Halves and Quarters
Split the shape fairly. Is that a half or a quarter?
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
Splitting shapes into equal parts, and naming a half and a quarter.
Fractions begin as fair shares of a shape, with no symbols at all. The emphasis is on equal parts, since "split into four" and "split into four equal parts" are different claims and children routinely conflate them.
- The underlying idea
- Equal partitioning precedes fraction notation.
- Where this sits in Illustrative Mathematics
- 1st grade Unit 7: Geometry and Time
- Sources
- Illustrative Mathematics / Kendall Hunt (2024) · Fuchs et al. (2013) all references →
Related measured skill: ALPACA · Early operations. What this means