In my work with children who have trouble with math I have used various methods and strategies to develop and enhance the mathematical thinking and, among many other useful manipulatives, one of the better ways to help them is by the consistent use of number lines. Moving slowly with them from the number path to the number lines, then to double number lines and eventually even to circular number lines and number lines on a grid to form graphs. View my Masterclass Smart Number Lines

There is a large number of mathematical concepts that can be modeled in various ways. We bombard them with  stacks of counters, Cuisenaire rods, base ten blocks, and pizza slices. This may lead to students believing that they are learning many separate topics that each come with their own model, and they often fail to see the connection between topics and across models.

The number line can be the anchor we can tie other models to.

I’ll share the step-by-step progression of understanding mathematical concepts based on an increasingly sophisticated number line. We start from counting and take it to reasoning about the additive and multiplicative connections between quantities as basis for proportions, percentages, unit-conversion, and algebra. One overarching model helps students see the red thread in the relationship between operations and concepts. The number line can be the anchor to which other models may be tied

Briefly I will go over some research about the benefits of working with number lines and then we’ll walk through some examples of using number lines for the various operations.