Paula Beardell Krieg posted: " Lots of cut squares Continuing on from last post, I'm practicing how I want to talk to my aspiring-teacher friend about fractions, This is really just a set-up for the next post. I don't want to offend anyone who likes to talk about fractions" Playful Bookbinding and Paper Works
Continuing on from last post, I'm practicing how I want to talk to my aspiring-teacher friend about fractions,
This is really just a set-up for the next post.
I don't want to offend anyone who likes to talk about fractions in terms of pizza slices, but my daughter and I agree, we never want to see a round fraction-pizza ever again.
There is a place for circles in math, but in the early stages of learning fractions, the pizza doesn't give a solid foundation that multiplication and division of fractions can be built on.
For that we need squares.
Squares inside squares
This is good news. Not only are squares delightful in every way, but they underlie so many concepts in math that every opportunity to cozy up to them is worth pursuing.
This means that the hexagon fractions picture in my last post were just meant for decoration. It didn't occur to me that they would provoke some discussion. I have to say I enjoyed the engagement and the opportunity to chat that the hexagons inspired. No more hexagons for now, though, going full steam ahead with squares. Tomorrow.
A preview: the language we use around the multiplication and division of fractions feels like someone is trying to trick us. For instance:
Is half of two-thirds the same as two-thirds divided by one-half?
Even if you know the answer, you had to stop and think about it. I suspect that nearly no regular people (aka people who are not mathematicians) knows WHY two-thirds divided by one-half is one and one-third. This upsets me. I know that no one lied to me when they told me to flip and multiply, but they weren't telling me the whole truth either.
No comments:
Post a Comment