Fractions on a Number Line Worksheets

Fractions on a number line show a fraction as a distance from zero, instead of as a slice of a shape. Children learn that 3/4 is a point on the line between 0 and 1, found by cutting the line into 4 equal spaces and counting 3. Practice with fractions on a number line builds the idea that fractions are numbers, and not only pieces of a shape. The three PDFs on this page cover lines from 0 to 1 and from 0 to 2, with answer keys, and they follow standard 3.NF.A.2 of the Common Core standards for grade 3 fractions.

Why number lines?

A number line shows that a fraction is a number with its own place between whole numbers. To find 3/4, cut the space from 0 to 1 into 4 equal jumps and count 3 of them. Grade 3 children learn to show fractions on number lines (Common Core 3.NF.A.2), and the number line is the model used for fractions all the way to grade 6.

What is on this page

• Name the dot: count the jumps from 0 to the dot and the jumps in one whole.
• Label the line: write every fraction between 0 and 1.
• From 0 to 2: fractions like 5/4 that are bigger than 1.

Tip

Count the spaces, not the marks. A line from 0 to 1 with 4 spaces has 5 marks, and children who count marks often write fifths instead of fourths.

Fractions on a number line worksheets: what is in the set

There are 3 fractions on a number line worksheets on this page, and every one has an answer key except for any cut-out games. The first set names the dot, the second asks children to label every mark, and the third extends the line to 2.

Fractions on a number line: how to read one

To read fractions on a number line, count the equal spaces between 0 and 1. That number is the denominator. Then count the spaces from 0 to the point, and that number is the numerator. A line with 4 spaces shows fourths, and a dot 3 spaces from zero is at 3/4. Each space is one unit fraction long, so the line is a ruler for fractions. Wikipedia’s article on the number line explains how the same line is used for whole numbers, decimals and negative numbers. This table shows the lines that appear in the worksheets, with the length of one space if the line is 10 cm long:

The last column shows why fractions need equal spaces. On a 10 cm line cut into 8, each space is 1.25 cm, so a child measuring with a ruler has to read between the marks. Cutting a line into halves, then into halves again, is the easiest way to make fourths and eighths. The blank number lines page has printable lines that children can cut into equal spaces and label.

Number line fractions grade 3: count the spaces, not the marks

The number line fractions grade 3 standard 3.NF.A.2 asks children to represent a fraction 1/b on a number line by cutting the interval from 0 to 1 into b equal parts. The most common error is to count the marks. A line with 5 marks, counting 0 and 1, has only 4 spaces, so it shows fourths. Counting spaces is the key skill for fractions on a number line. This table shows how the number of marks changes the denominator:

The picture of the “jumps” in the diagram above helps: each jump is one unit fraction, and the point 3/4 is where the third jump lands. Children who draw the jumps as arcs rarely count marks by mistake.

Fractions greater than 1 number line: past the first whole

The third set on this page is a fractions greater than 1 number line set, with lines from 0 to 2. The pattern does not stop at 1: the jumps of 1/4 go on, and the fraction 4/4 is the same point as 1. The next mark is 5/4, which is one whole and one fourth. This table lists the fourths from 0 to 2, with each as a whole or mixed number:

Thirds work the same way, with 3/3 at 1 and 6/3 at 2:

A line from 0 to 2 with fourths has 9 marks and 8 spaces, so a child who counts all the spaces would say eighths. The denominator is the number of spaces in one whole, which is 4. The numerators go past the denominator, and children see for the first time that a fraction can be bigger than 1. Fractions on a number line do not stop at 1. This idea is the start of the improper fractions and mixed numbers on the fractions of a number and mixed numbers page.

Labeling fractions on a number line: one point, many names

When children are labeling fractions on a number line with different denominators, they find that the same point can have several names, which is why fractions on a number line are a good way to show equivalent fractions. The point halfway between 0 and 1 is 1/2 on a line with 2 spaces, 2/4 on a line with 4, and 3/6 on a line with 6. The table shows which of five common points land exactly on a mark when the line is cut into 2 to 12 spaces:

A line must be cut into a multiple of the denominator for a point to land exactly on a mark. A line with 12 spaces has a mark for every fraction in the table, which is one reason why twelfths are so useful. The same idea is the basis of the equivalent fractions page.

