*[Rescued from my old blog. Image via Wikipedia.]*

**Math concepts:** greater-than/less-than, addition, subtraction, multiplication, division, fractions, negative numbers, absolute value, and multi-step problem solving.

Have you and your children been struggling to learn the math facts? The game of ** Math Card War** is worth more than a thousand math drill worksheets, letting you build your children’s calculating speed in a no-stress, no-test way.

## Set Up

You will need several decks of *math cards*. Don’t rush to look for these at your school supply store or try to order them through your favorite website. Math cards are normal, poker-style playing cards with the jack, queen, king, and jokers removed. Make one deck of math cards per player. A math deck contains 40 cards, so a single game of ** Addition War** lets a child work 20 problems, and he hears his opponent work 20 more—and if your children are like mine, they will rarely want to stop at just once through the deck.

As my students learn their math facts, they need extra practice on the hard-to-remember ones like 6 × 8. With a normal deck of cards, however, I find they turn up far too many problems like 1 × 9 or 2 × 7. To give a greater challenge to older children, I make each player a double deck of math cards, but I remove the aces, deuces, and tens. This gives each player a 56-card deck full of the toughest problems to calculate.

[This is an old, classic children’s game. I’ve often been amazed how such a simple thing can keep my kids occupied for hours. In our variations, because the math card decks are only 4/5 the size of a regular card deck, we give each player his own pack of cards. We don’t shuffle the decks together at the beginning, although I suppose you could—that would be more like the traditional game, which (at least in our house) is usually played with a single deck shuffled and split between the players.]

## How to Play

* Basic War*—Each player turns one card face up. The player with the greatest number wins the skirmish, placing his own and all captured cards into his prisoner pile. Whenever there is a tie for greatest card, all the players battle: each player lays three cards face down, then a new card face up. The greatest of these new cards will capture everything on the table. Because all players join in, someone who had a low card in the initial skirmish may ultimately win the battle. If there is no greatest card this time, repeat the 3-down-1-up battle pattern until someone breaks the tie. The player who wins the battle captures all the cards played in that turn.

## Endgame

When the players have fought their way through the entire deck, count the prisoners. Whoever has captured the most cards wins the game. Or shuffle the prisoner piles and play on until someone collects such a huge pile of cards that the others concede.

## Variations

For most variations, the basic 3-down-1-up battle pattern becomes 2-down-2-up. For advanced games, however, the battle pattern is different: in case of a tie, the cards are placed in a center pile. The next hand is played normally, with no cards turned down, and the winner of that skirmish takes the center pile as well.

**Addition War—**Players turn up two cards for each skirmish. The highest sum wins.

**Advanced Addition War—**Turn up three (or four) cards for each skirmish and add them together.

**Subtraction War—**Players turn up two cards and subtract the smaller number from the larger. This time, the greatest difference wins the skirmish.

**Product War—**Turn up two cards and multiply.

**Advanced Product War—**Turn up three (or four) cards and multiply.

**Fraction War—**Players turn up two cards and make a fraction, using the smaller card as the numerator. Greatest fraction wins the skirmish.

**Improper Fraction War—**Turn up two cards and make a fraction, using the larger card as the numerator. Greatest fraction wins.

**Integer Addition War—**Black cards are positive numbers; red cards are negative. The greatest sum wins. Remember that -2 is greater than -7.

**Integer Product War—**Black cards are positive numbers; red cards are negative. The greatest product wins. Remember that two negative numbers make a positive product.

**Wild War—**Players turn up three cards and may do whatever math manipulation they wish with the numbers. The greatest answer wins the skirmish.

**Advanced Wild War—**Black cards are positive numbers; red cards are negative numbers. Players turn up four cards (or five) and may do whatever math manipulation they wish with the numbers. The greatest answer wins the skirmish.

**Reverse Wild War—**Players turn up three cards (or four, or five) and may do whatever math manipulation they wish with the numbers. The answer with the lowest absolute value (closest to zero) wins the skirmish.

