13.1 Elementary Education K-6 Subtests & Competencies (Language Arts/Reading, Social Science, Science, Mathematics)

Elementary Education K-6 Subtests & Competencies

Quick Answer: The FTCE Elementary Education K-6 (Test Code 060) is the cornerstone Subject Area Examination for Florida elementary certification. It features four modular subtests: Language Arts & Reading (601), Social Science (602), Science (603), and Mathematics (604). Candidates may complete all four subtests in a single 4-hour-and-30-minute session or test across multiple appointments. Each subtest is scored on a criterion-referenced scale requiring a scaled score of 200 to pass. Passed subtests are permanently banked, while unpassed subtests may be retaken independently after Florida's statutory 31-calendar-day waiting period under Florida Administrative Code Rule 6A-4.0021.

---

1. Examination Architecture & Modular Administration

The Elementary Education K-6 examination assesses pedagogical subject-matter competency across the core curriculum taught in Florida kindergarten through sixth-grade classrooms. Unlike single-session exams, Test 060 employs a modular architecture designed for candidate flexibility.

+---------------------------------------------------------------------------------------------------+
|                     FTCE ELEMENTARY EDUCATION K-6 (TEST CODE 060) SPECIFICATIONS                  |
+------------------------------------+----------------+-------------------+-------------------------+
| Subtest Name & Code                | Question Count | Testing Time      | Specialized Tools       |
+------------------------------------+----------------+-------------------+-------------------------+
| Subtest 1: Language Arts & Reading | ~50 Multiple-  | 1 Hour 5 Minutes  | None                    |
| (Test Code 601)                    | Choice Items   | (65 Minutes)      |                         |
+------------------------------------+----------------+-------------------+-------------------------+
| Subtest 2: Social Science          | ~45 Multiple-  | 1 Hour 5 Minutes  | None                    |
| (Test Code 602)                    | Choice Items   | (65 Minutes)      |                         |
+------------------------------------+----------------+-------------------+-------------------------+
| Subtest 3: Science                 | ~45 Multiple-  | 1 Hour 10 Minutes | None                    |
| (Test Code 603)                         | Choice Items   | (70 Minutes)      |                    |
+------------------------------------+----------------+-------------------+-------------------------+
| Subtest 4: Mathematics             | ~35 Multiple-  | 1 Hour 10 Minutes | On-Screen 4-Function    |
| (Test Code 604)                    | Choice Items   | (70 Minutes)      | Calculator & Formulas   |
+------------------------------------+----------------+-------------------+-------------------------+
| Full Battery (All 4 Subtests)      | ~175 Multiple- | 4 Hours 30 Minutes| Calculator (Math only)  |
| Single Appointment                 | Choice Items   | (270 Minutes)     |                         |
+------------------------------------+----------------+-------------------+-------------------------+```

### Strategic Modular Scheduling vs. Full-Battery Testing

Candidates may choose between two scheduling formats:
1. **Full Battery in One Sitting:** Scheduling all four subtests in a single 4.5-hour appointment. This minimizes test center travel and testing fee overhead, but requires sustained cognitive endurance.
2. **Split Modular Appointments:** Scheduling subtests individually or in pairs across multiple test dates. Candidates seeking targeted preparation often take Language Arts & Reading with Social Science on one date, and Mathematics with Science on another.

> **Key Rule (Score Banking & Retakes):** Under **Florida Administrative Code Rule 6A-4.0021**, once a candidate earns a passing scaled score of 200 on any individual subtest, that score is **permanently banked** and never expires. If a candidate fails one subtest (e.g., Mathematics 604) but passes the other three, they must only retake Mathematics 604. Retakes require waiting exactly **31 calendar days** from the test administration date.

---

## 2. Subtest 1: Language Arts and Reading (Test Code 601)

The Language Arts and Reading subtest assesses comprehensive foundational literacy instruction grounded in the **Science of Reading**, text analysis across literary and informational genres, writing instruction under the **Florida B.E.S.T. Standards**, and diagnostic literacy assessment.

