The Spiral of Theodorus Block Kit allows students of any age to experiment with square roots and irrational numbers in physical form. This kit, though simple in design, provides a setting for age-appropriate discussions of the structure and behavior of a whole new type of number. Young children can use the kit to explore right triangles and ramps. Elementary school children can use the triangles to make their first foray into indirectly defined quantities. They can work to make Theodorus’ spiral and other related shapes, and depending on their age level, elementary school children can explore the Pythagorean theorem and square roots. Middle school students can use the triangles to test equivalencies with square roots, and explore abstract concepts like a sequence of geometric shapes based on the Fibonacci numbers. High school students can use the kit to explore a proof of irrationality for non-square integer roots, a method for approximating square roots and, using the Spiral of Theodorus, approximating the number p.
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