## Update

** Multi-Digit War—**Turn up two or three cards and create a 2-digit or 3-digit number.

** Multi-Digit Subtraction War—**Turn up three cards. Make two of them into a 2-digit number, then subtract the third. Example: Suppose you turn up 3,4, and 5. Should you arrange them as 54-3 or 45-3 or 35-4 or . . . ?

** Multi-Digit Product War—**Turn up three cards. Make two of them into a 2-digit number, then multiply by the third. Example: Suppose you turn up 3,4, and 5. Should you arrange them as 5×43 or 4×53 or 3×54 or . . . ?

** My Closest Neighbor**—Instead of turning up cards at random, each player draws a hand of five cards. Then turn up a target card such as “Closest to 1/2” and try to make a fraction from two cards in your hand that will be near the target but not equal to it. Chris posted a set of printable target cards at her blog. I modified the game for regular playing cards: Fraction Game: My Closest Neighbor.

** Logarithm War**—Requires a special deck of cards. Download from Kate’s blog: This Game Really Is Worth 1000 Worksheets in doc or pdf format.

** Logs and Trig War**—Jim extended Kate’s logarithm war to include trig functions. Double the cards, double the fun! Download from Jim’s blog: War: what is it good for?

** Math War Trumps**—Players alternate choosing “trump” for the math card battles. After the cards are turned up, the player whose turn it is gets to say which operation (+, –, ×, ÷) to do.

** Speed Racer**—For two players of evenly-matched ability. Each player turns up one card, and the first player who calls out the correct sum (or difference, or product) of those two cards wins the pair.

**Can you think of another variation to share?**

If you enjoyed this post, check out my *Math You Can Play* book series featuring math games for all ages.

**Hat tips:** Marni suggested the *Mult-Digit* variation in the comments section below, but I didn’t think to add it as an update until Mary from the Albany Area Math Circle suggested the *Multi-Digit Product War* variation in a comment on another post. And then her extension of the game made me think of the *Multi-Digit Subtraction War* variation. Math tutor and games enthusiast Nancy Rooker suggested the *Trumps* variation in an email. Amy suggested the *Speed Racer* variation.

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Ooooh. I’ve been looking for some more fun ways to drill math facts with my son. I like this. I especially like that it’s not going to cost me an arm and a leg. We’ve also found that he enjoys Timez attack (www.bigbrainz.com), which is a free computer game that drills multiplication facts, and Totally Tut, a math game from Discovery Toys (http://www.amazon.com/Learning-Resources-Totally-Math-Operations/dp/B00004TDKR)

But I’m always on the lookout for a new way of helping him learn these things.

Hi, Amy!

We also enjoyed Totally Tut. One of my dd’s is a maniac for anything Egyptian, so we had to have that game. We downloaded Timez Attack, but my kids found it too repetitive, though it does have cool graphics. Did you know you can also practice multiplication on the Free Rice website? And without time pressure.🙂

* http://freerice.com/#/multiplication-table/17485Oh, what a great idea! My son is forever wanting to play cards, so he’ll love this.

Thanks, I’ll definitely check it out. Today I picked up some playing cards while at the store, and was just checking back to remind myself which cards to remove….

(And Timez Attack is getting a bit boring around here too now. Very glad I didn’t pay for the full version.)

I just read your post! We’ve played this game (we called it “factor war”) after learning it from an Uncle. One great variation for more advanced players is to play one card at a time, and then on the second, decide whether to add or multiply (you would keep in aces and deuces for this) thereby requiring two calculations at times….. Thanks for all the great ideas on your blog!

Thanks,

This will be great for decks that don’t have all the cards.

This is fabulous! My kids love to play War, and I didn’t even think of altering it to work on our math facts. Thanks!!!!

Very nice! Where does it come from?

I will experiment with my niece and nephew.

