Last updated 2026-09-22. Written by the TernQuest team. This guide is for parents of 2nd graders (and 3rd graders still shaky on it) who have watched a subtraction problem end in tears and want a way to teach it that makes sense instead of a trick to memorize.
What is regrouping in subtraction?
Direct answer: Regrouping is trading one ten for ten ones (or one hundred for ten tens) so there are enough in a column to subtract. In 52 minus 17, you cannot take 7 ones from 2 ones, so you break one of the 5 tens into ten ones: now you have 4 tens and 12 ones, and 12 minus 7 is 5, 4 tens minus 1 ten is 3 tens, answer 35. Nothing is borrowed and nothing is owed; a ten was simply exchanged.
By the end of 2nd grade, children are expected under the California Common Core standards to add and subtract within 100 fluently and within 1000 using place-value strategies, though your school's pacing may differ. Regrouping is where many 2nd graders first hit a wall, and the wall is almost never the procedure. It is place value.
Quotable version: "Regrouping is a trade, not a borrow: one ten becomes ten ones, and the number does not change."
Why do you have to teach place value first?
Direct answer: Because regrouping only makes sense if the child knows that the 5 in 52 means five tens, not five. A child who sees 52 as "a five and a two" has no reason to believe that crossing out the 5 and writing a small 1 next to the 2 is anything but magic. When the procedure is taught before the idea, it is memorized, then forgotten, then guessed at.
The check before you start
Ask your child: "In the number 52, what does the 5 mean?" If the answer is "five tens" or "fifty," go ahead. If the answer is "five," stop and spend a few days on place value with objects first; place value explained for parents has the bundling activities. You are not wasting time; you are removing the reason for the tears.
How do you teach it with blocks?
Direct answer: Model the top number with tens rods and ones cubes (or bundles of ten straws and single straws), then physically try to take away the bottom number. When there are not enough ones, trade one rod for ten cubes and try again. Do this for several problems before any of it is written down.
Step by step with 52 minus 17
- Build 52: five tens rods, two ones cubes.
- Try to take away 7 ones. There are only 2. Say it out loud: "Not enough ones. I need to trade."
- Take one tens rod and trade it for ten ones cubes. Now there are 4 rods and 12 cubes. Ask "Is it still 52?" (Yes; count it.)
- Take away 7 cubes. 5 cubes are left.
- Take away 1 rod. 3 rods are left.
- Read the answer: 3 tens and 5 ones, 35.
Do this with at least a handful of problems over a few days. The child should be the one deciding when to trade and doing the trade. Your only lines are "Do you have enough ones?" and "Is it still the same number?"
What is the right language: borrowing or regrouping?
Direct answer: Use whatever word your child's teacher uses so school and home match, but explain it as a trade either way. "Borrowing" suggests something will be paid back, which confuses children who then wonder when to give it back. "Regrouping" or "trading" says what actually happens: one ten is exchanged for ten ones.
Phrases that help:
- "Do you have enough ones to take away 7?"
- "Trade a ten for ten ones."
- "Is it still the same number?" (This is the sentence that prevents the number from mysteriously changing in the child's head.)
- "Now subtract the ones, then the tens."
Phrases to avoid: "cross out the 5 and make it a 4," said without the blocks. That is the procedure with the meaning stripped out, and it is the source of the errors below.
What are the common errors and what do they mean?
Direct answer: The big three are subtracting the smaller digit from the larger one regardless of position (52 minus 17 becomes 45), forgetting to reduce the tens after trading (52 minus 17 becomes 45 another way), and regrouping when it is not needed. Each points to a specific gap, so the error tells you what to reteach.
| What the child writes | What went wrong | What to reteach |
|---|---|---|
| 52 − 17 = 45 (did 7 − 2) | Subtracted smaller from larger; no trade | Place value + the "enough ones?" question, with blocks |
| 52 − 17 = 45 (12 − 7 = 5, but kept 5 tens) | Traded but did not reduce the tens | "Is it still 52?" check with rods after trading |
| 45 − 12 regrouped anyway | Regroups on every problem | Ask "enough ones?" first, every time |
| 100 − 37 stalls | Two trades in a row (hundred to tens, ten to ones) | Model with a hundred flat, rods and cubes before writing |
| 60 − 24 = 44 | Zero in the ones treated as "nothing to trade" | Trade a ten into the empty ones column; 0 becomes 10 |
The first row is by far the most common, and it is worth naming for your child: "You can't take 7 from 2, so what do we do?" If the answer is "take 2 from 7 instead," the place-value idea is still missing, and the blocks go back on the table.
What does a worked-example ladder look like?
Direct answer: A ladder is a sequence of problems that adds one new difficulty per rung, so the child is never facing two new things at once. Climb one rung per session and go back down a rung when errors appear. Each rung should be done with blocks first, then written next to the blocks, then written alone.
| Rung | Example | New idea |
|---|---|---|
| 1 | 47 − 23 | Two-digit, no regrouping (warm-up; confirms columns) |
| 2 | 52 − 17 | One trade: ten to ones |
| 3 | 60 − 24 | Trade with a zero in the ones |
| 4 | 345 − 128 | Three-digit, one trade |
| 5 | 345 − 172 | Three-digit, trade hundred to tens |
| 6 | 423 − 187 | Two trades |
| 7 | 500 − 236 | Two trades across zeros |
| 8 | 1000 − 437 | Three trades across zeros (a 3rd grade stretch) |
Rungs 1–4 are 2nd grade territory. Rungs 5–8 arrive over 2nd and 3rd grade; do not push to rung 8 in one week. One clean rung a day, with the "is it still the same number?" check, is the pace that sticks.
How do you keep it from ending in tears?
Direct answer: Keep sessions short, let the child own the blocks, and treat errors as information rather than failure. Most subtraction tears come from a child who has been told the procedure and cannot make it work; the blocks give them something to reason with instead of something to remember.
Three rules that help:
- Five problems, not twenty. A page of thirty regrouping problems is an endurance test, not practice.
- Say the reasoning, not the steps. "Not enough ones, so I trade" beats "cross out, write one, subtract."
- Check with addition. 35 + 17 should give 52. Checking their own answer turns a red X into a puzzle the child solves.
If subtraction has already become a source of dread, our post on math anxiety in kids covers how to lower the stakes before adding practice. And to see where regrouping fits in the whole year, the 2nd grade math skills checklist lists every expectation.
TernQuest's 2nd grade map has regrouping games with place-value visuals and hint-based help from Pip, and they are a fine place for the repetition once the trade makes sense. They are not the place to start: for the first week, real blocks on a real table are better than any screen, because the child needs to physically make the trade.
Related reading
- Place value explained for parents — the prerequisite; if "the 5 means five," start here.
- 2nd grade math skills checklist (2026) — where subtraction within 100 and 1000 fits among the year's skills.
- Math anxiety in kids: signs and what to do — if the tears are already there.
Next step
Once your child can trade a ten with blocks and explain why, let them practice in TernQuest, which is free to start for one child and runs in the browser. The weekly report will tell you if the smaller-digit error is creeping back.