As you are working with your children, remember that math instruction has changed since we were in elementary school. You probably remember adding with carrying. "5 + 9 = 14. Put down the 4, carry the 1..." Children can still solve addition problems this way. The only thing different for that method, is that we call it regrouping. They don't carry the one, they regroup the 10 (or the hundred). We will learn to add three digit numbers using the traditional algorithm (regrouping) tomorrow.
There are two major challenges with regrouping. First, it's important that children have lined up the numbers properly. The digits in the hundreds place, tens place and ones place need to be lined up. It's not accurate to combine 3 from the ones place with 4 from the tens place. Also, children tend to forget that the little 1 they are "regrouping" is really a ten. It's important for them to remember that so they can develop a sense of the numbers.
So we learn to add with partial sums to reenforce the meaning of the numbers we are using. Here's how it works:
For this method, the mathematician actually starts with the hundreds column. Below the problem you show the sum of each column. As you can see, 400 + 300= 700. When all of the columns have been added, you add all of the sums.
As always, don't hesitate to contact me with any questions, comments or concerns.