Mathionaire
Play a math game based on the popular "Who Wants To Be A Millionaire?" television show. While that show asked questions relating to general knowledge, this variant is all about testing a child's numeracy skills. Before playing, make a batch of game cards, each of which contains a numeracy question and a choice of four answers, similar to the format of the questions on the television show. The questions can get harder so that the game becomes more challenging as the child progresses.
This game is based on an online version found on the Netrover math website. The game on the website is designed for solitary play, but a few adaptations will encourage interaction between the child and an adult "host." To play, ask the child each of the questions in turn. To further increase the similarities between this game and its television counterpart, introduce a currency system. For instance, give the child a candy reward or other small prize if he answers a certain number of questions correctly.
Mind Reader
This simple game can be used to help children learn the order of numbers. Think of a number, typically between 1 and 100, although the scope of the game can be reduced for a younger child. The child tries to guess the number in as few attempts as possible. After every guess the child makes, give her a clue such as "it's a number between 11 and 20" to help narrow her guesses. For older children, turn the game into a math game by giving more complex clues, such as "it's a prime number" or "it's divisible by 4."
Number Hat
This game, described on the Teaching Ideas website, is most suitable for use in a teaching classroom with children around kindergarten age. Create a hat or crown of some kind and decorate it as you like. At the beginning of the game, while one child is wearing the hat, attach a piece of paper with a number written on it to the hat so that the rest of the class can see, but the child wearing the hat can't. The rest of the children in the class then collectively work out what number needs to be added to the hat's number to make 10 and hold up their fingers to indicate this number. The child in the hat must then announce the number based on his classmates' clue.