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

Pick's theorem as a system of equations

http://illuminations.nctm.org/LessonDetail.aspx?ID=L624

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)
Provider
National Council of Teachers of Mathematics

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Students will gather three examples from a Geoboard or other representation to generate a system of equations that will provide the coefficients for Pick’s Theorem.

Students will:

  • Create three figures and measure the number of perimeter pins, number of interior pins, and the resulting area.
  • Use the data to construct a system of equations.
  • Use algebraic manipulations to solve the system to find the coefficients of Pick’s Theorem.

NCTM Standards and Expectations covered in this lesson include:

  • Understanding and performing transformations such as arithmetically combining, composing, and inverting commonly used functions, using technology to perform such operations on more-complicated symbolic expressions.
  • Interpreting representations of functions of two variables.

North Carolina Curriculum Alignment

Mathematics (2004)

Grades 9–12 — Algebra 1

  • 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 4.02: Graph, factor, and evaluate quadratic functions to solve problems.
    • 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.
    • Objective 4.04: Graph and evaluate exponential functions to solve problems.