Pythagoras - Practice

This math unit begins by developing students' understanding and application of the Pythagorean theorem in calculating the lengths of the missing sides of right triangles. Initial topics involve finding these lengths using equations, radical forms, and decimal representations, with a focus on reinforcing the theorem through various problem scenarios. The unit progresses into geometric applications of these concepts, incorporating Cartesian grids where students calculate distances between points using the Pythagorean theorem expressed as radical distances. The latter part of the unit introduces Pythagorean triples—sets of integer side lengths forming right triangles. Students first identify and solve problems with these triples, learning to find both individual side lengths and the hypotenuse, including scaled scenarios that demonstrate real-world applications. Ultimately, this unit enhances students' geometric calculations precision and deepens their understanding of fundamental relationships in right triangles using the Pythagorean theorem and its extensions to complex geometric contexts.