Monday, March 25, 2013
Ratio, Rate and Proportion Series - Post 2
I wrote an epistle reflecting on our past three sessions but somehow it did not publish. Now, I am trying to reconstruct what I wrote.
On Tuesday, we introduced fraction as number and fraction as ratio on the Cartesian coordinate plane. Both operate differently due to the continuous nature of fraction as number and the discrete nature of fraction as ratio. What they both have in common however is the visual representation that allows us to see what it means to have a common denominator. Too often that is an abstract concept that students can determine but which many just do not understand. The way in which we introduce division can set up our students for success or for reliance on cutesy sayings rather than helping them understand we are simply looking to see how many groups of something we have or how many items each member of a group will get.
Using the graphs to convert ratios to percents is also a valuable tool for students especially when thinking about slope as percent…think about a 40% grade on a hill. Students need to be able to move seamlessly within the ratio, decimal/percent representations and this is yet one more model to use.
On Thursday, we really worked hard solving problems on the Cartesian coordinate plane. It is really challenging to use a model for the first few times. None of us were taught this as students yet the CCSS progressions insist that our students use it as a problem solving strategy. This model really emphasizes the concept of ratio as being discrete and answering the question "How Many?" But, what I found most interesting is how hard it is for some of us to move to a “relative” representation rather than an exact numerical one. This is really a stretch since we have not been trained to think that way. What an advantage your students will have from their exposure to thinking like this!
The highlight of the week was our field trip to the Science Museum. I was really impressed with the depth of conversation around the different exhibits especially the Mt Everest exhibit. I was listening to a news show this morning and they mentioned that the base camp is 17,000 ft above sea level. Imagine!!! Tom mentioned how cold it must be, but I was thinking about the thin air. I had trouble breathing atop Pike’s Peak which is a measly 14,000+ feet above sea level. Of course today hikers bring portable oxygen tanks, but imagine Sir Hillary doing it au natural.
The other interesting point for me was seeing the difference between the pencils made to a scale of 12:1 versus a scale of 10:1. The end products were amazing.
I look forward to reading your posts.