Btw, in my family we “replay” the prisoners until the winner has all the cards. Games can continue for days. With my sister’s kids, I reduce the deck to 9 – A or 2 – 10 or whatever, (keeps changing, depending on their age and the time we have), and I also sometimes strip out one suit. Playing until total victory with a short deck takes 10 – 20 minutes.

Jonathan

Do you mean, where does the game come from? I have no idea! It’s possible I read something like this somewhere once upon a time, but I don’t remember. We have played traditional War since forever (we replay the prisoners, too, but I wear out and give up long before anyone has all the cards). One day, I was looking for a warm-up game for my younger math club kids, and I thought of the simpler variations. From there, it wasn’t very hard to expand the game to fit older students, too.

Just looking for math drill ideas and got your site from the 4real boards. This is great. Can’t wait to try it.

I love these ideas. Teaching my children the automaticity and the cognitive understanding of basic skills has been my challenge. I will certainly use these ideas.

I noticed that some of the responders were looking for computer programs to teach math facts. The best one I’ve found is http://www.AMatterofFacts.com

It is web-based with arcade games that motivate children to practice. It also tracks their work and prints out a list of trouble facts and flash cards specific each child. You kids will want to work on their math facts all the time.

I can’t believe it, but we also play one variation you don’t have. My 9 year old didn’t come with a math gene, and even early math concepts are hard for him. Basic War is just greater than/less than, and we’ve played War turning 2 or 3 cards over just to help him get that down further. Also helps with place values.

Hi, Marni,

That sounds like a great variation! How do you tell which card goes in the tens or hundreds column? Or do you just each make the biggest number you can? Or for a change, you could arrange them to make the smallest possible number, and then have whichever is less win.

I do have a few place value games (based on some they used to play on the old Square One TV show — showing my age!), but I haven’t posted any of them yet. Someday…

How about using Uno cards? Instead of the Wild card changing the color, it could be used for any number the player wants it to be.

How about using red cards as positive #s, and black cards as negative numbers? (because red electrical terminals are positive, black are negative). Then you can add another dimension to the game – you can have them break ties using the absolute number, or as +/-

Good idea, Linda! We also do this in my kids’ favorite math game — “Hit Me,” which is described near the end of my post on teaching negative numbers. One of these days, I should make that game into a post of its own…

I just discovered your site today — it’s time to go home, but I don’t want to leave as I keep on finding more and more great activities.

I am a math coach working with students from Gr. 1 – 8 and already I have found activities for all age groups.

Thanks much — I will definitely be a frequent visiter.

thank you for your web site and the blogs for helping teach math. I am a new teacher (third career so I am older) but enjoy teaching. I find today that I am exhausted and lack energy and hope that my plans go well on Monday as I face teaching math and language arts to my resource room 6th and 7th graders. teaching is a joy. it is also extremely hard work! thank you for your support and ideas. I needed your site today to help me not feel so alone out here with my lesson ideas. sincerely, carol mauger

These are some great ideas! I have been playing versions of this concept over the past few years. The students are always engaged for a long period of time. I really like some of the additional ideas found here. Thanks!

Thanks you for this idea. I am going to try it with some of my math-challenged older students. If I make it into a fun, class competition with some prizes, maybe I can help the students improve their math knowledge and skills without them knowing it and complaining about it.

A Math War tournament? Sounds like fun! I hope you’ll let us know how it works out in your class.

Hello – While doing research for a Graduate Action Research project I came upon your blog on “Aha” – since procrastination had set in I “played around” on your site and came to this blog. I have one more idea that will make the challenge level even greater! Kids (and adults) are adept at reading number but the VALUE of a number is not always as concrete. With your deck of cards in hand, CUT OFF the corner numbers from the cards leaving only the subitized pattern (also known as the visual cluster) of the number left. For example: the 5 of diamonds card – cut off the number 5 in each diagonal corner, this will leave the visual pattern of 5 diamonds on the card – similar to the 5 pattern seen on a die or domino. Do this with all of the cards and this will change the entire game as the child/student/adult will have to group the pattern and perform the operation. One could buy these cards already cut, http://www.mathematicsforall.org/2009/List%20of%20Games.doc could be a link to help you find them (they are pricey and even though our busy time is worth something it is still cheaper to just cut the numbers off the corners and start playing)

