I’ve been thinking about a more effective way (for me) to teach proportionality (to 7th graders). I never have wanted to reduce it, like so many textbooks and videos and apps do, to a series of how-to lessons and repetitive just-do-it-this-way practice. You know what I mean; Lesson 1: How to write a ratio. Lesson 2: How to write a unit rate. Lesson 3. How to write and solve proportions: Method1: cross products Method 2: equivalent fractions. Lesson 4: How to… make everyone think learning math is only about following directions to get the right answer. Yuck.
In spite of my best efforts to teach for understanding, I
think know I’ve missed the mark. Fortunately, I’ve had lots of glorious time lately to read incredible blogs and do some heavy self-reflecting. Here’s where I stand currently regarding teaching proportionality:
WHAT IF… I build a series of lessons (primarily exploratory activities and worthwhile tasks, discussion and reflection, but also instruction and practice) that explore the Big Essential Idea of Relationship. Have all lessons contain this common, recurring thread: proportionality is about a consistent relationship between two things that change together (co-vary). This idea needs to be explicitly noticed and talked about from multiple perspectives– in rates, in probability, in percent change, in similar figures, in scale drawings, in proportional contexts, graphs and slope, tables, equations, in formulas– and in experiencing all these things, students develop a solid understanding of relationship, a foundational algebra concept, make oodles of connections, and all the while develop a meaningful set of skills.
Just wondering, how do you address the relationship concept in your classes? I’ve got some ideas brewing for a series of posts.
BTW, the other two 7th grade BEIs are, IMO, Equality and Operation.