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After completing a unit on polygons and finding the sum of the angles in a polygon the students were given a two day activity to build an arch based upon a 18 sided polygon. Students had to decide the number of degrees which the trapezoidal block had to contain so that it would form an arch when 9 blocks were used. Each arch is based upon an 18-sided polygon. Each block is made up of two trapezoids and four rectangles
On the first day the students performed several calculations and decided the measurements they would use for their blocks. Each class was given the task of building three arches. Each group would be responsible to build 9 identical blocks and two abutments. On the second day the students were given oaktag to use for their blocks. With the use of compasses, protractors, and scissors the students build blocks which were as identical as possible.
Once the blocks were built it was time for the test. Would the 9 blocks fit together to form an arch which would be free standing between two books? Some the blocks were more successful than others. In each class two of the arches were able to stand without the use of tape. Students first built the arches on a shelf at desk level. Then after they were sure the arch would stand the students rebuilt the arch on top of the cabinets so it would not be disturbed by people walking by.
Students use their knowledge of regular polygons to determine that there will be a 160 degree angle between the blocks. This means that each of the trapezoidal faces will have 80 and 100 degree angles. The students agree on the width of the block and the height of the block. Then each student build the net to make each block. As students get blocks complete, nine students put their blocks together to form an arch. The arches are then transferred to the top of the cabinets and they stay up there the rest of the school year.
The students are always amazed that the block stay in position with no extra tape, just the forces working between the blocks. Books are used as abutments. Some groups learned that measuring had to be extremely accurate if the arches were going to fit together properly using 9 trapezoidal blocks. With only a few degrees error it was not possible to build some of the arches. Those groups had to just mark the activity as a learning activity.
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