Helping Students Master Adding and Subtracting with Regrouping

The Importance of Mastering Regrouping

Across grade levels 3rd-6th there are several math skills that are arguably significantly harder than others to master. Consequently, these are also usually the skills that are the most critical to master because they 1.) continue to show up year after year, but in increasingly more complex versions, and/or 2.) are prerequisites for learning and mastering another more, complex skill.

It’s important for teachers and parents to understand that when a child/student isn’t grasping one of these skills, if time isn’t taken to help them achieve mastery, they won’t just suffer temporarily or for the duration of the current math lesson or chapter, but most will likely struggle in many subsequent lessons in their current and future grade levels.

One of the first places this type of stumble can be commonly seen is when students must master adding and subtracting larger (3-digit) numbers with regrouping, usually in the 3rd grade. Students will continue to see regrouping though in later grades when adding & subtracting larger numbers, multi-digit multiplication problems, and more.

Challenges When Learning Adding and Subtracting with Regrouping

As crucial as regrouping is, many students do face challenges when learning this skill especially as the numbers become a bit larger. Why? Sometimes the obstacles are centered around the concept of regrouping itself, while others are related to the steps needed to complete the problem. Let’s take a look...

• Larger numbers mean more room for errors and careless mistakes.  Adding and subtracting 3-digit numbers means 3 potential columns to add or subtract which means more of a chance of one of those being calculated incorrectly. 
• Not being able to write neatly and use correct alignment.  I can’t tell you how many times I’ve heard the heartbreaking teacher story of how a student is a whiz at adding and subtracting with regrouping, but when given a problem to solve in a horizontal format (i.e. 345 - 136 =) was unable to copy it down with correct alignment and thus ending up getting it wrong on a test.
• Lack of fact fluency. While most 3rd graders should be able to fluently add and subtract single digit numbers, students who are not as fact fluent will often face challenges working through problems that require multiple steps. When they can't recall basic facts quickly, they can spend so much time counting on their fingers or drawing tally marks on their paper to try and figure out the answer to a math fact that they lose track and forget what step they need to do next. 
• Struggles with executive functioning. To solve an addition or subtraction problem with regrouping successfully, students must be able to remember all the steps they need to complete. Students who struggle with executive functioning can become overwhelmed or distracted with problems like these that require multiple steps. See Math Tips & Strategies for Students with IEPs for strategies that can help.
• Finally, just regrouping - enough said. It can just be a tough skill to learn! Understanding the concept of regrouping, when & why to do it and mastering the practical steps to do it correctly can all be challenging on their own. Which number gets "carried over"? Where do you put it? What if there is a zero in the problem? 

Common Mistakes Students Make When Regrouping

There are many mistakes students might make related to regrouping when adding or subtracting. Here are some common variations to look out for:

Mistake #1 - Not carrying over a digit at all! 

Mistake #2 - Not adding in the number that was carried over.

Mistake #3 - Carrying over the ones digit instead of the tens.

Mistake #4 - Not recognizing when regrouping is necessary and just subtracting the top number from the bottom number.

Mistake #5 - Not changing the value of the number that is being borrowed from.

Mistake #6 - Not correctly borrowing across zeros.

Remember, it is also beneficial to model common errors for students so that they can recognize if/when they make them.

How to Effectively Teach Adding and Subtracting with Regrouping

While learning regrouping skills may present challenges, there are definitely teaching strategies that can make the learning process smoother and help your students achieve mastery. 

1. Review, review, review!

Even though your 3rd grade students should have added and subtracted 2-digit numbers in 2nd grade, that was forever ago to a kid! Take time to review, model and practice procedures for adding and subtracting 2-digit numbers that do not require regrouping first. In addition, strong fluency with those addition and subtraction facts are a must, so start reviewing those daily ahead of time so that your students are sharp and ready.

2. Use a memorable saying or chant.

You know the ones. So cheesy but also so memorable and definitely effective in helping students be successful in both remembering and identifying when regrouping is necessary. While there are several to choose from, some of the most common and my personal favorites are: "10 or More, Carry Next Door" for adding and "If there’s more on the floor, go next door. If there’s more on top, no need to stop!” for subtracting. These also make for great regrouping anchor charts or posters. 

3. Provide Visual Supports

When you read the words visual supports, I bet you thought of the posters and anchor charts hung around the classroom or given to students that contain rules, steps, acronyms, mnemonic phrases and example problems. These types of visual aids are great to have in your classroom to enhance your instruction and serve as helpful reminders for students when solving problems.

However, did you know that there is another type of visual support you can provide your students if needed to help ease them into solving problems independently? The type of visual support I am referring to is provided on their practice problems and worksheets as extra cues and guidance to help them work through problems with more confidence.

A great visual support that is extremely helpful for Adding and Subtracting with Regrouping are boxes, grids or blanks that provide students with the opportunity to practice neat handwriting, correct number alignment, and even can go so far as to provide a space to write a number that has been regrouped cueing them that hey! you need to write something here. These supports are very beneficial when students are just beginning to practice solving problems on their own and like all forms of scaffolding, can be gradually removed.

4. Scaffold the practice problems or worksheets. 

You can’t expect most 3rd graders to make the leap from subtracting 86 - 32 to 304 - 146 after one or even more instructional lessons. Your instruction and subsequent guided practice and independent practice problems can be scaffolded as much or as little as needed based on the learning pace and needs of your class or individual student.

For this skill, I recommend starting with smaller numbers and working up to larger ones. Likewise, I also guide students through mastering problems that only require regrouping once before I even think about giving them a problem where they will have to regroup twice. More complex problems like subtracting across zeros should be saved for after subtracting with regrouping once and twice are mastered.

Mastering addition and subtraction with regrouping is a critical milestone in a child's mathematical journey. By providing a strong foundation in these skills, you're setting your students up for success in future math concepts. 

PS - If you need more help with Adding and Subtracting with Regrouping or love the resources you have seen in this article, be sure to visit our store and specifically check out:

• Addition with Regrouping - 3rd Grade Lesson Bundle with Worksheets
• Adding Within 1,000 with Regrouping Worksheet Set (worksheets only)
• Subtraction with Regrouping - 3rd Grade Lesson Bundle with Worksheets