Using NIM in the classroom

First off, there’s MANY different ways to play NIM. I first learned about it form another classroom teacher, but I could finally understand the game when Jon Orr posted about it. He also did this sweet youtube video of him playing it with his daughters.

I introduced it to my class, and they love being in pairs up at the markerboards to play it.

So how can I make this game into a lesson? Into a mini-unit? And does it have enough math content associated with it to warrant that much valuable class time?

I feel like the easy answer is to go to the Math Process Standards (MP1-7). I mean, if you want to do something kind of fun in math and can’t tie it to any content standards, then you can EASILY tie it to at least a few Process Standards.

But I want this to be real and have value.

There aren’t many sixth grade standards that align very well to this: arithmetical standards use larger numbers and more operations. If I bent-over backwards I might be able to tie it into GCF or LCM.

But instead, I’ll look at how the game can be broken down, and about many of my kids’ weaknesses when it comes to math facts.

For arithmetic math facts, a lot of my students have weakness in the 7’s, 8’s, and 9’s. I have no idea why. But maybe if they had to count by 7’s, 8’s, and 9’s more, the patterns might be stuck in their heads better.

I’m also thinking about Pam Harris‘s 2nd part of her research. The first part is her awesome work on Development of Mathematical Reasoning and Problem Strings. But the 2nd part focuses on what to do AFTER your problem strings. After you drop the knowledge bomb of exciting ways to think about mathematics, what’s the NEXT step?

Rich tasks via Math Congresses. HERE’s a nice blog about math congresses, or you can look at this brief synopsis here:

I think that NIM has pedagogical use if used at the beginning of the year as a tool to get kids used to the mindset of your classroom, the structure of your math congresses, and slight review of the trickier math facts.

Here’s how.

FULL DISCLOSURE: I haven’t tried this at the beginning of the year, yet. When I do I’ll totally either write a new post or fix this one. But we are playing it NOW (November) and the kids really seem to like it and be open to talking strategy. I also have Vertical Non-Permanent Surfaces (synopsis HERE, original research HERE) around my room, which will totally help with collaboration.

First week of school. Do some killer addition problem strings from “Lessons and Activities for Building Powerful Numeracy” for the first 30ish minutes. Take a break with “I have, you need“, though I steal it and call it my own for the kids. I call it the “Schneider Game”, and don’t tell them the rules of it.

NIM: Day 1

Then I move into NIM. I play one game Me VS them to have them get the rules. That’s all they seem to need before they’re convinced that they have a “good strategy” (SPOILER: they don’t). But in each class that I played it with, they all did a frustrated sigh/sound of surprise when I got them down to “4”. If I could bottle that sound…

So here’s where it will get weird. My END goal is to have them not only find the pattern for victory, but also know how to identify the pattern not only when they take 1,2,3 away, but also when they take 1,2,3…,x away. And how it doesn’t really matter how many THINGS that they start with. I want them to know how to win no matter what the conditions I give them are.

So I’ll allow the students to pick their pairs, and then go around the room to a board. They’ll take their name tents and put them on the boards so I can know their names while they’re working.

Every side of the room will be given different constraints:

  • Left–> Starting #: 22, Takeaway Options: 1,2,3
  • Back –> Starting #: 22, Takeaway Options: 1,2
  • Right –> Starting #: 22, Takeaway Options: 1,2,3,4

They’ll play, and I will ask them to keep their games on the board so that they can keep track of it and see patterns.

The goal of the first day is to get them familiar with the game and have them recognize the first number that they can force their opponent too which would give them the game. At the end of class I’ll make sure to have gone around and drop the question: I wonder if you can win if you force them into a BIGGER number (I haven’t perfected the question yet, something like that).

NIM: Day 2

After “I have, you need”, they go back up in pairs to play their game. I interrupt the left side of the room and ask questions for them to think about the number BEFORE the number that they found (Example: if they’re doing 1,2,3, then once they get their opponent to a “4”, then they win, so I need them to reason how they can force their opponent into a “4” SPOILER: it’s 8). I do the same thing with the other two walls. After the third wall, I’ll watch the groups and either encourage them to use that 8 more effectively (if they aren’t), or ask them what number they can get to BEFORE the 8).

The goal at the end of Day 2 is for them to be aware that there IS a strategy, even though they only have a couple of the pieces to it.

NIM: Day 3

I start at the other side of the room while they’re playing, and talk about what they’ve discovered. A group has most likely figured out the counting up by… and is eager to share. We break apart why it works, and after they play a game of it I change their starting number to a good prime, like 31 to see how they do. I do the same thing for the other groups.

By the end of Day 3 they all know the winning strategy for their given numbers, no matter how many I give them to start with. I tell them that they’ll be presenting to the other groups that DIDN’T have their number tomorrow.

NIM: Day 4

No problem string today. It’s all about presentations!

They spend the first 10 minutes creating their examples and explanations on the whiteboard, and then a group from each of the other walls comes over and looks at it. This next part I stole from “Building Thinking Classrooms“. And that’s the group who MADE the presentation does not get to present. The other groups look at their work and say what the group that made it was thinking. What their strategy was. The reason for this is that when someone presents their own work, no one listens, but if someone else interprets and presents their work, then EVERYONE listens.

The groups spend 10 minutes at each location, learning the others’ strategies and asking questions.

We come back together as a whole class and discuss take-aways with me writing what they got on the board. When it’s all up, I’ll ask them for patterns that they see with the numbers, or things that they notice or wonder.

I’m hoping that someone sees that if they add one more to the choices, then they get how much that they have to count by, but that could be hoping for too much…

NIM: Day 5

Problem strings resume, and we go back over the strategies that we found. They beat me in a game. And now for the FUN part.

In their same paired-groups, I send them back to the boards, but THIS time I increase the amount that they can take away: 1-6, 1-7, and 1-8, and I increase the number that they start with to 50.

Their goal is to find the winning strategy.

Before this, they SHOULD already be hyper-sensitive to counting by 3s, 4s, and 5s. Now I hope that they’ll be the same for 7s, 8s, and 9s….

But we’ll see!

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