# Lesson Plan: Rational and Irrational Numbers Mathematics • 8th Grade

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to identify and tell the difference between rational and irrational numbers.

#### Objectives

Students will be able to

• define what makes a number rational or irrational, in particular,
• if a number can be written in the form , then it is rational,
• if it is a repeating decimal number (e.g., 0.66666…), then it is rational,
• if it is a terminating decimal number (e.g., 0.259574), then it is rational,
• if a decimal number is neither terminating nor repeating (e.g., ), then it is irrational,
• understand that rational and irrational numbers are disjoint sets,
• identify rational numbers and prove that they are rational using the above properties,
• identify irrational numbers such as roots of nonperfect squares or cubes and pi,
• identify whether the solution of a simple equation will be rational or irrational without finding its value.

#### Prerequisites

Students should already be familiar with

• rational numbers and how they can be written as ,
• square and cube roots of perfect squares and cubes,
• two-step equations.

#### Exclusions

Students will not cover

• finding approximate values of irrational numbers and expressions,
• representing irrational numbers on the number line,
• ordering rational and irrational numbers,
• real numbers as a set.