Making the Invisible Visible: Ten-Frames for Teaching Regrouping
How visual scaffolding with ten-frames helps students understand the 'make ten' strategy in addition with regrouping, and when to fade this support.
Making the Invisible Visible: Ten-Frames for Teaching Regrouping
When you ask a child "What is 7 + 5?", they might count on their fingers, use mental strategies, or if they're just learning, stare blankly while their brain tries to process what you're asking. But when you show them ten-frames, something magical happens: the abstract becomes concrete, and the "make ten" strategy becomes obvious.
What Are Ten-Frames?
A ten-frame is a simple 2×5 rectangular grid—ten boxes arranged in two rows of five. Originally developed for teaching number sense and subitizing (instantly recognizing quantities), ten-frames have become an essential tool for teaching addition, especially when regrouping (carrying) is involved.
The genius of ten-frames is their structure: two rows of five boxes make visualizing groups of ten natural. When you see 7 dots in a ten-frame, you immediately see "5 plus 2 more":
When you add 5 more dots and the frame fills up, you physically see the creation of a complete ten, plus extras that don't fit:
Why Ten-Frames Matter for Regrouping
Regrouping in addition—the concept that when you add numbers and get more than 10 in a place value, you "carry" to the next column—is one of the first abstract mathematical concepts children encounter. And it's hard.
Consider the problem 47 + 38:
- When adding the ones place: 7 + 8 = 15
- That's "1 ten and 5 ones"
- The ten gets carried to the tens place
This is abstract. What does it mean that 15 is "1 ten and 5 ones"? Why does the "1" move to the tens column? For many students, this becomes a mechanical procedure they follow without understanding.
Ten-frames make this visible.
When you represent 7 + 8 with ten-frames:
- You have a ten-frame with 7 filled boxes
- You have 8 more to add
- First, 3 boxes fill up the remaining spaces in the ten-frame → you made a ten!
- The remaining 5 boxes overflow into a second ten-frame
- Result: 1 full ten-frame (= 10) + 5 extra boxes = 15
The regrouping isn't a mysterious rule anymore—it's a physical consequence of filling up frames.
How We Use Ten-Frames in Our Worksheet Generator
Our addition worksheet generator integrates ten-frames directly into problem layout to scaffold the regrouping process. Here's how it works:
Ten-Frames Appear When Regrouping Happens
The worksheets show stacked ten-frames below each place value column that needs regrouping:
- Bottom frame: Shows the overflow from the current place value (the "extra" ones that make regrouping necessary)
- Top frame: Shows where that overflow goes (carried to the next place value)
- Color-coded: Place value colors (blue for ones, green for tens, yellow for hundreds) help connect the frames to their respective columns
For example, in 47 + 38:
- When adding the ones column (7 + 8), a ten-frame appears below the ones column
- The bottom portion shows the 5 extra ones (in blue) that remain after making a ten
- The top portion shows the 1 ten (in green) that gets carried to the tens column
- Students can literally see how the overflow becomes a carry
Visual Examples
Let's compare the same problem with and without ten-frames to see the difference:
With Ten-Frames: Visual Support for Regrouping
Ten-frames appear below the ones column, showing how 7 + 8 = 15 breaks down into 1 ten (carried) and 5 ones (remaining). The bottom frame (blue) shows the 5 ones that stay, while the top frame (green) shows the 1 ten that gets carried.
Without Ten-Frames: Abstract Representation
The same problem without ten-frames requires students to mentally visualize the regrouping process.
Notice how the ten-frames make the invisible visible. In 47 + 38, when adding the ones column:
- Students see 7 + 8 creates enough to fill one complete ten-frame (10) with 5 left over
- The filled frame (green, top) represents the carry to the tens place
- The 5 remaining boxes (blue, bottom) stay in the ones place
- This visual directly maps to writing "1" in the carry box and "5" in the ones answer
Pedagogical Progression: When to Show Ten-Frames
Like all scaffolding, ten-frames should be introduced when needed and faded when mastered. Our worksheet generator supports three levels of ten-frame scaffolding:
1. Beginner Level: Learning with Ten-Frames
Use when: Introducing regrouping for the first time
A simpler problem (28 + 15) with ten-frames. Students see 8 + 5 = 13, which requires regrouping. The ten-frame shows this as 1 full ten (carried) plus 3 ones (remaining).
At this level, ten-frames appear when problems involve regrouping. This helps students:
- Build visual familiarity with the ten-frame representation
- Practice the "make ten" strategy with concrete support
- Develop number sense about what sums greater than 10 look like
- Connect the visual representation to the carry notation
Key insight: Start with problems that have single-digit sums needing regrouping (like 8 + 5, 7 + 6, 9 + 4), where the ten-frame pattern is clearest.
2. Intermediate Level: Ten-Frames for Multiple Regroups
Use when: Students understand basic regrouping but need support for complex problems
A more complex problem (57 + 68) that requires regrouping in BOTH place values. Ten-frames appear below both the ones column (7 + 8 = 15) and the tens column (5 + 6 + 1 = 12), showing students how each overflow creates a carry.
