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

Important Announcement about Online Courses and LEARN NC.

Important Message about LEARN NC

LEARN NC is evaluating its role in the current online education environment as it relates directly to the mission of UNC-Chapel Hill School of Education (UNC-CH SOE). We plan to look at our ability to facilitate the transmission of the best research coming out of UNC-CH SOE and other campus partners to support classroom teachers across North Carolina. We will begin by evaluating our existing faculty and student involvement with various NC public schools to determine what might be useful to share with you.

Don’t worry! The lesson plans, articles, and textbooks you use and love aren’t going away. They are simply being moved into the new LEARN NC Digital Archive. While we are moving away from a focus on publishing, we know it’s important that educators have access to these kinds of resources. These resources will be preserved on our website for the foreseeable future. That said, we’re directing our resources into our newest efforts, so we won’t be adding to the archive or updating its contents. This means that as the North Carolina Standard Course of Study changes in the future, we won’t be re-aligning resources. Our full-text and tag searches should make it possible for you to find exactly what you need, regardless of standards alignment.

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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.