Follow up an introduction to your class on rational and irrational numbers by distributing flash cards with numbers and symbols. These cards will include symbols such as pi and the mathematical constant "e" (an irrational number), as well as numbers expressed as fractions, decimals and sums. Divide your class into groups and ask them to organize themselves into a line so their numbers are in ascending order. Then ask everyone holding a rational number to go to one side of the classroom and everyone holding an irrational number to go to the other side. This will allow your class to get a better view of rational and irrational numbers.
Divide your class into three groups and assign each group a different method of representing a number: fractions, decimals or percentages. First, ask them to draw a picture representing their method. For example, a picture of a pie with a quarter missing could represent a fraction. A sprinter breaking a world record could represent decimals. Ask each group to come up with as many different places as they can where they have seen their method of representation used. This will get them to think about real world applications of mathematics and which method is best suited for certain situations.
Despite their cumbersome nature, irrational numbers still can be graphed along a standard number line. For example, an irrational number beginning with 3.994258673 and recurring indefinitely may have many more digits but will still always be smaller than 4, just as it will always be smaller that a number beginning in 3.995. To demonstrate this, give your students a list of square roots and other representations of irrational numbers, and ask them to graph them on a number line. They will soon see even irrational numbers can be put into basic mathematical parameters.
For this activity, you will need an egg timer and some open space in your classroom. Assemble your class in the middle of the floor and ask them to get their calculators ready. Set the timer for a very short time, give your students a square root to work out and tell them to find out if it is rational or irrational. All who think the answer is rational, go to the left wall; all who think it is irrational, go to the right. Keep reducing the time on the timer and making the roots more difficult until there is only one person left who has gotten every answer correct. This game builds an understanding of rational and irrational numbers as well as developing calculator skills for more difficult exercises later.