Pick's theorem as a system of equations

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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