Fraction Number Line
Halves, thirds, fourths and eighths — find them on the line.
New to fractions? Start here.
A short lesson where one bar gets cut up while you watch, so you can see for yourself that one half and two quarters are the same amount. About about 5 minutes.
Show me how fractions work →
Why are one half and two quarters the same?
For grown-ups
- How long: 10 to 15 minutes is plenty. Short and frequent beats long and occasional — the early-numeracy trials with the largest effects ran eight weeks or less.
- When they get one wrong: the page shows the working. Read it together rather than moving straight on. Feedback that explains is worth several times more than feedback that only marks right or wrong, and that gap is wider in maths than in any other subject.
- Not timed: thinking time is the point of a book. Let silences run.
- Print it too: doing the same problems on paper a few days later is worth more than doing twice as many today.
What this practises
Locating a fraction on a number line, building it from unit fractions, and seeing which fractions are equivalent.
A fraction placed on a number line is a fraction understood as a number, rather than as one whole number stacked on another. That shift is the single best predictor of later fraction competence, and the number line is the representation that produces it — which is why this is the flagship of the site.
- The underlying idea
- Fraction as a number with a position, not as one whole number over another.
- Where this sits in Illustrative Mathematics
- 3rd grade Unit 5: Fractions as Numbers
- Sources
- Fuchs et al. (2013) · What Works Clearinghouse (2020) · Institute of Education Sciences / What Works Clearinghouse (2021) · Schneider et al. (2018) all references →
Related measured skills: MagPI · Number line estimation, ALPACA · Elementary operations. What this means