Exploring and applying Pythagoras’ theorem

These four lessons targeting students Year 8, can be used as stand alone or as a sequence of lessons. The series of lessons progressively introduce, explore, and apply the theorem in various contexts. Students investigate practical and theoretical problems involving right-angled triangles, discover Pythagorean triples, and learn to calculate unknown side lengths using visual and algebraic proofs. The lessons aim to deepen students' understanding of the theorem's applications and its connections to algebra and measurement.

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  • How old is the (Pythagorean) theorem? Image
    How old is the (Pythagorean) theorem?

    Students learn about Pythagoras’ theorem and its application in calculating lengths in right-angled triangles. They explore the statement of the theorem, some of its history, a simple geometric proof and visual demonstrations of the theorem.

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  • Pythagoras investigations and applications Image
    Pythagoras investigations and applications

    Students work in small groups to investigate the application of Pythagoras’ theorem to problems in a practical or theoretical context. They apply the ‘context > representation > exploration > interpretation > investigation’ cycle to questions of interest or problems in a context involving right-angled triangles and lengths and communicate their findings to others.

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  • Pythagorean triples Image
    Pythagorean triples

    The purpose of this lesson is to have students undertake a mathematical exploration to find Pythagorean triples, that is, sets of positive integers {a, b, c} such that a^2 + b^2 = c^2.

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  • Pythagoras: Cartesian coordinate plane Image
    Pythagoras: Cartesian coordinate plane

    This lesson has students calculate the distance between any two points on the Cartesian coordinate plane using Pythagoras’ theorem and then develop a set of steps that outline the process.

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