Ten-Frame Dual Stage & Carry Shelf
The foundational tactile laboratory for early numeracy, subitizing, number bonds, and place-value regrouping. Features a precision dual 2×5 counting stage with inset square sockets, an integrated elevated carry shelf for base-ten regrouping, 20 high-contrast bi-color square miniblocks (19×19mm), and a solid 2U cube "10" Carry Block housed neatly in a modular 3×1 Gridfinity storage box.
Building Intuitive Number Sense
Moving beyond finger counting to spatial base-10 mental models.
1. Instant Subitizing
The 2×5 array teaches students to recognize "seven" immediately as "five on top and two on the bottom." This structural visualization replaces tedious one-by-one counting.
2. Making Ten Strategy
To solve \(8 + 5\), students place 8 counters on the first frame and see 2 empty slots. Moving 2 counters from the second frame fills the ten-frame, showing \(8 + 5 = 10 + 3 = 13\).
3. Physical Carry Mechanism
When ten counters accumulate in the frame, they are consolidated and transferred to the raised carry shelf. The mathematical act of "carrying a ten" becomes a concrete physical memory.
Interactive Ten-Frame & Regrouping Simulator
The Video Showcase: Mechanical Animation, Unboxing & Classroom Lesson
Experience the complete journey from modular Gridfinity tray kinematics and zero-plastic unboxing to early number sense and base-10 regrouping on a classroom desk.
Mechanical & CAD Animation
Exploded 3D view showing dual-tier 2×5 counter receptacles, tiered carry-shelf retention, and 3x1 Gridfinity nesting.
Instant Subitizing: Recognizing 7 as 5 + 2
Filling top row of 5 instantaneously and adding 2 bottom counters. Students subitize quantities under 180ms without counting fingers.
Make-Ten Regrouping: 8 + 5 = 10 + 3
Sliding 2 counters from Frame 2 across to complete Frame 1 into a full 10, leaving 3 counters on the carry shelf for place-value addition.
Archival Reference & Video QR Card (135×90mm)
Included inside every box. Scan Side B to jump straight to this 3-video learning portal or inspect Side A for part replacement IDs.
Zero Plastic Wrap. 100% Archival Packaging Architecture.
Every StackCalc kit arrives in a custom 200 lb-test kraft mailer engineered for classroom unpacking, permanent drawer storage, and zero unrecyclable film.
Crushproof Corrugated Mailer
Engineered with interlocking friction tabs. Withstands 200 lbs of side-wall compression without foam peanuts or shrink wrap.
Laser-Engraved Archival Card
Resting directly on top of the bin. Side A catalogs all part manifests; Side B embeds deep QR routing to video lessons and single-piece replacement.
Tiered Receptacle Caddy
20 bi-color 19mm square miniblocks and the green 2U carry cube nest into precision sockets with perimeter finger notches, preventing accidental scatter while enabling rapid clearing.
Gridfinity 3x1 Modularity
Integrates instantly with standard 42mm desktop grids. Stacks seamlessly under our SC-6 or SC-32 RPN hardware calculators.
From the Teacher's Manual: Unit Lab Sheet
Most traditional math teacher manuals treat manipulatives as optional afterthoughts. In the StackCalc curriculum, every manipulative unit includes a dedicated, reproducible lab sheet connecting hands-on tactile geometry directly to hardware calculator execution.
Lab 02: Dual-Tier Subitizing, Making 10 & Place Value Regrouping
Investigation Goal: Ground place-value intuition in physical capacity. Use the 2×5 ten-frame sockets to subitize quantities 1–10 without counting one-by-one, slide completed tens to the elevated carry shelf, and execute multi-digit regrouping on the SC-32 RPN stack.
Start with an empty 2×5 primary ten-frame tray. Explore how numbers decompose into the benchmark anchor 5 and the base anchor 10:
| Addition Expression | Starting Frame Count | Counters to Complete 10 | Counters on Lower Tier | Regrouped Form (Tens + Ones) |
|---|---|---|---|---|
| \(8 + 4\) | 8 counters | 2 counters (from 4) | 2 counters remaining | 1 Ten + 2 Ones = 12 |
| \(7 + 6\) | 7 counters | 3 counters (from 6) | 3 counters remaining | 1 Ten + 3 Ones = 13 |
| \(9 + 7\) | 9 counters | 1 counter (from 7) | 6 counters remaining | 1 Ten + 6 Ones = 16 |
Execute the regrouping decomposition \(7 + 5 = (7 + 3) + 2\) on the SC-32 RPN stack:
Build a Complete Hands-On Place Value Station
Anchor early arithmetic and multi-digit regrouping in physical dual-tier capacity, reinforced by dedicated student lab sheets and RPN entry.
SC-32 Scientific RPN Maker Kit
Introduce students to Postfix stack entry where numbers are entered first and operators act immediately, mirroring the physical act of gathering counters before executing addition.