+---------------------------------------------------------------------------------------------------+ | SUBTEST 1: LANGUAGE ARTS & READING (601) COMPETENCY BREAKDOWN | +------------------------------------------------------------------------+--------------------------+ | Competency 1: Knowledge of the reading process | 44% | | Competency 2: Knowledge of texts and text analysis | 16% | | Competency 3: Knowledge of the writing process | 10% | | Competency 4: Knowledge of literacy instruction and assessments | 20% | | Competency 5: Knowledge of communication and media literacy | 10% | +------------------------------------------------------------------------+--------------------------+```

Competency 1: Foundational Literacy & The Science of Reading

Elementary educators must master the five essential pillars of reading identified by the National Reading Panel, augmented by oral language and structured literacy principles:

• Phonological & Phonemic Awareness: The hierarchy of phonological skills progresses from broad phonological awareness (word awareness, rhyming, alliteration, syllable segmentation/blending, onset-rime manipulation) to discrete phonemic awareness (isolating, blending, segmenting, adding, deleting, and substituting individual phonemes).
  • Example: Segmenting the word "stop" into four distinct phonemes: /s/ /t/ /o/ /p/.
  • Instructional Strategy: Elkonin sound boxes, push-and-say tokens, and multisensory phoneme mapping.
• Phonics & Word Recognition: Explicit, systematic phonics instruction linking graphemes to phonemes. Concepts include:
  • Six Syllable Types: Closed (cat), Open (he), Vowel-Consonant-e / VCe (cake), Vowel Team / Digraph (boat, rain), R-Controlled / Bossy R (car, bird), and Consonant-le (table, candle).
  • Syllabication Rules: VC/CV (divide between consonants: rab-bit), V/CV (divide before single consonant: ti-ger), VC/V (divide after consonant for short vowel: rob-in).
  • Morphological Analysis: Root words, prefixes (e.g., un-, re-, dis-), suffixes (inflectional -ed, -ing, -s; derivational -ful, -tion, -ment).
• Fluency: The Bridge between word recognition and comprehension. Fluency consists of three core components:
  • Accuracy: Correct word identification (target >95% in instructional text, >98% in independent text).
  • Automaticity (Rate): Words Correct Per Minute (WCPM) measured against seasonal grade-level norms (Hasbrouck-Tindal oral reading fluency chart).
  • Prosody: Expressive reading with appropriate phrasing, inflection, intonation, and adherence to punctuation marks.
  • Evidence-Based Interventions: Repeated readings, paired reading, choral reading, and reader's theater. Unscaffolded round-robin reading is considered ineffective and pedagogically unacceptable.
• Vocabulary Development: Direct and indirect vocabulary acquisition using Beck & McKeown's Three-Tier Model:
  • Tier 1 (Basic): Everyday conversational words (house, run, happy) requiring minimal direct instruction.
  • Tier 2 (High-Utility Academic): Cross-curricular academic words (analyze, contrast, synthesize, evaluate) that form the primary focus of direct classroom instruction.
  • Tier 3 (Domain-Specific): Specialized technical words tied to specific disciplines (photosynthesis, isotope, peninsula) taught in context.
• Reading Comprehension: Constructing meaning through metacognitive and structured comprehension routines:
  • Metacognitive Strategies: Self-monitoring, generating questions, visualizing, inferencing, and summarizing.
  • Reciprocal Teaching: A four-strategy collaborative framework comprising Predicting, Clarifying, Questioning, and Summarizing.

Competency 2: Text Analysis, Literary Genres & Craft

• Literary Text Elements: Plot exposition, rising action, climax, falling action, resolution, theme vs. main idea, character development (protagonist, antagonist, static vs. dynamic), setting, and point of view (First-Person I/we, Second-Person you, Third-Person Limited he/she knows one character's thoughts, Third-Person Omniscient all-knowing narrator).
• Informational Text Structures: Description, Chronological/Sequence, Cause and Effect, Problem and Solution, and Compare and Contrast. Identification via signal words and graphic organizers.
• Author's Craft & Figurative Language: Metaphor, simile, personification, hyperbole, alliteration, onomatopoeia, imagery, tone vs. mood.

