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K04 • Lesson 16 of 105

Multi-Digit Addition with Regrouping

Students learn to add two- and three-digit numbers using the standard algorithm, with a focus on regrouping (carrying). They begin with base-10 block models to see why 10 ones become 1 ten, then transition to the written vertical method. Problems progress from two-digit plus two-digit with one regrouping to three-digit problems with multiple regroupings.

K-2 Foundations • K-2

Prerequisites: E02, K01, K02

Key Concepts

  • vertical addition algorithm
  • regrouping ones into tens when adding
  • regrouping tens into hundreds when adding
  • estimating sums to check reasonableness

Multi-Digit Addition with Regrouping

When we add big numbers, we line them up by place value and add one column at a time, starting from the ones (the right side). Sometimes a column adds up to 10 or more, and we need to regroup (also called "carrying").

Setting Up Vertical Addition

  1. Write the numbers one above the other.
  2. Line up the ones under ones, tens under tens, hundreds under hundreds.
  3. Draw a line underneath and a plus sign on the left.
  4 5
+ 3 2
-----

Worked Example 1: Adding Without Regrouping

Add 45 + 32.

  1. Ones column: 5 + 2 = 7. Write 7 in the ones place.
  2. Tens column: 4 + 3 = 7. Write 7 in the tens place.
45 + 32 = 77

When You Need to Regroup

If a column adds to 10 or more, write the ones digit below the line, and carry the tens digit to the next column.

Worked Example 2: Two-Digit Addition with Regrouping

Add 47 + 36.

  1. Ones column: 7 + 6 = 13. That is more than 9! Write the 3 below. Carry the 1 above the tens column.
  2. Tens column: 1 (carried) + 4 + 3 = 8. Write 8 below.
  1
  4 7
+ 3 6
------
  8 3

Answer: 83

Worked Example 3: Three-Digit Addition with Regrouping

Add 278 + 365.

  1. Ones: 8 + 5 = 13. Write 3, carry 1.
  2. Tens: 1 + 7 + 6 = 14. Write 4, carry 1.
  3. Hundreds: 1 + 2 + 3 = 6. Write 6.
278 + 365 = 643

Estimating Sums

Before you add, estimate to check if your answer makes sense. Round each number to the nearest ten (or hundred), then add.

47 + 36 is close to 50 + 40 = 90 (actual answer 83 -- close!)

Watch Out!

Do not forget to add the carried digit! It is the most common mistake. After you write the carry number above the next column, make sure you include it when you add that column.

Check Your Work

You can add the numbers in the opposite order. Addition works in any order! If 47 + 36 = 83, then 36 + 47 should also equal 83.

Real-World Connection

If you have 47 stickers and your friend gives you 36 more, how many do you have? Line them up and add: 47 + 36 = 83 stickers!

Practice Problems

1. Add: 56 + 23

Show Answer

56 + 23 = 79. Ones: 6+3=9. Tens: 5+2=7. No regrouping needed.

2. Add: 68 + 27

Show Answer

68 + 27 = 95. Ones: 8+7=15, write 5 carry 1. Tens: 1+6+2=9.

3. Add: 345 + 278

Show Answer

345 + 278 = 623. Ones: 5+8=13, write 3 carry 1. Tens: 1+4+7=12, write 2 carry 1. Hundreds: 1+3+2=6.

4. Add: 199 + 1

Show Answer

199 + 1 = 200. Ones: 9+1=10, write 0 carry 1. Tens: 1+9=10, write 0 carry 1. Hundreds: 1+1=2.

5. Estimate 287 + 415 by rounding to the nearest hundred, then find the exact answer.

Show Answer

Estimate: 300 + 400 = 700. Exact: 287 + 415 = 702. The estimate was very close!

Lesson Summary

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