1.)The teacher will need to define and describe each classification of the real number system. It is a good idea to illustrate the progression through time. For example, when students were in kindergarten they had only an understanding of numbers that they could count, hence the term counting numbers (or natural numbers). In first grade they understood zero and how it functioned as a placeholder. In seventh grade they learned to use integers. In Algebra II they will learn an entirely new number system, complex numbers.
2.)Use the diagrams in the attached slideshow presentation to further illustrate the attributes of each classification.
3.)Select six students to sit in chairs in the front of the room facing the class. The first round should probably be with students who have a good understanding of the concept.
4.)Give each student a sign to wear: (in this order) Real, Rational, Irrational, Integer, Whole, Natural.
5.)The remaining students will draw numbers from a container. As each student reads his/her number, the students in the front will stand if the number meets the constraints of their classification.
6.)Teacher observation and assessment will determine how many rounds are played. When the teacher feels the connections have been made, a discussion will evolve. Students will begin to see that Irrational and Rational never stand at the same time. They will also see that Real always stands. If Natural is standing, then Whole and Integer will also. Allow students to make these observations. Do not rush the process.
7.)Give the students the practice sheet for classwork or homework.
8.)Be sure to give enough guided practice before assigning independent work.