Power play

Purpose

The purpose of this activity is to engage students in evaluating powers of whole numbers and generalise the repeating sequence in the ones digit of those powers.

Description of Mathematics

The background knowledge presumed for this task is outlined in the diagram below:

This activity should be used in a ‘free exploration’ way with an expectation that students will justify the solutions that they find.

Activity


The last (ones) digit of 32 is 9 since 3 x 3 = 9
The last (ones) digit of 33 is 7 since 3 x 3 x 3 = 27
The last (ones) digit of 34 is 1 since 3 x 3 x 3 x 3 = 81.

What is the ones digit of 32019?

Do similar patterns exist in the powers of other whole numbers? For example, what is the ones digit of each of the following?

  • 52019
  • 22019
  • 42019
  • 82019
  • 72019

The procedural approach (show more)

  • The student uses calculations, with the support of digital technology, to identify elements of repeat in the ones digit of powers.

The conceptual approach (show more)

  • The student uses multiplicative thinking, particularly division with remainders, to predict the ones digit of powers.

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