Number Lines for Kids: Free Printable Number Lines and the Open Number Line

A number line is a straight line with numbers marked at equal spaces, starting at 0, so every number sits as far from 0 as it is big: 3 is three equal steps from 0. On a number line you count the jumps between the marks, not the marks themselves, and that is what makes it a tool for adding and subtracting. Three jumps to the right of 5 land on 8, so 5 + 3 = 8.

The free printable number lines here run from 0 to 10, 0 to 20, and 0 to 100, with blank and open lines, missing-number puzzles, and jump practice with answer keys, all in black and white with no sign-up. Schools start young children on a number path of numbered squares and bring in the number line by second grade. There the open number line, a line with no marks at all, is a common way to add and subtract within 100.

What is a number line?

A number line is a straight line with a mark at every whole number, the marks an equal distance apart, and 0 at the left end. Each mark has its numeral under it, and an arrow at the right end shows that the numbers keep going. A number is a distance from 0: 7 is seven equal steps along. That is why the spaces must be equal, and why the line starts at 0, where the first step begins. The Common Core standard 2.MD.B.6 asks second graders to “represent whole numbers as lengths from 0 on a number line diagram with equally spaced points”.

A ruler is a number line too: the Common Core Standards Writing Team, in its Progressions for the standards, calls rulers, yardsticks, and measuring tapes “special number line diagrams”. Bigger numbers sit farther right, so comparing two numbers means finding the one farther along.

A number path is not a number line, and a young child usually meets the path first. A number path is a row of squares numbered from 1 to 10, like the track on a board game. On a path a child counts squares; on a line a child counts jumps between marks. The Progressions call the path “a count model, not the measurement model”, because its numbers “count separated things rather than consecutive length units”. A child meets it in a number path game or the counting strips a kindergartner fills in.

Some classrooms call a number line a number track, though strictly a track is a path. A line with no marks is an empty, blank, or open number line.

Free printable number lines: 0 to 10, 0 to 20, 0 to 100, and blank

The free number lines come as seven PDFs: four lines to keep on the table, and three practice sheets with answer keys.

• Number Line 0–10, 3 pages. A long 0–10 line and six desk strips. Print this one for a kindergartner counting on.
• Number Line 0–20, 3 pages. A 0–20 line with longer marks at 5, 10, 15, and 20, and four desk strips. Print this one for first-grade adding and subtracting.
• Number Line 0–100, 4 pages. A 0–100 line by tens, and the same line by ones in five strips that tape end to end. Print this one for second grade.
• Blank Number Lines, 4 pages. Lines with 11 or 21 marks and no numbers, and open lines with no marks. Print these when homework says “draw a number line”.
• Number Line Missing Numbers, 6 pages. Lines with numerals left out, some starting at 30, 57, or 88, and a key. Print this one after the 0–20 line.
• Adding and Subtracting on a Number Line, 6 pages. Problems within 10, then 20, each on its own printed line for your child to draw the jumps, with a one-page key.
• Open Number Line, 6 pages. Two-digit adding and subtracting on open lines, with a one-page key.

Every line starts at 0, including for parents who searched for a 1–20 line. The 0 is where the first jump starts, so a line that starts at 1 has lost a space. Tens are marked with longer, heavier ticks, never with color, so every line prints in black and white. None of the problems is numbered, and each key is laid out like the page it answers.

Free PDF · no sign-up

Free printable number lines

Seven free PDFs in black and white, with no account and no email, in teaching order: number lines from 0 to 10, 0 to 20, and 0 to 100, blank and open lines, then missing numbers, jumps, and open number line practice. Print the 0–10 line for kindergarten, the 0–20 line for first grade, and the 0–100 line for second grade. The three practice sheets each have an answer key, and every PDF ends with a page of instructions for grown-ups on why, what for, and how to use it.

1. 1Number Line 0-10 (PDF)11 numbers · 3 pagesDownload
2. 2Number Line 0-20 (PDF)21 numbers · 3 pagesDownload
3. 3Number Line 0-100 (PDF)101 numbers · 4 pagesDownload
4. 4Blank Number Lines (PDF)15 number lines · 4 pagesDownload
5. 5Number Line Missing Numbers (PDF)98 missing numbers · answer key included · 6 pagesDownload
6. 6Adding and Subtracting on a Number Line (PDF)12 problems · answer key included · 6 pagesDownload
7. 7Open Number Line (PDF)24 problems · answer key included · 6 pagesDownload

What grade uses number lines?

