What do rulers, tape measures, bathroom scales, and thermometers all have in common?

They’re examples of number lines!

Number lines are not only essential to the tools we use every day, but they’re also an important sense-making model for early elementary and secondary mathematics. When students draw a number line, they’re learning the foundation of number sense and linear space, which are concepts that form the basis for more complex mathematical subjects like pre-algebra, algebra, geometry, and statistics.

How can teachers use this tool in the primary grades to help students develop a linear view of numbers and prepare them for upper-level math understanding? Elizabeth Peyser, national director of content and implementation at Curriculum Associates, and co-author Jessica Babo recently published a paper on the importance of the number line called *Linking Number Sense to Linear Space* in the National Council of Teachers of Mathematics (NCTM) journal, *Mathematics Teacher: Learning and Teaching PK–12*. Check out their hands-on tips for using this important tool in the classroom!

## In Kindergarten, Use Number Paths to Connect Linear Space with Quantity

In kindergarten, students begin working with numbers and start to develop an understanding of positioning and how to establish a linear view of numbers using a number path. They learn to count by ones and tens and are also introduced to the position of a number relative to 100. This is an important time for learners to use tangible objects and manipulatives to count, group, and sort so they can arrange what they’ve counted and begin to work with a number path. When students cover a box on the number path with an object, for example, they begin to see that the quantity takes up the whole space. This connection of quantity to linear space is an important foundation for understanding number lines.

## In First Grade, Use Connecting Cubes to Help Students Understand Quantities

In first grade, teachers can further develop this linear view of numbers by providing activities that use connecting cubes and a number path. Ask students to take four cubes and place them over the first four spaces of a number path. As students follow the number path, they’ll start at the far-left edge of the "1" box and should say the quantities aloud as they place down each cube. This will help them understand that they must travel the entire length of each box to have that quantity.

## In Second Grade, Introduce the Number Line with Zero

While the number path taught in kindergarten and first grade does not include a box for zero—that would imply that zero has a quantity—an important transition takes place in second grade when students are formally introduced to the number line. Teachers should explain that with a number line, the far-left edge of the "1" box serves as the zero starting point.

## Use Connecting Cubes to Help Students Understand Spatial Distance

Connecting cubes are also an effective way to help learners in the primary grades create number lines of equal spaces. Ask students to lay connecting cubes on a piece of paper, draw a line underneath, and use the edges of the boxes to make tick marks to mark the boundaries of the spaces. Students should then use the number line to count quantities. Have them start at the far-left edge of the number line—or the first tick mark—travel the whole space, and land on the tick mark called "1." By connecting number path spaces to the spaces between tick marks, students will begin to understand that "0" to "1" is one whole space, "1" to "2" is one whole space, etc.

## Introduce Fractions Using the Number Line

When students begin working with fractions on the number line, they should mark where the whole number begins and ends, and they can then partition that whole into equal parts. Students should start by using the whole number marked by "0" and "1" on the number line and define it with tick marks. Learners can then partition that whole into three equal spaces for thirds or four equal spaces for fourths. When students start at zero and travel one piece of size 1/4, they land on the tick mark called "one-fourth."

These hands-on learning techniques in the primary grades will help teachers solidify students’

understanding of the number line and lay the groundwork for secondary math concepts like fractional computations, graphing on coordinate planes, and ratios and proportions. These all lead to linear algebra—which is about a line!

### Interested in learning more about the development of number lines?

Read *Linking Number Sense to Linear Space* in the NCTM journal, *Mathematics Teacher: Learning and Teaching PK–12*.

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