Lattice Land: Polygon Exploration - Preview

Lattice Land: Polygon Exploration

Subject: Mathematics
Time: 1-2 Class Periods (45 minutes each)



In this Lattice Land unit, students will be exploring the lattice and lattice polygons--an array of dots on a plane, such that there is one dot at each coordinate (x,y), where x and y are integers. In other words, {(x,y)|x,y∈Z}. This lesson can be the first in a unit using Lattice Land, a stand-alone exploration of geometric entities, or it may follow the series on Lattice Land Triangles or Lattice Land Squares. Students are asked to identify and define geometric entities: points, line segments, triangles, etc. There are some familiar geometric objects that cannot be drawn in Lattice Land, for example the circle. Students should explore some of these impossible Lattice shapes and discuss theories for why they are impossible. These discussions should also help cement what does and does not define a polygon. Students should also feel free to get creative. They can draw diagrams of their choosing, and may opt to explore in depth topics in symmetry, patterns, or optical illusions, and the like.

Lattice Land is an array of dots on a plane where every dot represents a point (x,y) on the coordinate plane, where x and y are both integers. One way to think about the Lattice is to picture a floor filled with square tiles, but you are only able to step on points where the corners of the tiles meet. You may also draw line segments connecting any lattice point to any other lattice point. This is your only restriction when drawing 2-dimensional shapes in Lattice Land.

It is up to you to define your terms carefully in this Lattice universe. Terms may include: triangle, square polygon, regular polygon, line, segment, circle, distance, perimeter, area, and more.

Compatible With




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Computational Thinking in STEM
  • Modeling and Simulation Practices
    • Using Computational Models to Find and Test Solutions
  • Computational Problem Solving Practices
    • Troubleshooting and Debugging
  • Systems Thinking Practices
    • Communicating Information about a System
    • Investigating a Complex System as a Whole
    • Understanding the Relationships within a System

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