Spirolaterals

Making spirolaterals is a way to bring Math and Art together. A spirolateral is geometric art made up of spirals and structures that are formed using a pattern of numbers, in the same way you would build code to get a robot to move on the Lightbot app. You can find patterns anywhere.

We are going to make spirolaterals using patterns from multiples and factors.

Step One: Pick a factor. The simplest factor to work with is 3, so let’s start here. Find all the multiples of 3 up to the factor of 12 (use your multiplication chart, skip count by three, or use repeated addition).

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36

Step Two: In order to find your pattern, you must have only single digit numbers. For all the 2-digit multiples, add the digits together to form a single digit:

Step Three: Head to your graph paper. Find a starting place that is close to the middle of the page.

  • Draw a line that is 3 spaces to your right.
  • Turn your notebook 90 degrees.
  • Draw a line that is 6 spaces to the right.
  • Turn your notebook 90 degrees.
  • Draw a line that is 9 spaces to your right.
  • Turn your notebook 90 degrees.
  • Continue turning your notebook 90 degrees and follow the pattern of 3, 6, 9 until you meet back up with your starting place.

Lines will overlap, so make sure to be careful to keep your place on the graph paper.

Some factors take longer to find the pattern, like the factor of 4. You will have to go past the factor pair of 4 x 12 to find the pattern. To get a better idea of how it works, watch the video on making the Spirolateral with the pattern using multiples of 4.

Using the Math and Art section of your Math Journal, find as many patterns using multiples up to 12, and make spirolaterals for as many as you like. Share your photos or videos with me, sonia@seredipityschool.com, and I will share them here. Have fun!

Shout out to Sarah Apple who brought spirolaterals to my attention, THANK YOU!!

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