Teaching Subtraction With Regrouping in 2nd Grade Small Groups

Subtraction with regrouping means decomposing a ten into ten ones (and, with three-digit numbers, a hundred into ten tens) when a column doesn't have enough to subtract from directly. Students need to understand this as breaking apart an existing unit into smaller units of the same total value, not as a symbol-manipulation rule applied to whichever digit is smaller. The teacher's job is to connect a base-ten block model or place-value chart directly to the written notation, so every mark on the page has a physical meaning behind it. A common 2nd grade instructional focus is two-digit regrouping before extending the same reasoning to three-digit numbers, where a ten and a hundred may both need to be decomposed in the same problem.

Where This Skill Fits

2nd Grade Place Value and 1st grade addition and subtraction within 20 → 2-and-3-digit subtraction with regrouping (decomposing tens and hundreds) → 3rd grade multi-digit operations and multiplication and division foundations.

Essential Prerequisite Skills

Subtraction fluency within 20
Understanding of tens and ones as composed units (place value to 1,000)
Ability to represent a two- or three-digit number with base-ten blocks
Comfort composing and decomposing a ten from base-ten blocks (built during place value work)

Helpful Prior Knowledge

Familiarity with a place-value chart as a recording tool
Experience composing a new ten during addition with regrouping, since decomposing is the reverse action
Comparing two-digit and three-digit numbers using place value rather than guessing from digits alone

What's Different About Subtraction's Trigger

Addition regrouping is triggered by a column total that's too large — more than 9 — which the student resolves by composing a new, larger unit. Subtraction regrouping is triggered by the opposite condition: a column that doesn't have enough to subtract from. The student isn't combining anything; they're checking whether the top number's digit in a given column is large enough to subtract the bottom number's digit from, and if it isn't, they open up one unit from the next column over to get more of the smaller unit to work with. This "not enough" trigger can be harder for students to recognize than addition's "too many" trigger, because there's no visible overflow to notice — the student has to actively compare two digits and predict a problem before doing any subtracting. Decomposing a ten into ten ones (or a hundred into ten tens) doesn't change the total value of the number; it just represents the same quantity using more of a smaller unit, which is the reverse of what happens when addition composes a larger unit from smaller ones.

Common Student Thinking / Misconceptions

Student may think: "The top number in the ones column is smaller than the bottom number, so I just subtract the smaller from the bigger no matter which is on top."

What this may reveal: This may indicate the student hasn't yet connected the digits to actual quantities and is instead treating subtraction as "always take the smaller digit away from the larger digit," which produces a wrong answer whenever the top digit is genuinely too small.

Possible teacher response: Have the student build the top number with blocks and physically attempt to remove the bottom number's ones, so they can see there simply aren't enough ones there.

Student may think: After decomposing a ten into ten ones, the student forgets to reduce the tens column by one, since a ten rod was taken away from it.

What this may reveal: One possibility is that the student sees the new ones appearing in the ones column but doesn't track that they came from somewhere — the tens column isn't being treated as one unit smaller now.

Possible teacher response: Ask the student to physically move a ten rod out of the tens group and trade it for ten unit cubes, then recount what's left in the tens column before continuing.

Student may think: When subtracting a three-digit number, the student decomposes a hundred into tens but doesn't check whether the tens column now also needs to be decomposed further into ones.

What this may reveal: This can suggest the student is treating decomposing as a single event tied to whichever column looked short first, rather than a check that applies to every column in order.

Possible teacher response: After decomposing the hundred, ask, "Now that we have more tens, do we still have enough ones, or do we need to open up a ten too?" as a standard question for every column.

Student may think: "There's a zero in the tens place, so I can't take anything from it — I'll just skip that column."

What this may reveal: This may indicate the student doesn't yet understand that a zero can be decomposed too, by reaching one column further to the hundreds to open up a new ten.

Possible teacher response: Model this case slowly with blocks, showing that a hundred flat can be exchanged for ten ten-rods when the tens column shows zero.

Student may think: The student assumes decomposing changes the value of the number, worrying that "breaking apart" a ten makes the number smaller.

What this may reveal: This may suggest the student hasn't yet internalized that a ten and ten ones represent the exact same quantity, just grouped differently.

Possible teacher response: Have the student count the total value before and after the exchange to confirm it hasn't changed, only the grouping has.

Useful Visual Models

Base-Ten Blocks — This model can help students physically exchange a ten rod for ten unit cubes (or a hundred flat for ten ten-rods), making the decomposing action concrete before it's written as notation. A limitation is that blocks become unwieldy with larger three-digit numbers, so students eventually need to transition to a place-value chart.
Place-Value Charts — A place-value chart can help students record the decomposing exchange in an organized way and connect it directly to the columns used in an efficient written method. A limitation is that it's more abstract than blocks, so it works best as a bridge after the block model, not as the first introduction to regrouping.

Small-Group Teaching Sequence

A short small-group lesson (roughly 15–30 minutes) might look like this: Activate Prior Knowledge (2–4 min) — quickly represent a two-digit number with base-ten blocks and identify the tens and ones. I Do (4–6 min) — teacher models one regrouping problem with blocks and a place-value chart side by side, narrating the decomposing exchange. We Do (5–8 min) — teacher and students build and record 1–2 problems together, with the teacher asking questions rather than giving the steps. You Do (4–8 min) — students solve 2–4 problems independently with blocks or a chart available. Quick Check (2–3 min) — one problem plus a short explanation to gauge whether the student can say why they're decomposing a ten, not just complete the steps.

