Classifying rational and irrational numbers

This lesson develops the concept of distinguishing between rational and irrational numbers. In particular, students will enhance their ability in:

• Classifying numbers as rational or irrational.
• Moving between different representations of rational and irrational numbers.

 An initial activity asks students to classify a list of numbers as rational or irrational. There then follows a claim that 0.57575757… is irrational, with a conversation shown between two people. Students must comment on the validity of each claim made by the people having the conversation.

There is a collaborative activity where numbers must be placed under five headings:

• Non-terminating non-repeating decimal
• Non-terminating repeating decimal
• Irrational number
• Terminating decimal
• Rational number

A hint sheet is provided to guide students with their work.

There are pre-lesson and post-lesson formative assessment tasks. Detailed teacher notes give suggestions on questioning and how to use the resources. Full solutions are given for each of the sections.

This is a concept development lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.