Long Multiplication
Break it into parts, multiply, put it back together.
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
Multiplying a two-digit number by one digit, then by two digits.
Concreteness fading: the area model is visible for the early pages, then withdrawn, so partial products are understood before they become a written ritual. Two-digit by one-digit is secure before two-digit by two-digit appears.
- The underlying idea
- Partial products, with the area model faded once the structure is understood.
- Where this sits in Illustrative Mathematics
- 4th grade Unit 6: Multiplying and Dividing Multi-digit Numbers
- Sources
- Illustrative Mathematics / Kendall Hunt (2024) · Fyfe et al. (2014) · Barton (2018) all references →
Related measured skills: CALF · Multi-digit ×, ALPACA · Elementary operations. What this means