November 18, 2019

When given an opportunity to “make something” in my Math 229 class at Grand Valley, I decided to construct a math game. There are a lot of different directions one can take when creating a math game, but one of my favorite memories from high school is playing euchre in my AP Calculus class. Thus, I decided to create a math game using a standard deck of playing cards, something that is also easy to come across no matter your location. I call it “Number Wars.”

The object of the game is similar to the card game “War” where you win by collecting the whole deck of cards in your own hands by the end of the game. The matter in doing so is different, though.

The game has two players, and each player starts with half the deck (26 cards each) flipped face side down in hand. Next, player 1 and player 2 each lay down two cards in the shape of a square. (See figure 1)

The fastest of the two players will point to “Which card does not belong.” (Originally, I had thought to lay down one card each, but there would be no math competition to the game, only speed.) In the case of figure 1, one could claim that 7 does not belong because it is a prime number whereas 4, 9, and 8 are all composite numbers. Each claim for the card must based in mathematics. Another claim could be that 7, 8, and 9 are consecutive numbers, so 4 is the card that does not belong.

Another case could be figure 2. One could claim that the 6 does not belong because 2+3=5. A second claim could be that the 5 does not belong because 2*3=6, and the next could be based in prime/composite numbers, etc. We see here that there are several different combinations of cards where we choose that one does not belong.

One addition I am making to the number sets is that all face cards are negative values, so Jack = -1, Queen = -2, and King = -3. With this rule, we can also include natural numbers as a qualifier for “Which one doesn’t belong.”

Claims could include but are not limited to:

- Prime vs. composite
- Multiples of 3 vs. not
- Natural number vs. negative
- Consecutive numbers
- Even vs. odd (though, try to stray from this)
- The adding of cards
- The multiplication of cards

If the player who is fastest to pointing to the card that does not belong can say WHY it does not belong within 5 seconds and the other player agrees, they win the four cards and add them to the deck.

If the player points but cannot answer as to why the card is different, the other play has 20 seconds to supply an answer, and then they can claim the win.

If in the case that neither player can supply an answer for which card does not belong, the four cards are put aside and whichever player wins the next round takes the last four cards in addition to that round’s cards. An example of this would be if two aces and two 2s were played; there is no answer to this round. (This is a flaw to the game that I am still working on.)

This process continues until one player has all of the cards, and the player that loses will have lost all of their cards.

When using this game in a lesson, one could introduce the game as well as cover different options for claims that the students could use to qualify which card does not belong. This would help the students move more quickly in the game and eliminate the number of times the partners would not be able to come up with a reason for a set of cards.

“Number Wars” practices number sequences, grouping, and basic math operations. Any age group of students could play this game as long as an introductory level of algebra is present. The player who wins should have a higher fluency in these definitions and number groups, but the two partners should have approximately equal knowledge to keep the game fair. If “Number Wars” is played during a math class, though, this should not be a concern.

**ADDED AFTER SUGGESTIONS **

December 9, 2019

After playing the game a few times and having some peers play it with my instruction, I realized a couple places in the game could use some fine-tuning. One problem that we consistently ran into was that it felt like the game would never end! The hope is that Number wars is to be played when opponents have equal math backgrounds, but we found that this drags the game on until one person forfeits unconsciously or openly. I am open to suggestions on this matter.

Another problem with the game that came up was the speed element. A lot of my opponents lost because, of course, I created the game; thus, I am more familiar with it and those properties needed to win. This would also present a problem if used in a classroom where the students may even have the same math background, but it takes one student longer than another to evaluate the four cards and weigh their similarities and differences. Therefore, I would like to amend the rules of Number Wars to hopefully get rid of this speed element. This will encourage students who we want to be engaged by the game to really get engaged.

Along with the same idea from before where if one opponent cannot get an answer, the other opponent has the chance to answer, now, the players will take turns. Four cards will be laid down, two from each player. Next, Player 1 will attempt to name which card does not belong, and Player 2 will time 15 seconds (the time can be adjusted if more or less is needed on average). If Player 1 cannot answer within those 15 seconds, Player 2 can answer. This will keep Player 2 engaged while Player 1 is making up their mind and also keeps the competition in it. Whoever wins that round takes the cards. Once that turn is over, the roles switch. Four cards are laid down again, but now it is Player 2’s turn to have the first guess, and Player 1 will time and get the second opportunity if Player 2 cannot answer.

This amendment may make the game last even longer, but hopefully, it gets rid of academically unsafe element of speed in a math class.

Not sure if this comment was posted: I am very curious about this game. Have you tried it with anyone? I’m wondering how to take speed out of it… but haven’t tried it yet as is – always dangerous when giving feedback. Have you tried it? Speed in classroom games can discourage the players we most want playing.

Maybe if you did turns… could have player whose turn it is fill in any gaps and their two cards. Point to a card and give the reason. Other player points to another and gives a reason. If you can point to another and give a reason, you score that stack. Other player fills in the gap and plays two more on their spots. If at some point a player can’t give a reason, the other gets a chance to score. Winner is the player with the most cards at the end. The stacks would make some cards more valuable than others, adding strategy.

Only thing you need as a blogpost is this post was supposed to have a connection to the SMPs. You could do it in terms of making the game or playing the game. It would be nice to have an example played out in the post.

Cs: 4/5

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From Twitter:

Joe Schwartz @JSchwartz10a

I’d take the speed element out as well. Also include color, suits, and face cards in reasons why WODB.

Jim Doherty @mrdardy

Then maybe the winner is the one who can come up with the most reasons why a certain card ‘does not belong’ not speed here, but depth and persistence emphasized

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What a great idea for a game. I know that it may be hard to compete with speed in the game, but i’m curious to see how that may be fixed. Maybe a point system could be assigned to each “which doesnt belong reason”. So maybe even vs odd isn’t worth many point, but prime vs composite, or a more important concept that you wish for them to learn would be worth more points. And the players can each come up with as many “Which doesnt belong reasons” as possible to earn the most points.

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