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Discovering Pick's Theorem on a Geoboard

Draw polygons on dot paper, count points, and discover a formula for area using only dots.

Grade 10Math OlympiadMathGeometryLogicNumber SenseAdvanced50 to 90 min4 materials

What you'll learn

  • Count interior and boundary lattice points
  • Form a conjecture from a table of data
  • Test and justify a formula

Objective

Collect data on polygons drawn on a grid, find the formula connecting area to interior and boundary points, and test it.

STEM concepts

Lattice polygonsConjecturePattern findingProof
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Materials and safety
Step-by-step instructions
Prediction, test sheet and results
Why does it work, challenge and project report

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