Regrouping

This week we have reviewed addition and subtraction with regrouping. Earlier in the year we added and subtracted with two digits, but this week we worked with three digit numbers. 

As you are working with your children, remember that math instruction has changed since we were in elementary school. You probably know regrouping as 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).

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.

We also learned a new strategy for adding. It's called the partial sums method. Many of the kids aren't big fans of it, but it reenforces each mathematician's number sense. Here's how it works:

   439

+ 398

  700
  120
    17
  837

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. 

We also practiced subtraction with regrouping. Unfortunately, there is not a partial sums method to subtraction. Therefore, we focused on the traditional algorithm. When subtracting, children typically encounter two problems. Sometimes, they try what I call the "flip trick." For example, in the following problem: 

   523

-  394

You probably know to start with the "ones place." That's the column on the far right. Mathematicians look at that and realize they can't take 4 away from 3. Some third graders try the "flip trick" and take the 3 away from the 4 instead. Mathematically, of course, this doesn't work. 

The other problem many students encounter is forgetting to use regrouping. In the above example, they regroup from a ten to the ones column. This should make 13 ones and 1 ten. However, kids often forget to record this work, and therefore subtract inaccurately. 

Subtraction with regrouping can be tricky, but I know all our students can do it!

As always, don't hesitate to contact me with any questions, comments or concerns.