Fraction number line

What the number line shows

A number line shows a fraction as a single number with its own place, not just as a piece of a shape. Choose a line from 0 to 1, 0 to 2 or 0 to 3 and split each whole into 2, 3, 4, 5, 6, 8, 10 or 12 equal parts. Drag the purple point to any mark, or use the arrows. The readout names the point as a fraction, as a mixed number once it passes 1, in simplest form when that is different, and as a decimal. When a decimal goes on forever, such as for 1/3, it is rounded and marked with ≈.

Why a number line matters

Children who only see fractions as slices of pizza often struggle to believe 5/4 is a real number, since you cannot shade 5 of the 4 slices of one pizza. On a line, 5/4 is simply one more jump of a fourth past 1. The line also connects the different ways of writing a number: 5/4, 1 1/4 and 1.25 are the same point. Counting jumps from 0 makes both numbers in a fraction meaningful. The denominator tells you how many equal jumps make 1, and the numerator tells you how many jumps to take.

Common mix-ups

• Counting tick marks instead of spaces. A line from 0 to 1 cut into fourths has 5 marks but only 4 spaces, and each space is 1/4.
• Counting the mark at 0 as the first jump. The first jump ends at 1/4.
• Thinking fractions only live between 0 and 1. Set the line from 0 to 3 to see 7/4, 2 and 11/4 on the same line.
• Reading 0.5 as 1/5. Put the point on 5/10 and the readout shows 1/2 and 0.5: five tenths, not one fifth.

A 10-minute activity

• Minutes 1 to 3: set 0 to 1 with 4 parts. The child drags the point to each mark and says the fraction aloud: one fourth, two fourths, three fourths, four fourths or 1 whole.
• Minutes 4 to 6: switch to 0 to 2 and keep counting past 1. Ask the child to say 5/4 as a mixed number before checking the readout.
• Minutes 7 to 9: press Challenge three times. The labels turn off, so the child places each number by counting jumps and presses Check.
• Minute 10: ask which is closer to 2, 7/4 or 9/4, and how the line shows it. They are both 1/4 away.

Where it fits by grade

• Grade 3: understanding a fraction as a number on the number line by marking off lengths of 1/b from 0 (Common Core 3.NF.A.2).
• Grade 4: fractions greater than 1 and mixed numbers, and decimal notation for fractions with denominator 10 (4.NF.C.6).
• Grade 5: placing fractions and mixed numbers to estimate sums and differences and check answers.
• England: Year 3 pupils count up and down in tenths, Year 4 pupils count in hundredths, and Year 5 pupils convert between mixed numbers and improper fractions.

Learning more

Fractions on a number line appear throughout Eurekami's lessons, from first steps with unit fractions to mixed numbers. The skill map shows which fraction skills a child has mastered, and Daily Practice mixes in short review questions so older skills stay fresh.