Classroom Visual Companions & Station Lab Guides
Welcome to the StackCalc Visual Companion & Station Guide Library. Unlike generic online worksheet generators that produce detached drill sheets that fight against district-adopted curricula, StackCalc companion guides operate as Tactile Learning Lab Station Guides aligned directly to textbook chapters across:
- Singapore Dimensions Math (Pre-K through Grade 8 & Additional Math)
- Bridges in Mathematics (Kindergarten through Grade 5)
- Big Ideas Math & Secondary / AP Standards (Grades 6 through 12+, AP Stats, AP CSP)
Every guide is 100% pre-generated as a publication-grade 2-page PDF in two distinct versions: - Form A (Classroom Master): For station rotations, collaborative desk labs, and direct teacher facilitation. - Form B (Retake & Homework Variant): Features fresh problem numbers with identical pedagogical depth for independent practice or retake assessments.
// DISTRICT PILOT & DEPARTMENT CHAIR SUITE
1-Click Teacher Evaluation Kit (.ZIP)
Evaluating StackCalc for your grade-level team or district adoption? Download our complete 9-resource evaluation archive: includes the District PO Order Requisition Form (Net-30 Terms), Signed IRS Form W-9 Onboarding Packet, 34-page Teacher Facilitator Guide, sample CPA math labs, 3 textbook station guides (Singapore, Bridges, Big Ideas), and an official Texas UIL tournament sprint test with scoring keys.
The 2-Page Station Companion Architecture
+===================================================================================+
| PAGE 1: STUDENT STATION COMPANION & VISUAL LAB GUIDE |
+-----------------------------------------------------------------------------------+
| HEADER: Curriculum • Grade Level • Chapter Number & Title • CCSS Alignment |
| STUDENT BENCH BAR: Name, Date, Target Calculator Model, Check Score (___ / 4) |
| STUDENT SELF-CHECK RULE: "Solve with blocks and pencil first! Calculator is ONLY |
| used to verify answers on the 4-line LCD screen." |
+-----------------------------------------------------------------------------------+
| ZONE 1: TACTILE STATION TUTORIAL & CPA PROGRESSION |
| [Col 1: 2D Blueprint] [Col 2: Desk Setup] [Col 3: Step-by-Step LCD Trace] |
| Millimeter-precision Concrete bench setup MODE: [123] Base-10 Arithmetic |
| vector CAD schematic paired with pictorial 1. [4] X: 4 (Operand 1) |
| from physical STL sketch guidelines 2. [ENTER] Y: 4 | X: 4 (Lift) |
| library (catalog.py) (tape / bond model) 3. [1] Y: 4 | X: 1 (Operand 2) |
| 4. [+] X: 5 (Stack Drop) |
| EXPECTED LCD: 5 counters |
+-----------------------------------------------------------------------------------+
| ZONE 2: 4 AUTHENTIC MATH PRACTICE PROBLEMS |
| • Problem Statement & CCSS Standard |
| • Left Panel: Spacious "Manipulative Model & Desk Sketch" drawing workspace |
| • Right Panel: Clean "Final Math Answer" underline & [ ] "Verified on SC-6" box |
+===================================================================================+
| PAGE 2: OFFICIAL TEACHER FACILITATOR GUIDE & DIAGNOSTIC KEY |
+-----------------------------------------------------------------------------------+
| BOX 1: HARDWARE STATION INVENTORY & 3D PRINT PREPARATION |
| • Station Kit, CAD Blueprint ID, Target Device (SC-6 Elementary vs SC-32 Scientific) |
| • CAD / STL Source File, Standard Gridfinity Footprint, Recommended PLA Filaments|
+-----------------------------------------------------------------------------------+
| BOX 2: CANONICAL SOLUTIONS & RPN STACK TRACE TABLE |
| • Prompt #, Standard, Expected Math Answer (Gold Badge), Keystroke & Register Flow|
+-----------------------------------------------------------------------------------+
| BOX 3: TEACHER DIAGNOSTIC GUIDE: MISCONCEPTIONS & REMEDIATION |
| • Key misconception to observe during station rotation |
| • How physical blocks and RPN stack foster immediate student self-correction |
| • Station facilitation and desk pacing guidance |
+-----------------------------------------------------------------------------------+
| BOX 4: 4-TIER CLASSROOM SCORING & MASTERY RUBRIC |
| • Exemplary (18-20 pts) • Proficient (14-17 pts) • Developing • Intervention |
+===================================================================================+
Pedagogical Guiding Principles
1. Authentic Math Problem Solving (No Calculator Write-In Cells)
Students are learning mathematics, not calculator operation. Practice problems feature spacious drawing canvases for tape diagrams, bar models, number bonds, or area matrices. Students solve with physical blocks and paper first. There are strictly zero calculator button fill-in blanks.