Competency 3: Writing Process & Florida B.E.S.T. Standards

• Stages of the Writing Process:
  1. Prewriting: Brainstorming, researching, clustering, outlining, establishing audience and purpose.
  2. Drafting: Putting ideas into continuous prose without premature editing.
  3. Revising: Modifying content, organization, voice, sentence fluency, and word choice (A.R.R.R. — Add, Rearrange, Remove, Replace).
  4. Editing: Correcting surface-level mechanics, capitalization, spelling, grammar, and punctuation (C.O.P.S. — Capitalization, Organization, Punctuation, Spelling).
  5. Publishing: Sharing the finalized text with an intended audience.
• Writing Modes: Narrative, Informative/Explanatory, and Opinion/Argumentative writing with text-based evidence synthesis.

Competency 4: Diagnostic Literacy Assessment & Interventions

• Informal Reading Inventories (IRI): Determining reading levels:
  • Independent Level: 95–100% word accuracy, >= 90% comprehension.
  • Instructional Level (ZPD): 90–94% word accuracy, 75–89% comprehension (ideal for guided reading).
  • Frustrational Level: <90% word accuracy, <75% comprehension (text is too difficult; requires intensive scaffolding).
• Running Records & Miscue Analysis (MSV Framework):
  • M = Meaning (Semantic Cue): Did the error make sense in the context of the passage?
  • S = Structure (Syntactic Cue): Did the error fit the grammatical rules and part of speech of the sentence?
  • V = Visual (Graphophonic Cue): Did the error look like the target printed word (matching initial, medial, or final letters)?

---

3. Subtest 2: Social Science (Test Code 602)

The Social Science subtest evaluates subject-matter expertise across history (with distinct emphasis on Florida history), geography, civics and government, economics, and pedagogical assessment strategies.

+---------------------------------------------------------------------------------------------------+
|                     SUBTEST 2: SOCIAL SCIENCE (602) COMPETENCY BREAKDOWN                          |
+------------------------------------------------------------------------+--------------------------+
| Competency 1: Effective instructional practice & assessment of social sciences| 19%               |
| Competency 2: Time, continuity, and change (history)                   | 26%                      |
| Competency 3: People, places, and environment (geography)              | 18%                      |
| Competency 4: Government and the citizen (government & civics)         | 20%                      |
| Competency 5: Production, distribution & consumption (economics)       | 17%                      |
+------------------------------------------------------------------------+--------------------------+```

### Competency 1: Historical Inquiry & Source Analysis
- **Primary vs. Secondary Sources:**
  - *Primary Sources:* First-hand, contemporary accounts created during the time period under study (diaries, letters, photographs, treaties, speeches, raw census records, artifacts).
  - *Secondary Sources:* Interpretations, summaries, or analyses written after the event by non-participants (textbooks, scholarly biographies, historical encyclopedias, documentary films).
- **Historiographical Literacy:** Identifying historical point of view, evaluating author bias, corroborating multiple sources, and interpreting historical timelines, demographic charts, and thematic maps.

