Column Subtraction: How to Teach Borrowing
Borrowing is the hardest part of column subtraction. Explaining it with stick bundles turns the mysterious "little one on top" into a clear action.
Where children stumble
The problem 52−27 requires borrowing a ten: 7 cannot come out of 2. A child without the mechanics writes a "little one on top" at random — hence chaotic answers. Borrowing gets mastered with objects before digits.
Borrowing with sticks
Step 1 — Build the number
The number 52 from sticks: five bundles of ten plus two loose. The task — remove 27, meaning two bundles and seven sticks.
Step 2 — Not enough ones
Removing 7 sticks from 2 fails. The fix — untie one bundle: a ten scatters into ten ones. Now there are twelve ones and four bundles.
Step 3 — Subtract
From 12 sticks remove 7 — five remain. From 4 bundles remove 2 — two remain. The answer is 25. The child performs the borrow by hand and sees its meaning.
Step 4 — Move to paper
The same problem now in columns. A dot above the tens — a memory of the untied bundle. The written steps mirror the stick actions one to one.
No borrowing: 47−23, 68−35, 59−17
Borrowing: 52−27, 43−18, 61−36
With zero: 50−24, 70−38
Three digits: 152−87 (after two-digit confidence)
Common mistakes
- Flip subtraction: 7 will not come out of 2, so the child computes 7−2. Sticks cure it: removing 7 from 2 visibly fails
- Forgotten reduction of the tens after borrowing — the dot above the column reminds
- Borrowing where none is needed — before each column ask: "are there enough ones?"
Checking with addition
Answer plus subtrahend equals the starting number: 25+27=52 — the solution holds. The checking habit saves test scores.
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