Playing Games: The Future of Learning Early Mathematics
Both my kids learned about prime numbers, factorial, roots, and exponents outside of school — and earlier than they would have in traditional curriculum paths.
Like many kids, mine play video games. My son is infatuated with Fortnite and my daughter with Minecraft and Overcooked 2(a hilarious co-operative cooking game). But, they never say no to playing board/card games that involve math — Yahtzee, Prime Climb, and Albert’s Insomnia(pictured above).
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.
Last week, we got lucky. We pulled out the numbers 3, 4, 7, and 12. The only card restriction is that you can’t use a card more than once. You don’t have to use all the cards, but again, you can’t duplicate a use of card(ie. 3 x 3).
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.
We have been playing with these set of 4 cards for the last week, every night before bed. They have their snacks and pj’s on.
We are now at 130…
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.
110 = (12- 7)!-3! -4
111 = (12 -7)! -3^sqrt4
112 = (12–7)! -sqrt4 -3!
113 = (12 -7)! -3 -4
114 = (12–7)! -3!
115 = (12–7)! -3 -sqrt4
116 = (12–7)! -4
117 = (12 -7)! -3
118 = (12 -7)! -sqrt4
119 = (12 -7)! -4 +3
120 = (12–7)!
5!, even before this game, was a math fact etched into their brains. It is actually been said probably more than what is 2 x 2. Because of this, both my kids now know up to 7! The simple idea of multiplying 1 x 2 x 3 x 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 kids that is kind of a “desert” for prime numbers — their are only two, 113 and 127. Which meant, that maybe there were different ways to construct most of the numbers in this zone. 119 is 17 x 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 the beauty of mathematics.
It doesn’t get better than this.
Which is why mathematical games, already been installed in many classroom around the world, need to be formally implemented as critical pieces for learning about mathematics through the most important reason to learn mathematics — for the joy and love of it.
It is no coincidence then that this year’s NCTM has a new strand in which presentations can occur(side note: it is also the one I will be presenting under in San Diego)
In the book Math Recess: Playful Learning in an Age of Disruption(out in Spring 2019), we talk about the value of play and go into detail about many games/resources/ideas that flesh out the practical ideas of math fluency with the loftier ideas of nurturing a love for mathematics.
Math games are the most natural and organic way for children to enter and explore the world of mathematics. Obtaining strong number fluency — and a desire to know more — will not just help school success.
It will go a long way in creating a lifetime interest in mathematics, which for me, is the only goal I am interested in…well, at least for my own kids:)
Note: Will update to let you know how far we get! 144(12 ^sqrt4) will be an anchor pretty soon!