Fractions on a number line: what children learn
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 labeled, so they have to count the equal parts to find the right spot.
Supports part of Common Core 3.NF.A.2. This focused game does not cover the entire standard.
Common Core connection: 3.NF.A.2. This is focused practice for part of the standard.
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. Color 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 liter, 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 students 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?
Free printable game and worksheet
The free printable starts with a game sheet, such as a color-by-answer picture, an answer maze or a secret-code joke, followed by a worksheet. Both use the same checked questions as the online game, and the answers are on the last page. Print it, or save it as a PDF from your browser’s print menu.
Open the free printable game and worksheet
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.
How should I choose this game for my learner?
Supports part of Common Core 3.NF.A.2. This focused game does not cover the entire standard.
What is the US equivalent?
Common Core standard 3.NF.A.2 (Grade 3): understand a fraction as a number on the number line.