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The Pythagorean theorem can be modeled both algebraically and geometrically. Using both models at the middle school level can help students see that algebra and geometry are related, and that they connect with other content areas in the curriculum. The NCTM Standards' electronic example, Understanding the Pythagorean Relationship Using Interactive Figures, provides a visual perspective. The Pythagorean theorem can be used to solve the problems listed below. Some, such as The Mad Hatter's Gone! and Canadian Soccer, use 3,4,5 triangles that simplify calculations. Others, like A Stellar Garden and The Spiral on the Can, will lead to approximations when using a calculator, or to solutions containing irrational numbers. Background information on The Pythagorean Theorem can be found in the Dr. Math FAQ, or by searching the Math Forum's Internet Mathematics Library for pythagor or Pythagorean theorem (that exact phrase). Access to these problems requires a Membership. |
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