Fraction number line: ordering and measuring

The fraction number line is also the best way to see which fraction is greater, because the one farther to the right is the greater, so fractions on a number line are ordered from left to right. This table puts eleven fractions in order, with the decimal and the gap from the fraction before it:

Fractions can also be measured. If a number line is a 10 cm strip, some fractions land exactly on a mark of a ruler in tenths of a centimeter, and some do not:

Thirds and sixths never end as decimals, which is the first hint that some fractions are not terminating decimals, and eighths need two decimal places. The decimals worksheets page continues this idea.

Common mistakes with fractions on a number line

These are the mistakes that teachers see most often with fractions on a number line, with what went wrong and the fix:

Fractions on a number line word problems

Fractions on a number line appear in trails, rulers and races. Ask children to draw a number line for each story and mark the point before they write the fraction:

Games and activities for fractions on a number line

Children learn fractions on a number line best when they play with it. These games use things that are found at home or in a classroom:

• Human number line: tape a line on the floor, mark 0 and 1, and ask children to stand at 1/4, 1/2 and 3/4
• Hopscotch fractions: draw a hopscotch with 8 squares, and hop to 5/8
• Ribbon fractions: fold a ribbon into 4 or 8 equal parts, and mark the fractions with clips
• Clothesline: hang fraction cards on a string between 0 and 1, in order
• Number line bingo: a card with fractions, and calling cards with a dot on a line
• The number line tool: try the number line tool online, and mark a fraction between 0 and 1

Extra support and extra challenge with fractions on a number line

For children who need more support: use a paper strip folded into halves, fourths and eighths, because fractions on a number line are easier when the child can fold the line, and start with lines that already have all the marks. Count the spaces out loud, and use arcs for the jumps. Practice lines from 0 to 1 before lines to 2, and do only the first worksheet at the start.

For children who need more challenge: ask for the fraction halfway between 1/4 and 1/2, for a point that has the names 2/6 and 1/3, and for a line from 0 to 3 cut into thirds. The “Number Lines From 0 to 2” worksheet is a good challenge, and so is a line that does not start at 0.

How to tell that a child is ready to move on from fractions on a number line

1. The child counts the spaces, not the marks, to find the denominator.
2. The child reads a fraction from the number of jumps from 0.
3. The child labels every mark between 0 and 1.
4. The child places fractions greater than 1 on a line to 2.

When all four are true, move on to the equivalent fractions page or the comparing fractions page.

A 20-minute lesson on fractions on a number line

A short lesson is the best way to introduce fractions on a number line. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:

Where fractions on a number line fits across the grades

No skill stands alone. This table shows what children learn before and after fractions on a number line, with the standard that goes with each step:

The number line connects fractions with whole numbers and decimals. The whole sequence is on the fractions worksheets page.

Helping at home with fractions on a number line

Parents do not need to be experts to help with fractions on a number line. These suggestions work well, and each takes only a few minutes:

• Practice fractions on a number line with a ruler cut into eighths, and find fractions of an inch.
• Draw a number line on the sidewalk with chalk, and hop to fractions.
• Use a measuring cup: it is a number line with fractions on the side.
• Ask the child to put 1/2, 1/4 and 3/4 in the right order on a string.
• Praise “I counted the spaces”, since that is the key idea.

How to check progress in fractions on a number line

A teacher or parent can check progress with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:

A five-day plan for fractions on a number line

Most children need about a week of short sessions for fractions on a number line. This plan follows the order of the worksheets on this page:

When the plan is complete, move on to the equivalent fractions page. The whole sequence is on the fractions worksheets page.

Read the guide: Fractions on a Number Line: How to Teach Comparing and Equivalent Fractions, for the ideas and steps behind this page.