Evaluating statements about rational and irrational numbers

This lesson develops the concept of reasoning about the properties of rational and irrational numbers. In particular, students will enhance their understanding of:

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

Students are given eight statements relating to rational and irrational numbers. They must classify each statement as, ‘Always’, ‘Sometimes’, or ‘Never true’. There are number cards that students match to statements to exemplify the statement. An example of a statement to be evaluated is:

‘The sum of a rational number and an irrational number is irrational’

There is an extension task that includes further statements to classify. An example is:

‘If the circumference of a circle is rational, then the area is rational’

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.