Master Curriculum Alignment Matrix
This alignment matrix provides classroom educators and curriculum coordinators with an exact, cross-referenced mapping of StackCalc Physical Manipulatives, Handheld RPN Calculator Keystroke Flows, and the corresponding chapters in major national curricula.
Our Hardware-First Pedagogy: StackCalc does not manufacture generic plastic toys like geoboards, plastic tree connectors, or plastic stack holders. Every manipulative in our learning lab is an authentic, precision Gridfinity instrument designed to pair directly with a dedicated button or calculation mode on our SC-6 Elementary and SC-32 Scientific RPN calculators. The calculator's default 4-line reflective LCD (with toggleable 2-stack mode for number racks and dice) is the live operational stack.
1. Overview by Educational Unit & Textbook Chapter Cross-Reference
| Unit # | Unit Title | Target Grade | Authentic Manipulative | Calculator Keycap Flow | Companion Book Chapter & Lesson Plans | Primary Standards |
|---|---|---|---|---|---|---|
| 01 | Counting & Cardinality | Pre-K β K | Ten-Frame Studio (2x5 Grid + Counters) | [β¦] Ten-Frame / [COUNT] Rack & 1 [ENTER] 1 [+] |
SC-6 Manual, Ch. 3 & App. B (Lessons K.1βK.4) | CCSS.MATH.K.CC.A.1, K.CC.B.4 |
| 02 | Place Value & Regrouping | Grades 1 β 2 | Place Value Studio (Units, Tens, 100s) | [NUM] Whole-Number Stack & [β¦] Carry Bundling |
SC-6 Manual, Ch. 3 & App. B (Lessons 1.1β2.2) | CCSS.MATH.1.NBT.B.2, 2.NBT.A.1 |
| 03 | Doubles & 12-Frame Regrouping | Grades 1 β 2 | Math Domino Studio (12-Frame Tray) | N [ENTER] [+] (Instant Double) & [REP] |
SC-6 Manual, Ch. 4 & App. B (Lessons 1.3β2.3) | CCSS.MATH.1.OA.C.6, 2.OA.B.2 |
| 04 | Equal Groups & Multiplication Arrays | Grades 2 β 4 | Counting Tiles (144-Tile Studio, 13U) | [REP] Skip-Counting, [Γ] Array & [Γ·R] Remainder |
SC-6 Manual, Ch. 4 & App. B (Lessons 3.1β4.1) | CCSS.MATH.2.OA.C.4, 3.OA.A.1, 3.OA.B.5, 3.MD.C.7 |
| 05 | Fraction Equivalence & Operations | Grades 3 β 5 | Fraction Studio (84mm Whole Towers) | [SIMP], [β°] [FDISP], Two-Dot Syntax [.] N [.] D |
SC-6 Manual, Ch. 5 & App. B (Lessons 3.3β5.2) | CCSS.MATH.3.NF.A.3, 5.NF.A.1 |
| 06 | Prime Factorization & Number Theory | Grades 4 β 6 | Prime Factor Studio (Logarithmic Blocks) | [PRIME] & [g] [FACT] Prime Decomposition |
SC-6 Manual, Ch. 7 & App. B (Lessons 5.4β6.2) | CCSS.MATH.4.OA.B.4, 6.NS.B.4 |
| 07 | Planetary Geared Elapsed Time | Grades 3 β 5 | Clock & Interval Timer System | [π] Modulo-60 H.MMSS Arithmetic Mode |
SC-6 Manual, Ch. 9 & SC-32 Manual, Ch. 4 | CCSS.MATH.3.MD.A.1, 4.MD.A.2 |
| 08 | Geometric Polynomial Factoring | Grades 8 β 10 | Algebra Studio & Factoring Stage | [β±] [POLY] Cubic/Quadratic Solver & [β±] [SOLVE] |
SC-32 Manual, Ch. 7 & SC-32 Manual, Ch. 3 | CCSS.MATH.8.EE.A.2, HSA.SSE.A.2 |
| 09 | Discrete Probability & Statistics | Grades 7 β 9 | Probability Dice & Modular Spinner | [π²], [Ξ£+], [xΜ], [β±] [s,Ο] Accumulators |
SC-6 Manual, Ch. 7 & SC-32 Manual, Ch. 9 | CCSS.MATH.7.SP.C.5, 7.SP.C.7 |
| 10 | Trigonometric Coordinates & Radians | Grades 11 β 12 | Precision Acrylic Trig Volvelle | [SIN], [COS], [RAD], [β°] [βΈΞΈ,r] |
SC-32 Manual, Ch. 4 & SC-32 Manual, Ch. 5 | CCSS.MATH.HSF.TF.A.1, HSF.TF.A.2 |
| 11 | Parenthesis-Free Multi-Step Math | Grades 5 β 8 | SC-6 & SC-32 4-Line Hardware LCD Stack | 4-Line Live Registers (\(X, Y, Z, T\)) & [β°] [LASTX] |
