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In the first lesson of this unit, students use pattern recognition to determine that the length of a diagonal of a square is equal to the side length times √2. They then attempt to discover the Pythagorean theorem by examining similar patterns for rectangles.
Individual Lessons
Lesson 1 - Squares, Diagonals, and Square Roots Students explore the relationship between the lengths of the sides and diagonals of a square. Students will use their discoveries to predict the diagonal length of any square. Lesson 2 - Exploring Diagonals and the Pythagorean Theorem Students further explore square roots using the diagonals of rectangles. Using measurement, students will discover a method for finding the diagonal of any rectangle when the length and width are known, which leads to the Pythagorean Theorem.
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