Solitaire 1 player

Math Concepts: sorting, order, array, probability, greater than / less than

See this video - The Mathematics of Solitaire - 56 mins. courtesey of Stanford University

1. The object of the game is to create four piles of cards - one per suit - in ascending order.
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2. Start building the layout. An example of this is to the right. Put down one card face up and lay six cards face down next to it. Then, put one card face up on top (but lowered slightly) of the first face down card, then put a facedown card on top of the other five cards. Continue doing this, so that each pile has one face up card on top and so that the left pile has one card, the next has two, then three, four, five, six, and finally seven.                                 
   
3. Put the remaining cards in a separate pile and set it either above or below the piles. This pile is where you will go to get more cards if you run out of moves.
4. Leave room at the top for four piles of cards.
5. Look at the cards on the table that are faceup. If there are any aces, place them above the seven piles. If there are no aces, rearrange the cards you have, moving only the faceup cards. When you place a card on top (slightly lower so that you can still see both cards), it must be a different color than the card you are placing it on top of and have a value of one less. Thus, if you have a six of hearts, you can either place a five of spades or a five of clubs on top. Keep placing the cards on top of each other until you cannot move anymore. Each pile should be alternating in color and move in descending order.
6. The card on top of each of the seven piles should be faceup. So, if you move a card, remember to turn the card underneath it over.
7. If you have an ace above the piles, you may move cards of the corresponding suit on top of the pile in ascending (A,2,3,4,5,6,7,8,9,10,J,Q,K) order. #Each slot is for a suit and you have to find the first card which is the A and then go to 2,3,4,5,6,7,8,9,10,J,Q,K with each suit.
   

   You start with A and make way to king for each suit
8. If you run out of places to go/combination of cards, you can search for cards in the deck by turning over three cards and use them too. Most of the time, there is a A in there so look there first!
9. If you have a card that's under the deck, you can move cards around and find places that you can hold and grab that card and take it to the slot.
   

   Image2: More Images of How to Play
10. If you use all the cards in one of the seven piles, you may place a king (but only a king) in the empty space.

Math Card War  2 players

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

The game of Math Card War is worth more than a thousand math drill worksheets, letting you build the students calculating speed in a no-stress, no-test way.

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 catalog. 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!

To give a greater challenge to more advanced students, 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.

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.