Two-Digit Addition With Regrouping

The hard case: when the ones place adds up to 10 or more, we have to bundle.

What we're learning

• What "regrouping" (or "carrying") actually means — at the bundles-of-ten level
• The procedure for adding two-digit numbers when the ones overflow
• Why we move a 1 to the tens column

Why this is the moment kids get stuck

27 + 38. The ones add up to 7 + 8 = 15. We can't write 15 in the ones column — there's only room for one digit. What do we do?

This is where many adults remember being told "carry the 1" with no explanation, and it became a magic procedure they followed without understanding. We're going to do better.

Use the bundles

Get the bundling materials from the Tens and Ones lesson — popsicle sticks rubber-banded into tens, plus loose ones.

Build 27: 2 bundles + 7 loose. Build 38: 3 bundles + 8 loose.

Push them all together. Count the loose ones: 15.

Now here's the key move. Take 10 of those loose ones and bundle them. You now have:

• The original 5 bundles
• 1 NEW bundle (made from the loose ones)
• 5 loose ones left

That's 6 bundles + 5 loose = 65.

The "carrying" we do on paper is just shorthand for that physical bundling.

Now on paper

     1            ← the carried "1" (one new bundle)
   2  7
 + 3  8
 ------
   6  5

Step by step:

1. Add the ones: 7 + 8 = 15.
2. Write the 5 in the ones place.
3. Write the 1 (which is really one bundle of ten) above the tens column.
4. Add the tens: 1 + 2 + 3 = 6.
5. Write the 6 in the tens place.

Read the answer: 65.

Try it together

Use the bundles for the first few. Then transition to paper-only.

• 18 + 27 (bundles overflow: 8 + 7 = 15)
• 35 + 46 (5 + 6 = 11)
• 49 + 39 (9 + 9 = 18; both digits help build the new bundle)
• 64 + 28 (4 + 8 = 12)
• 55 + 25 (5 + 5 = 10 exactly — interesting case, ones digit becomes 0)

That last one is worth lingering on. 5 + 5 = 10 means exactly one new bundle and zero loose ones. The ones digit of the answer is 0. It feels weird the first time.

Watch for

• Forgetting to add the carried 1. They write the 5 in the ones place, then add 2 + 3 = 5 in the tens place, getting 55 instead of 65. Catch it gently: "Don't forget the new bundle we just made."
• Carrying when they shouldn't. Some children will see two two-digit numbers and instinctively carry, even when the ones don't overflow. Slow them down: "Add the ones first. Is the answer 10 or more? Yes? Then carry."
• Confusion about the WRITTEN 1. When you write "1" above the tens column, your child may read it as "one." Remind them: that 1 stands for one bundle, which is ten. It's there because we made a new bundle.

Where this is going

The third lesson in this module: make a ten as a mental strategy that bypasses paper for a lot of two-digit addition. After that we move to subtraction with regrouping (which is exactly this idea in reverse — and is harder for most kids).