we see our list of number sentences, how could we have done it better?

Profanity aside, those are some things we want to hear our students say and ask in the classroom.  They are evidence of having a mathematical mindset and provide a wealth of opportunities for teachers to structure the flow and sequence of discussion.

Here were some key takeaways that came out during our reflection conversation about the educational value of playing “How close to 100?”

  • The game promotes social interactions and gets kids engaged with each other.
  • It has a wonderful balance between giving students freedom of choice (where to put the array) and freedom from choice (have to put it somewhere).
  • The game incorporated a layer of strategy and anticipation that lays an excellent foundation for talking about probability.
  • The strongest math student doesn’t always win.
  • All students can feel successful and develop math confidence.
  • It’s a puzzle!  Everyone loves puzzles!
  • It reinforces a spatial understanding of multiplication.
  • It is fertile ground for using peer-to-peer academic language.

And here were some variations and wonderings that they had about the game moving forward:

  • Allow students to be able to have some passes for rolls.
  • Modify the rules for ending.  When is the game over?
  • How could we do a collaborative whole class version?
  • What would a 3-D version look like with three dice?
  • You could roll several times (like 3 times) and decide where you want to put them all.
  • You could choose if you want to put it on your grid or your opponents grid.  And where to put it.
  • We play until we’re bored.  When bored, we change the rules.
  • How could we rework the number sentences to incorporate the distributive property.  For example, 6(4) = 6(3 + 1) = 6(3) + 6(1).  Could we allow students to then make their 6 x 4 array a 6 x 3 and a 6 x 1 array and allow them to graph them separately.

Thanks for checking in math nerds.  I invite you to experience the game in your PDs or classrooms and share any mathusiams with us here in the comments section.  Please be in touch.

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