Toothpick Shapes’ Sequences

Posted August 27, 2015

by Lensyl Urbano

Toothpick shape sequences.

Toothpick shape sequences.

Using a sequence of connected shapes to introduce algebra and graphing to pre-Algebra students.

Make a geometric shape–a square perhaps–out of toothpicks. Count the sides–4 for a square. Now add another square, attached to the first. You should now have 7 toothpicks. Keep adding shapes in a line and counting toothpicks. Now you can:

  • make a table of shapes versus toothpicks,
  • write the sequence as an algebraic expression
  • graph the number of shapes versus the number of toothpicks (it should be a straight line),
  • figure out that the increment of the sequence–3 for a square–is the slope of the line.
  • show that the intercept of the line is when there are zero shapes.

Then I had my students set up a spreadsheet where they could enter the number of shapes and it would give the number of toothpicks needed. Writing a small program to do the same works is the next step.

Citing this post: Urbano, L., 2015. Toothpick Shapes' Sequences, Retrieved February 26th, 2018, from Montessori Muddle: .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

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