How to Explain Regrouping to a Child (So It Actually Makes Sense)

What Is Regrouping?

Regrouping is trading between place values:

In addition: "Carrying" — trading 10 ones for 1 ten
In subtraction: "Borrowing" — trading 1 ten for 10 ones

Kids learn the procedure but often don't understand WHY it works.

Why Kids Get Confused

They see regrouping as a mysterious rule:

"Cross out the number and make it smaller"
"Put a little 1 next to the other number"

But they don't understand they're trading equal values.

The Secret: Make It Physical First

You need base-10 blocks, or make your own:

Small cubes = ones
Sticks of 10 = tens
Flat squares of 100 = hundreds (if needed)

No blocks? Use:

Pennies and dimes (10 pennies = 1 dime)
Single straws and bundles of 10
Drawing dots and circled groups of 10

Teaching Addition Regrouping

Problem: 27 + 15

Step 1: Build both numbers with blocks

27 = 2 tens, 7 ones
15 = 1 ten, 5 ones

Step 2: Combine the ones

7 ones + 5 ones = 12 ones
"We have 12 ones. That's more than 10!"

Step 3: Trade 10 ones for 1 ten

Take 10 ones away, add 1 ten
Now we have: 4 tens, 2 ones

Step 4: Count the result

4 tens + 2 ones = 42

The "why": We trade because each place can only hold digits 0-9.

Teaching Subtraction Regrouping

Problem: 42 - 17

Step 1: Build 42 with blocks

4 tens, 2 ones

Step 2: Try to take away 7 ones

"We only have 2 ones. We can't take 7 from 2."

Step 3: Trade 1 ten for 10 ones

Now we have: 3 tens, 12 ones
"We still have 42 — just arranged differently!"

Step 4: Now subtract

12 ones - 7 ones = 5 ones
3 tens - 1 ten = 2 tens
Answer: 25

The "why": We're not changing the number, just rearranging it so we can subtract.

The Key Phrase to Use

"Trade, don't change."

We're trading 1 ten for 10 ones (or vice versa). The total value stays the same. We're just making it easier to work with.

Common Mistakes (And Fixes)

Mistake: Subtracting smaller from larger (42 - 17 = 35) Fix: Always check: "Do I have enough ones to subtract?"

Mistake: Forgetting to reduce the tens when borrowing Fix: Physical blocks make this obvious — you removed a ten!

Mistake: Carrying but not adding the carried number Fix: Practice with blocks until the trading is automatic

When to Move to Paper

Only after they can do it physically without help:

Build it with blocks
Write the problem while using blocks
Imagine the blocks while writing
Do it on paper alone

Don't rush this progression!

Practice Resources

2nd Grade Subtraction — Two-digit with regrouping
3rd Grade Subtraction — Three-digit with regrouping