Table of Contents Appendix E-examples Resources

Investigating the Concept of Triangle and Properties of Polygons: Creating Polygons Making Triangles Creating Polygons

This two-part example describes activities that use interactive geoboards to help students identify simple geometric shapes, describe their properties, and develop spatial sense. The first part, Making Triangles, focuses attention on the concept of triangle, helping students understand the mathematical meaning of a triangle and the idea of congruence, or sameness, in geometry. In this second part, Creating Polygons, students make and compare a variety of polygons, describing the salient properties of the shapes they create. Both parts help students reach the goals described in the Geometry Standard.

• As many different-sized squares as possible
• Many different hexagons
• The polygon with the fewest number of sides
• The polygon with the largest number of sides you can make
• Polygons with every number of sides between the fewest and the largest

[How to Use the Interactive Figure]

[Stand-alone applet]

Learning about Polygons in the Classroom

Through small-group or informal class discussions, teachers help students learn geometric vocabulary as well as learn about properties of different polygons. Some properties of figures will be easier to identify than others as students plan how to create a figure on a geoboard. For example, polygons are made with straight lines, as modeled by a band connecting two nodes, and polygons are closed figures. Students can learn the names of the specific figures they create as they talk about the hexagons that have six sides and the quadrilaterals that have four sides.

Students can make their favorite polygon on a geoboard and describe it to the class. Teachers might ask if any figures are congruent and how students might justify their claims. Students can sort the polygons and describe why they are grouped in certain ways.

Working with interactive computer geoboards make exploring polygons easy for students who have difficulty managing the rubber bands. Because students have a broad work space, they can make a large variety of polygons. There is room to create multiple convex and concave figures, and they can view all of them at once. Filling the polygons with color helps young students notice the number of sides and, because open figures cannot be shaded, reinforces the understanding that polygons are closed figures. As with physical geoboards, the lines created by the bands are straight, not curved.

Take Time to Reflect

In what ways, other than with geoboards, can you help students learn properties of polygons? What experiences, knowledge, and vocabulary should students have in order to develop an understanding of properties of polygons?

Making Triangles

Creating Polygons

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