If there’s one skill that often trips up elementary students, it’s adding and subtracting with regrouping. You probably know the feeling—students can sometimes rattle off the algorithm, but the moment the numbers get bigger (or the problem involves regrouping across multiple places), the errors pile up.
That’s because many of us were only taught the standard algorithm with little connection to why regrouping works. Students memorize “carry the one” or “borrow from next door,” but they don’t understand what those phrases mean in terms of place value. Without that foundation, mistakes are common—and they stick around year after year.
That’s why I recommend teaching addition and subtraction with regrouping using the CRA method (Concrete–Representational–Abstract). This gradual approach helps students truly understand place value, making the algorithm more meaningful and less error-prone.
What is the CRA Method?
CRA stands for Concrete–Representational–Abstract. It’s a sequence of learning that builds deep understanding:
- Concrete: Students use hands-on tools (like base-10 blocks or place value discs) to model numbers.
- Representational: Students draw models, often on place value charts, to represent what they did with manipulatives.
- Abstract: Students use numbers and the standard algorithm to solve problems.
The key to CRA is bridging each step: when moving from building to drawing, have students build first, then draw. When moving from drawing to the algorithm, encourage them to notate what’s happening in their drawings alongside the steps.
Concrete: Building Numbers and Regrouping with Manipulatives
Start with manipulatives like base-10 blocks or place value discs. These tools make place value visible and regrouping concrete.
Addition Example: To add 47 + 36, students build each number on a place value chart. They combine the tens and ones. When they have more than 10 ones, they physically “bundle” 10 ones into 1 ten and move it to the tens column.
Subtraction Example: For 52 – 28, students build 52. When they try to take away 8 ones, they see they don’t have enough. They “unbundle” 1 ten into 10 ones and then subtract.
The language of bundle and unbundle is much clearer than “carry” or “borrow.” It reinforces place value and shows students what’s really happening.
Representational: Drawing Place Value Models
Once students are comfortable with manipulatives, have them begin drawing what they build. Place value charts are especially helpful at this stage.
Addition: Students draw tens and ones, cross out 10 ones to regroup as a ten, and redraw it in the tens column.
Subtraction: Students cross out a ten, replace it with 10 ones, and then subtract.
Encourage students to build and then draw at first. This bridges their concrete understanding to representational thinking. Eventually, they can draw directly without manipulatives.
Abstract: Using the Standard Algorithm
Finally, students are ready to transition to the standard algorithm. The key here is to connect it back to the drawings so the algorithm doesn’t feel like random steps.
- When adding, instead of just saying “carry the one,” ask: Where did that extra ten come from? Students should relate it to the bundle they created when adding ones.
- When subtracting, instead of “borrowing from the neighbor,” students should see that they’re unbundling a ten to make 10 ones.
At this stage, encourage students to draw and notate alongside their algorithm work. For example, when regrouping in subtraction, they can show the cross-out and redraw in their place value sketch. This dual representation cements their understanding and ensures they aren’t just memorizing steps.
Why CRA Matters for Regrouping
Without CRA, students often:
- Forget steps of the algorithm.
- Misapply “borrow” and “carry” without understanding.
- Get unreasonable answers and don’t notice.
With CRA, students:
- See regrouping as place value-based, not magic.
- Build confidence in moving between strategies.
- Retain their understanding long after the test.
Helpful Resources for Teaching Regrouping
If you’re ready to make regrouping less frustrating for your students, these resources can help:
1. Guided Notes: My addition and subtraction guided notes walk students through regrouping step by step using CRA. They’re scaffolded so you can use them for whole-group instruction, small groups, or independent reference.
2. Interactive Worksheets: These interactive worksheets come with QR codes linking to mini-lesson videos. Perfect for students who need extra support or review at home.
3. Math Escape Rooms: Want to add excitement to regrouping practice? Addition and subtraction escape rooms turn practice into a fun challenge where students solve problems to unlock codes. These are great for test prep, centers, or whole-class review and make regrouping practice feel like a game instead of a worksheet.
Teaching regrouping doesn’t have to feel like pulling teeth! With the CRA method, your students will finally understand what it means to bundle and unbundle, setting them up for success in future math concepts.
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