Simplifying radicals war

We played this game in, like, October. It’s based off of someone else’s hard work—probably this post, but, you know, October.

I’m presenting my version of it though because I did a little work to find what I think is a better rule-set. One of the problems that you run into if you use the “normal” values for cards (jack = 11, queen = 12, king = 13) is that the majority of the numbers you get (around 60%) aren’t able to be simplified. In my version, 61% of the possible numbers can be simplified, while also having enough variety to keep it interesting. (It’s possible to make almost all of the possibilities simplifiable, but you have to use only 2, 4, 8 and that’s a little boring…)

Here are the rules. It’s based on War and involves two players:

  • Remove all 3s, 7s, 10s, and jokers from the deck.
  • Jacks count as 4. Queens count as 8. Kings count as 12. Aces count as 1.
  • Each player starts with half the deck.
  • Each player draws a card. Use the two cards to form the radicand by concatenation. So if the two cards drawn are 5 and 2, the square root is \sqrt{52}. A king and a queen makes \sqrt{128}. Students will need to agree on a method for determining which number comes first.
  • Both players try to simplify the radical as quickly as possible. I’m not usually into speed-math, but sometimes it’s okay, I suppose.
  • Whoever simplifies the square root first gets to keep both cards. The goal is to collect the whole deck.
  • If the square root isn’t able to be simplified, players take their cards back and try again. You can also play by switching the order of the cards if the first order didn’t work and only taking the cards back if neither order works.

Click here for a copy of the slide I used in the classroom. It’s the same as above, but with some pictures. It’s kind of ugly…