Cas Dunlap

US Math - Planning periods A1, A4, B4
Teacher Toolbox Tool: Project-Based Learning
  • Major PBL Project: Pythagorean Proof Demonstration
    • Students selected a proof of the Pythagorean Theorem with a primarily visual line of reasoning.  The proofs they chose from were historically significant, allowing a tie-in to Practice P6 (Connects and relates knowledge in and across disciplines)
    • Students constructed a set of wooden blocks with specific side ratios in the Design Den, then used their constructed blocks to demonstrate their selected proof, either in person or in a video.  (Practice P5: Develops a product or concept for public consideration)
    • PBL Result: Students gained a deeper understanding of one of the most famous theorems in history, and they strengthened their design, construction, and presentation skills.

Parish Profile Practices 2013-14

    P4. Imagines alternatives and generates solutions for problems.

  •  Students consistently solve in-class problems and occasionally work projects in which they do not have a "blueprint" solution, but must figure out how to apply knowledge:
  • Using trigonometry to measure heights of various objects in the atrium.
  • Combining algebraic and geometric techniques to figure out the weight of the pillars in the hallway.
  • Using calculus techniques to cut out a box that will hold the maximum possible number of packing peanuts (using actual packing peanuts to test)
  •  Notes, HW, and assessments invariably contain problems designed to have more than one possible approach; we often review multiple paths, sometimes students will informally demonstrate their different ideas (those who do this frequently can tie-in to P1 and/or P2).

    P6. Connects and relates knowledge in and across disciplines.

  • English - examine mathematical vocabulary, word origins, and Greek and Latin roots that apply in non-math situations (this often ties to World Languages as well); students explain things in their own words, often using complete, well-written sentences
  • History - occasional historical notes about Ancient Greeks and Geometry
  • Physics - students construct a Geometric proof of a major optics equation while learning the scientific side of it in Physics
  • Philosophy - we study introductory Logic in our concepts of proof and validity; in Honors Geometry we also look at some of Zeno's paradoxes that question the discrete vs continuous nature of space and time
  • Higher Mathematics (it's different enough that I'm counting it as cross-disciplinary) - Problems of the Week introduce Honors Geometry students to Abstract Algebra (Finite and Cyclic Group Theory) and its applications in Cryptography and Combinatorics.

  P10. Leads with wisdom, honor, and service to make a positive impact in the world.

  • Honors Geometry has a "Community Participation" component.  In order to satisfy it, students tutor other students, represent Parish in mathematics competitions, help out with middle school programs, or otherwise contribute their mathematical skill outside of the classroom.

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