Before students can move on to distinguishing rational numbers from irrational numbers, they must have a strong grasp of just what makes a number rational. A rational number can be converted into a simple fraction. Divide the class into small teams and reveal identical columns of numbers on the board. The teams should elect a member to go to the board and turn each number into a fraction. Reassure the kids that all the numbers are rational. The first team to finish wins a prize.
This game is targeted at individuals. Students can play this at a computer or with a sheet of paper. The problems presented should be identical to make the game fair. Present them with a list of rational numbers written in various forms. These could be decimals, fractions, square roots, integers and other forms. The point of the game is to put them in order from least to greatest as fast as possible. For team fun, you can give kids placards with rational numbers on them and ask them to line up in order.
You can adjust the number bin game to make it as hard as you want. After presenting the kids with two bins, tell them that one is for rational numbers and the other is for irrational. Give them a deck of cards with numbers written on them and ask students to place each card in the correct bin. If you want this to be easy, only hand them cards with simple fractions and a few obviously irrational numbers form your lesson, such as the square root of two. Later, as they acquire competency, you can add trickier cards to the deck.
A lot of famous irrational numbers are written as square roots. For example, the square root of two is one of the numbers ancient mathematicians first identified as a number that could not be written as a fraction. More advanced students should play games which only present numbers which are written as square roots. Some, such as those they have seen in lessons, will be easy to identify as rational or irrational. Throw in previously unseen square roots to increase the challenge of the game.