ABSTRACT
My school is an urban school with a high percentage of students qualifying for free or reduced lunch. The teachers in my school expect a high level of engagement, and use the teamwork aspect of our instruction to teach students how to work together and to lead. Many of these students haven’t been expected to act as leaders in the past, so at first this is difficult. But we are persistent, and they begin to see that, buried deep within them, is powerful number sense that can be used to solve problems. I have noticed that many students enter my middle school classroom with very little proportional sense. Some have learned to cross multiply, but are not sure why it works, or even when to use it—and when NOT to. Others have trouble understanding that there are multiple quantities to work with, and those that do recognize the different quantities don’t always see the relationships that link them. In a way, I find this to be a lucky break, almost a clean slate upon which to help my students develop the reasoning they will use later in algebra, geometry and measurement.
