The Standard Algorithm
The written methods, at full size. Two digits by two, and long division.
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 multi-digit numbers and dividing by two digits, fluently.
Grade 5 is where Illustrative Mathematics expects the standard algorithms to become fluent, having built them from partial products in grade 4. This book assumes that groundwork and drills the compressed form — with a partial-product page every third item so the compression stays connected to what it compresses.
- The underlying idea
- The standard algorithm is the endpoint of a progression, not the starting point: it compresses partial products into a notation that only makes sense once the parts are understood.
- Where this sits in Illustrative Mathematics
- 5th grade Unit 4: Wrapping Up Multiplication and Division with Multi-Digit Numbers
- Sources
- Illustrative Mathematics / Kendall Hunt (2024) · Fyfe et al. (2014) · Codding et al. (2011) · Fuchs et al. (2012) all references →
Related measured skills: CALF · Multi-digit ×, CALF · Multi-digit ÷, ALPACA · Elementary operations. What this means