Friday, August 6, 2010

Working with Slope and Fractions

If you get a chance, check out NCTM's August 2010 edition of Mathematics Teaching in the Middle School. Ivan Cheng has written an article "Fractions: A New Slant on Slope", about using slope to add, subtract, and multiply and divide fractions that I think is an interesting and fun read. Basically, when you graph a line with a slope of 1/2 (y=1/2x) starting from the origin, all the coordinates on that line will be equivalent to 1/2. i.e. 3/6, 5/10, etc. The fun starts when you start adding and subtracting fractions using slope. Graph another line such as y=2/3x will notice that the lattice points of the two lines will line up on the common denominators (the x-coordinates or 6 in this case). From there the adding and subtracting is pretty easy. Not necessarily a method I would use to introduce adding and subtracting with fractions - fraction bars, number lines, and manipulatives are what I prefer- but this method using slope was sure fun to do! I have never thought about teaching fractions with slope before- but this year when we work with slope, I plan on having my students get out their whiteboards and do some fraction work as well! It will be a fun review of fractions with a twist, and hopefully deepen their understanding of slope as well!

1/2 + 2/3 = 3/6 + 4/6 or 7/6

This method reminded me of something one of my algebra students came up with a couple of years ago to order fractions from least to greatest which I wrote a post about earlier. He graphed the fractions on the coordinate grid (y/x) and extended a line from the origin to the point. Going from left to right, the fractions were in order.

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