2. Student Self-Check Rule (No Cheating)
A clear instructional banner enforces that the calculator is strictly a self-checking device. When a student enters their solution into the StackCalc 4-line LCD screen, any discrepancy immediately prompts them to re-inspect their physical bench model or regrouping, turning mistakes into productive struggle without requiring teacher intervention.
3. Exact Continuous Squircle App Buttons
All buttons in keystroke sequences and LCD traces are rendered with millimeter-precision touch squircles featuring dark trench bezels matching the StackCalc iOS/macOS production app (HardwareReplicaKeyCap.swift).
4. Step-by-Step LCD Stack Trace
Zone 1 (Right Panel) illustrates worked-out examples with the stack after each keypress: explicitly starting with the Mode Key ([PV], [FDISP], [🕒], [EQN], [DEG]), followed by operands, automatic stack lift (Y: val | X: val), and operator stack drop transitions (X: result).
1. Singapore Dimensions Math (Pre-K to Grade 8 & Add Math)
The Singapore Math method utilizes the Concrete-Pictorial-Abstract (CPA) pedagogical sequence, emphasizing Number Bonds, Bar Models, Bridging Through 10, and Place Value Discs.
| Grade Level | Chapter / Unit & Topic | Target Calculator | Primary Manipulative & CAD Blueprint | Form A (Classroom Master) | Form B (Retake / HW Variant) |
|---|---|---|---|---|---|
| Kindergarten (KA) | Chapter 1: Numbers to 5: Counting & Cardinality | SC-6 Elementary | Ten-Frame Studio (ten_frame_tray) |
Download Form A ↓ | Download Form B ↓ |
| Kindergarten (KA) | Chapter 2: Numbers to 10: Ten-Frame Structure | SC-6 Elementary | Ten-Frame Studio (ten_frame_tray) |
Download Form A ↓ | Download Form B ↓ |
| Kindergarten (KA) | Chapter 3: Comparing Numbers within 10 | SC-6 Elementary | Number Rack (number_rack) |
Download Form A ↓ | Download Form B ↓ |
| Kindergarten (KA) | Chapter 4: Number Bonds to 5 & 10 | SC-6 Elementary | Math Domino Studio (number_bond_stage) |
Download Form A ↓ | Download Form B ↓ |
| Grade 1A | Chapter 2: Number Bonds to 10 & Complements | SC-6 Elementary | Ten-Frame Studio & Math Dominoes (number_bond_stage) |
Download Form A ↓ | Download Form B ↓ |
| Grade 1A | Chapter 3: Addition as Putting Together & Part-Part-Whole | SC-6 Elementary | Math Domino Studio & Number Rack (number_rack) |
Download Form A ↓ | Download Form B ↓ |
| Grade 1A | Chapter 7: Numbers to 20: Place Value & Staging | SC-6 Elementary | Place Value Studio (place_value_tray_whole) |
Download Form A ↓ | Download Form B ↓ |
| Grade 1A | Chapter 8: Making 10 to Add (Bridging Through 10) | SC-6 Elementary | Ten-Frame Studio (ten_frame_shelf) |
Download Form A ↓ | Download Form B ↓ |
| Grade 2A | Chapter 1: Numbers to 1,000: Hundreds, Tens & Ones | SC-6 Elementary | Place Value Studio (place_value_base_ten) |
Download Form A ↓ | Download Form B ↓ |
| Grade 2A | Chapter 4: Multiplication & Doubles: 2, 5 & 10 Facts | SC-6 Elementary | Math Dominoes & Counting Tiles (four_color_tile_tray) |
Download Form A ↓ | Download Form B ↓ |
| Grade 3A | Chapter 3: Multiplication & Division: Arrays & Groups | SC-6 Elementary | Interlocking Cubes & Gridfinity Baseplate (gridfinity_baseplate) |
Download Form A ↓ | Download Form B ↓ |