SC-6 Manual, Ch. 2 & SC-32 Manual, Ch. 2 | CCSS.MATH.5.OA.A.1, 6.EE.A.2 |
2. Framework-Specific Cross-Reference Tables
2.1 Common Core State Standards for Mathematics (CCSS-M)
| CCSS Standard | Description | StackCalc Unit & Manipulative | Calculator Key Flow & Book Chapter |
| :--- | :--- | :--- | :--- |
| **K.CC.B.4** | Understand the relationship between numbers and quantities; connect counting to cardinality. | **Unit 01:** Ten-Frame Studio (2x5) | `1 [ENTER] 1 [+]` step counter advance (**SC-6 Manual, Ch. 3**) |
| **1.NBT.B.2** | Understand that the two digits of a two-digit number represent amounts of tens and ones. | **Unit 02:** Place Value Studio | `[NUM]` Place Value mode with decimal stack (**SC-6 Manual, Ch. 3**) |
| **1.OA.C.6** | Add and subtract within 20 using strategies such as making ten and doubles. | **Unit 03:** Math Domino Studio (12-Frame) | `N [ENTER] [+]` (Instant double fact, **SC-6 Manual, Ch. 4**) |
| **2.OA.C.4** | Use addition to find total number of objects in rectangular arrays; write an equation. | **Unit 04:** Counting Tiles (Planar Array Studio) | Array rows: `ROW [ENTER] COL [Γ]` (**SC-6 Manual, Ch. 4**) |
| **3.NF.A.3** | Explain equivalence of fractions and compare fractions by reasoning about their size. | **Unit 05:** Fraction Studio (84mm Whole) | `2 [.] 4 [SIMP]` & `[β°] [FDISP]` (**SC-6 Manual, Ch. 5**) |
| **4.OA.B.4** | Find factor pairs for whole numbers 1β100; recognize prime and composite numbers. | **Unit 06:** Prime Factor Studio (Logarithmic Blocks) | Stack prime blocks to target height; press `[g] [FACT]` (**SC-6 Manual, Ch. 7**) |
| **6.NS.B.4** | Find greatest common factor ($\le 100$) and least common multiple ($\le 12$) of whole numbers. | **Unit 06:** Prime Factor Studio | Compare overlapping logarithmic factor stacks for shared and union factors (**SC-6 Manual, Ch. 7**) |
| **3.MD.A.1** | Tell and write time to the nearest minute and measure time intervals in minutes. | **Unit 07:** Clock & Interval Timer | `[π] 9.45 [ENTER] 3.35 [+] => 13.20` (**SC-6 Manual, Ch. 9**) |
| **5.NF.A.1** | Add and subtract fractions with unlike denominators by replacing with equivalent fractions. | **Unit 05:** Fraction Studio Towers | `1 [.] 2 [ENTER] 1 [.] 4 [+] => 3/4` (**SC-6 Manual, Ch. 5**) |
| **6.EE.A.2** | Write, read, and evaluate expressions in which letters stand for numbers. | **Unit 11:** SC-32 Hardware LCD Stack | `A [ENTER] B [+] C [Γ]` (Postfix order, **SC-32 Manual, Ch. 2**) |
| **7.SP.C.7** | Develop a probability model and use it to find probabilities of events. | **Unit 09:** Probability Dice & Spinner | `Sample Value [Ξ£+]` (Statistical accumulator, **SC-6 Manual, Ch. 7**) |
| **HSA.SSE.A.2**| Use the structure of an expression to identify ways to rewrite it (Factoring Quadratics). | **Unit 08:** Algebra Studio & Stage | `1 [ENTER] 5 [ENTER] 6 [ENTER] 0 [β±] [POLY]` (**SC-32 Manual, Ch. 7**) |
| **HSF.TF.A.2** | Explain how the unit circle in the coordinate plane enables trigonometric extension to all reals. | **Unit 10:** Unit Circle Trig Volvelle | `[RAD] 5 [ENTER] [β±] [Ο] [Γ] 6 [Γ·] [COS]` (**SC-32 Manual, Ch. 4**) |
2.2 Bridges in Mathematics (The Math Learning Center)
| Bridges Grade & Unit | Chapter / Topic | StackCalc Manipulative Equivalent | Pedagogical Bridge to RPN Calculator & Manual Chapter |
