Applying properties of exponents

This lesson develops the concept of using the properties of exponents. In particular students will:

• Recall and use the properties of exponents to generate equivalent numeric expressions.
• Identify the appropriate property to use and apply it correctly.
• Check the numerical value of an expression involving exponents without using a calculator.

The initial task is to re-write a series of calculations using only powers of two. For example:

4 x 8 = 32 can be written as 2² x 2³ = 2⁵

The idea is developed further in a collaborative exercise where cards showing single exponents must be matched with ones that show a calculation involving exponents. Some cards have been left blank, so students must fill these in with their own calculations to complete the exercise.

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.