Ask students to form three teams. The "Integers" team must make a paper disk with a 5-inch radius, the "Rational Numbers" teams must make an 8-inch radius disk and the "Irrational Numbers" team must make a 12-inch radius disk. Each team must fill its disk with random integers (0, 1, -12), rational (0.75, 1/3=0.333, 5/11=0.454545...) and irrational numbers (pi, square root of 2=1.4142135...). Glue the "Irrational numbers" disk on a large sheet (A3 size), followed by the two smaller ones to form three concentric circles. The contents of the large sheet form the real numbers sphere.
Draw a long real number line on the board. Put 0 in the middle and place positive integers (up to 10) on the right side and negative integers on the left side. Give simple operations to students and ask them if it is possible to place them on the line. For example, -20/5 goes to the line, as it equals -4, 6/5 goes to the line, as it makes 1.2. However, the square root of -1 does not go to the real number line, as there is no number multiplied by itself to give -1 (or -2 or -3 and so forth).
You can use real numbers to represent a quantity, such as the distance between two spots on a map, the weight of a person, the salary of a worker or the temperature of a place. Bring measuring tools in class, such as a scale and a thermometer. Ask students to use their rulers to measure the length and width of their textbooks and notebooks, measure the temperature in the room and outdoors with the thermometer, as well weigh different items on the scale. Explain that any number able to describe a quantity or characteristic of real-life items is a real number.
The term "real" does not mean that we encounter them exactly in everyday life. For example, 0.5 denotes something half, but it is impossible to cut a real thing measuring 1 (inch, meter, mile) in half and have 0.5 (inch, meter, mile). To make students understand this, ask them to cut out a square with a 1-inch side. Instruct them to cut the square in two equal parts (not diagonally). Go over each student and use a ruler and a magnifying glass to show that, even for millimeters, the side is not 0.5 inches.