Children meet the number line in stages: a number path in kindergarten, counting on and back along a 0–20 line in first grade, and the number line diagram itself in second grade, where the Common Core first names it in 2.MD.B.6.

Grade	What children do	Common Core	Texas (TEKS)
Pre-K and kindergarten	Count on a number path and in board games; count forward from any number	K.CC.A.2 (counting forward; no number line standard)	None for the line
1st grade	Count on and back to add and subtract within 20, often on a 0–20 line or path	1.OA.C.5, 1.OA.C.6 (counting on; no line named)	1.2(F), open number lines
2nd grade	Show numbers as lengths from 0, and sums and differences within 100, on a line	2.MD.B.6; strategies for 2.NBT.B.5	2.2(E), 2.2(F), 2.9(C)
3rd grade	Round between tens, and place time intervals and fractions on a line	3.MD.A.1, 3.NF.A.2	3.2(C), 3.3(B), 3.7(A)

The Common Core waits on purpose. Its writing team says in the Progressions that number line diagrams use length units, “which are more difficult to see and count than are objects”. It also says the standards follow a National Research Council recommendation not to use number lines in kindergarten and first grade.

Texas starts sooner: its first graders order numbers on open number lines (1.2(F)). Its second graders locate a number on an open number line and name the number at a point on a number line (2.2(E), 2.2(F)), the year Common Core brings in the number line diagram. First-grade classrooms in other states use 0–20 lines for counting on too, so a first grader bringing one home is normal.

Fractions on a number line are a third-grade skill.

The hundreds chart is the other big tool of these grades, and it shows tens where a line shows distance. A kindergartner who cannot use a number line yet is on time.

How to use a number line with your child

Use a number line with your child in routines of a few minutes, in the order a child meets them: walk it, find a number, count on, count back, then find the missing numbers. Start with tape on the floor, then move to the printed 0–10 or 0–20 line.

1. 1

   Walk a floor number line

   Put painter's tape on the floor and mark it from 0 to 10, one big step apart. Your child stands on 0 and steps along, saying each number as they land on it. A child who walks to 6 has taken six steps from 0, which is what 6 means on a number line.

2. 2

   Find a number

   Ask your child to put a finger on 7, then ask which number is one jump before 7 and which is one jump after it. Ask for numbers in a mixed order, so your child finds each one by where it sits rather than by reciting from 0.

3. 3

   Count on from any number

   Start on 6 and jump four times, saying 7, 8, 9, 10 as the finger lands. Never say the 6: it is where the jumps start. Counting forward from a given number is the Common Core kindergarten standard K.CC.A.2, and counting on to add is first grade's 1.OA.C.5.

4. 4

   Count back

   Start on 10 and jump back one mark at a time to 0, saying each number as the finger lands. Then start on 20. Texas asks kindergartners to count forward and backward to at least 20 (TEKS K.2(A)).

5. 5

   Find the missing numbers

   On the missing-numbers sheet, some numerals on each line are left blank, and some lines start at 30, 57, or 88 instead of 0. Your child works out each blank from where it sits. Texas asks second graders to name the whole number that corresponds to a specific point on a number line (TEKS 2.2(F)).

Finding the number one jump before or after 7 is one more and one less on a line. Fingers work as well as a line for small numbers. The line lets a child start at 8 and count on 5 without holding up 8 fingers first: the step from counting on fingers to counting on in the head.

How do you add and subtract on a number line?

To add on a number line, start on the first number and jump right; to subtract, start on the first number and jump left. Count the jumps, not the marks, and the answer is where you land. Each jump is one step of the same size, so three jumps add 3 wherever they start. Here is how a child says each problem aloud:

• 5 + 3. “Start on 5. Jump to 6, jump to 7, jump to 8. Three jumps, so 8.”
• 12 − 4. “Start on 12. Jump back to 11, 10, 9, 8. Four jumps back, so 8.”
• 8 + 5, making ten. “Jump 2 to get to 10, then 3 more to 13.” Splitting the 5 into 2 and 3 to reach 10 is the making ten strategy that first grade’s 1.OA.C.6 names, and two ten frames show the same step with counters.
• 13 − 9, as a distance. “How far is it from 9 to 13? Start on 9 and count up: 4 jumps.” Counting up to subtract uses the relationship between addition and subtraction, another strategy 1.OA.C.6 lists.

When a word problem compares two amounts, a tape diagram shows the difference as the extra piece of the longer of two bars.

On homework, count your child’s arcs and check that each spans one space. The Adding and Subtracting on a Number Line sheet practices jumps within 10, then 20, and its key draws them.

What is an open number line?

