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What secrets are hidden in squares? While the Pythagoreans are best known for their triangle theorem, they were in fact religious cult who believed in the god of mathematics. Pythagoras and his followers believed that everything in the universe could be described as a ratio of two numbers...and tenet that was quickly challenged.

In this lesson, students use concrete models to explore square numbers and square roots and confront the philosophical and moral questions posed by the existence of irrational numbers.

- Sometimes humans are persecuted for proclaiming their truths because it threatens a status quo.
- For the Pythagoreans, numbers were a religion and they expected them to reveal the truth of the universe.
- The Pythagoreans persecuted Hippasus when he shared his discovery of irrational numbers, because that “truth” was inconveniently in conflict with the Pythagoreans' understanding at the time.

- Develop a geometric understanding of square root; reason about and find square roots of rational numbers
- Identify the "square root of 2" as
*irrational* - Use rational approximations of irrational numbers and locate them on a number line