Regrouping

Math: Addition and Subtraction with Regrouping

We spent quite a while working on addition and subtraction with regrouping. We used Place Value Parkway in Number Talks and while working in our journals to support visual learners. We also used Base-Ten blocks to physically group and "move" ones, tens, hundreds, etc. to the correct place.

Students were able to move into using the standard algorithm very easily because of their understanding of place value.  

For example, in the problem below, they know they are not  "carrying the one", they are moving "1 group of 10" to the tens column. 

Here are pictures of addition regrouping using Base-Ten blocks, and a snapshot of a journal piece using the standard algorithm.

For regrouping in subtraction, we used stories of the numbers on Place Value Parkway having parties or going trick-or-treating to help understand the process of moving groups of numbers from one "house" to another. This helped TREMENDOUSLY when subtracting across a zero. 

Example:

   502 - 268

Student oral reasoning: 

"First, I start in the Ones House. 

I can't take away 8 pieces of candy if I only have 2.  So now I will go next door, but there is no one home in the Tens House! 

I have to keep walking down the block to the Hundreds House.  

I knock on the door and ask if I can move 100 to the tens place. They say yes, so when I move the 100 in 10 groups of 10, there are 4 Hundreds left, and now there are 10 tens in the Tens House. 

I still can't subtract yet, so I have to ask the Tens if I can move a group of Ten to the Ones House. 

They say yes, too. 

When I do that, there will only be 9 groups of 10 left in the Tens House, and now there are 12 ones in the Ones House. 

Now I can subtract.  

12 - 8 = 4

90 - 60 = 30

400 - 200 = 200

So my answer is 234."

Without the understanding of place value, students would simply be "borrowing" and "crossing out" like I learned when I was in school. I never knew what I was doing; I was just following the procedure my teachers taught me! Now, our students can do the standard algorithm just like the "Old Way", but they actually understand what they are doing. 

Amazing, isn't it??