Many of us successfully solve ratio problems partly
because we know how to represent them algebraically and can solve for the
unknown, and some of us because we have innate or developed number sense and
can “see” the relationships between and among quantities that are being
compared. We are lucky again partly because as adults we have been working on
these types of relationships for a long time and have been successful
implementing the algorithms we were taught.
BUT, think back to when you were
learning about ratios and did not understand what it meant to be related to
some other value. I recall being told that the ratio of two things were in a 5
: 7 ratio and there were a total of 763 items. I sat mesmerized when my math
teacher proceeded to write 5x + 7x = 763. It was like magic. At no time was I
shown a visual representation of what was going on nor was I encouraged to
think about the fact that there was a multiplicative relationship happening.
When I finally realized that teaching as telling is totally ineffective I
became a deeper thinker, sought out ways in which to help students visualize,
touch and manipulate the mathematics and relate it to things they are
interested in I discovered my students, no matter how old, started to progress
in their own learning.
I hope that after today’s class the inclusion of the
bar model makes sense to you and it is something that you can bring into your
own battery of teaching strategies. Modeling how the original problem looks and
comparing it to the results after an activity has occurred allows students to
make sense of a given situation and adds sense making to doing the mathematics.
Anne