| Grade 3A | Chapter 5: Multi-Step Word Problems & Bar Models | SC-6 Elementary | Interlocking Cubes & 4-Line Hardware LCD Stack (stack_board) |
Download Form A ↓ | Download Form B ↓ |
| Grade 3B | Chapter 9: Fractions: Equivalence & Common Denominators | SC-6 Elementary | Fraction Studio Towers (fraction_tray) |
Download Form A ↓ | Download Form B ↓ |
| Grade 3B | Chapter 10: Time: Modulo-60 Arithmetic & Elapsed Minutes | SC-6 Elementary | Classroom Planetary Geared Clock (clock_dial) |
Download Form A ↓ | Download Form B ↓ |
| Grade 4A | Chapter 5: Fractions: Mixed Numbers & Addition | SC-6 Elementary | Fraction Studio (fraction_blocks) |
Download Form A ↓ | Download Form B ↓ |
| Grade 5A | Chapter 2: Fractions: Adding with Unlike Denominators | SC-6 Elementary | Fraction Studio Towers (fraction_tray) |
Download Form A ↓ | Download Form B ↓ |
| Grade 6A | Chapter 1: Negative Numbers, Zero Pairs & Absolute Value | SC-6 Elementary | Ten-Frame Studio (number_rack) |
Download Form A ↓ | Download Form B ↓ |
| Grade 6A | Chapter 3: Algebraic Expressions & Postfix Traversal | SC-6 Elementary | Interlocking Cubes & 4-Line Hardware LCD Stack (tree_board) |
Download Form A ↓ | Download Form B ↓ |
| Grade 7A | Chapter 4: Linear Equations & Stage Balancing | SC-32 Scientific | Algebra Studio & Factoring Stage (algebra_stage) |
Download Form A ↓ | Download Form B ↓ |
| Grade 8A | Chapter 5: Quadratic Factorisation & [EQN] Root Solver | SC-32 Scientific | Algebra Studio & Factoring Stage (algebra_tiles) |
Download Form A ↓ | Download Form B ↓ |
| High School (Add. Math) | Chapter 7: Circular Measure & Trigonometric Ratios | SC-32 Scientific | Unit Circle Trigonometry Volvelle (unit_circle_volvelle) |
Download Form A ↓ | Download Form B ↓ |
| High School (Add. Math) | Chapter 9: 2D Vector Decomposition & Resultants | SC-32 Scientific | Unit Circle Trigonometry Volvelle (unit_circle_volvelle) |
Download Form A ↓ | Download Form B ↓ |
2. Bridges in Mathematics (Kindergarten to Grade 5)
Bridges in Mathematics (The Math Learning Center) uses visual models including the Number Rack (Rekenrek), Open Number Lines, Open Arrays, Combinations to 10, and Tile Rectangles.
| Grade Level | Chapter / Unit & Topic | Target Calculator | Primary Manipulative & CAD Blueprint | Form A (Classroom Master) | Form B (Retake / HW Variant) |
|---|---|---|---|---|---|
| Kindergarten | Unit 1: Numbers to 5 & 10: The Step Counter & Ten-Frame | SC-6 Elementary | Ten-Frame Stage & Two-Color Discs (ten_frame_tray) |
Download Form A ↓ | Download Form B ↓ |
| Kindergarten | Unit 2: Numbers to 10: Five-Structure & Five-Frames | SC-6 Elementary | Ten-Frame Stage (ten_frame_tray) |
Download Form A ↓ | Download Form B ↓ |
| Kindergarten | Unit 3: Combinations to 10 with the Number Rack | SC-6 Elementary | Number Rack (number_rack) |
Download Form A ↓ | Download Form B ↓ |
| Kindergarten | Unit 4: Paths to 20: Comparing Groups on the Number Rack | SC-6 Elementary | Number Rack (number_rack) |
Download Form A ↓ | Download Form B ↓ |
| Grade 1 | Unit 1: Numbers All Around Us: Rekenrek Subitizing & Ten-Structures | SC-6 Elementary | Number Rack (number_rack) |
Download Form A ↓ | Download Form B ↓ |
| Grade 1 | Unit 2: Developing Strategies with Dominoes & Doubles | SC-6 Elementary | Math Domino Studio (number_bond_stage) |
Download Form A ↓ | Download Form B ↓ |
