Geometry and the Geoboard

Jacqueline Darling             Simmye Anderson Community Academy
1733 E. 84th Street            6315 S. Claremont Avenue
Chicago IL 60617               Chicago IL 60625
312-375-2987                   312-535-9070

Objective(s):
  
    The 6th grade student will be able to:
    1.  Discover the fun of using the geoboards as they learn many mathematical 
        concepts.
    2.  Visualize the concepts of squares, rectangles, triangles and polygons.
    3.  Explore line segments, areas, and perimeters.
    4.  Demonstrate the phenomenological approach in learning geometry.
    5.  Understand the multicultural aspect of geometry and the geoboard.

Materials:
  
    Geoboard
    Geobands  
    Dot paper         
    Overhead projector (optional)
    Activity sheets
   
Strategy:

    Discuss with the students the origin and the various types of geoboards 
    (square and circle).  Issue the geoboards and the geobands to each student.
    Let the students explore different shapes on their own.  Elicit from the
    student ways the geoboard can be used to explore different geometric
    shapes. 
    Introduce dot paper to the students.  Use the overhead projector to show the 
    relationship between the geoboard and the dot paper. 
    Explain the coordinates on the geoboard and let the students find points.  
    Show what one square unit is on the geoboard. 
    Give example of a line segment on the geoboard.  Let the students practice 
    making line segments, horizontally, vertically, diagonally, and shortest to 
    the longest. 
    
    Activity 1.
      Locate the circled points on your geoboard.  Name them.  (On the overhead 
      projector select points to circle.)
    
    Activity 2.
      The game Tic Tac Toe is an appealing way to introduce a coordinate system 
      for graphing.  Start with a five by five array of dots on the chalkboard.  
      The plastic geoboard for the over-head projector works well for this 
      activity. 
        Ask a student to name two numbers.  Ask another student to name two 
      numbers.  Mark one team's points with X's and the other teams's with O's.  
      Three in a row wins.  Teams take turns giving you pairs of numbers.  If a 
      pair is given that does not fit on the graph, that turn is lost.  If a 
      pair is called and that dot has already been marked, that turn is lost.  
      After playing this game a few times, change the rules so that it takes 
      four in a row to win. 

    Activity 3.
      Make the figures shown on the overhead projector on your geoboard.
      (Display and label various polygons A, B, C, etc. and let A have
      an area of 6 square units).  Copy on dot paper.             

    Activity 4.
      Using the activity sheets you made in Activity 3, find the areas of the 
      polygons. 
      The geoboard is not needed for this activity.
      Count the squares in example (a).  How many do you see?  The number
      of squares in the figure is called the area of the figure.  The
      area of the figure in example (a) is 6.  Notice we have put the
      6 inside the figure.  Write the correct area inside of each of
      the other figures.

Performance Assessment:

    In the previous activity you were to make different figures on your geoboard 
    with different areas.  Now, see how many figures you can  make on your 
    geoboard, all of which have an area of six square units.  This larger number 
    allows much more variety.  Be sure to check the area on your geoboard and 
    sketch it.  Remember, by different we mean different size and shapes.  (You 
    will need to distribute dot paper.)    
    
Conclusions:

    Geoboards enable us to count units of area of geometric figures.
   
References:

    Meserve, Bruce E., Sobel, Max A., Dorsey, John A., Contemporary Mathematics, 
    4th. Edition, Prentice Hall, 1987. 

    Cech, Joseph P. and Tate, Joseph B., Geo-board Activity Sheets, Ideal School 
    Supply Co. , Oak Lawn, Il. 60453, 1989.