Adding two-digit numbers without regrouping means adding ones to ones and tens to tens separately. For example, 23 + 14 = (20 + 10) + (3 + 4) = 30 + 7 = 37. This foundation precedes regrouping situations.
You already know two things that make this possible: how to add numbers within 20, and how place value splits any two-digit number into tens and ones. Two-digit addition without regrouping combines both skills at once.
The central idea is column independence: ones only talk to ones, and tens only talk to tens. When you see 23 + 14, think of it as two separate mini-problems stacked side by side. The ones column: 3 + 4 = 7. The tens column: 2 + 1 = 3 (meaning 20 + 10 = 30). Put them together: 37. You never need to mix the columns, because the ones total (7) stays safely under 10.
You can also think of it as decomposing numbers — a skill you've practiced. Break 23 into 20 + 3, and break 14 into 10 + 4. Then rearrange: (20 + 10) + (3 + 4) = 30 + 7 = 37. Both approaches — the column method and the expanded-form method — give the same answer because they both respect place value.
The phrase "without regrouping" is the key qualifier here. Regrouping becomes necessary when the ones column sums to 10 or more — for instance, 27 + 15 has ones summing to 12, which spills over into the tens place. This lesson deliberately stays in cases where that doesn't happen (ones digits sum to 9 or less), so you can build fluency with the column procedure before adding the extra step of carrying. Master the clean cases first; then regrouping is just one additional rule on top of exactly what you're doing now.