Grown-ups, when was the last time you played with a number line?

I always carry paper and pencils with me so I can draw number lines, area models, and graphs. I often find myself engaged in exciting math conversations (yep, even at the airport, on planes, or in restaurants) that necessitate the use of these simple, yet powerful, visual models!

As a sense-making model for early elementary and secondary mathematics, there’s just no topping the humble number line. When students draw a number line, they’re learning the foundation of number sense and linear space, forming the basis for more complex mathematical subjects like pre-algebra, algebra, geometry, and statistics.

How can you use this tool in the primary grades to help your students build that critical foundation? Let's break it down with some hands-on tips for using number lines 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 a linear view of numbers. By using tangible objects and manipulatives to count, group, and sort, students 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 key for understanding number lines.

## In first grade, use connecting cubes to help students understand quantities.

In first grade, you can further develop this linear view of numbers with activities using 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 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. Explain to your students that with a number line, the far-left edge of the “1” box serves as the starting point zero.

## In second grade, use connecting cubes to draw equally spaced number lines.

Connecting cubes are also an effective way to help young learners 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. Start at the far-left end of the cube train, draw a tick mark, and label it “0.” Students have to travel the entire cube to the seam with the next cube, and that’s where they will place the tick mark labeled “1.”

By connecting number path spaces to the spaces between tick marks, students begin to understand that “0” to “1” is one whole space, “1” to “2” is one whole space, etc.

## In third grade and above, 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. Have them start by using the whole number marked by “0” and “1” on the number line and define it with tick marks. Next, they 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 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, after all, about a line!

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

Read *Linking Number Sense to Linear Space* by Elizabeth Peyser and co-author Jessica Babo in the National Council of Teachers of Mathematics journal, Mathematics Teacher: Learning and Teaching PK–12.