### Competency 2: Florida and United States History
- **Indigenous Peoples of Florida:** The Calusa (coastal southwest Florida, known for shell mounds and maritime engineering), Timucua (northeast/central Florida, agricultural and palisaded villages), Apalachee (northwest Panhandle, extensive maize farming and trade), and Tequesta (southeast coast).
- **Spanish Exploration & Early Settlement:**
  - *1513:* Juan Ponce de León arrives on the Florida coast, naming it *La Florida*.
  - *1565:* Pedro Menéndez de Avilés establishes **St. Augustine**, the oldest continuously occupied European settlement in the continental United States, and constructs the Castillo de San Marcos.
  - *Colonial Rivalry:* Spanish, French (Fort Caroline), and British control (Treaty of Paris 1763 traded Florida to Great Britain; Treaty of Paris 1783 returned Florida to Spain).
- **Territorial Florida, Seminole Wars & Statehood:**
  - *Adams-Onís Treaty (1819):* Spain formally ceded Florida to the United States (effective 1821).
  - *Seminole Wars:* First (1817–1818), Second (1835–1842, led by Osceola; most costly Indian War fought by the US), and Third (1855–1858) Seminole Wars, resulting in forced removal of Indigenous populations to Indian Territory, while resilient bands retreated into the Everglades.
  - *1845 Statehood:* Florida entered the Union on **March 3, 1845**, as the 27th state (admitted as a slave state paired with Iowa as a free state).
- **Industrial Transformation & Modern Florida:**
  - *Henry Flagler:* Constructed the Florida East Coast Railway and luxury hotels, opening southern Florida and Key West to tourism and agricultural commerce.
  - *Henry Plant:* Developed the Atlantic Coast Line Railroad and Tampa Bay Hotel, transforming the Gulf Coast into an industrial shipping hub.
  - *Citrus, Cattle, Phosphate, and Tourism:* Core economic drivers throughout the 19th and 20th centuries, culminating in post-WWII aerospace expansion (Cape Canaveral / NASA) and theme park development.
- **United States History Highlights:**
  - *American Revolution & Constitutional Era:* Declaration of Independence (1776), Articles of Confederation weaknesses, Constitutional Convention of 1787, Federalist vs. Anti-Federalist debates, Bill of Rights (1791).
  - *Civil War & Reconstruction:* Sectionalism, Missouri Compromise (1820), Compromise of 1850, Emancipation Proclamation (1863), 13th, 14th, and 15th Amendments (Reconstruction Amendments).
  - *20th Century & Civil Rights Movement:* Industrialization, Progressive Era reforms, Great Depression and New Deal, WWI and WWII, Cold War containment, *Brown v. Board of Education* (1954), Civil Rights Act of 1964, Voting Rights Act of 1965.

### Competency 3: Geography & Spatial Thinking
- **Five Themes of Geography:**
  1. *Location:* Absolute (latitude/longitude coordinates) vs. Relative (position relative to landmarks).
  2. *Place:* Physical characteristics (landforms, climate, biomes) and human characteristics (culture, language, religion, population density).
  3. *Human-Environment Interaction:* Adaptation (building stilt homes in flood zones), modification (canals, deforestation, damming rivers), and dependency (relying on the Everglades aquifer for freshwater).
  4. *Movement:* Spatial transfer of people (migration, immigration), goods (trade, shipping), and ideas (cultural diffusion, telecommunications).
  5. *Region:* Formal regions (defined by political boundaries or uniform climate), Functional regions (nodal, defined by focal connection like a transit system or newspaper distribution area), and Perceptual/Vernacular regions (informal cultural constructs, e.g., 'The Deep South', 'The Rust Belt').
- **Map Projections & Geographic Tools:** Mercator (distorts area near the poles, preserves directional compass bearing for navigation), Robinson (visually balanced compromise with curved meridians), Topographic maps (contour lines indicating elevation change).

### Competency 4: Civics, Government & Florida Constitution
- **Principles of Constitutional Government:** Popular sovereignty, limited government, separation of powers, checks and balances, federalism (enumerated, reserved, concurrent powers), and judicial review (*Marbury v. Madison*).
- **Three Branches of Government:**
  - *Legislative:* Bicameral US Congress (Senate and House of Representatives; makes federal laws, controls purse strings). Florida Legislature (Florida Senate and Florida House of Representatives).
  - *Executive:* President, Cabinet, federal agencies (enforces laws, Commander-in-Chief). Florida Governor, Lieutenant Governor, and elected Cabinet (Attorney General, Chief Financial Officer, Commissioner of Agriculture).
  - *Judicial:* US Supreme Court and federal appellate/district courts (interprets laws, evaluates constitutionality). Florida Supreme Court, District Courts of Appeal, Circuit Courts, and County Courts.
- **Civic Rights & Responsibilities:** Mandatory obligations (paying taxes, serving on juries, obeying laws, selective service registration) vs. voluntary civic participation (voting, petitioning government, attending school board meetings).