| Grade 1 | Unit 3: Adding, Subtracting & Combinations of 10 | SC-6 Elementary | Ten-Frame Studio (ten_frame_shelf) |
Download Form A ↓ | Download Form B ↓ |
| Grade 1 | Unit 4: Leapfrogs on the Number Line: Skip Counting | SC-6 Elementary | Counting Tiles & Number Rail (four_color_tile_tray) |
Download Form A ↓ | Download Form B ↓ |
| Grade 1 | Unit 6: Figure the Facts with the Number Rack: Teen Numbers | SC-6 Elementary | Number Rack (number_rack) |
Download Form A ↓ | Download Form B ↓ |
| Grade 2 | Unit 1: Figure the Facts: Addition Strategies & Near Doubles | SC-6 Elementary | Number Rack (number_rack) |
Download Form A ↓ | Download Form B ↓ |
| Grade 2 | Unit 2: Place Value & Bundling Tens into Hundreds | SC-6 Elementary | Place Value Base-Ten Studio (place_value_base_ten) |
Download Form A ↓ | Download Form B ↓ |
| Grade 2 | Unit 3: Addition & Subtraction Within 100: Jump & Split Strategies | SC-6 Elementary | Stack Stage Rail & Interlocking Cubes (stack_board) |
Download Form A ↓ | Download Form B ↓ |
| Grade 2 | Unit 6: Geometry & Fractions: Partitioning Equal Shares | SC-6 Elementary | Fraction Studio Proportional Towers (fraction_tray) |
Download Form A ↓ | Download Form B ↓ |
| Grade 3 | Unit 1: Addition & Subtraction Patterns on the Open Number Line | SC-6 Elementary | Stack Stage Rail & Interlocking Cubes (stack_board) |
Download Form A ↓ | Download Form B ↓ |
| Grade 3 | Unit 2: Introduction to Multiplication: Equal Groups & Arrays | SC-6 Elementary | Gridfinity 4x4 Coordinate Baseplate & Cubes (gridfinity_baseplate) |
Download Form A ↓ | Download Form B ↓ |
| Grade 3 | Unit 4: Measurement & Fractions: Unit Fractions & Tower Heights | SC-6 Elementary | Fraction Studio Proportional Towers (fraction_blocks) |
Download Form A ↓ | Download Form B ↓ |
| Grade 3 | Unit 5: Multiplication, Division & Area: Open Arrays | SC-6 Elementary | Gridfinity 4x4 Coordinate Baseplate & Cubes (gridfinity_baseplate) |
Download Form A ↓ | Download Form B ↓ |
| Grade 4 | Unit 1: Multi-Digit Multiplication: Partial Products & Ratio Tables | SC-6 Elementary | Gridfinity Baseplate & Stacking Blocks (gridfinity_baseplate) |
Download Form A ↓ | Download Form B ↓ |
| Grade 4 | Unit 3: Fractions & Decimals: Proportional Towers & Two-Dot Notation | SC-6 Elementary | Fraction Studio Towers (fraction_tray) |
Download Form A ↓ | Download Form B ↓ |
| Grade 4 | Unit 4: Measurement & Angles: Modulo-60 Clock Navigation | SC-6 Elementary | 4-Quadrant Modulo-60 Clock Dial (clock_dial) |
Download Form A ↓ | Download Form B ↓ |
| Grade 5 | Unit 1: Expressions, Equations & Volume: Postorder Traversal & Cubic Units | SC-6 Elementary | 4x4 Expression Tree Case & Cubic Blocks (tree_board) |
Download Form A ↓ | Download Form B ↓ |
| Grade 5 | Unit 2: Adding & Subtracting Fractions with Unlike Denominators | SC-6 Elementary | Fraction Studio Towers (fraction_tray) |
Download Form A ↓ | Download Form B ↓ |
3. Big Ideas Math & AP Standards (Grades 6 to 12+)
Big Ideas Math (Ron Larson & Laurie Boswell) and Advanced Placement standards bridge middle school conceptual mastery into formal secondary algebra, calculus, and computer science. Visual models feature the Balance Scale, Polynomial Algebra Tiles, Area Matrices, Unit Circle Volvelles, and Expression Tree Boards.
