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Amy Bode

Pop quiz! What’s the Pythagorean theorem? If you need help jogging your memory, just ask Ms. Joy Perley’s 5th grade math MTSS group. They completed a week-long, hands-on exploration of the Pythagorean theorem.

Ms. Perley is the PS-8th grade Advanced Learning Teacher. Students are assigned to her small groups through MTSS, or Multi-Tiered System of Support, which provides every elementary school student with small group instruction and individualized attention, no matter whether they need academic support, enrichment, or extension. Small groups are developed through data-driven decisions, so every student receives individually-customized instruction at exactly the level they need.

Even though the Pythagorean theorem is introduced in 8th grade, Ms. Perley’s 5th grade students were up for the challenge. But to keep them engaged, she got creative! To understand this fundamental theorem, students started off by drawing on centimeter grid paper to discover that the sum of the squares of a right triangle's sides a and b is equal to the square of the triangle's hypotenuse c.

They then manipulated paper squares and triangles to complete the well-known Proof by Rearrangement. Having solidified their understanding of what Pythagoras actually proposed, students then applied the formula to solve a variety of problems involving Pythagorean triples (sets of three positive integers a, b, c); for each problem, they either had to determine a certain side length, a triangle's perimeter, the area of a triangle, or the area of a square of a specific side.

For the culmination of the project, students then learned about radicals by creating a Spiral of Theodorus, a series of right triangles arranged so that the hypotenuse of the previous triangle becomes a leg of the next triangle.

For many students, it was their first time working with square roots; each student used their creativity to turn their spiral into a colorful rendering of an animal, such as a parrot, dragon, hermit crab, or a snail. Finally, the class created display folders of the various steps as a take-home reminder of all that they had learned.