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.