Pick's Theorem as a System of Equations—Investigating Pick's Theorem

This Pick's Theorem as a System of Equations—Investigating Pick's Theorem lesson plan also includes:

Pick the values of the coefficients and constants. After finding different values that define the relationship between the area of geoboard figures and perimeter and interior pins, pupils work to find the coefficients that define the equation. They use a system of equations to calculate the missing values to the equation in the second lesson in a series of three on Pick's Theorem. Scholars may use a system of three equations in three unknowns or matrices to arrive at the equation.

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CCSS: Adaptable
Instructional Ideas

  • Conduct a mini-lesson on solving systems of equations using matrices
  • Use different values for A, P, and I to confirm the same equations hold
Classroom Considerations

  • The class should be familiar with solving systems of equations
Pros

  • Provides suggestions for extensions
  • Includes a series of questions teachers can use to assess knowledge
Cons

  • None