I love language almost as much as I love numbers, so I tend to get excited about vocabulary. We talk about Latin roots in my class, and why we use the terms we do in math class. I have always stressed “constant” and “variable,” but I really got excited when I saw how contrasting the variety of possible scale factors in a table with the constancy of the “constant of proportionality” highlighted the concept of a mathematical constant. By talking about proportional tables and asking questions like “What’s the same throughout the table and what keeps changing?” my students have already heard me say the word “constant” (with something I could point to) more times than all of last year. When we start to write equations, it will be the word “variable,” and I expect that the idea of a variable will make perfect sense in the context of the proportional relationships and tables. And by spending as much time as we are going to on proportional y = ax equations before we move on to y = ax + b, students will have a deeper understanding of the subtler differences between constants, constant terms, and coefficients.
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