Fractions on a number line: what children learn
In Year 3, pupils learn to recognise and use fractions as numbers: unit fractions such as ⅓ and non-unit fractions such as ⅗, with small denominators. Placing fractions on a number line is one of the clearest ways to see that a fraction is a number with a size, not only a part of a shape.
In this game the line runs from 0 to 1 and is split into equal parts, from halves up to tenths. Children move the marker to the right fraction. Only 0 and 1 are labelled, so they have to count the equal parts to find the right spot.
This topic covers the Year 3 statutory requirement in the National Curriculum in England (Number – fractions): pupils should be taught to “recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators”. Year 3 pupils are usually aged 7–8.
For families following US standards, the closest Common Core standard is 3.NF.A.2, which is taught in Grade 3.
How to play
Move the marker to the right place on the number line, then press Check. You can drag, tap the line or use the arrow keys. Each game has 8 rounds. After you press Check, a green arrow shows the correct position if you were not quite right.
Step by step
- Count the equal parts. Count the gaps between 0 and 1, not the tick marks. If there are 5 gaps, each step is one fifth.
- Read the denominator. The bottom number of the fraction should match the number of equal parts. ⅗ needs a line split into fifths.
- Count the numerator in steps. For ⅗, count three steps from 0: one fifth, two fifths, three fifths.
- Sense-check against a half. ⅗ is more than half, so it should be past the middle of the line.
Worked examples
Example 1: Put ¾ on a line split into quarters.
Working: There are 4 equal gaps. Count 3 from 0.
Answer: One step before 1
Example 2: Put ⅙ on a line split into sixths.
Working: One step from 0. It is a small fraction, close to 0.
Answer: First tick after 0
Example 3: Put 5/10 on a line split into tenths.
Working: Count 5 steps of one tenth. 5/10 is exactly halfway, the same as ½.
Answer: The middle of the line
Common mistakes and how to fix them
- Counting tick marks instead of gaps. Colour each gap as you count it, or count jumps with a finger.
- Thinking ⅛ is bigger than ¼ because 8 is bigger than 4. Compare lines split into quarters and eighths. More parts means each part is smaller.
- Placing the numerator as a whole number (putting ¾ at '3'). Remind children the whole line is only from 0 to 1.
Activities to try at home
- Fold a paper strip into halves, then quarters, then eighths, and label the folds.
- Use a measuring jug or ruler: where is ¼ of a litre, or ½ of 10 cm?
- Ask 'is this more or less than a half?' about fractions you see on food packaging.
Ideas for the classroom
- Hang a 0 to 1 washing line and ask pupils to peg fraction cards in the right places.
- Compare number lines split into different numbers of parts and find equivalent fractions, such as 2/4 and 1/2.
- Extend beyond 1, as the curriculum suggests: where would 5/4 go?
Printable worksheet
The printable worksheet uses the same question generator as the game, so it practises exactly the same skills. It comes with a separate answer sheet on the second page. Print it, or save it as a PDF from your browser's print menu.
Frequently asked questions
What is a unit fraction?
A fraction with 1 as the numerator, such as ½, ⅓ or ⅕. A non-unit fraction has a numerator bigger than 1, such as ⅗.
Why use a number line for fractions?
It shows that fractions are numbers with a position and a size, which helps children compare them and later add them.
Which denominators does the game use?
2, 3, 4, 5, 6, 8 and 10, which are the 'small denominators' that Year 3 pupils work with.
What is the US equivalent?
Common Core standard 3.NF.A.2 (Grade 3): understand a fraction as a number on the number line.