Mixed Number Line
Past one and under two. Where does 7/4 go?
For grown-ups
- How long: 5 to 10 minutes is plenty. Short and frequent beats long and occasional — the early-numeracy trials with the largest effects ran eight weeks or less.
- The strategy to reinforce: “Whole first” — Decide which two whole numbers it sits between, then split that gap. If they stall, remind them of this rather than giving the answer.
- 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.
- On the timer: it is off unless you turn it on, and it is never needed. Use it only once the skill is comfortable, never to introduce it.
- 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
Placing mixed numbers and improper fractions on a 0–2 line.
An improper fraction on a nought-to-two line is the clearest test of whether a child treats a fraction as a number: 7/4 has to go somewhere specific, and "seven over four" gives no help in finding it.
- The underlying idea
- A fraction greater than one still has a single position on the line.
- Where this sits in Illustrative Mathematics
- 5th grade Unit 2: Fractions as Quotients and Fraction Multiplication · 5th grade Unit 3: Multiplying and Dividing Fractions
- Sources
- Fuchs et al. (2013) · Schneider et al. (2018) · Institute of Education Sciences / What Works Clearinghouse (2021) · Riconscente (2013) all references →
Related measured skill: MagPI · Number line estimation. What this means