# Toothpick Shapes’ Sequences

#### Posted August 27, 2015

#### by Lensyl Urbano

*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 23rd, 2017, from *Montessori Muddle*: http://MontessoriMuddle.org/ .**Attribution (Curator's Code )**: Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.