## Real Numbers

### Xiuqing LiEscambia County Schools

#### Description

Students examine the concept of integers, rational numbers, irrational numbers, real numbers, complex numbers and understand their relative size.

#### Objectives

Understands the relative size of integers, rational numbers, irrational numbers, real numbers and complex numbers.

#### Materials

-Transparency
-Student worksheet-One per student (See associated file)

#### Preparations

1. Prepare a transparency copy of the attached file showing definitions and examples of terms.
2. Prepare a student worksheet (one per student) as a method to assess the students.

#### Procedures

Students should have prior knowledge of the concepts of natural numbers, whole numbers, origin, positive numbers, and negative numbers.

Review prerequisite concepts.

1. Discuss the following with students: -The concept of numbers has been around for a long time. For example, say you were a business person selling pencils and a customer wanted to buy some of your product from you. Now, if he were to ask for 2 pencils, what kind of number is 2?- Lead students to reply that it is a whole number or natural number.

2. Continue discussing: -If you had sold out of pencils and you had to promise to give him two pencils next week, how would you express that you owe him two pencils?- Lead students to reply that the business person owes the customer two pencils which could be written -2.

3. Explain the concept of an integer on the overhead by using the transparency (see associated file.) The set of integers is whole numbers and their opposites. (-3, -2, -1, 0, 1, 2, 3)

4. Draw a real number line and ask students to label several integers on the real number line. (see attached file)

5. Then, on the real number line, write down points that are not integers, and explain the concept of rational number. A rational number is a number that can be written in the form of m/n, where m and n are integers and n does not equal to zero. (see attached file)

6. Show several examples of rational numbers. Explain that the rational number include integers.(see attached file)

7. Explain that at times, there are numbers that cannot be expressed as m/n. Give several examples of each. (see attached file)

8. Explain the concept of irrational numbers. (see attached file)

9. Explain the concept of real numbers. The real number line includes both rational and irrational numbers. (see attached file)

10. Review these definitions with students. Call on students randomly to name an example of each term and then list it on the board. When there is a numerical example of each term, ask students how these numbers could be compared/ordered from smallest to largest. Lead students to say that we could use a number line if necessary but that they have to be in similar form in order to compare them. Help students to see that decimals are one form that might lend itself to comparing the numbers.

11. Ask 8 more students to give examples of each of the terms and then to list them on the board. Allow students to practice on a piece of paper ordering the numerical examples. After a couple of minutes, give the correct order and answer any questions about those missed.

12. Give students the worksheet in the file and collect when finished.

#### Assessments

Formatively assess the students on the worksheet. Note those who are having difficulty. They may need additional practice.