36-Page Spiral Student Workbook
Features 4 foundational place-value investigations: visual subitizing 1–10, Making-10 bridge facts, two-digit addition with carry, and subtraction decomposition.
Tactile Math Dominoes
Double-six tactile dominoes with recessed pip wells and subitizing partition lines. Ideal for early addition doubles and decomposition alongside ten-frames.
Technical Specifications
Tactile proportions and modular classroom storage.
| Outer Dimensions | 126.0 mm (L) × 42.0 mm (W) × 36.0 mm (H) • Standard 3x1 Gridfinity bin |
| Ten-Frame Grid | Dual 2×5 recessed counting pocket array with debossed five-structure center bar |
| Counters Included | 20 precision two-tone tokens (20.0 mm diameter × 5.0 mm thick • Coral on Top / Teal on Bottom) |
| Carry Shelf | Raised 8.0 mm second-tier shelf for regrouped base-ten bundles |
| Material | Non-toxic matte PETG polymer • Washable with warm water and soap |
| Industrial Design & CMF | Tactile square tiles with dished finger wells • 45° edge relief • Standard 3x1 42 mm Gridfinity footprint with interlocking dovetails |
| Curriculum Standards | Common Core: CCSS.MATH.CONTENT.K.OA.A.3, K.OA.A.4, K.NBT.A.1, 1.OA.C.6 • TEKS: 111.2.b.2, 111.3.b.3 • Grades K–2 |
| Procurement Classification | UNSPSC: 60101700 (Math Manipulatives) • NIGP: 785-70 • Title I Early Numeracy & Head Start Grant Eligible |
What's in the Box
Complete hands-on early numeracy workstation.
Safety, Compliance & Guarantees
Durable, non-toxic materials engineered for elementary classrooms.
WARNING: CHOKING HAZARD – Small parts. Not for children under 3 years. This product contains small counters (\(18.0\,\text{mm}\) diameter). Designed for educational numeracy instruction for Grades K–3 (ages 5 and up) under adult supervision.
Molded from odorless, non-toxic, BPA-free PLA biopolymer. 100% free of lead, phthalates, and PVC. Washable with warm water and soap or standard classroom disinfectant wipes.
Counters get misplaced in kindergarten and 1st grade rooms. Order individual replacement counters or tray segments anytime for just $2.49 with free envelope shipping.
Designed and manufactured by StackCalc in California under strict dimensional tolerances and quality control.
Pedagogical Verification & Classroom Architecture
Concrete-Representational-Abstract (CRA) tactile mechanics, subitizing geometry, and storage standards.
Elevated Carry Shelf
Physically elevates 10 grouped counters onto a discrete upper tier, translating abstract base-ten regrouping into spatial movement and tactile motor memory before symbolic notation.
Finger-Lift Perimeter Chamfers
Counters feature 19×19mm footprints with precision 0.8mm edge chamfers. Designed specifically for early childhood fine motor dexterity, preventing frustration and counter slippage.
42mm Gridfinity Ecosystem
Fits standard open-source 42mm Gridfinity classroom storage drawers. Form-fitted dual 10-wells provide instant visual inventory audits during 30-second classroom cleanup transitions.
Frequently Asked Questions
Teaching mechanics, subitizing, and grade recommendations.
What is subitizing and how do ten-frames build it? +
Subitizing is the ability to instantly recognize the number of objects in a small group without counting them one by one. The standard 2×5 ten-frame layout provides a structured visual anchor: students quickly see 7 as 'a full row of 5 plus 2 more', building foundational mental math fluency.
How does the elevated carry shelf assist with addition? +
When adding \(8 + 5\), students place 8 counters on the lower tray, add 2 counters from the second group to 'make ten', and slide the full tray onto the elevated upper carry shelf. The remaining 3 counters stay on the lower tray, visually proving that \(8 + 5 = 10 + 3 = 13\).
Are the bi-color counters magnetic or interlocked? +
The counters feature perimeter finger-relief notches and nest securely inside circular dished pockets. High-contrast Glow Red and Glow Yellow dual-face coloring allows teachers and students to model addition combinations and number bonds (e.g. 6 Yellow and 4 Red = 10) with zero slipping.
What if counters get lost? +
Under our "Anti-Heartbreak" lifetime guarantee, teachers and parents can order individual matching replacement counters or trays anytime for just $2.49 with free envelope shipping.
3D Print Ten-Frames in Your School
Download our print-tested STL models for the ten-frame tray, carry shelf, and two-tone counters. Prints in under 2 hours.
The Ten-Frame Dual Stage introduces early learners to base-ten place value and regrouping. As students develop computational speed, these physical groupings translate directly into the stack push/pop operations of our SC-6 and SC-32 calculators.