| :--- | :--- | :--- | :--- |
| **Kindergarten Unit 1** | Numbers to 5 & 10 | Ten-Frame Studio (2x5 Grid + Counters) | Placing physical counters increments Register X via `[β¦]` and `1 [+]` (**SC-6 Manual, Ch. 3**). |
| **Grade 1 Unit 2** | Addition & Subtraction to 10 | Math Domino Studio (12-Frame Tray) | Left and right domino pips mirror lifting Part 1 to Register Y via `[COUNT]` and executing `[+]` (**SC-6 Manual, Ch. 3**). |
| **Grade 1 Unit 3** | Tens & Ones / Bicycle Shop | Place Value Studio (Units & Tens Trays) | Physical carry bay demonstrates bundling 10 ones into 1 ten, verified in `[NUM]` mode (**SC-6 Manual, Ch. 3**). |
| **Grade 2 Unit 1** | Figure the Facts / Number Racks | Math Domino 12-Frame Tray (6x2) | Red/white bead slider groupings map to `[COUNT]` and domino doubles (`N [ENTER] [+]`, **SC-6 Manual, Ch. 4**). |
| **Grade 3 Unit 2** | Introduction to Multiplication | Counting Tiles (144-Tile Planar Arrays) | Four-color 2D arrays on desk correspond to stack multiplication (`ROW [ENTER] COL [Γ]`, **SC-6 Manual, Ch. 4**). |
| **Grade 3 Unit 4** | Measurement & Elapsed Time | Clock & Interval Timer System | Planetary gear mesh physically demonstrates modulo-60 time addition via `[π]` (**SC-6 Manual, Ch. 9**). |
| **Grade 4 Unit 1** | Multiplicative Thinking & Factors | Prime Factor Studio Logarithmic Blocks | Stacking prime factor blocks physically multiplies them ($h_1 + h_2 = 42\log(p_1 \times p_2)$); verified with `[g] [FACT]` (**SC-6 Manual, Ch. 7**). |
| **Grade 4 Unit 3** | Fractions & Decimals | Fraction Studio Proportional Towers | Comparing block heights against 84mm Whole matches `[SIMP]` and `[β°] [FDISP]` (**SC-6 Manual, Ch. 5**). |
| **Grade 5 Unit 1** | Expressions, Equations & Volume | SC-6 & SC-32 4-Line Hardware LCD Stack | Postfix execution mirrors order of operations naturally without parentheses errors (**SC-6 Manual, Ch. 6**). |
2.3 Big Ideas Math (Larson & Boswell)
| Big Ideas Grade & Book | Chapter / Topic | StackCalc Manipulative | Exploratory Activity, Keystroke Flow & Book Chapter |
| :--- | :--- | :--- | :--- |
| **Grade 1** | Chapter 3: Addition Strategies | Ten-Frame Studio + Carry Shelf | Exploration: "Making 10 to Add". `8 [ENTER] 2 [+] 3 [+] = 13` (**SC-6 Manual, Ch. 3**). |
| **Grade 1** | Chapter 7: Count & Model Numbers | Place Value Studio (Units & Tens) | Exploration: "Modeling Numbers to 100". Group ten 1s into one 10-bar, enter in `[NUM]` (**SC-6 Manual, Ch. 3**). |
| **Grade 2** | Chapter 3: Addition by Doubles | Math Domino Studio | Exploration: "Doubles & Near-Doubles". Snap double tile, execute `N [ENTER] [+]` (**SC-6 Manual, Ch. 4**). |
| **Grade 3** | Chapter 2: Multiplication Concepts | Counting Tiles (144-Tile Studio) | Exploration: "Four-Quadrant Array Area Models". Build 12x12 grid, evaluate `12 [ENTER] 12 [Γ] = 144` (**SC-6 Manual, Ch. 4**). |
| **Grade 3** | Chapter 12: Time and Measurement | Clock & Interval Timer | Exploration: "Elapsed Time on a Clock". Rotate bezel to measure elapsed minutes, verify with `[π]` (**SC-6 Manual, Ch. 9**). |
| **Grade 4** | Chapter 7: Understand Fractions | Fraction Studio Towers | Exploration: "Decomposing Fractions". Match three 1/8 blocks to 3/8, verify with `3 [.] 8` (**SC-6 Manual, Ch. 5**). |
