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Doodles

How it works

You probably know how to draw a 5-pointed star without picking up your pencil or retracing any lines. Is it possible to draw a 6-pointed star without picking up your pencil or retracing any lines? Are there images that you can't draw without picking up your pencil or retracing lines? Is there a general rule you can use to help you determine which images you can and can't draw without picking up your pencil or retracing lines?

Intro handout
Doodles handout

Why we like this activity:

  • It’s fun! Trying to draw different images without picking up your pencil or retracing lines is a compelling challenge.

  • It helps to develop algorithmic reasoning.

  • It helps to develop combinatorial reasoning (reasoning about discrete features (like the number of points where lines intersect, and the number of lines connected to each of these intersections) as opposed to continuous ones (like the exact shape of the lines)).

  • It requires students to engage in mathematical habits of mind:

    • Making observations / finding similarities and differences / looking for patterns / making and testing predictions / understanding and explaining when exploring which images you can draw without picking up your pencil or retracing lines, and which ones you can't.

    • Finding and using strategies to draw images without picking up your pencil or retracing lines.

  • It has a low floor and a high ceiling: The images start out pretty simple, so it's possible to figure out how to draw them using trial and error. As the images get more complex, it becomes useful to strategize to try to figure out whether or not it's possible to draw an image without picking up your pencil or retracing lines, and if it is possible, how to do it.

To find out more about our approach to math and math education, click here.