This activity is best for elementary age students. Have the students create a number line. Use whole numbers or even whole and halves or quarters depending on the grade level. Have the students use marker or crayon to write on the number line. Use marbles or another similar sized indicator to use as a marker. The students place the marker anywhere on the number line and have another student name the value of the place holder. Add some difficulty to the activity by having the students name other ways to say the value, such as in fraction form, decimal or even in square root form.
Write a variety of numbers on index cards. Each index card should have an irrational or rational number on it. In addition, each student should have a card. Ask the students to divide into irrational and rational numbers. Check to make sure everyone is where they should be. Have the students place themselves on the number line in numerical order. For younger students or students who are just learning about irrational numbers, feel free to allow them to use their calculator. This activity allows for the students to learn about real numbers, both irrational and rational. This activity also teaches the students teamwork and leadership.
Any board game that involves counting both positive and negative numbers to move around the board is a fun way for younger children to learn about real numbers. By giving children a colorful playing piece or even a themed playing piece, they get the benefit of playing a game and also learning their numbers, more specifically whole numbers. Even creating a math-themed game out of construction paper is an excellent way to teach about whole numbers.
Write on an even number of index cards square roots, pi, cube roots, fractions and decimals. Each card should have a matching card. One card should have the number in one form while the other card has another form. For example, if one card has the symbol for pi on it, its matching card should have the decimal 3.1415. Include definition cards with the correct term. Students should be teamed up in groups of two to four players. Place all the cards face down. Students take turns flipping over two cards until all the cards are matched. Students with the most matches win.