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.
Anne