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K–12 teaching and learning · from the UNC School of Education

Rediscovering the patterns in Pick's Theorem

http://illuminations.nctm.org/LessonDetail.aspx?ID=L623

A lesson plan for grades 9–12 Mathematics

Provider: National Council of Teachers of Mathematics


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This lesson, one from a multi-part unit, challenges students to use a geoboard, geoboard applet, or Geometer’s Sketchpad® to discover the pattern of Pick’s Theorem. Illuminations provides an activity sheet, links to a geoboard applet, and detailed instructions for completing the lesson.

Students will:

  • Investigate several geoboard figures to determine the pattern between the number of perimeter pins, the number of interior pins, and the resulting area.
  • Create an equation using symbolic algebra to represent the pattern.

NCTM Standards and Expectations:

  • Interpret representations of functions of two variables.
  • Generalize patterns using explicitly defined and recursively defined functions.
  • Make decisions about units and scales that are appropriate for problem situations involving measurement.

North Carolina Curriculum Alignment