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Hi everyone!
Today we're going to talk about regrouping in two digit addition.
When we write numbers with two digits we have to pay attention to WHERE the numbers are
written, because how much they are worth changes based on where they are.
This is called place value.
When we're adding two digit numbers we only have two places to worry about, and those
are the tens column and the ones column.
So, to demonstrate, if we write the number '32,' then the 3 goes in the tens column and
the 2 goes in the ones column.
Because the two is in the ones column it is worth 2 one-unit blocks, but the 3 is in the
tens column, which means that it is worth 3 block stacks of ten units each.
That 3 is really worth 30.
Now let's try adding something to our 32: 11.
11 is the same as one one-unit block and one ten-unit block stack.
We're going to start by counting all of our ones - because we always start with the ones
column.
So, we have one, two, three ones blocks, so we put a 3 in the ones column.
Next we count our tens: one, two, three, four.
We have four tens, so we put a four in the tens column.
Okay.
That means that 32 + 11 is 43.
That was easy.
But what happens if we want to add 29 instead of 11?
29 is the same as 9 one-unit blocks and 2 ten-block stacks.
So, let's count all of our ones again.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
2 + 9 equals 11, but we can't write that in our ones column!
Our ones column is only for numbers less than 10.
So we have to change ten of our ones into a ten-block stack, something we call 'regrouping.'
That means we only have one single block left.
So in the ones column, we will write 1.
But now we have to do something with that ten-block stack.
Where do tens go?
In the tens column!
So we move it over into our tens column, which sometimes we call 'carrying,' and now we're
going to count how many stacks of ten we have.
We have 1, 2, 3, 4, 5, and then the one that came over from the ones column - 6.
We have 6 tens!
So we write 6 in our tens column.
We have 6 in the tens column, and 1 in the ones column: 61.
32 + 29 equals 61.
Let's try another problem, but this time let's pretend that we have boxes of cookies.
Each box can only fit 10 cookies.
So first we have 29 cookies, that's 2 boxes of 10 cookies and 9 individual cookies - and
we want to add to that 17 more cookies, that's one box of 10 cookies and 7 individual cookies.
So we'll start by adding our individual cookies, because we always start in the ones column.
Let's count.
We have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 cookies, and we're going to stop for a minute and put
those cookies into a box, then we're going to count the rest of the cookies.
We have 1, 2, 3, 4, 5, 6 cookies left.
So in our ones column, we have one box of 10 cookies, and 6 individual cookies, or 16
cookies: 9 + 7 equals 16.
Now we have to move our full box of cookies out of the ones column and over to the tens
column with all of the other boxes.
Then we only have 6 cookies left in the ones column, so we'll write '6' in our ones column.
Let's count how many boxes of 10 cookies we have now!
1, 2, 3, then the one that came over from our ones column - 4!
We have four boxes of 10 cookies, so in our tens column we write 4.
So, we have 4 in our tens column, and 6 in our ones column: 46.
29 + 17 equals 46.
Now that you know how to add two digit numbers together and regroup them, try some problems
on your own!