9-1 Figures on Rectangular and Circular Geoboards
NCTM Standard: “The study of geometry in grades 3-5 requires thinking and doing. As students sort, build, draw, model, trace, measure, and construct, their capacity to visualize geometric relationships will develop. At the same time they are learning to reason and to make, test, and justify conjectures about these relationships” (2000, 165).
Purpose: To use rectangular geoboards to illustrate geometric figures and circular geoboards to study inscribed and central angles.
Materials:
· Rectangular and circular geoboards
o Material card 8 rectangular geoboard – online geoboard paper (please print and bring to class for work – may want more than one page to work on)
o Material card 26 circular geoboard – online circular geoboard paper (please print and bring to class for work – may want more than one page to work on)
· Protractor is on material card 19, but you should bring your own with you to class and for the test
· Scissors are needed for activity 1 – supposed to bring to class regularly, please be sure to have them with you for this lesson
Introduction:
· Geoboard is a popular manipulative for showing geometric concepts and investigations
o Most familiar geoboard is square shaped, 5x5 (25 pin)
o Rubber bands can be used to form line segments, angles, and polygons
· Circular geoboards helpful for developing angle concepts
o We will use 25 pin variety – 24 pins equally spaced in a circle and 1 pin in the center
o Can construct polygons on circular geoboard that cannot be shown on the square geoboard
o Will be used to form central and inscribed angles
o Will help us determine relationship between central and inscribed angles
· Geoboard paper can be used in place of actual boards – we will use paper for all of our activities
o What is gained by using paper instead of geoboards?
o What is lost by using paper instead of geoboards?
· Geoboards provide insights because
o Ease figures can be shaped and reshaped
o Encourage experimentation and creativity
· We will begin the following questions together
o 1. Determine all possible triangles with the same base and the third vertex on a pin. One is shown here, find the rest.
o 2. Seen here are three line segments of different lengths. Geoboard line segments begin and end on a pin. How many geoboard line segments of different lengths are possible? Record your solution and be prepared to defend your answer.
o 3.
§ Make the largest square possible
§ Divide the square into two congruent figures (if the figures are congruent the areas are likewise congruent)
§ You have been provided with 4 examples –
§ Find 7 more examples of congruent halves
o 6. Central angle is 15° because 124×360°=15° or (360° ÷24=15°)
§ Central Angles: angle with vertex in center of a circle
§ Intercepted Arc: portion of a circle cut off by the rays of the central angle
§ Name the central angle of given figure
§ Draw the central angle for the given degrees
o 7. ÐABC is inscribed and intercepts the arc AC
§ Inscribed Angles: an angle where the vertex is on the arc and the sides contain endpoints on the arc
§ Use your protractor to measure these angles to the nearest 0.5 degrees
§ ÐABC = 60°
· Get a partner – no more than one group of 3 if there are an odd number of students present
o Complete problems 1- 8 with your partner in class
o Be sure to request assistance from the instructor or another classmate if you need any help
· See the assignment sheet for homework assigned. This homework will NOT be collected for a grade unless the instructor specifically requests students to turn it in before the end of class. It would then be due the following class meeting.