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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 Algebra 1

Provider: National Council of Teachers of Mathematics

About this resource

Appropriate grades
9–12
Subjects
mathematics (algebra, measurement)
Provider
National Council of Teachers of Mathematics

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Creative Commons License

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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

Mathematics (2004)

Grades 9–12 — Algebra 1

  • Goal 1: Number and Operations - The learner will perform operations with numbers and expressions to solve problems.
    • Objective 1.02: Use formulas and algebraic expressions, including iterative and recursive forms, to model and solve problems.
  • Goal 4: Algebra - The learner will use relations and functions to solve problems.
    • Objective 4.01: Use linear functions or inequalities to model and solve problems; justify results.
      • Solve using tables, graphs, and algebraic properties.
      • Interpret constants and coefficients in the context of the problem.
    • Objective 4.03: Use systems of linear equations or inequalities in two variables to model and solve problems. Solve using tables, graphs, and algebraic properties; justify results.