Do the following spirograph designs using the specified rings and wheels. Record your data and the prime factors for the number of teeth on the outer ring and the inner wheel. You can make a factor tree to find the prime factors.
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96 = |
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36 = |
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96 = |
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52 = |
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96 = |
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63 = |
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105 = |
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36 = |
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105 = |
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63 = |
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Small ring = 96 teeth |
Large ring = 105 teeth |
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Small wheel = 36 teeth |
Medium wheel = 52 teeth |
Large wheel = 63 teeth |
From your table, determine a method you can use to predict the number of petals in a spirograph design using the number of teeth on the outer ring and the inner wheel.
Use this method to predict the number of petals in the following designs:
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Use this method to determine a number of teeth on the outer ring and the inner wheel that could make a design with the specified number of petals (there are many possible answers). Try to give a reasonable number of teeth (single digit numbers are not reasonable).
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Why do you think you were not asked to make a spirograph using an outer ring with 105 teeth and an inner wheel with 52 teeth?
Extra Credit
Explain why this method of predicting the number of petals on a spirograph design using the number of teeth on the outer ring and the inner wheel should work. You may find it helpful to consider some simple cases, and consider the number of revolutions it takes to complete the design.