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4.2.2 Creating Polygons


4-2_CreatingPolygons  Creating Polygons (applet)

 Students make and compare a variety of polygons, describing the salient properties of the shapes they create.

Task 

Make these figures on the geoboard:

  • 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

 

[Stand-alone applet]

How to Use the Interactive Figure

We will refer to the pegs that the rubber band is attached to as nodes. To begin, click on the rubber-band box and drag a rubber band to the geoboard. Click on a node to attach one end of the rubber band to that node. Move the mouse and click on another node to attach the other end of the rubber band to that node.

  • To attach the rubber band to more than two nodes, drag the rubber band from the middle.
  • To move a rubber band to a new node, click on the current node and drag the rubber band to the desired node.
  • To remove a rubber band from a node, click on the node to select it (a double circle appears), then click on the Delete Node button.
  • To delete a rubber band, click on it to select it, then click the Delete Band button.
  • To clear the geoboard, click on the Clear All button.
  • To color the interior of a shape, click on the rubber band and then click on a color.   

 

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?

 


Also see: 

  • 4.2  Investigating the Concept of Trangle and Properties of Polygons

    • 4.2.1  Making Triangles
     



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