Teaching students how to add and subtract mixed numbers in 5th grade is a major skill tested on SBAC. Don’t quote me, but it often feels like a large portion of the test focuses on fractions, and there is always a performance task that requires students to add or subtract mixed numbers.
Adding and subtracting like fractions is something most 5th graders understand easily. However, many students hit a wall when regrouping mixed numbers is introduced.
What It Means to Regroup Mixed Numbers
I’ve found a reliable way to help students be successful with this skill, but first, it’s important to understand what regrouping mixed numbers actually means.
When you add mixed numbers and end up with a fraction greater than one—also called an improper fraction—you need to regroup. There are two ways to do this:
- Break out the whole number (decompose)
- Divide the improper fraction
I use a mnemonic to help students remember that they must divide and regroup, which I explain in the video.
On-grade-level students usually understand this concept fairly quickly, while struggling students often want to divide first.
How to Teach Adding Mixed Numbers with Regrouping
Regrouping should be taught as its own lesson. I recommend spending an entire day explaining and practicing this skill before students apply it to real problems.
I explain to students that sometimes when they add mixed numbers, their answer will include a whole number and an improper fraction, and that regrouping is simply a skill they need to practice.
I often have students pretend their answer is something like 4 wholes and 5/3 and we practice regrouping these examples on their whiteboards. Then the independently practice with the worksheet above. You can find it HERE.
Once students feel confident, we move on to independent practice using a worksheet I created. After they master regrouping, they apply the skill to adding mixed numbers the next day.
How to Teach Subtracting Mixed Numbers with Regrouping
After students are comfortable adding with regrouping, we move on to subtracting mixed like numbers.
Most students don’t struggle with borrowing from the whole number. The tricky part comes when they must combine the fractions, which is why clear instructions and visuals are so important.
Regrouping—or borrowing—means breaking down the whole number when the fraction is not large enough to subtract. Students borrow from the whole number to make the fraction larger. I remind them that we are simply renaming the fraction because the value of the mixed number stays the same.
The Best Strategy: Use Visual Models
The best strategy to teach students how to regroup a mixed number is by using visual models. When your students “see” that they can change whole numbers into fractions, they realize that wholes and fractions are equivalent, and they understand what it means to regroup.
From Visual Models to the Algorithm
Once your students have a conceptual understanding of what it means to regroup with visual models, it’s time to focus on solving problems with only numbers. Tell your students that they can always fall back on drawing pictures, but the faster way is to use numbers to represent the pictures we draw.
Here are the steps to regroup when subtracting mixed numbers:
Step 1: Write the number that comes BEFORE the whole number
Step 2: Write a fraction equal to ONE using the denominator
Step 3: Add the fractions together
Step 4: Subtract the mixed numbers
Final Thoughts
Teaching students how to regroup mixed numbers and handle improper fractions may take time, but with a focused lesson and plenty of practice, they’ll eventually get it. I use these worksheets to teach adding and subtracting with mixed numbers using like denominators.
By breaking down the skill into manageable steps and using hands-on activities, you can help your students master this tricky concept.
Remember, it’s all about patience and practice. Once they get the hang of it, they’ll be ready to tackle more complex problems. You got this! Giselle
P.S. If you are an upper elementary teacher and you teach fraction as division, you have to download my free worksheets below. They teach students the concept of fractions as division in a visual way, and there is also a worksheet to teach finding a fraction of a whole number.
For more blog posts about teaching fractions, make sure to read:
How to Introduce Fractions as Division with Visual Models – Free PDF Worksheets Inside
Mastering Mixed Numbers & Improper Fractions: Visual Strategies for 5th Grade
Step-by-Step Directions To Teach Equivalent Fractions in 5th Grade