The game of Prime Climb
Prime Climb is a wonderful game by Dan Finkel (aka @MathforLove), which you can find out more about here. The board is a path made of the numbers from 0 to 101, coloured by an ingenous and beautiful system. Each player has two pawns which they move around the board by applying numerical operations to the number the pawn is sitting on. If you finish on a red prime you get an action card to use now or later. If you finish on another pawn, they go back to start.
The first time I played it at work back in December 2016, we had so many players we decided to play in teams of two. I have to say I enjoyed playing in teams so much more than playing for myself. There was someone to talk to about how we would move our pieces and I have to say the talking about what was happening in the game was the most fun part for me.
— Matt Skoss (@matt_skoss) December 14, 2016
The idea of bodyscale Prime Climb
Playing in pairs gave me this most fabulous idea. Each team had two players and each team had two pawns. What if the players were the pawns? What if we could actually walk on the board? That would totally take this game from wonderful to wonderfully awesome!
Unfortunately, the rigours of life and work meant that the idea had to go on the backburner for five months. Moreover, I had a couple of issues to work out with the walk-on version: how would I deal with the fact that I need two 10-sided dice, and what do I do about the deck of action cards you draw when you land on a prime? It occurred to me I could use spinners instead of dice, but try as I might I couldn’t find any that would allow me to make the spinner myself.
But then a couple of things came together that made the dream possible. First, I was in the Reject Shop and found travel Twister for $2 each, which meant I finally had a cheap spinner I could use instead of dice. Also, one of my staff/students played the game at a games night and reported his frustration that you couldn’t move the other players more often. This gave me an idea of an easy way to replace the cards by simply spinning one spinner and allowing you to apply that to the other players. Finally, I was home sick with a chest infection with plenty of time to individually design all the cards and easy access to a laminator. And with that, Bodyscale Prime Climb was born! I was itching to try it out at the next available One Hundred Factorial session.
Playing bodyscale Prime Climb for the first time
And it really was wonderfully awesome when we did play. We laid out all the cards in a back-and-forth line on the floor.
— David Butler (@DavidKButlerUoA) May 31, 2017
From the outset we had people walking up interested in what was happening and trying to figure out the colouring scheme on the cards. It was one of the best levels of engagement I’ve seen at One Hundred Factorial this year.
We played with three teams of two using the same rules as for ordinary Prime Climb, except for what happens when someone lands on a prime. In that case, the team spins one spinner, and then applies that number with a + or a – to any player on the board (whether in their team or not). We also ignored the usual rule for rolling doubles (which is to actually count it as four of that number) to counteract the extra freedom expected from our new land-on-a-prime rule. Here’s an action shot:
— Amie Albrecht (@nomad_penguin) May 31, 2017
I thoroughly enjoyed the game because of how it felt and because of the talk it generated.
The feeling while playing it was very different from the hand-scale Prime Climb. There was something totally engaging about standing on the board. You could really feel how far you had to move to get where you want to go, and you had to look all around you for numbers you might be able to get to. Bumping people back to start felt so much more intense when you actually forced a person to walk all the way back to zero.
The talk between players was also very different from the hand-scale Prime Climb. I already mentioned how I loved the talk that happened when we played in pairs before, but this was at a whole different level. It’s impossible to hide your discussion when your partner is standing three metres away from you! This meant that all our talk was much more public so that everyone could follow what was happening, even the bystanders trying to figure out what we were doing. Also, because the board was so big and pointing was therefore so inaccurate, we had to be a lot more explicit about our language to each other. On the other hand, having the pawns being different people meant it was easier to talk about where they went. There was a lot of talk like “If we add 2 to me and multiply you by 3, then…”.
One lesson we learned along the way was that we really shouldn’t have tried to get both players to 101 but instead have the shorter goal of just getting one player to 101. This would have made for a much quicker game and allowed us to play more than one in the time we had, and to more quickly get our bystanders into the game. I’d also like to get some coloured hats or sashes or something to wear so that it’s easier for observers to tell who is on what team.
I’m not 100% sure that our land-on-prime rule was the best replacement for the cards. It would be kind of cool if you could save them up to use on a later turn, but my memory’s just not that good and I don’t want anything that requires us to pass out or hold onto cards. One alternative that just occurred to me is that if you land on a prime, you can add or subtract one of the prime factors of the number where the other player is standing to any pawn on the board. That would make it very highly strategic!
The spinners worked really well. To start with, I held the spinners and did it for everyone. Later when we had an extra person, they became the spinner like in a game of Twister. It worked really well to have this extra person because they could freely move around to help people think and explain what we were doing to observers. I’ll have to appoint an official spinner next time I play!
I do think that maybe I could make some dice instead of spinners using 12-sided dice. I have no shortage of 12-sided objects to use as dice right now! My idea was to have 1-10 on each dice, but then an extra 2, 5 on one and an extra 3, 7 on the other. I think it might work really well. Still, I will miss the spinners, which had a certain charm about them.
The moveable board
One thing I didn’t really expect was the swirling vortex of ideas that were created by having the board made up of cards. The moment we started playing I started thinking about all sorts of ways that I could rearrange the structure of the board and thereby change the way the game felt.
The first thing I want to try is setting it up with one long straight line. Then there would be a real feeling of distance when you multiply or divide. Indeed, you could guess where double or triple your number is by doubling or tripling the distance between you and the 0 card. I also want to try it in the traditional 100’s chart with each row going left-to-right to match up how movement across that chart feels. Adding 10 would be a particularly pleasant experience I’d wager.
I also wonder how the game might work if we arranged the cards not in numerical order. Then to add or subtract, we’d have to actually calculate where to go rather than just step it out. I’m not sure I want to lay them out completely randomly, because it would be very hard to find the number you wanted. What if you laid it out like the 100’s chart but started a new line every time you got to a red prime? What if you had all the composite numbers in order in one row and the primes in order in another? What if you made a big Venn diagram of the multiples of 2, 3, 5, 7? I want to feel the feeling of what it’s like to adding or multiplying in these situations and move from one collection of cards to another. Not to mention the very interesting task of simply arranging the cards themselves!
On that note, I actually reckon I might make a small version of the Prime Climb cards to use in the original game. How cool would it be to sit and sort the coloured numbers to see what sorts of patterns you could find before actually playing the game? (EDIT Aug 2017: Amie Albrecht has done just this with her class of pre-service teachers. Check it out!)
So stay tuned! At the July One Hundred Factorial session I want to try all the variations we have the energy to try and see how they turn out. And then a week later I’ll be at Twitter Math Camp and I’ll be trying it again there. I’m going to have so much to write about so check in in a couple of months to see how I went ok?
If you want to make your own bodyscale Prime Climb board (or indeed a set of Prime Climb number cards) then you can access a PDF of the cards and the spinner template at the link below. (I don’t recommend printing it at home because of the density of the ink! Best to use your workplace’s laser photocopier/printer.)
If you do play it then please let me know! I’d love to see how it turned out for you.