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Lesson Plan

Recognize patterns that make Pythagorean Triples

teaches Common Core State Standards CCSS.Math.Practice.MP1
teaches Common Core State Standards CCSS.Math.Content.8.G.B.7
teaches Common Core State Standards CCSS.Math.Practice.MP2
teaches Common Core State Standards CCSS.Math.Practice.MP8
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Big Ideas: Some sequences of geometric objects change in predictable ways. Known elements in a pattern can be used to predict other elements. This lesson explores some patterns found in Pythagorean Triples. The task asks students to find algebraic and geometric patterns between the numbers in Pythagorean triples that are primitives and to generalize patterns for finding a Pythagorean triple. Students start by comparing the side lengths of skateboard ramps to look for similarities in the types of numbers and their relationships to each other. Students then choose one set of Pythagorean triples to explore in detail and to develop an algebraic expression that will generate more triples in that set. This task can be very open-ended or more structured depending on how much guidance is given. Vocabulary: Pythagorean triple, primitive triple, hypotenuse, leg, square of a number, square root Special Materials: calculator (optional) graph paper or isometric dot paper (optional)
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