# Prime Climb: Where mathematics meets play

## Dan Finkel’s board game is a triumph of game-based learning

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I am generally sceptical of games involving maths — out of experience rather than principle. I have chanced away too many afternoons to games that wear the false promise of mathematical learning. Too often, they are shrouded in a context that is quite removed from the mathematics itself.

It was with cautious optimism, then, that I took to Prime Climb. Cautious because I carry the scars of failed attempts to fuse learning with games. But optimistic because this game is a creation of math educator, Dan Finkel.

Prime Climb is more than a board game. It is a way of seeing and understanding numbers, and of uncovering the role of primes in multiplication. I have previously written of the joys of the Prime Climb coloured number grid, where every number is coloured according to its prime number decomposition. The grid is enthralling, mystifying and revelatory all at once.

But would it hold up to the scrutiny of a maths lesson? The ten primary students of my weekly maths club are willing and eager guinea pigs . The students vary in age, current ability and confidence. All have mathematical potential ready to be developed. Some have encountered primes, others have barely grasped the fundamentals of multiplication. My task, as their maths coach, is to prepare activities that engage them as a collective, while also hitting their individual sweet spot of challenge — the so-called ‘low floor/high ceiling’ criteria of task design.

Is Prime Climb up to it? You betcha.

The first session was the appetiser. Taking my lead from Dan’s own lesson resources, I introduced the grid gradually, first displaying the numbers 1–20, then 1–60 and finally 1–100. Two questions guided our inquiry: *what do you notice? What do you wonder?*

The litmus test for the board game was a set of quick warm up activities that are based on the game’s rules. The test was passed with all the flying colours of the Prime Climb grid. Students wrestled with options as they sought to reach a number target given a starting point and possible operations (this activity resembles my own favourite number game from Countdown).

Onto the main course in session two, with the unveiling of the Prime Climb board game, where the grid now takes the form of a spiral. This time taking my cues from the *Gaming Gurus* of my local board game café, I was careful to introduce the rules of Prime Climb in deliberate sequence. In fact, most of them came naturally to the students. Prime Climb borrows from the randomness of *Snakes & Ladders* and the combative strategy of *Ludo*. Each player’s objective is to guide their two pawns through the number spiral until they reach 101. On each turn players roll a pair of dice, using each one in turn to either add, subtract, multiply or divide the number corresponding to their current pawn tiles. If they land on a prime number, they pick up a bonus card. If one pawn reaches another’s space, it bumps them back to the start.

Left unattended, students may proceed as if Prime Climb is just another stab at number play. But the game is laced with prime number representations, down to the colouring of each number tile. This gives teachers plentiful opportunities to pause and prompt students with situational questions that are embedded in the gameplay. Every turn involves choices, and students can be pressed to consider the ‘optimal’ move; often a trade-off between their carnal impulse to ‘bump’ players back to the start and their competitive urge to reach the end (it never ceases to amaze me how readily students gravitate to the former). Choice brings flexibility and Prime Climb champions number sense by helping students to see pattern and structure in their calculations.

Prime Climb appeals to students across the fluency spectrum. The ingenuity of Prime Climb is that the colouring system acts as an optional scaffold when students combine numbers. To compute *8*12*, for example, the most fluent students can head straight to 96. But speed is not the aim of the game here, and students can derive just as much pleasure by inferring their destination from the colours of relevant tiles.

Example: an eight comprises three oranges (one for each factor of two: 8 = 2*2*2), a 12 comprises orange-orange-green (green denotes three and 12 = 2*2*3), so 96 must comprise the combined amount of five oranges and a green. The hunt is on, fuelled by pattern recognition rather than blunt recall of number facts. The reverse operation of division is just as intuitive, except now the colours are being peeled away.

The end result is a heightened engagement with number operations that supports both fluency and understanding. For students encountering primes for the first time, Dan’s representation brings home the multiplicative essence of these numbers in a way that symbolic treatments rarely achieve. And for those already acquainted with primes, the game offers a peek into their limitless mysteries. Students may ponder whether numbers can be coloured in more than one way (the answer to which is what makes primes so remarkable). Or whether those red tiles will cease to appear on large boards (also remarkable).

Prime Climb is playful learning as it should be, where the play actually reinforces students’ discovery and understanding of mathematical concepts. It takes a creative mathematics educator like Dan Finkel to achieve that balance. It is obvious from the design of Prime Climb that Dan’s pedagogical aims fuel every aspect of gameplay.

My students have since been asked to rank Prime Climb against our other maths club activities. We’ve had fun with some Martin Gardner classics, Jo Boaler’s paper-folding exercises and NRich’s store of exploratory problems. The results are in, with Prime Climb emerging a clear victor — all ten students placed it at the summit.

Prime Climb is a remarkable achievement. Here’s hoping it leaps into classrooms and homes the world over.