Multiplication wheel: A different kind of table
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Multiplication wheel

You can create:

  • Multiplication wheels
  • Colorful patterns on your wheels
  • Conjectures and theories about times tables patterns


This activity is inspired by Robinsunne's "multiplication clock." The idea is quite simple: you create concentric circles, separate them into as many segments as you want for your tables, and fill them with multiplication results. Figuring out how to draw concentric circles and separate them evenly is a good engineering and geometry problem, though the site has detailed directions.

The most interesting thing, of course, is how to color your multiplication wheels. For example, you can make all numerals for even numbers one color and all numerals for odd numbers another color. What pattern will you see? Why? Try it with multiples of different numbers, say three or five, for more pattern fun. You can highlight full squares (number times itself) for a very special spiral. Any pattern you pick will produce interesting results.

If you want to play with many patterns, it may be easier to copy and then print your concentric circles. However, drawing circles is usually a fun tactile experience. You can use multiplication wheels to decorate your walls, at least for the duration of the study. I usually attach them with a nail or a pushpin in the middle, so they rotate. Remember to share your creations!

Because this activity gives a fresh representation on times tables; it has interesting potential for "text design" (or rather, numerals design). People who like to play with numerals will probably like it.

As you go

  • Look at the wheel for any patterns in numbers. Color your patterns.
  • Think of other wheels and round models people use, such as the color wheel, the seasons wheel, the clock - all of them are multiplicative in some way!

Higher and deeper

  • Counting on wheels (or in cycles) is the basis of modulo arithmetic, a branch of number theory.
  • Circle is a powerful metaphor of time and life cycles, widely used in art and psychology.
  • Many coding systems use wheels; mathematics of wheel and cyphers is quite rich.
Created: December 6, 2008, 8:22 am, by MariaD
Last edit: December 6, 2008, 8:22 am, by MariaD ( Edit, History )
Co-author: MariaD