Math Forum - Problems Library - Middle School, Pythagorean Theorem

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Middle School: Pythagorean Theorem

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.

Building on Water - Judy Ann Brown
Pre-Algebra, difficulty level 4. Find the area of a circular pond not covered by a rectangular building. ... more>>

Canadian Soccer - Judy Ann Brown
Pre-Algebra, difficulty level 2. Find the distance a player runs to complete three "Double V" laps. ... more>>

Judy and Jen's Garden Problem - Terry Trotter
Algebra, difficulty level 2. Judy and her daughter Jen make up math problems while working in their vegetable garden. ... more>>

Lucie and Daryl's Bike Ride - Terry Trotter
Algebra, difficulty level 2. A sister and brother who ride bikes provide us with a math challenge concerning distance, rate, and time. ... more>>

The Mad Hatter's Gone! - Leanne Gater
Math Fundamentals, difficulty level 4. Explore a coordinate plane and help the Cheshire Cat find his favorite cheese. ... more>>

Partial Area - Judy Ann Brown
Pre-Algebra, difficulty level 3. Find the area of the portion of the circle that is not included inside the inscribed square. ... more>>

The Spiral on the Can - Ethel Breuche
Algebra, difficulty level 3. By using the Pythagorean theorem, students can find the length of the spiral painted on a can. ... more>>

A Stellar Garden - Bill Marthinsen
Pre-Algebra, difficulty level 3. Martha Stewart wants to rebuild her ugly garden. She needs help calculating the areas in the new garden. ... more>>

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