Evaluating Statements about Rational and Irrational Numbers

Mathematical goals

This lesson unit is intended to help you assess how well students reason about the properties of rational and irrational numbers. In particular, it aims to help you identify and assist students who have difficulty:

  • Finding irrational and rational numbers to exemplify general statements.
  • Reasoning with properties of rational and irrational numbers.


The lesson unit is structured in the following way:

  • Before the lesson, students attempt the assessment task individually. You review students’ work and formulate questions that will help them improve their solutions.
  • During the lesson, students work collaboratively in small groups, reasoning about general statements on rational and irrational numbers. Then, in a whole-class discussion, students explain and compare different justifications they have seen and used for making their classification decisions.
  • Finally, students work alone to improve their individual solutions to the assessment task, before working on a second, similar task.

Materials required

  • Each student will need a mini-whiteboard, pen, eraser, and a copy of Rational or Irrational? and Rational or Irrational? (revisited).
  • For each small group of students provide a copy of the task sheet Always, Sometimes or Never True, a copy of the Poster Headings, scissors, a large sheet of paper, and a glue stick.
  • Have several copies of the Rational and Irrational Numbers hint sheet and the Extension Task for any students who need them and calculators for those who wish to use them.
  • There is a projectable resource with task instructions and to help support discussion.

Time needed

15 minutes before the lesson for the assessment task, a 60-minute lesson, and 20 minutes in a follow-up lesson. All timings are approximate, depending on the needs of your students.