# What is Regrouping in Addition and Subtraction?

We are sure you can envision the looks of terror and panic if you utter the word “regrouping” in your math class.  The concept can even make parents and teachers tremble in fear wondering how to effectively teach the strategies needed to solve problems involving regrouping.  Take a deep breath and relax the grip you have on your marker, all is well, and all will learn thanks to a few of our tips and clarifying questions.

What is Regrouping?

Understanding the “what” is an essential step towards easing the anxieties that you or your students may have about regrouping.  Essentially, regrouping is what your mathematicians will need to do when solving addition in subtraction problems that require making groups of ten to solve multi-digit problems.  If you can count to ten and count by tens, you are in great shape!  In addition, we call regrouping “carrying” and in subtraction, we call it “borrowing.”

Ways to enhance your understanding of regrouping include using base ten blocks and understanding place values.

When do students start learning how to regroup?

According to the Common Core State Standards, students are expected to be able to regroup by the end of second grade.  However, first-grade students are expected to be able to “use place value understanding and properties of operations to add and subtract” by the end of the year.  All the skills needed for regrouping are built upon and many first graders will practice the skill.  It’s second-grade where they are expected to master the skill.

Perhaps the most important key is for your students to understand the “why” and be able to explain why these strategies work.  One of the second-grade standards (CCSS.MATH.CONTENT.2.NBT.B.9) includes being able to, “explain why addition and subtraction strategies work, using place value and the properties of operations.”

More commonly referred to as carrying, regrouping in addition, is the process in which we have a sum of two numbers in the same place value that exceeds ten.  When counting and adding, only the numbers 0-9 can fit in any singular place value.  Once you get to ten, it’s time to regroup, and the number will extend to the tens place.  Whether it’s 9+1 or 9+7, our number will become two digits.

Let’s take 9+7 as an example to start.  When you combine them, you now have one group of ten and six ones left over.  The one group of ten goes into the tens place and the leftover six goes in the ones place and you wind up with 16.

That may seem easy enough, but what if we are adding:

 2 9 + 1 7

If we start in the ones place we get 9+7=16.  The six will stay in the ones place, but we will carry the one group of ten into the tens place and get:

 1 2 9 + 1 7 6

Now, we are adding the groups of ten together.  1 group of ten (10) + 2 groups of ten (20) + 1 group of ten (10) = 4 groups of ten (40).  If you have the 4 groups of ten (40) and add the 6 groups of one (6) you get 46.

 1 2 9 + 1 7 4 6

What is Regrouping in Subtraction?

With subtraction, we refer to regrouping as borrowing, because now we are deconstructing our place values to solve our problem with a positive number.  Think of borrowing as the tens being moveable, but not necessarily flexible.  You can only borrow in tens, hundreds, thousands, etc., but never in ones.  In the following example, borrowing allows us to regroup our tens to solve a subtraction problem correctly.

 3 1 – 1 4

In the problem, 31-14, we start in the ones place to subtract.  However, if we subtract 1-4 we would get -3 which is not an accurate representation on the whole problem we are trying to solve.  Therefore, any time we try to subtract a smaller number by a larger number in multi-digit subtraction we use the process of borrowing.  Here, we will borrow one group of 10 from 31 and add that to the 1 in the tens place to get:

 2 3 11 – 1 4

Now we can simply subtract 11-4 to learn that we have 7 ones left.

 2 3 11 – 1 4 7

Finally, we have 2 groups of ten (20) and subtract that by 1 group of ten (10) and are left with 1 group of ten to be placed in the tens column.

 2 3 11 – 1 4 1 7

Breaking borrowing and carrying down step-by-step is an effective way to teach regrouping.  Additionally, we highly suggest using base tens and other manipulatives to help students grasp an understanding of why this process works.

Here are some additional regrouping resources on the web:

Grade 2 ” Number & Operations in Base Ten
http://www.corestandards.org/Math/Content/2/NBT/