Let's talk about place values...

 I don't know about you, but when I learned about numbers and adding or subtracting it was all about how to count (1 - 2 - 3 - 4 - etc) and learning how many items that "number name" represented. Then I learned to count one number and add on more. When adding and subtracting was taught it was all about carrying and borrowing with no real explanation of what I was doing when I "carried" or "borrowed", and by then I was expected to just have all my addition and subtraction facts memorized. I knew on some level what I was doing, but I honestly had never really thought much about it until my kids were in elementary school and then more when I took a math class while working on my master's degree. What we are doing now helps to ensure that our kids know WHY they carried that number or what is happening when they borrow. 

Let's look at this standard (one of the expectations for first graders in Georgia to learn):

MGSE1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones – called a “ten.” b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

The way that math is taught now is that students by kindergarten are taught about the "one's place" and "tens place", maybe even the "hundreds place". When they look at the number 25 they can tell you it is "two tens" and "five ones". Further, they can show you with manipulatives. That would look something like this:

Each blue "tower" is 10 and then each yellow square is a 1. So this represents two tens and five ones. You might have seen your child work with "ten frames", with those students come to know that when they see a full 10 frame they can say, "brain 10" and they don't have to count each marker in the ten frame. The same is true with the above "base ten blocks". The students know a rod is 10, and a block is 1. If they don't already, they soon will also know that a "flat" is 100 and a "cube" is 1,000

"flat": "cube": 

This sets up to to be ready for the next standard:

MGSE1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of ten (e.g., 24 + 9, 13 + 10, 27 + 40), using concrete models or drawings and strategies based on place value, properties of operations, and/or relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Let's look at 24+9. The way I was taught was:

I was told to "carry the 1". But really, we aren't carrying a ONE. We are carrying the TEN. Which you can see if you do it this way:

 

The student can immediately see that there are at least two tens, but then they will count the blocks - 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 --> Now there is a full "rod" and 3 more:

So now they can see WHY you would "carry the 1". 

They can count the rods and see that there are 3, so they have a "3" in the tens place - because they can see that there are three tens. They also can see that there are three ones, so they write "3" in the ones place. They know that the answer is 33 and they are visually able to see why.

I hope that this has helped to explain why we are doing math this way at this point in your child's eduction. This is going to help them understand the why behind what they are doing which is going to lead to better conceptual understanding.