Quandaries and Queries


I am a teacher's aide working with ESL students in all subject areas.  This question is 7th grade Math.
  My name is Lindsay
 "There are two gears, a small one on the left and a larger one on the right.  The gear on the right makes 1 revolution.  The gear on the left makes two revolutions.  Suppose the gear on the right is turned through an obtuse angle.  Will the gear on the left make a full turn?"
  Thank you very much for your assistance.


Hi Lindsay,

Imagine that a dime and a quarter were the correct sizes. Put them on your desk touching each other with the dime on the left, the quarter on the right and both with the faces oriented upwards. The instructions say that if you keep them touching and roll them together one revolution of the quarter, so that Washington's face is back right side up then Roosevelt's face will have turned upside down and then right side up twice.

Imagine that you roll the quarter clockwise. If you roll the quarter 90 degrees then Washington's head will be pointed to the right and Roosevelt's head will be upside down. An obtuse angle is between 90 degrees and 180 degrees so roll the quarter a little more but not far enough to put Washington's head upside down, that would be 180 degrees. Roosevelt's head moves in a counterclockwise rotation but doesn't reach an upright position. So the dime didn't make a fill turn.



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