Why am I starting a blog about building fluency with a deep dive into number lines?
That’s a good question.

First, it’s a topic that offers up a “hmm, why did a student do that” moment with relatively little effort. The first post in this series focused on a basic number line problem, that when given to an academically diverse set of students in grades 3-8, will generate any number of incorrect answers. In addition, the justifications for the incorrect answers will reveal that a good number of students don’t understand the basic measurement concepts that govern number line representations. When I find problems that reveal a blatant and pervasive misconception with an important mathematical idea, it makes me want to dig deeper.

Second, number line representations show up everywhere we look in grades 3-12 math and beyond. Think about it: line plots, axes on a coordinate grid, double number lines, bar models, and continuous data representations all rely on students understanding how number lines work. In addition, number lines (axes) are fundamental to the study of algebra, geometry, trigonometry, calculus, and beyond. If a student doesn’t understand the basics of how number lines work, their academic career in math is likely to be shortened or significantly undermined.

Third, it’s a topic that teachers of many grade levels can appreciate. This blog is not targeted at any specific grade level band, even though many future topics will target a specific grade level range. To start things out, I tried to pick a topic that might interest a wide spectrum of math teachers and administrators.

Finally, I wanted a math topic that didn’t carry a lot of math-ed “baggage.” For example, had I picked whole number addition and subtraction, most of us would have started with very specific opinions. By choosing number lines, an important topic that carries very little controversy, we can nail down some areas of agreement before we tackle the “gloves are coming off” topics in math-ed.

So, let’s geek out on number lines with whole numbers!