Visualising Indices TN

Teacher Notes

This is short, effective and fun. Helping students discern between 2 to the power of 3 and 2 x 3 is a constant need and having some of these pictures on the wall of the classroom could really help with this. Thinking about how these picture are put together helps to bring across the power and structure of exponential growth and students will really have to think about it to make the pictures work.


The following is some practical advice about how the activity might be run.

Time needs

This need not take more than an hour and could be done quicker, depending on how pretty you want the final results to look. For that reason it can easily be continued outside the classroom with students creating some serious works of art!

Starting and finishing

  • Start by showing one of the pictures from the activity page like the image above and ask students to think about a mathematical title for it. Try to tease out the mathematical structure behind it.
  • Once the structure is established, show one or two other examples and maybe create one as a group together quickly.
  • Lead a discussion where students advise each other on the care required in choosing a title. For example, 6 to the power of 7 is likely to be a real challenge!
  • Students work individually on pictures of their own. The numbers they choose to use can be used for differentiation.
  • Create a gallery of their pictures and ask the students to say which numbers have been drawn.


A display of the work is the most important and powerful record of this activity. If students can keep their own copy with the worksheet this can be a useful reminder as well.


The main area students can have difficulty with is the distinction between the base and the exponent. For example, if drawing 3 to the power of 4, what impact does the number 3 have and what impact does the number 4 have on the picture? Students may need help with this distinction.

Obviously the bigger the number being attempted, the greater the thought required in planning the drawing. This is an obvious extension opportunity. In order to plan 6 to the power of 7, students will really have to understand what it means and how many objects they will have to draw! They may reconsider!

In the end this is as stated at the beginning, short, effective and fun.

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