Just an idea –

Melissa

That’s an interesting idea, Melissa. I wonder how my math club students would react to cards without numbers. Something new to try next semester…

I’ve played logarithm wars with previous students. It went so well that I’m playing “Slope Wars” tomorrow with my Algebra I class. They have just been introduced to the slope formula and each card has two points listed. They’ll have to calculate then compare. I love this because they will also have to compare fractions (which is also a weakness).

Thanks! These are all great additions to my arsenal of math games, they are the BEST! I was already doing some, but never thought of some of these alternatives!

Awesome! I never knew there were so many variants. Very nice!

but I do have one suggestion

I would think red cards should be positive and black cards to be negative because should your child go into electronics he won’t get confused about electricity. Red wires being positive, black wires being negative.

Unless of course you talking about the stock market where red ink is negative and black ink is a positive thing. However mixing up electricity I think is far more dangerous. … just a thought.

Thank you for all of the variations. I’m putting on a pi day event for local homeschoolers and will be putting out a few decks of cards with these rules as one of the available activities.

That sounds like fun, JoAnn!

If you need more Pi Day ideas, I have quite a few in my Happy Pi Day post.

Red-negative and black-positive, on the other hand, is the convention in finance, so it’s just a matter of preference either way.

For a slightly more difficult set of games, you can extend the values up to 14 by using Rook cards.

You’re right on the colors, silverpie, and red=negative is what I usually do when we play card games with negative numbers. But it’s just a matter of preference, and of being consistent within the game.

I’m not familiar with Rook cards. How many are in a deck, and what values do they have? If it goes 1-14 (or even better, 0-14), they would make excellent math cards for a wide variety of games.

Rook cards are 1-14 in four colors (black, red, green, yellow), plus one unnumbered card (which could be used for a 0). A face-down card would be another way to represent zero, as could a face card from a standard deck (queen would be my pick, since Q looks a lot like 0).

Thanks, silverpie! I never played Rook, but the cards sound wonderful.

In my math books, I’m writing the games for standard playing cards, but they are best for just the numbers 1-10. Now I will insert a paragraph mentioning Rook cards as an alternative, especially for older students who will enjoy the challenge of bigger numbers. For example, Rook cards would be fun to use in the 24 game.

Hi Denise…

Just happened to find your blog and truly your article on the Game that is worth 1000 worksheets inspires me!

Will definitely use it on my Grade 1 students soon. We are about to learn number bonds next week and your writing is very helpful!

Thank you🙂

This is so great, thank you! I’m a nanny and the boy I nanny really needs help with his multiplication. I’ve been playing uno with the 4 yr old, to teach her numbers in general (we say what the number is when we put it down) and I just played war with her yesterday using some pennies to represent how many each number is so she can obviosly see which is greater.

When I was teaching my sister math (she was homeschooled) we played a version of go fish in which you made matches that equal ten (we would use numbers 1-9). She was being taught math using an abacus (as was I and my dad, and all three of us are amazing at math) and memorizing all the numbers that add to make ten is very important.

Thanks again for all these ideas! I can’t wait to play them!

Katie

Thanks for these great variations on the standby. Headed for long train ride. Was just starting to pack games. This will save us a lot of space and provide hours of fun – and may practice unbeknownst to them.🙂

I love this post. I am involved with my childrens schools parent committee. Currently our schools are focusing on increaseing knowledge and understanding of math. For Christmas we plan on giving decks of cards to each family and would like to include card games for them to play. I would love to pass this post on to the families in our school. I will give your website full credit…would love to know it this would be OK with you.

Thanks

Sue

Thank you for asking, Suzanne. I’ll send you an email.

I like the use of something that everyone can afford. Thanks for all the variations. I will pass it on to my grandchildren!

