Addition With Regrouping Up to 20

When you add two numbers and the ones digits add up to more than 10, you cannot leave the answer as a two-digit "ones" count. Instead, you trade 10 ones for 1 ten. This trade is called regrouping (sometimes called "carrying"). Addition with regrouping up to 20 means every sum you work with, from the smaller addends to the final total, stays at or below \( 20 \).

For example, \( 9 + 6 \) cannot stay as "15 ones." Instead, it becomes 1 ten and 5 ones, written as \( 15 \). Before learning to regroup, it helps to be comfortable with addition facts up to 20 and simple strategies for adding with digits up to 20, since regrouping builds directly on those skills.

Our number system is based on groups of ten. Any time a group of ones reaches 10 or more, those ten ones can be exchanged for a single ten. Regrouping keeps every digit in its correct place value spot, tens in the tens place and ones in the ones place, so the number is written correctly and can be used in later, larger calculations.

Without regrouping, a student might write \( 8 + 7 \) as "15" without understanding that the 1 stands for a whole ten. Learning to regroup builds the foundation for adding two-digit numbers later on.

The most common way to regroup when adding up to 20 is the make-a-ten strategy. Follow these steps:

1. Look at the larger addend and figure out how many more it needs to reach 10.
2. Split the smaller addend into two parts: the amount that completes the ten, and what is left over.
3. Add the leftover part to the new ten.

Here is the strategy applied to \( 8 + 7 \):

\( 8 \) needs \( 2 \) more to make \( 10 \). Split \( 7 \) into \( 2 + 5 \). Then \( 8 + 2 = 10 \), and \( 10 + 5 = 15 \). So \( 8 + 7 = 15 \).

A place value chart makes the trade from ones to tens easy to see. The figure below shows \( 8 + 7 \): fifteen ones are first collected together, then 10 of them are regrouped into 1 ten, leaving 5 ones.

Example 1: \( 6 + 9 \)

\( 9 \) needs \( 1 \) more to reach \( 10 \). Split \( 6 \) into \( 1 + 5 \). Then \( 9 + 1 = 10 \), and \( 10 + 5 = 15 \). So \( 6 + 9 = 15 \).

Example 2: \( 7 + 8 \)

\( 7 \) needs \( 3 \) more to reach \( 10 \). Split \( 8 \) into \( 3 + 5 \). Then \( 7 + 3 = 10 \), and \( 10 + 5 = 15 \). So \( 7 + 8 = 15 \).

Example 3: \( 9 + 9 \)

\( 9 \) needs \( 1 \) more to reach \( 10 \). Split the other \( 9 \) into \( 1 + 8 \). Then \( 9 + 1 = 10 \), and \( 10 + 8 = 18 \). So \( 9 + 9 = 18 \).

Regrouping becomes much easier once addition facts are automatic, so keep reviewing basic pairs alongside this strategy. You may also want to strengthen related skills such as using a number line to add up to 20, which gives another visual way to see numbers move past 10. Practicing with real objects, ten-frames, or counters before moving to pencil-and-paper problems helps the "make a ten" idea feel concrete rather than abstract.

As you practice, always ask: does this sum go past 10? If yes, regroup those ten ones into a ten before writing the final answer. Repeating this check consistently is the key to mastering addition with regrouping up to 20.

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