| **Grade 6** | Chapter 1: Numerical Expressions & Factors | Prime Factor Studio | Exploration: "Prime Factor Trees & Factor Sockets". Stack factor blocks in towers, verify with `[g] [FACT]` (**SC-6 Manual, Ch. 7**). |
| **Grade 6** | Chapter 3: Algebraic Expressions | SC-32 4-Line Hardware LCD Stack | Exploration: "Parentheses-Free Operations". Evaluate multi-step arithmetic via RPN stack (**SC-32 Manual, Ch. 2**). |
| **Algebra 1** | Chapter 7: Polynomials & Factoring | Algebra Studio & Factoring Stage | Exploration: "Area Models for Quadratic Factoring". Form rectangle with $x^2 + 5x + 6$, solve roots with `[β±] [POLY]` / `[β±] [SOLVE]` (**SC-32 Manual, Ch. 7**). |
| **Precalculus** | Chapter 4: Trigonometric Functions | Unit Circle Trig Volvelle | Exploration: "Exact Surd Values on the Unit Circle". Align aperture to $5\pi/6$, compute exact cosine to 12 digits (**SC-32 Manual, Ch. 4**). |
2.4 Singapore Dimensions Math (Marshall Cavendish)
| Dimensions Level | Chapter & Lesson | Manipulative Setup | CPA Progression: Concrete → Pictorial → Abstract |
| :--- | :--- | :--- | :--- |
| **Dimensions KA** | Ch 4, Lesson 4.1: Number Bonds of 5 | Ten-Frame Studio (2x5 Grid) | **C:** Place 3 teal & 2 coral counters. **P:** Draw number bond circle. **A:** `3 [ENTER] 2 [+] = 5` (**SC-6 Manual, Ch. 3**). |
| **Dimensions 1A** | Ch 7, Lesson 7.1: Tens & Ones | Place Value Studio Trays | **C:** Group 10 unit cubes into 1 ten-rod. **P:** Base-10 column sketch. **A:** Enter in `[NUM]` mode (**SC-6 Manual, Ch. 3**). |
| **Dimensions 1A** | Ch 8, Lesson 8.3: Bridging Through 10 | Ten-Frame Stage + Carry Shelf | **C:** Move 2 counters from second group to fill first ten. **P:** Branching notation. **A:** `8 [ENTER] 2 [+] 3 [+] = 13` (**SC-6 Manual, Ch. 3**). |
| **Dimensions 2A** | Ch 4, Lesson 4.1: Doubles & Multiplying by 2 | Math Domino Studio (12-Frame) | **C:** Snap identical double tile. **P:** Draw 2 equal rows. **A:** `N [ENTER] [+]` (**SC-6 Manual, Ch. 4**). |
| **Dimensions 3A** | Ch 3, Lesson 3.1: Multiplication as Arrays | Counting Tiles (Planar Arrays) | **C:** Form 4x3 rectangular array. **P:** Bar model / array grid. **A:** `4 [ENTER] 3 [Γ] = 12` (**SC-6 Manual, Ch. 4**). |
| **Dimensions 4A** | Ch 3, Lesson 3.1: Fraction Equivalence | Fraction Studio (84mm Whole) | **C:** Line up two 1/4 blocks with one 1/2 block. **P:** Singapore Bar Model. **A:** `2 [.] 4 [SIMP] => 1/2` (**SC-6 Manual, Ch. 5**). |
| **Dimensions 5A** | Ch 1, Lesson 1.4: Prime Factorization | Prime Factor Studio | **C:** Stack factor blocks $[2], [3], [5]$ on desk. **P:** Prime factor tree diagram. **A:** Match composite factor heights and verify with `[g] [FACT]` (**SC-6 Manual, Ch. 7**). |
| **Dimensions 8A** | Ch 4, Lesson 4.2: Factoring Trinomials | Algebra Studio & Factoring Stage | **C:** Arrange $x^2, x, 1$ tiles into rectangle. **P:** Area model diagram. **A:** `[β±] [POLY]` root evaluation on SC-32 (**SC-32 Manual, Ch. 7**). |
| **Additional Math** | Ch 8: Circular Measure & Radians | Acrylic Trig Volvelle | **C:** Rotate outer angle dial. **P:** Coordinate point on unit circle. **A:** Convert degrees to exact radians with `[RAD]` (**SC-32 Manual, Ch. 4**). |
3. Printable Reference Books, Teacher Solution Keys & Station Cards
Explore our spiral-bound reference handbooks ($16 print editions) and download our complete open-source classroom teacher guides and student station materials: