Carry and Borrow
The four cases: add with and without a carry, subtract with and without a borrow.
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
Two-digit addition and subtraction, with and without regrouping.
Four procedures that fail separately, so they are practised separately and then interleaved: add without carrying, add with carrying, subtract without borrowing, subtract with borrowing. Interleaving matters here — mixing the four is what forces a child to read the problem rather than repeat the last method.
- The underlying idea
- Regrouping as composing and decomposing a unit of ten.
- Where this sits in Illustrative Mathematics
- 2nd grade Unit 2: Adding and Subtracting within 100 · 2nd grade Unit 7: Adding and Subtracting within 1,000
- Sources
- Illustrative Mathematics / Kendall Hunt (2024) · Rohrer et al. (2020) · Barton (2018) all references →
Related measured skills: CALF · Adding, no carry, CALF · Adding with carry, CALF · Subtracting, no borrow, CALF · Subtracting with borrow. What this means