Q&A #145

Geoboards in geometry

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From: Suzanne (for Teacher2Teacher Service)
Date: May 11, 1998 at 10:52:31
Subject: Re: Geoboards in geometry

Geoboards are useful in many areas. They can be used to create shapes with a 
number of different lines of symmetry. The students can create a shape and 
then find the lines of symmetry. 

By using more than one board they can create a shape and on the next board 
demonstrate a transformation such as a reflection or a rotation. 
Geoboards are great for studying area and to compare the area of various 
shapes with the perimeter. One thing that you must be careful of in studying 
perimeter with students this age is using shapes with diagonals. They tend to 
think that from one peg to the next peg is one unit. Using rectangles they 
can clearly see that a 1 x 4 rectangle has a perimeter of 10 units and and a 
2 x 2 has a perimeter of 8 units, but they have the same area.  
Geoboards are great to use in finding areas of many shapes because fractions 
come into play as well. Many geoboards are set up to have 16 square units. 
The students could create a design and find what fractional part each shape 
is of the total shape. Different requirements could be made, such as there 
must be at least five bands used, or there must be at least 4 congruent 
shapes included in the design, or there must be at least 4 diagonals. Have 
them keep track of the number of pegs enclosed in the shape, the number of 
pegs in the outline, and the area of the shape to see if they can find any 
relationship. There is a theorem called Pick's Theorem that states I + E/2 - 
1 = A (I = points inside the shape, E = points on the edges, A = area).

Using dot paper to record the things they do is also a way to allow them to 
see patterns develop and to gain better understandings. This also allows for 
some great writing experiences. 
There really are many more ways that geoboards can be used but these are a 
few that might get you started. I understand why they enjoy geoboards. They 
provide fun hands-on activities. 
- Suzanne 

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