Composing and Decomposing Tens

The four cases: adding with and without composing a ten, subtracting with and without decomposing one.

Book Add and subtract within 100 2.NBT.B.52.NBT.B.7 CALF · Adding, no carry CALF · Adding with carry CALF · Subtracting, no borrow CALF · Subtracting with borrow

▤ Print this All of 2nd grade

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 composing or decomposing a ten.

Four procedures that fail separately, so they are practised separately and then interleaved: adding with and without composing a ten, subtracting with and without decomposing one. Interleaving matters here — mixing the four is what forces a child to read the problem rather than repeat the last method. The words are Illustrative Mathematics’: its grade 2 lessons are titled “How Do We Compose a Hundred?” and “Compose Three-digit Numbers”, and carry, borrow and regroup appear in none of them. Compose and decompose also name what actually happens to the ten, where borrowing implies a debt that is never repaid. The trick box keeps one bridge to the older words, because the adult holding the sheet was taught those.

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