### Competency 5: Principles of Economics
- **Fundamental Economic Concepts:** Scarcity (unlimited wants vs. limited resources), opportunity cost (the value of the next best alternative forgone when making a decision), factors of production (Land, Labor, Capital, Entrepreneurship).
- **Market Dynamics:** Law of Supply (higher price increases quantity supplied), Law of Demand (higher price decreases quantity demanded), equilibrium price, price ceilings, and price floors.
- **Economic Systems:** Traditional (custom and barter), Command (state-controlled planning), Market (private enterprise, price mechanism), and Mixed economies (contemporary US model combining private markets with regulatory oversight).

---

## 4. Subtest 3: Science (Test Code 603)

The Science subtest assesses scientific inquiry, laboratory safety regulations, the **5E instructional model**, and disciplinary knowledge across physical, Earth/space, and life sciences.

+---------------------------------------------------------------------------------------------------+ | SUBTEST 3: SCIENCE (603) COMPETENCY BREAKDOWN | +------------------------------------------------------------------------+--------------------------+ | Competency 1: Knowledge of effective science instruction | 20% | | Competency 2: Knowledge of the nature of science | 18% | | Competency 3: Knowledge of physical sciences | 20% | | Competency 4: Knowledge of Earth and space | 19% | | Competency 5: Knowledge of life science | 23% | +------------------------------------------------------------------------+--------------------------+```

Competency 1 & 2: Inquiry, Safety & The Nature of Science

• The 5E Inquiry Instructional Model:
  1. Engage: Capture student interest, elicit prior knowledge, and introduce a driving phenomenon or question.
  2. Explore: Hands-on collaborative investigation, manipulating materials, collecting empirical data without direct teacher lecturing.
  3. Explain: Students verbalize conceptual understandings using evidence; the teacher introduces formal scientific vocabulary and clarifies misconceptions.
  4. Elaborate: Students apply newly acquired concepts to novel scenarios, engineering design challenges, or cross-disciplinary problems.
  5. Evaluate: Formative and summative assessment of student mastery, self-assessment, and rubric-based reflection.
• Laboratory Safety Protocols:
  • Personal Protective Equipment (PPE): Splash goggles (ANSI Z87.1 approved), aprons, heat-resistant gloves.
  • Emergency Safety Equipment: Eyewash station (must flush eyes continuously for at least 15 minutes), safety shower, fire blanket, ABC fire extinguisher.
  • Chemical Handling & Storage: Maintain updated Safety Data Sheets (SDS), store flammables in dedicated fire-rated cabinets, never dispose of hazardous chemicals down standard classroom sinks, label all secondary containers with GHS pictograms.
• Nature of Science Principles:
  • Hypothesis vs. Theory vs. Law: A hypothesis is a testable, falsifiable proposition. A scientific theory is a well-substantiated, comprehensive explanation of observable natural phenomena supported by vast empirical evidence (e.g., Theory of Plate Tectonics, Cell Theory). A scientific law is a descriptive statement or mathematical equation summarizing observed relationships under specific conditions (e.g., Law of Conservation of Mass, Newton's Laws of Motion). Note: Theories do NOT become laws with additional proof.
  • Experimental Variables: Independent variable (the single manipulated factor changed by the experimenter), Dependent variable (the measured outcome or response), Controlled variables/Constants (all variables kept strictly identical across experimental and control groups to maintain internal validity).