This is the "smart scaffolding" level. Ten-frames appear only when they're needed—when a column sum exceeds 10. This:
- Reduces visual clutter on simpler problems
- Draws attention to where regrouping is happening
- Lets students practice both with and without visual support
- Shows how regrouping can cascade across multiple place values
Key insight: Problems with multiple regroups (like 57 + 68) are where ten-frames really shine—students can see the parallel structure of "making tens" in different place values.
3. Never Show Ten-Frames (Advanced Level)
Use when: Students have internalized the regrouping concept
At advanced levels, ten-frames are removed entirely. Students should have developed mental models for regrouping and can work abstractly with just carry boxes and place value colors (which also fade over time).
The "Make Ten" Strategy in Action
Ten-frames teach more than just regrouping—they teach a fundamental mental math strategy called "make ten." Here's how a child thinks through 7 + 8 using ten-frames:
Step 1: "I have 7"
Child sees: The top row is full (5), bottom row has 2. Three empty boxes remain to make a complete ten.
Step 2: "I can take 3 from the 8 to fill my frame"
Child thinks: "8 is really 3 and 5. I'll use the 3 to complete my ten-frame, and I have 5 extras."
Step 3: "Now I have 10 + 5 = 15!"
Child concludes: "One complete frame is 10, plus 5 more makes 15. So 7 + 8 = 15!"
This strategy becomes automatic through ten-frame practice. Eventually, students can mentally visualize the frames without seeing them, dramatically improving addition fluency.
Research Foundations
The use of ten-frames for teaching addition aligns with established learning science:
Concrete-Representational-Abstract (CRA) Sequence: Students learn best by progressing from concrete manipulatives → visual representations → abstract symbols. Ten-frames serve as the representational bridge between counting physical objects and working with pure numbers.
Making Thinking Visible: Regrouping is an abstract mental process. Ten-frames externalize this process, allowing teachers to see what students understand and where they struggle.
Cognitive Load Theory: Visual scaffolds like ten-frames reduce extraneous cognitive load (figuring out how to represent the problem) so students can focus on germane load (understanding the mathematical relationships).
When to Fade Ten-Frames
The goal isn't to use ten-frames forever—it's to use them as a bridge to abstract understanding. Signs that students are ready to move beyond ten-frames:
- Automatic recognition: They can instantly recognize ten-frame patterns without counting
- Mental visualization: They describe using ten-frames even when not shown ("I made a ten with the 7 and 3")
- Fluent regrouping: They correctly regroup without visual support on most problems
- Preference for speed: They start viewing ten-frames as "extra work" rather than helpful
Our scaffold fading system automates this progression: use the "Less support" difficulty adjustment to reduce ten-frames from "always" → "when regrouping" → "never" as students demonstrate mastery.
Try It Yourself
Our worksheet generator at abaci.one/create/worksheets/addition gives you complete control over ten-frame scaffolding:
For early learners:
- Set difficulty to "Beginner" or "Early Learner"
- Ten-frames will appear when problems involve regrouping
- Problems start simple to build confidence
To practice the "make ten" strategy:
- Use "More support" to set ten-frames to "always"
- Generate problems with moderate regrouping (pAnyStart = 0.5-0.7)
- Students see ten-frames on every problem to build pattern recognition
To fade scaffolding gradually:
- Start at "Early Learner" (ten-frames when regrouping)
- Use "Less support" to reduce other scaffolds first (carry boxes, colors)
- Finally use "Less support" again to remove ten-frames
- Students transition smoothly from concrete to abstract
The Bigger Picture: Adaptive Scaffolding
Ten-frames are one component of our larger scaffolding system. The power comes from adaptive, conditional scaffolding that appears exactly when needed:
- Ten-frames when regrouping
- Carry boxes when carrying
- Place value colors for larger numbers
- Answer boxes for alignment practice
This creates worksheets that provide just enough support for each problem's complexity, following Vygotsky's Zone of Proximal Development: challenging enough to promote learning, supported enough to prevent frustration.
What's Next
We're exploring extensions of the ten-frame approach to:
- Subtraction with borrowing: Showing how taking away requires "breaking" a ten
- Decimal addition: Using ten-frames to show regrouping across the decimal point
- Fraction concepts: Visual representation of part-whole relationships
The code for our ten-frame implementation is open source: github.com/antialias/soroban-abacus-flashcards
See the technical details in our typstHelpers.ts file, which generates the ten-frame visualizations.
Feedback Welcome
We'd love to hear from teachers using ten-frames:
- Are the stacked frames (showing both the overflow and the carry) helpful or confusing?
- Should we add configuration for single vs. double ten-frames?
- What other visual representations would support regrouping?
Share your thoughts via GitHub issues or try the worksheet generator and let us know how it works with your students.
The ten-frame scaffolding system described here is part of our 2D difficulty research. Students progress through a pedagogically-constrained space where problem complexity and instructional support balance appropriately for each learner. Read more in our 2D difficulty post.