Fear of Fractions

In Precalculus we just finished the first of the two most challenging units of the year.  Students had to draw graphs of sine and cosine functions that had been transformed in some way (stretched/compressed, moved vertically or horizontally, etc.).  The ultimate goal was to complete word problems that could be solved by writing a sine or cosine function to model the situation.  One would think that the most challenging part of this would be the word problems, but those actually went fairly well.  No, it was the fractions required to correctly label the scale on the x-axis that caused meltdowns even among some of my better students.

Note that if you just look at the fractions this student thinks the order should be 5/2, 1/4, 3/2, 1, 2/2, 2/3.  Yes, my high school graduates students who think that 3/2 is less than 1, 2/3 is greater than 1, and 2/2 is a different number from 1.  I just hope when they go to college they don't mention who their last math teacher was.