Competency 3: Physical Science

• Structure and Properties of Matter:
  • States of Matter: Solid (definite shape and volume, tightly packed vibrating particles), Liquid (definite volume, indefinite shape, sliding particles), Gas (indefinite shape and volume, high-speed dispersed particles), Plasma (ionized high-energy gas).
  • Physical vs. Chemical Changes: Physical changes alter form without altering chemical bonds (melting ice, dissolving salt in water, tearing paper). Chemical changes result in new substances with altered molecular identity (combustion, rusting of iron, baking bread, acid-base neutralization; indicated by gas formation, precipitate formation, unexpected color change, or temperature change).
  • Atomic Structure: Protons (+1 charge, in nucleus), Neutrons (0 charge, in nucleus), Electrons (-1 charge, in electron shells). Elements, compounds, mixtures (homogeneous solutions vs. heterogeneous suspensions).
• Forces, Motion & Newton's Laws:
  • Newton's 1st Law (Inertia): An object at rest remains at rest, and an object in uniform motion remains in motion unless acted upon by an unbalanced external force.
  • Newton's 2nd Law ($F = ma$): Acceleration is directly proportional to net force and inversely proportional to mass.
  • Newton's 3rd Law (Action-Reaction): For every action force, there is an equal and opposite reaction force.
• Energy Forms & Circuits:
  • Forms of Energy: Kinetic, potential (gravitational, chemical, elastic), thermal, electrical, radiant/light, and sound energy. Law of Conservation of Energy (energy cannot be created or destroyed, only transformed).
  • Circuits: Closed complete circuit vs. open circuit. Series circuits (single path; if one bulb disconnects, all go out; resistance increases additively) vs. Parallel circuits (multiple independent branches; if one bulb burns out, others remain lit; standard for residential wiring).

Competency 4: Earth and Space Science

• Geology & Plate Tectonics:
  • Earth's Layers: Crust (continental and oceanic), Mantle (lithosphere and asthenosphere mantle convection driving plate motion), Outer Core (liquid iron-nickel generating Earth's magnetic field), Inner Core (solid iron-nickel under extreme pressure).
  • Plate Boundaries: Divergent (plates move apart; mid-ocean ridges, rift valleys), Convergent (plates collide; subduction zones, deep ocean trenches, volcanic mountain ranges), Transform (plates slide horizontally past one another; strike-slip fault lines, severe earthquakes like the San Andreas Fault).
  • The Rock Cycle: Igneous (cooled magma/lava; basalt, granite), Sedimentary (weathering, erosion, deposition, compaction, cementation; sandstone, limestone), Metamorphic (heat and pressure altering existing rock without melting; marble, slate).
• Hydrology, Weather & Florida Meteorology:
  • Water Cycle: Evaporation, Transpiration (water loss from plant stomata), Condensation, Precipitation, Infiltration/Percolation, Runoff.
  • Atmospheric Layers: Troposphere (where all weather occurs, temperature decreases with altitude), Stratosphere (contains protective ozone layer absorbing UV radiation), Mesosphere, Thermosphere, Exosphere.
  • Florida Weather: Humid subtropical/tropical savanna climate; high convective thunderstorm frequency due to sea breeze convergence; hurricane formation over warm ocean waters (>= 80 deg F / 26.5 deg C).
• Astronomy & Planetary Systems:
  • Seasons: Caused strictly by Earth's 23.5 degree axial tilt as it revolves around the Sun—NOT by distance from the Sun (Earth is closest to the Sun at perihelion in January).
  • Lunar Phases: New Moon, Waxing Crescent, First Quarter, Waxing Gibbous, Full Moon, Waning Gibbous, Third Quarter, Waning Crescent (complete cycle = 29.5 days).
  • Eclipses: Solar Eclipse (Sun - Moon - Earth alignment; Moon casts shadow on Earth), Lunar Eclipse (Sun - Earth - Moon alignment; Earth casts shadow on Full Moon).

