One of the cheapest and easiest math manipulative to use is a deck of cards. Cards not only have numbers but a set of objects to represent the numbers making it as useful as counting bears for teaching young mathematicians. Most people can dig up a deck of cards making this a convenient math manipulative as well.
Counting. Simple counting is easily taught by using the number cards and the Ace for a one.
Sorting and Patterns. Have your child sort the cards by color and shapes. Mix it up by allowing your child to create patterns with respect to colors, shapes, and numbers.
Addition War. Divide the deck in two and give one half to your child and keep one for yourself or another child. Each player will lay down two cards. The two cards that add up to the greater number is the winner. The winner keeps the winning hand. Play continues until all cards are played. The one with the most cards is the final winner.
Subtraction War. Play as described above except this time the winning hand is the one with the two cards with the greatest distance.
Multiplication War. Play as described above except multiply the two cards.
Anything Goes War. Each player lays down two to four cards. The players have the choice of adding, subtracting, multiplying, or a combination to come up with the highest amount. Winning hand is kept by the player who laid it down. The player with the most cards at the end of the game wins.
Memory and Matching. Lay the cards face down and have the child pick up one and then pick up another. If the card matches or adds to a particular number previously decided on, then he removes the the cards from the play area. Play continues until all the cards have been matched.
5 Digit Winnings. Remove kings and jacks from the deck. Ace is one and Queen is zero. Players take turns drawing one card at a time, trying to create the largest 5 digit number possible. As each card is drawn it is placed (and cannot be moved) into the ones, tens, hundreds, thousands, or ten-thousands place. When the sixth card is drawn, the player can choose one of the cards on the table to discard and replace it with the sixth card. Largest 5 digit number wins. Make this game easier or harder by varying the number of digits.
Guess the Addends. (You can use this for multiplying as well.) You will need three players for this game. Remove the face cards and keep the ace to represent one. Cards are dealt evenly among two players. The third player then directs the players to take one card off the top of the deck and hold it to their foreheads facing out so only the other person and the 3rd player can see the card. The 3rd player gives the other players the sum of the cards. Now each player takes turns guessing the number of their own card. The first player to guess correctly wins.