In 7.RP.a.1, students need to be able to calculate unit rate, including rates that have complex fractions. I tried a method for dividing fractions using graph paper that I found at Fawn Nyugen's site. Definitely great for my visual learners. Through the process I found students really just had trouble understanding whether the quotient should be a number greater than 1 or a number less than one, so that became our focus. By drawing out the fractions using the same wholes, they could see which was larger. I kept coming back to...is this similar to a "10/2" problem, which is more than 1, or a "2/10" problem, which is less than one. I did really like the method though!
Some of my not so very visual students did really struggle with it. Common misconceptions: When students created the rectangles to represent the fractions some of them really struggled to draw an accurate representation of the fraction. For example, if they chose a 4x5 rectangle because they were trying to model 4ths and 5ths, when they tried to shade 3/4 they would shade 3 sets of 4 squares rather than 3 rows out of the 4 rows in their rectangle.
This links to the activity sheet I used with my students. The end of the document has pictures from Fawn's website!
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