Competency 5: Life Science

• Cell Biology & Energetics:
  • Cell Theory: (1) All living organisms are composed of one or more cells; (2) The cell is the basic structural and functional unit of life; (3) All cells arise from pre-existing cells.
  • Organelles: Nucleus (contains genetic material), Mitochondria ("powerhouse", site of cellular respiration producing ATP), Ribosomes (protein synthesis), Chloroplasts (site of photosynthesis in plant cells containing chlorophyll), Vacuoles (large central water storage in plant cells), Cell Wall (rigid cellulose structure in plants/fungi), Cell Membrane (semipermeable phospholipid bilayer).
  • Photosynthesis: 6CO2 + 6H2O + Light Energy -> C6H12O6 + 6O2.
  • Cellular Respiration: C6H12O6 + 6O2 -> 6CO2 + 6H2O + 36-38 ATP.
• Genetics & Heredity:
  • Mendelian Inheritance: Alleles (dominant vs. recessive), Genotype (genetic makeup: BB, Bb, bb) vs. Phenotype (physical expressed trait: brown eyes, blue eyes), Homozygous vs. Heterozygous, Punnett Square probability calculations.
  • DNA Structure: Double helix composed of nucleotides (phosphate group, deoxyribose sugar, nitrogenous bases: Adenine pairs with Thymine, Cytosine pairs with Guanine).
• Ecology & Ecosystem Dynamics:
  • Trophic Levels & Energy Pyramids: Producers (autotrophs) -> Primary Consumers (herbivores) -> Secondary Consumers (carnivores/omnivores) -> Tertiary Consumers -> Decomposers (detritivores). Only 10% of energy is transferred from one trophic level to the next (90% lost as metabolic heat).
  • Symbiotic Relationships: Mutualism (+/+, both benefit), Commensalism (+/0, one benefits, other unaffected), Parasitism (+/-, one benefits at host expense).

---

5. Subtest 4: Mathematics (Test Code 604)

The Mathematics subtest assesses mathematical pedagogy, conceptual problem-solving, error diagnostics, and content aligned to the Florida B.E.S.T. Mathematics Standards.

+---------------------------------------------------------------------------------------------------+
|                        SUBTEST 4: MATHEMATICS (604) COMPETENCY BREAKDOWN                          |
+------------------------------------------------------------------------+--------------------------+
| Competency 1: Integers, decimals, and fractions in base-10             | 29%                      |
| Competency 2: Knowledge of algebraic reasoning                         | 15%                      |
| Competency 3: Measurement, data analysis, and statistics               | 14%                      |
| Competency 4: Knowledge of geometric concepts                          | 15%                      |
| Competency 5: Student reasoning and instructional practices            | 27%                      |
+------------------------------------------------------------------------+--------------------------+```

### Competency 1: Mathematics Pedagogy & The CRA Framework
- **The Concrete-Representational-Abstract (CRA) Sequence:**
  1. *Concrete Stage:* Students manipulate physical objects to build conceptual understanding (base-ten blocks, counters, fraction tiles, algebra tiles, geoboards).
  2. *Representational (Semi-Concrete) Stage:* Students transition from physical objects to visual pictorial representations (drawings, bar models / tape diagrams, number lines, area models, ten-frames).
  3. *Abstract Stage:* Students solve mathematical problems using symbolic notation, numerical algorithms, and algebraic formulas.
- **Diagnostic Error Analysis:** Identifying underlying conceptual misconceptions vs. procedural slips:
  - *Example Misconception (Fractions):* Adding across numerators and denominators (1/3 + 1/4 = 2/7). The teacher must scaffold understanding by having the student model fractions using equal-sized fraction tiles on a number line to show common denominators are required for equivalent unit partitioning.
  - *Example Misconception (Decimals):* Believing 0.35 is larger than 0.8 because 35 > 8. Scaffolding requires base-ten grid modeling to demonstrate that 8 tenths = 80 hundredths > 35 hundredths.