Very little explanation and setup time! We get to use all of our time for actual practice. Love the versatility.

Wow! I’ve been looking for some additional math activities for my students who finish early to do. My kids will have fun with these!

I liked the different ideas on how to use the war game. I will use these.

Great ideas! Thanks. My son learns best with games. (He hates doing worksheets!) I used to play war as a kid, and I’ve totally forgotten about it.

My 1st grader and I used a deck of cards to practice addition and subtraction facts. We made 5×5 bingo boards with numbers 1-25 randomly placed. Then we each drew 2 cards at a time and could add or subtract any way to mark off answers on our boards. We used the full deck (jack=11, queen=12, etc) and two jokers as wild cards. We had to go through the deck multiple times to get just the right answers (by the end of the second game I let him draw one card and tell which card he needed to get the numbers left on the board).

That sounds like a fun game, Rachel. Thank you for sharing!

We used to play a similar game, making a chart like your Bingo board, but playing it like tic-tac-toe. The kids would draw cards (or throw dice), and they could choose whichever operation they wanted to use. The goal was to mark three squares in a row, but the cards added randomness to make it more challenging.

I like this idea! I have an 8 year old who is still struggling with the most basic math concepts. This is very promising. Going to pick up a deck (or 2) of cards tomorrow.

This is a great idea for Adult Basic Education! We (Goodwill Goodskills – an Americorps Adult Literacy program) will use it with our participants who are relatively new to number manipulation.

I play math war games a lot! Here are some variations:

I often have them play multiplication war, but if some students need extra practice on a specific portion of their times tables, such as 7’s, I have them find a 7 in the pile before handing out their cards and place it face up. This card remains during the entire game. Players take turns laying down a card next to the 7, and first one to say what seven times that new number is, wins the one card.

Another teacher that I work with came up with a Rounding War Game:

Divide up cards as if playing regular war. Each student puts down 2 or 3 cards (depending on how large a number you tell them to make) in a line to make one big number. If there is a zero at the beginning of the number they can shift it to another place, otherwise they can’t move the cards after being placed down. The students race to see who can round the number first, and say it out loud. You can decide ahead of time what place they will be rounding to, and have all students round to that place the whole game, or you can have students take turns calling out a place to round to before they both lay down their 2-3 cards.

Great suggestions here! My class (5th-7th grade) has had fun with fraction war and exponent war. With exponent war you just set down 2 cards each and compute as if the second card is the exponent of the first card. Fun stuff🙂

Hi, m new to this place. Here’s a variation I have used with 2nd graders : let all have black cards numbered 1, 2, 3, 4. In a row, the first one forms the biggest possible number with the 4 cards. The next one should form the next biggest, the next one the next biggest and so on……this may first be started with three digits. At the next level, you choose a set of 4 cards randomly, like 2,5,9,6 and play the same game.

That’s a great game, Chitkala! Thanks for sharing.

When we play we calculate the value of the “prisoners” not just count them. Great extra adding practice especially as kids start to use good strategies like trying to make tens and then counting the tens!

That’s an interesting extension of the game, Susanna. Do you add them up as you go along, or all at once at the end? And do you keep score and go for a certain total number of points?

Hey man, great article! I actually got further with my son playing with a deck of cards than I have in years with expensive workbooks/lesson plans. Thanks for taking the time to write this.

Hi, Jeremiah! I’m glad the game is helping your son. The key difference between this and a worksheet is that games are low-stress. Even though your son is still practicing math facts, it doesn’t feel as abstract and alien as a page of calculations can feel. Also, quality time playing with a parent is always good, right? 🙂

I know another game that can be done as a whole class activity or small group. Take your math cards and start with only aces, twos, threes, fours and fives tell students that the total of the cards is 60 and that you will take one card out and they must figure out which card it is. Showing students one card from the deck at a time they must add the numbers in their heads start off slowly until students learn patterns with their addition. At the end of the cards your total will be somewhere between 55-59 and students will be able to figure out the card that you have taken out. As students confidence grows add in more cards but make sure you tell them what the new total is.

