Addition with regrouping is a very difficult concept for students to learn. They need a solid foundation in place value in order to comprehend the concept. Without a strong sense of place value, regrouping will be difficult for them. It is often asked why we teach things differently from the way we grew up. The answer is simple. We need to teach the WHY before we teach the HOW. We want to give student’s a lot of options and flexibility when it comes to solving problems because each child learns differently.
In this post, I am going to share 4 different strategies that I have used in my own classroom that you can use to help your students better understand the concept of regrouping.
At the beginning of our addition with regrouping unit, I always make this anchor chart. As a new strategy is introduced, it is added to our whole group chart. I also have my students create the same chart in their math journals. This is helpful for them to look back on when they need extra support.
Let’s take a closer look at these four strategies.
Base Ten Model
It is essential that you introduce the concept that you use manipulatives. I recommend using base ten blocks because your students should be familiar with them from your place value unit. You can also use other fun tools such as pipe cleaners to represent the tens and pom poms to represent the ones.
I always give them a place value mat placed inside a plastic sleeve. This allows the student to also write or draw using a dry erase marker. They can also be used over and over again. Here is how this strategy works using the example 47+36=.
- Build out both addends with base ten blocks. First, they will build 47 and then they will build 36.
- Add up the ones first. Explain that when the sum is more than 10, we have to regroup.
- Review place value by asking if we can exchange any of our ones. Yes, we can. Have them trade out ten ones for a ten.
- Ask them how many ones do we have left? Write that answer in the ones place of the sum.
- Last, add the tens to solve for the sum.
It is also important for them to be able to draw out this strategy on paper because they won’t always have access to the manipulates they need to solve, but they will have a piece of paper and pencil available to them. The strategy works the same way when drawing it out.
- Draw out both addends.
- Add up the ones first. When the sum is more than 10, have them circle ten ones and then mark them out with an X.
- They will add a tens block to the first addend.
- Then, they can count and solve for the sum.
Expanded Form Method
The next strategy I’m going to share is the expanded form method. This is another strategy that can be extremely beneficial if your students have a strong understanding of place value and expanding numbers. Each addend will be broke apart to show the value of tens and ones. This helps students see that the value of a digit. For example in the number 87, when we expand it, we get 80+7. This helps them see that the value of the 8 is 80 rather than just 8. Here is how it works using the example 47+34
- Expand the first addend. >>> 40+7
- Expand the second addend and write it underneath. >>>30+4
- Solve vertically based on place value, starting with the ones. Then add the tens.
- Solve for the sum.
A benefit to this strategy is that it removes the regrouping step when the numbers are expanded.
Number Line Strategy
Using an open number lie to solve two-digit addition with regrouping problems is the third strategy I’m going to share. This strategy focuses on “hopping” along a number aline to solve for the sum of a given problem. Large hops are drawn for plus 10 and smaller hops are drawn for plus 1.
To help students visualize this concept, I teach them to include base ten blocks first. When they become more comfortable with this strategy then they can take them away. Here is how it works using the example 36+38.
- Identify the larger addend by circling it.
- Draw an open number line.
- Write the larger addend and the start of the number line.
- Then, students use base ten blocks to build the other addend horizontally across their number line.
- Draw large hops over the tens to show plus 10 and small hops over the ones to show +1.
- Count and solve for the sum.
When it comes to putting pencil to paper, your students can easily do the same strategy. If they need to draw base ten blocks along their number line they can. Our goal is for them to be able to mentally add.
The standard algorithm is probably how you learned addition with regrouping growing up. This is the strategy that your students parents will be the most familiar with.
I like to use the saying, “If it’s ten or more, carry next door.”
One tip that can be helpful is to give your students a highlighter to highlight the ones place first. This helps them visualize to add the ones place first followed by the tens. Students are trained to read from left to right, this makes going the opposite direction difficult for some students.
Here is how this strategy works using 68+37.
- Write 68+37 vertically, lining up the tens and ones.
- Highlight the ones place and add it first. If the sum is ten or more, they will carry next door.
- 8+7 = 15. Have the write 15 out to the side, next to the ones place.
- Since the sum is more than 10, they must regroup. Have them draw an arrow from the 1 of the 15 to above the tens place. They’ll write a 1 above the 6.
- The 5 from the 15 will be moved to the answer. Write it in the ones place of the sum.
- Last, add the tens place.
At the end of our unit, we always make these Addition with Regrouping Strategy Flipbooks. These help us review and they can keep them to use as a reference later on.
Once you have exposed your students to multiple regrouping strategies, this allows them to choose the one that works best for them and explore it further with additional practice. Here are some resources that you may find helpful
Addition with Regrouping: This guided math unit includes 2 weeks worth of lesson plans to teach two-digit and three-digit addition with regrouping. There are activities for whole group lessons, independent practice and small group instruction. The activities include lots of hands on practice with manipulatives, interactive journal activities, and math stations to use all year long.
Regrouping Task Cards: This is a set of task cards that include addition and subtraction word problems.
If you are looking for strategies for teaching addition and subtraction without regrouping, check out the blog posts below.
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