Math = Love: Prime Climb Game and an Interesting Problem

## Sunday, October 18, 2015

### Prime Climb Game and an Interesting Problem

At my last math teachers' circle meeting, we played a new-to-me game: Prime Climb.

This game has one of the most beautiful, math-y game boards I've ever seen.

Now, I can't really talk about the actual game all that much because we didn't play by the actual rules.  In the actual game, players have two pawns.  We used one.  In the actual game, there are action cards.  We didn't use these at all.

Here's how we did play:

Roll two ten-sided dice. (0-9)

Add, subtract, multiply, or divide the value of each die to your current place on the board.  For example, if I'm on START and roll a 3 and 7, I can add 3 and add 7 to end on 10, add 3 and multiply by 7 to end on 21, add 7 and multiply by 3 to end on 21, or add 7 and subtract 3 to end on 4.

You cannot go past 101.  You must apply the operations to the dice separately. And, if you land on the same number as another pawn, you send that piece back to start.

The first player to land on 101 wins.

As a roomful of math teachers, we loved the mental math aspect of this game.  My group didn't really want to be vicious and send others back to start, but I think my students would have zero problems with that!

After we played a round, our facilitator challenged us to list every single space on the game board that we could be on and in one roll end up winning.  Now, that was a fun problem to solve!  We got a lot of mileage out of this seemingly simple problem.  Especially because our answer was different than our facilitator's answer.  Then, she gave us 12-sided dice (1-12) to see how that changed our answer.  All in all, very interesting!

From these past few math teacher circles, I've discovered that while I'm not usually the fastest at solving problems in the group or the best at seeing unique ways of solving a problem, I do bring something to the group.  I'm really good at organizing information and illustrating the problem.  When I'm presented with a new problem, it takes me a while to process it.  My first instinct is to pause and process the problem, then I try to come up with a way to organize the information I have.  Only then, do I try to solve the problem.

Last month, with the lunes and balloons spherical geometry problem, this meant drawing the problem on a balloon.  My groupmates were easily solving the first few problems while I was still trying to wrap my mind around what we were doing.  However, as the problems became harder, they started using my physical representation to solve the problems.

With this Prime Climb problem, my first instinct was to draw a hundred chart to organize which numbers were one step away from winning and which numbers were more than one step away from winning.  Drawing a grid and writing out the numbers 1-100 was time consuming.  And, it seemed like my group was rushing ahead of me.  But, I persevered at creating my visual representation.  Once I started marking the numbers on my chart, my groupmates were all using my hundred chart to help come up with the next solutions.  In the end, everyone was copying from my chart to their notes.

Maybe this is why I'm so drawn to interactive notebooks.  I love organizing information.  I'm not the fastest at math.  I'm not the best.  I'm not the cleverest.  But, I am really good at visually organizing information.

So, has anyone played with the actual rules?  I'm trying to decide if this is a game I wan to invest in for my classroom.  The reviews on Amazon are all really good, but most mention playing with young children.

1. This game looks great! Either for my son or for my class, this game is on my Christmas list. I also found a "print and play" version on their website. This might be the best option for a class. Check it out! http://mathforlove.com/games/

1. Thanks for the link! They referenced this at our circle, but I hadn't looked at it myself.

2. Very cool that you played Prime Climb in your teacher circle! I love your information-organization approach to the problems.

If you or any of the other teachers or the circle leader are ever interested in getting in touch, don't hesitate to drop us a line.

To answer some of your questions, the official rules are similar to the simplified game you played in the circle. The main differences are that 1) you play with two pawns, which you can apply either dice roll to in whatever order you like, and 2) if you land on a red circle--i.e., a prime number greater than 10--you get to draw a Prime card. This gives you more potential targets for where to move on a turn: should you go close to 101, bump an opponent, or land on a prime and draw a card? The game ends up being more dynamic, and there is usually some fun choice to make.

There are a few other minor details to the rules, but those are the main elements. If you're interested, the official rules are here: https://www.dropbox.com/s/ia2wo2arkh6exyu/Prime-Climb-Updated-Rules-February-2015.pdf?dl=0

As for the appropriate age, we recommend the game for 10 and up, and a lot is possible with older kids. If you want to open the Pandora's box of probability, for example, there are all kinds of questions to ask. A series of questions I like is: what is the minimum number of rolls it takes to move one pawn from 0 to 101? What are the odds that you'll be able to achieve this journey in the minimum number of rolls?

There's also the possibility for modeling the game with a computer. A friend of mine programmed the expected number of moves it would take to win from any spot.

The game is also good for quick warm-ups. These ones were originally written with younger kids (i.e., 4th/5th graders) in mind, but I think they could be good for some flexible arithmetic practice for older kids too: ﻿﻿https://www.dropbox.com/s/0lsr43p4i9l20uf/Teaching%20with%20Prime%20Climb%20%28for%20Marbles%29.pdf?dl=0

We've been planning to write curriculum up for older grades as well, but haven't done so. Let me know if you'd like to collaborate on some high school level lessons/questions.

We've got some other graphics to accompany the game in the classroom. Email me at dan [at] mathforlove [dot] com and I'll send them to you.

1. Awesome information! Thank you so much!