K-12 Teaching and Learning From the UNC School of Education

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Learning outcomes

The students will be able to solve non-routine problems using the Pythagorean Theorem.

Teacher planning

Time required for lesson

90 minutes


  • calculators
  • graph paper or dot paper

Technology resources

Overhead Projector


Students should have worked on squares and square roots.


  1. Begin the lesson using the game called “What’s My Rule” for about 15 minutes (attached: What’s My Rule.doc, What’s My Rule.rtf). Show enthusiasm for all responses.
  2. Give the students the Ramp Question on the overhead (Ramp problem.doc, Ramp problem.rtf). Ask student to explain how they decided on their answer. After several student explanations, organize the class into pairs, putting students of a similar mathematical level together. Distribute activity sheet (Problem Centered problems.doc, Problem Centered problems.rtf) and ask the pairs to solve the problems and be prepared to explain their solutions to the class.
  3. While students are solving the problems, move around the room listening to the discussions but avoid answering questions directly. Do not tell students whether they are right or wrong and don’t give hints. This is an important learning time for them.
  4. Allow 20-25 minutes for discussion. Have the class come together and call on pairs to explain how they solved the problems. Feel free to ask clarifying questions but do not judge or tell students they are right or wrong. You may not have time for all problems to be discussed. The lesson could be spread over two days. There are many ideas to be discussed.


Give students problems where they use the Pythagorean Theorem to solve problems. I have listed a few sites where you can find these problem.

Supplemental information


  • Problem Centered Problems: doc | rtf
  • Ramp Problem: doc | rtf
  • What’s My Rule?: doc | rtf

  • Common Core State Standards
    • Mathematics (2010)
      • Grade 8

        • Geometry
          • 8.G.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

North Carolina curriculum alignment

Mathematics (2004)

Grade 8

  • Goal 3: Geometry - The learner will understand and use properties and relationships in geometry.
    • Objective 3.01: Represent problem situations with geometric models.
    • Objective 3.02: Apply geometric properties and relationships, including the Pythagorean theorem, to solve problems.