Grade 2 (some late grade 1, review in grade 3) · 2.NBT.5, 2.NBT.7 · the long version
How do I help my 2nd grader with borrowing?
Subtraction with regrouping (borrowing)
Your child was fine with 57 − 23. Then the homework turned into 52 − 38 and the answers went strange: 26, or 24, or a long silence. That's where subtraction starts needing the idea of a ten.
It's one idea: 52 is five tens and two ones, and when you need more ones you open a ten. Schools call that regrouping, decomposing, unbundling, or borrowing. Stuck children aren't stuck on the crossing-out; they are not yet opening a ten.
What it looks like with blocks
Put out five tens and two ones and ask for eight ones. There aren't enough, so a ten comes down and bursts into ten ones, and now taking eight is easy. Later, each cross-out on paper should remind your child of that burst.
The six ways it goes wrong
These mistakes aren't random. Researchers catalogued them decades ago, and nearly every wrong answer comes from one of a handful of rules.
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Smaller from larger
Takes the smaller digit from the bigger one in every column, whichever is on top. Never borrows.
52 − 38 they write 26 it is 14
Why children reach for it. Last year "you can't take 8 from 2" was true, and small-from-big always gives an answer. The most common pattern by far.
What replaces it. Stop talking about digits. Build 52 in tens and ones, ask for 8 ones, and let the ten split. The question is "where would eight ones come from?"
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Borrows, but never pays
Adds ten to the ones but leaves the tens alone. Looks like borrowing; the answer is ten too big.
52 − 38 they write 24 it is 14
Why children reach for it. The cross-out is the half of the move with nothing to show for it. The twelve ones are on the page; the missing ten isn't.
What replaces it. With blocks, have your child move the ten out of the tens pile before splitting it. On paper, say both halves out loud: "one ten comes down, four tens left, twelve ones."
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Borrowing through a zero
Turns the 0 into a 9 and gives the ones their ten, but never reduces the column left of the zero.
302 − 167 they write 235 it is 135
Why children reach for it. This one really is two moves: a hundred becomes ten tens, then one of those becomes ten ones. A child who learned "zero turns into nine" as a trick skips the hundred.
What replaces it. Build 302 with hundred-squares, tens and ones. No tens to open, so a hundred bursts into ten tens first, then one ten bursts. Watching that twice beats any rule about nines.
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Zero minus a number is the number
When the top digit is 0, writes the bottom digit as that column's answer.
40 − 27 they write 27 it is 13
Why children reach for it. Zero feels like nothing is there, so nothing happens, and the 7 passes straight through. Smaller-from-larger's cousin.
What replaces it. Ask it with objects: "you have no ones and I want seven. Now what?" The only honest answer is to open a ten, and then the column has a 10 on top.
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Zero minus a number is zero
When the top digit is 0, writes 0 for that column.
40 − 27 they write 20 it is 13
Why children reach for it. The other reading of zero: nothing there, so the answer is nothing. Children often hold this one and the previous one on different days.
What replaces it. Same move: a ten has to open. Then ask "can 20 really be left? 27 plus 20 is 47." Checking by adding back is a habit worth starting.
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Within twenty, digit by digit
Treats 13 − 5 as two separate digits: 3 and 5 give 2, the 1 stays. Smaller-from-larger before there were columns.
13 − 5 they write 12 it is 8
Why children reach for it. Children moved to written subtraction before they could take 5 from 13 in their head. Columns are hopeless until going back through ten is easy.
What replaces it. Step back from columns. Practise taking away past ten with fingers or a ten-frame: 13 take 3 is 10, then 2 more is 8. Come back to two digits once that's quick.
The five-minute check
A short run of problems on a phone or tablet, chosen as your child answers. If one of the six patterns is behind their mistakes, the check names it. Nothing to install, nothing stored.
Hand the phone over, or play it here. When it says all done, take it back and tap see what we found.
Start the five-minute checkWhat the school is probably doing
- Regrouping / decomposing
- The written method, through tens and ones first; the cross-outs record a ten being opened.
- Counting up on a number line
- From 38, jump 2 to 40, then 12 to 52: the difference is 14. No borrowing; it's how adults make change.
- Expanded form
- 52 − 38 as (40 + 12) − (30 + 8): the regrouping done in the open first.
- Base-ten blocks and drawings
- Sticks for tens, dots for ones. If your child draws these on homework, the lesson is working.
They're not the new way versus the right way, just one idea at different distances from the objects. Whichever way you learned, insist on knowing where the ten went.
Questions parents ask
What grade is this?
Grade 2 in the US (2.NBT.5), three-digit later the same year (2.NBT.7). Some schools start late in grade 1; most children are still settling it in grade 3.
Is regrouping the same as borrowing?
Yes. The word changed because nothing gets given back: a ten is opened, not lent. If borrowing works at your kitchen table, use it.
My child crosses out everything on the page. Is that bad?
Crossing out is the ritual; opening a ten is the idea. Crossing out every column, needed or not, is the ritual without the idea. Back to objects for a few days.
Should I teach it the way I learned?
Sure. The method you learned is still the method. Just build the number with objects first and ask "where did the ten go?" every time.
They can do it with blocks but not on paper.
That's the normal order. The gap closes when the two stay together: do a problem with blocks and write each step as it happens.
How long should we practise?
Five to ten minutes most days beats an hour on Sunday. Three or four problems done slowly with blocks are worth more than a page.
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