Teaching with number lines: what the research says, and how to use them from pre-K to 8th grade

What it is

A number line is a straight line with numbers placed at equal intervals. It shows two things that symbols alone don't: the order of numbers and the size of the gaps between them. 7 is after 6, and it's the same distance after 6 as 6 is after 5. Halfway between 0 and 1 is 1/2.

Teachers use several kinds:

• Marked number lines, with every whole number labeled, for counting and early addition.
• Open (empty) number lines, with only the numbers a student needs, for showing jumps in mental addition and subtraction.
• Fraction and decimal number lines, to show that fractions are numbers with a size, not just pieces of a pizza.
• Vertical number lines and thermometers, for negative numbers.
• Linear board games, where moving along a numbered path is a playful number line.

The number line is one of the six practices the What Works Clearinghouse rates Strong for elementary math intervention, alongside systematic instruction, precise math language, concrete and semi-concrete representations, deliberate teaching of word problems, and timed fluency activities.

Why it works

Understanding math depends on knowing how big numbers are, not just how to say them. A child who knows that 8 is much bigger than 2 can judge whether an answer makes sense; a student who places 1/3 and 1/4 correctly on a line won't think 1/4 is bigger because 4 is bigger than 3. The number line makes size visible and keeps the same picture across whole numbers, fractions, decimals and negatives.

Robert Siegler and Geetha Ramani's experiment shows how much a simple number line experience can matter early. Preschoolers from low-income families started behind better-off peers in estimating where numbers fall. After four 15-minute sessions playing a simple board game with numbers in a straight line, the difference disappeared. Children who played the same game with colors instead of numbers didn't improve, so it was the numbers in a line, not the game, that mattered.

For older students who struggle, the What Works Clearinghouse's 2021 intervention guide, from a panel chaired by Lynn Fuchs, rates using the number line to facilitate learning of concepts and procedures, build grade-level understanding and prepare for advanced math as Strong. The IES guide on organizing instruction rates connecting abstract and concrete representations of concepts as Moderate; the number line is a representation that sits between counters and symbols.

How to start, by grade

Examples

• First to 10 board gamePre-K–Kindergarten

  A strip of ten numbered squares in a straight line. Children spin a 1 or a 2 and move, saying the numbers on the squares they land on ("four, five"). Four short sessions over two weeks. It's the kind of game Siegler and Ramani tested, and it costs a sheet of paper.

• Jumps on an open number lineGrades 1–3

  For 38 + 25, a student draws a line, writes 38, jumps 20 to 58, then 5 to 63. The drawing makes the strategy visible to the teacher and to classmates, and shows why the answer is reasonable.

• Where does it go?Grades 3–5

  On a line from 0 to 2, students place 3/4, 1/2, 5/4 and 2/3, then explain their order. Students who think 1/4 is bigger than 1/3 have to confront where each one actually lands.

• Temperature and integersGrades 6–7

  A vertical number line drawn as a thermometer. "It's −3 degrees and the temperature rises 8 degrees." Students move up and land on 5. Then "falls 10 degrees" from 5 lands on −5. The moves build intuition before rules.

Common mistakes

Uneven spacing.

A number line only works if equal steps are equal distances. Model careful spacing, and use printed or digital lines when accuracy matters.

Fractions only as pie pieces.

Area models are useful, but they hide that fractions are numbers. Put fractions on number lines from the start of fraction teaching.

Using it once and dropping it.

The number line's value grows when it's the same model across whole numbers, fractions, decimals and negatives. Keep coming back to it.

Skipping zero.

Lines that start at 1, or don't show 0, hide the fact that a number's position measures its distance from zero. Include zero, especially for fractions, where 0 to 1 is the whole story.

Counting the lines instead of the spaces.

Young students often count tick marks rather than jumps. Teach that each jump is one, and start from zero.

Time and cost

Time: a few minutes inside existing lessons; a few short game sessions for young children.

Money: nothing. Masking tape on the floor, a printed line, a paper board game, or the free tool below.

Training: low to moderate. Using number lines well for fractions and integers is a skill worth some planning time, and it helps if every grade in a school draws them the same way, so students meet one familiar picture as the numbers get harder.

Debates and open questions

How strong is the evidence for whole classes? The Strong rating is from a guide about intervention for elementary students who struggle, and the board game study is a small experiment with preschoolers. Both point the same way, but more classroom trials would make the case for every class.

Is it the number line or the conversation? Much of the value may come from the talk around the line: estimating, explaining, comparing. The studies on this card don't separate the two.

Which kind of number line? Marked, open, fraction and double number lines each suit different tasks. The guide recommends the number line broadly; we haven't added studies comparing kinds.

Tools that do it

Free, on this site, nothing to sign up for. Class lists stay in your browser.

• Number line: a projector number line for whole numbers, fractions, decimals and negatives.
• Blank number lines: printable lines for students to label and use.
• Fraction bars: line up fraction bars with a number line to connect pieces and positions.
• Hundreds chart: pair with an open number line for adding tens and ones.
• Dice roller: roll for moves in a linear number board game.

Questions teachers ask

What's an open number line?

A line with no numbers marked except the ones a student needs. It's used to show mental addition and subtraction as jumps (for example, from 38 jump 20 to 58, then 5 to 63).

Why teach fractions on a number line?

Because it shows that fractions are numbers with a size and a place among other numbers, which pie pictures don't. It also makes comparing fractions and seeing equivalent fractions easier.

Do board games really help young children with math?

In Siegler and Ramani's experiment, four short sessions of a straight-line number board game closed the gap in number estimation between preschoolers from low-income families and their better-off peers; a color version of the game didn't.

How do I use a number line for negative numbers?

Extend the line to the left of zero, or draw it vertically like a thermometer. Model adding as moving right (or up) and subtracting as moving left (or down), and use temperature, sea level or money owed as contexts before introducing rules.

Is the number line just for struggling students?

The Strong rating comes from a guide about intervention, but the number line is used across math teaching for all students, especially for fractions and negative numbers.