New: 45-Day Big Ideas Middle School Catch-Up Workbook (SC-6 & Manipulatives)
Designed specifically for middle schoolers who struggle with multi-line handwritten work, resent "showing the same problem 3 ways," or feel behind in math:
| Grade Level | Chapter / Unit & Topic | Target Calculator | Primary Manipulative & CAD Blueprint | Form A (Classroom Master) | Form B (Retake / HW Variant) |
|---|---|---|---|---|---|
| Grade 6 | Chapter 1: Numerical Expressions & Factors: Prime Factorisation & GCF | SC-6 Elementary | Prime Factor Studio & Logarithmic Blocks (prime_studio_box) |
Download Form A ↓ | Download Form B ↓ |
| Grade 6 | Chapter 2: Fractions & Decimals: Dividing Fractions & Reciprocals | SC-6 Elementary | Fraction Studio Proportional Towers (fraction_tray) |
Download Form A ↓ | Download Form B ↓ |
| Grade 6 | Chapter 3: Algebraic Expressions & Properties: Order of Operations | SC-6 Elementary | 4x4 Expression Tree Case & Token Operators (tree_board) |
Download Form A ↓ | Download Form B ↓ |
| Grade 6 | Chapter 6: Integers & The Coordinate Plane: Negative Numbers & Zero Pairs | SC-6 Elementary | Number Rack & Zero-Pair Color Discs (number_rack) |
Download Form A ↓ | Download Form B ↓ |
| Grade 6 | Chapter 7: Equations & Inequalities: One-Step Equations & Balance Scale | SC-6 Elementary | Tactile Algebra Stage & Balance Blocks (algebra_stage) |
Download Form A ↓ | Download Form B ↓ |
| Grade 7 | Chapter 1: Adding & Subtracting Rational Numbers: Signed Stack | SC-32 Scientific | Stack Stage Rail & Color-Coded Tiles (stack_board) |
Download Form A ↓ | Download Form B ↓ |
| Grade 7 | Chapter 2: Multiplying & Dividing Rational Numbers: Sign Rules | SC-32 Scientific | Stack Stage Rail & Color-Coded Tiles (stack_board) |
Download Form A ↓ | Download Form B ↓ |
| Grade 7 | Chapter 3: Expressions & Equations: Two-Step Equations & Balance Stage | SC-32 Scientific | Tactile Algebra Stage & Tile Weights (algebra_stage) |
Download Form A ↓ | Download Form B ↓ |
| Grade 7 | Chapter 4: Ratios & Proportional Reasoning: Unit Rates & Proportions | SC-6 Elementary | Counting Tiles & Ratio Rail (four_color_tile_tray) |
Download Form A ↓ | Download Form B ↓ |
| Grade 7 | Chapter 8: Circles & Area: Circumference, Pi & Modulo Dial | SC-32 Scientific | 4-Quadrant Modulo Clock & Rotary Dial (clock_dial) |
Download Form A ↓ | Download Form B ↓ |
| Grade 8 | Chapter 1: Solving Multi-Step Equations: Variables on Both Sides | SC-32 Scientific | Tactile Algebra Stage & Tile Weights (algebra_stage) |
Download Form A ↓ | Download Form B ↓ |
| Grade 8 | Chapter 7: Real Numbers & The Pythagorean Theorem: Radicals & Square Roots | SC-32 Scientific | Gridfinity 4x4 Coordinate Baseplate & Triangles (gridfinity_baseplate) |
Download Form A ↓ | Download Form B ↓ |
| Algebra 1 | Chapter 7: Polynomial Equations & Factoring: Area Model & [EQN] Solver | SC-32 Scientific | Tactile Algebra Stage & Polynomial Tiles (algebra_tiles) |
Download Form A ↓ | Download Form B ↓ |
| Algebra 2 | Chapter 6: Exponential & Logarithmic Functions: Compound Interest & LN | SC-32 Scientific | Stack Stage Rail & Token Tiles (stack_board) |
Download Form A ↓ | Download Form B ↓ |
| AP Standards | AP Stats Unit 4: Probability & Combinatorics: Permutations & Combinations | SC-32 Scientific | Probability Spinner & Fair Dice Pack (probability_spinner) |
Download Form A ↓ | Download Form B ↓ |
| AP Standards | AP CSP Big Idea 2: Digital Information: Base Conversions & Two's Complement | SC-32 Scientific | 4x4 Expression Tree Case & Logic Bit Tokens (tree_board) |
Download Form A ↓ | Download Form B ↓ |