An open number line is a line with no marks and no numbers until the child puts them there. The child writes only the numbers a problem needs and draws jumps of any size, usually tens and ones. It is also called an empty or blank number line.

Take 38 + 25. Write 38 at the left end, jump 20 to 58, jump 2 to 60, then jump 3 to 63. Another child jumps 2 to 40 first, then 20 to 60, then 3 to 63. Both are right, and choosing the jumps is the point. The spaces do not have to be to scale, only in order: 58 sits to the right of 38 and to the left of 60.

The open line lets a child add and subtract within 100 by tens and ones, which is what second grade’s 2.NBT.B.5 means by “strategies based on place value”. It comes from the Netherlands. In a study of 275 Dutch second graders, Klein, Beishuizen, and Treffers found the empty number line “a very powerful model for the learning of addition and subtraction up to 100”. Texas starts it in first grade (TEKS 1.2(F)); in Common Core it goes with second grade’s two-digit adding and subtracting.

A marked, or closed, number line is for reading where numbers sit and for jumps of one; an open number line is for working out a sum. The Open Number Line sheet’s key shows one way to jump, and a different route to the same number is right too.

Why do schools teach number lines instead of the old way?

Schools teach the number line because it shows what adding and subtracting are: moving along, and the distance between two numbers. Here is 52 − 27 done the written way parents learned and on an open number line.

Step	The old way	On an open number line
1	Write 52 above 27, lining up the digits	Write 27 at the left and 52 at the right
2	2 is less than 7, so borrow a ten: 12 − 7 = 5	Jump 3 from 27 to 30
3	4 − 2 = 2 in the tens	Jump 20 from 30 to 50, then 2 to 52
Answer	25	3 + 20 + 2 = 25

The same 52 − 27 with base ten blocks needs one rod traded for ten units. A child can also start on 52 and jump back 20, then 7. A child who counts up from 27 to 52 can see the answer is a little more than 20, so an answer of 35 or 79 looks wrong straight away. The What Works Clearinghouse practice guide Assisting Students Struggling with Mathematics (2021) makes the number line one of its six recommendations for teaching children who struggle with math. How well children place numbers on a line goes with how well they do in math. A meta-analysis by Michael Schneider and colleagues found a correlation of .44 across 263 effect sizes, in samples with average ages from 4 to 14. That is a correlation, not proof that number lines raise math scores. Robert Siegler and Julie Booth found that between kindergarten and second grade, children’s estimates of where numbers go on a 0–100 line shifted from bunching the larger numbers together to spacing them evenly.

The number line comes before the old way, not instead of it. The Common Core expects the standard written method in fourth grade (4.NBT.B.4, “using the standard algorithm”), after the strategies. Why the rest of school math looks different now is the subject of new math explained.

Number line games

Number line games need only a printed line, painter’s tape, a die, or a few cards, and each one has a child saying where they land.

• Floor hop. Roll a die, jump that many spaces along a taped 0–20 line, and say where you land. First to 20 wins.
• Guess my number. Think of a number on the 0–20 line. Your child guesses, and you answer “higher” or “lower”, which makes it a comparing numbers game.
• Race to 20 and back. Race two counters to 20 with one die, then race back to 0, saying each subtraction aloud: “I am on 14 and rolled 3, so 11.”
• Clothesline estimation. Hang a string between a card marked 0 and a card marked 100, and ask your child where a card for 50 goes, then 25 and 90. Placing numbers on an empty line is the number line estimation task researchers measure.

Common number line mistakes (and what to do when it is hard)

The number line mistake to watch for first is counting the mark you start on, and the Progressions name the cause: children “attend to tick marks or numbers instead of lengths”. Each fix follows its mistake.

• Counting the starting mark. For 5 + 3 the child says “5, 6, 7” and lands on 7. Put a finger on 5 and say a number only when the finger lands.
• Jumping the wrong way to subtract. The child jumps right for 12 − 4. Say “take away means go back toward 0”.
• Starting at 1, or drawing uneven spaces. Start every marked line at 0, and use a printed line until even spacing is automatic. An open line may be uneven; a marked one may not.
• Reading a 0–100 line by tens as if each mark were 1. The child counts three marks from 0 and says 3, not 30. Read the numbers at the marks first.
• Losing count of big jumps on an open line. Write the size of each jump above its arc, then add those numbers.

When the number line is hard, make it easier instead of giving it up. Go back to a number path, where your child counts squares, or to the floor line or a ruler, and shorten the line to 0–10. If counting on is still hard after a few weeks of short practice, mention it to your child’s teacher, who can say what comes next.