The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 2.1: Classifying Counting Numbers, Whole

Numbers, Integers, and Rational Numbers

Classifying numbers presents problems for some students. Classifying rational numbers can pose

special problems.

1. Review the counting numbers, whole numbers, and integers with your students. You may
   find it helpful to refer to the student worksheet for this.


2. Define rational numbers as any number that can be expressed as the quotient of two integers.
   Rational numbers can be positive, negative, or zero.


3. Provide examples of rational numbers such as

3

5

,−

1

3

,− 2

1

4

, 4, 1.2, and 0.75. Remind your

students that whole numbers and decimals can be expressed as fractions.

4. Review the information and examples on the worksheet with your students.

EXTRA HELP:

Being able to classify numbers fosters overall understanding of numbers and their relationships.

ANSWER KEY:

(Counting numbers)15, 4, 21 (Whole numbers)15, 0, 4, 21

(Integers)15,−8, 0,−7, 4,−1,−150, 21 (Rational numbers)All of them

------------------------------------------------------------------------------------------

(Challenge)Agree. Explanations may vary. One explanation is that every integer can be

expressed as a rational number by writing the integer over 1, such as

2

1

. But fractions and
decimals are rational numbers that may or may not be integers, such as 0.3.

48 THE ALGEBRA TEACHER’S GUIDE