Playing Games: The Future of Mathematics
Both mathematics and games have long and illustrious histories. They both have represented the social and cultural thinking and imagination of the times. As well, they have played integral roles in promoting play through organization, rules, and, of course, imagination!
Using games in math classrooms has become a strong trend, especially in elementary and middle schools. Those that create a supportive social setting and amplify fluency of math facts are the ones that are most enjoyed by teachers and students.
While there are a myriad of games—and we will talk about many of them in the coming weeks—often the simplest games are the ones that have the strongest allure in terms of fun factor and longevity.
The game pictured above is called “Albert’s Insomnia.” I have been playing the game steadily for several years now. In fact, both my kids solidified their math facts by playing this game over and over and over again! In addition, they also learned about prime numbers, factorial, roots, and exponents outside of school—and earlier than they would have in traditional curriculum paths. The game is also a big hit with the Netmath team—especially when we go on the road to math conferences.
Like many kids, mine play video games. My son is infatuated with Fortnite and my daughter with Minecraft and Overcooked 2 (a hilarious cooperative cooking game). But they never say no to playing board/card games that involve math—especially Albert’s Insomnia. Every time we play Albert’s Insomnia, we randomly pull 4 cards out of the deck, and take turns using these numbers to construct answers from 1 to whenever a number can’t be made—that way we don’t make that into a winner/loser kind of thing. You are allowed to use any of the cards, up to all of them, to construct PEDMAS questions to get the target answers. For example, in the cards shown above, 4 – 3 = 1 and 12 – 7 – 3 = 2. For the number “3,” you simply allowed to point to it. You cannot use any card more than once.
There is a reason why this article contains a picture of the cards that we selected. They gave us a rich mathematical moment that we could not have anticipated. As mentioned above, my kids have learned all advanced operations through games. To be specific, this game.
We have incorporated factorial, roots and exponents in Albert’s Insomnia. As such 3 can be used as 3!, which is 6. We can take the square root of 4, which is 2. So, automatically there is also a 6 and 2 available in those cards. We also use exponents. So something like 144 can be constructed with only two cards—the “12” and the “4.” 12 is pointed to and then the 4 is moved into an exponent position, and is used as 2 by taking the square root.
Something interesting happened between 110 and 130. The number 120 became the anchor to all the answers. How did we get 120? 12–7 is 5, and 5! is 120. The symmetry to subtract from that value to produce numbers 110 to 119 was used to provide answers from 121 to 130 with addition.
Just having the numbers 3 and 4, with, of course, the advanced operations of factorials and roots, gave us every value from 1 to 9—see if you can find them! And, then my son pointed out that it will be easy to get the numbers from 121 to 129 because we will simply add all these values. It was a great moment in a game that was already becoming a fun marathon.
5!, even before this game, was a math fact etched into their brains. It has actually been said probably more than what is 2 × 2. Because of this, both my kids now know up to 7! The simple idea of multiplying 1 × 2 × 3 × 4 x … n is now entrenched in their wheelhouse of curiosity, expanding their view into the landscape of numbers.
One of the things that I brought up in the zone of 110 to 130 was to remind my kids—that are kind of a “desert” for prime numbers—there are only two, 113 and 127. Which meant that maybe there were different ways to construct most of the numbers in this zone. One hundred and nineteen is 17 × 7. There is already a 7 available. Can we construct 17 from 12, 4 and 3? We sure can! 12 + sqrt4 +3. Easy peasy lemon squeezy.
The core ideas of math fact fluency are flexibility, efficiency, accuracy, and automaticity. The core idea of a good game is its replay value. Even what happened in this game between the numbers of 110 and 130 is a treasure trove for all of the above.
My kids are learning math facts—advanced math facts—without worksheets/homework/school expectations. They are learning it for the sheer joy and love of mathematics. They/we are persevering towards a goal of getting as high a number as they/we can, strengthening the growth mindset they already possess—munching on snacks, in a comfortable environment, socializing with the beauty of mathematics.
This is what the beautiful cross-section of mathematics and games can look like!
Next time: Math Games from Around the World.