I Do Example

Problem: 42 − 17

"I'll build 42 with 4 ten rods and 2 ones. I need to take away 17, which means taking away 7 ones and 1 ten. Let's look at the ones column first — I have 2 ones, but I need to take away 7. Do I have enough ones? No, 2 isn't enough to take 7 from." (Teacher points to the 2 unit cubes.) "So I'll open up one of my ten rods and trade it for 10 ones." (Teacher physically trades 1 ten rod for 10 unit cubes.) "Now how many ones do I have? 2 plus the new 10 is 12 ones. And how many tens are left? I had 4, and I just traded one away, so I have 3 tens now." (Teacher records on the place-value chart: tens column shows 4 crossed down to 3, ones column shows 2 becoming 12.) "Now I can subtract: 12 ones minus 7 ones is 5 ones. 3 tens minus 1 ten is 2 tens. So 42 − 17 = 25." (Teacher writes 42 − 17 = 25 underneath, pointing to each digit's matching block.)

We Do Example

Problem: 53 − 28

"Let's build 53 with blocks. Look at the ones column — we have 3 ones, and we need to take away 8. Do we have enough?" (Students notice 3 is less than 8.) "What can we do since we don't have enough ones?" (Open up a ten rod and trade it for 10 ones.) "Once we trade, how many ones do we have now?" (3 plus 10 is 13.) "How many tens are left after we traded one away?" (5 tens minus 1 is 4 tens.) "Now can we subtract? What's 13 minus 8, and what's 4 tens minus 2 tens?" (5 ones, 2 tens.) "So what's 53 − 28?" (25.)

Second problem: 61 − 34. "Before we even build this, look at the ones digits — 1 and 4. Do you predict we'll have enough ones, or will we need to trade?" (Students predict we'll need to trade, since 1 is less than 4.) "How do you know how many tens are left once we've traded one away?"

You Do Examples

Students solve independently using base-ten blocks or a place-value chart, then record the standard notation alongside their concrete work:

32 − 15
70 − 26
216 − 138
84 − 49

Quick Check

Ask the student to solve 51 − 24 and explain their thinking aloud, then ask a second question: "How did you know you needed to trade a ten for ones before you even started subtracting?" A student who can both solve the problem and explain the "not enough" trigger in their own words shows a deeper understanding than one who reaches the correct answer through memorized steps alone. If the student demonstrates understanding — comparing the ones digits, recognizing there aren't enough ones, decomposing a ten, and correctly reducing the tens column — move toward three-digit regrouping or regrouping across a zero in the tens place. If the student needs more support — for example, getting the right answer but unable to explain why a ten was opened up, or subtracting the smaller digit from the larger one regardless of position — return to base-ten block practice with two-digit regrouping using smaller numbers before reintroducing the written notation.

If Students Demonstrate Understanding

Move to three-digit subtraction with regrouping in more than one column (e.g., 342 − 168, which requires decomposing both a ten and a hundred), and introduce subtraction across a zero (e.g., 400 − 165), where the tens column shows zero and the exchange must reach back to the hundreds.

If Students Need More Support

Return to place value work representing two- and three-digit numbers with base-ten blocks, then practice two-digit regrouping with smaller numbers (totals under 30) before reintroducing the written method. Avoid teaching this as an isolated rule with no place-value meaning attached to it — a teacher prompt like "Show me the trade with your blocks before we write anything" keeps the model and the notation connected.

Before → Current → Next Skill Relationships

Before: 2nd Grade Place Value and 1st Grade Addition & Subtraction
Current: 2-and-3-digit subtraction with regrouping (decomposing tens and hundreds)
Next: 3rd Grade Small Group Math — multi-digit operations and multiplication/division foundations

This page pairs with Teaching Addition With Regrouping: addition composes a new, larger unit when a column has too much; subtraction decomposes an existing unit when a column doesn't have enough. Teaching them side by side as opposite actions on the same place-value structure can help students see regrouping as one coherent idea rather than two unrelated procedures.

Related Misconceptions

Related Visual Models

Relevant SMS Resources

Browse more 2nd grade regrouping routines, task cards, and quick checks in the full catalog.

Teacher FAQ

Should I teach students to say "borrow a ten" or "the bottom number is bigger, so cross out and make it one less"?

No — avoid "borrow," "bottom bigger," and "cross out and make it one less" as instructional language. These are rules with no place-value meaning: nothing is actually being borrowed (it's never paid back), and "cross out and make it one less" describes a mark on paper instead of the real action of decomposing a ten into ten ones. Teach the exchange through base-ten blocks and a place-value chart instead, so students understand they're breaking apart one unit into smaller units of equal value.

How is this different from addition with regrouping?

Addition regrouping composes a new, larger unit when a column has too much (more than 9). Subtraction regrouping decomposes an existing unit into smaller units when a column doesn't have enough to subtract from. They use the same place-value structure but move in opposite directions.

What should I do when there's a zero in the column a student needs to decompose from?

Model it slowly with blocks — a zero in the tens place means the student needs to reach one column further, decomposing a hundred into ten tens before a ten can then be decomposed into ones. This case tends to need extra guided practice.

Should students always predict whether they'll need to regroup before subtracting?

Building that habit can help. Comparing the ones digits (and tens digits, for three-digit problems) before subtracting gives students a way to anticipate the "not enough" situation rather than discovering it partway through.

What if a student gets the right answer but can't explain the decomposing?

Treat that as a signal to slow down, not to move on. A correct answer without an explanation can suggest the student is following a memorized procedure that may not transfer to new problem types, such as subtraction across a zero.

When should three-digit subtraction with regrouping be introduced?

After students are consistently accurate and can explain their reasoning with two-digit regrouping, since three-digit problems may require decomposing a hundred and a ten in the same problem. Specific grade-level expectations and number ranges vary by state and curriculum.