I love this idea! I used it with my class for practising our times table facts and also for quick fire addition during mental and oral starters! Thanks so much! I mention it on my blog here: http://www.interactiveteacher.co.uk/?p=68

I have a very young dd who is absolutely in love with anything number/math related. Because of her age we do much of her ‘math’ in the form of games.

One other variation of war we play for money we call ‘Making change’ War. Each player turns over 2 cards for creating cents, or values under $1.00. We quickly count back the ‘change’ or difference between 100 and the value of the cards. Person with the most change wins the hand and player with the most money at the end is the winner.

We have also done this with 3 cards and then 4, to practice counting change to different values. I simply made a decimal card for each player to have in front of them.

Reblogged this on Teaching in These Fly Over States and commented:

My kids love playing this game when their morning math is done. It’s the best way to practice math facts and have fun.

What if one card is place in the center and each upturned card must be added, subtracted, or multiplied by that card to get the largest or smallest number? Or a die to roll for the same purpose.

I think I’ve seen a game like that online, Ellen, but I prefer the randomness of turning up both factors. When I want to practice a specific set of math facts, I like a simpler game: Once Through the Deck.

Here’s a variation that I don’t think I saw above: to practice quick calculations, whoever calls out the correct sum or product FIRST wins the hand. The value of the sum or product doesn’t matter.

Thank you, Amy. I didn’t have that variation listed, since my kids always disliked speed drills. I’ve seen the game played that way on other websites, though, and I’ll add it above. WARNING: You have to be careful that your players are equally matched.

True. I did try giving my second grader one extra “beat,” flipping his cards about a second sooner than my third grader. It leveled the playing field a bit. I think your update might want to say “each player turns up *two* cards.🙂

No, in the Speed Racer variation, both players are racing to determine the same number — whatever answer their two cards together make. I guess I should edit to make that clear. In the normal game, where each player turns up two cards, it doesn’t matter who says their answer first.

Ohhhhh, I get it. Thanks for the clarification! (Although you *could* play it with each player trying to call out the sum of two of their own cards. That’s how we’ve played for the last couple of days, although I had to be there as a “referee” to check the accuracy of the sums called out. Your way is better though because it eliminates the potential “unfairness” of one person getting an easier sum than the other.)

Yes, some answers are much easier than others. Even a young child with 2×1 could beat most adults racing to calculate 7×8.🙂

I would like to add my “Snakes and Ladders” imitation game that teaches prime and composite numbers. Please see the complete game board design and rules at: http://heliwave.com/PurePrimes.pdf

All copyrights are reserved by the author of the game, Ali Adams or http://www.heliwave.com.

I would love to have some school or a national government to introduce the game it into their school curriculum in order to encourage their pupils/citizens to appreciate the mystery of the distribution of prime numbers among the natural numbers from 1 to infinity.

Oh, did I say that 619 is the 114th prime number and 6*19 = 114🙂

View this in Notepad http://heliwave.com/114.txt

If anyone wishes to use a proper Prime Factorization calculator, please download a free one from http://primecalculator.codeplex.com

Peace to all …

God > infinity

Hi, Ali,

Thanks for the game idea!🙂

I’m not sure you quite understand how copyright works, though. While your pdf game board and rules are protected under copyright, the basic ideas of a game (such as move ahead at the odd numbers and backward at the evens) cannot be copyrighted. Ideas are not eligible for copyright. So anyone can use the game — they just can’t copy and sell your specific words and drawings.

I am looking forward to trying some of your games with my class, Denise. I know that they, and I, am tired of drills and worksheets! Thanks.

I hope your class enjoys the games!

My kids always liked this one, though it seems to me like the most “worksheety” of games — I guess because there’s no strategy, just luck. The kids don’t seem to mind, but I prefer games that require more thought. Depending on what topic you’re studying, I have several other options on my blog:

*blog posts labeled “Games”