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.


Students will be able to

  • define what makes a number rational or irrational, in particular,
    • if a number can be written in the form 𝑝𝑞, 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., 𝜋), 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.


Students should already be familiar with

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


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.

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