### Competency 2: Number Sense, Operations & Algebraic Thinking
- **Properties of Operations:**
  - *Commutative Property:* a + b = b + a and a * b = b * a (order does not alter sum/product).
  - *Associative Property:* (a + b) + c = a + (b + c) and (a * b) * c = a * (b * c) (grouping does not alter sum/product).
  - *Distributive Property:* a(b + c) = ab + ac.
  - *Identity Property:* Additive identity is 0 (a + 0 = a); Multiplicative identity is 1 (a * 1 = a).
  - *Inverse Property:* Additive inverse (a + (-a) = 0); Multiplicative inverse (a * (1/a) = 1, for a != 0).
- **Fractions, Ratios, Decimals & Percentages:**
  - *Fraction Operations:* Addition/subtraction with uncommon denominators via LCM/LCD; multiplication as area modeling ((a/b) * (c/d) = (ac)/(bd)); division via reciprocal multiplication ((a/b) / (c/d) = (a/b) * (d/c)).
  - *Unit Rates & Proportions:* Cross-multiplication and scaling ratio tables.
- **Algebraic Expressions & Equations:**
  - Solving multi-step linear equations: 3(2x - 4) + 5 = 29 -> 6x - 12 + 5 = 29 -> 6x - 7 = 29 -> 6x = 36 -> x = 6.
  - Linear inequalities: Reversing inequality sign when multiplying or dividing by a negative number.
  - Linear functions: Slope-intercept form (y = mx + b), calculating slope m = (y2 - y1)/(x2 - x1), interpreting rate of change and y-intercept in applied contexts.

### Competency 3: Measurement, Data & Probability
- **Measurement Conversions & Formulas:**
  - Customary units (12 in = 1 ft, 3 ft = 1 yd, 5280 ft = 1 mi; 16 oz = 1 lb, 2000 lb = 1 ton; 8 fl oz = 1 cup, 2 cups = 1 pt, 2 pt = 1 qt, 4 qt = 1 gal).
  - Metric system conversions via powers of 10 (Kilo, Hecto, Deka, Base, Deci, Centi, Milli: 'King Henry Died By Drinking Chocolate Milk').
  - Area formulas: Rectangle (A = lw), Triangle (A = 0.5bh), Parallelogram (A = bh), Trapezoid (A = 0.5(a+b)h), Circle (A = pi * r^2, Circumference C = 2 * pi * r = pi * d).
  - Volume & Surface Area: Rectangular prism (V = lwh, SA = 2lw + 2lh + 2wh), Cylinder (V = pi * r^2 * h).
- **Descriptive Statistics & Data Representations:**
  - *Measures of Center:* Mean (arithmetic average), Median (middle value in ordered dataset), Mode (most frequent value).
  - *Measures of Spread:* Range (Maximum - Minimum), Interquartile Range (IQR = Q3 - Q1).
  - *Data Displays:* Box-and-whisker plots (five-number summary: Min, Q1, Median, Q3, Max), histograms, stem-and-leaf plots, dot plots, scatter plots (identifying positive, negative, or no correlation).
- **Probability:** Theoretical probability P(E) = (Number of Favorable Outcomes) / (Total Possible Outcomes); Compound events; Independent vs. dependent events.

### Competency 4: Geometry & Spatial Reasoning
- **Classification of Polygons & 3D Solids:**
  - Triangles classified by sides (equilateral, isosceles, scalene) and angles (acute, right, obtuse). Triangle sum theorem: Interior angles = 180 degrees.
  - Quadrilaterals hierarchy: Trapezoid, Parallelogram, Rectangle, Rhombus, Square.
  - Polygons: Sum of interior angles of an n-gon = (n-2) * 180 degrees.
- **Coordinate Geometry & Transformations:**
  - Coordinate plane quadrants (I: +/+, II: -/+, III: -/-, IV: +/-).
  - Rigid Transformations (preserve congruence, shape, and size): Translation (slide), Reflection (flip over line of reflection), Rotation (turn around a point).
  - Non-Rigid Transformations: Dilation (expansion or contraction by a scale factor k, preserving similarity but altering side lengths).
  - Pythagorean Theorem: a^2 + b^2 = c^2 in right-angled triangles (common triples: 3-4-5, 5-12-13, 8-15-17).