A roadmap to raising an irreplaceable human.

Author

Jian W Dong, M.D., M.S.

K-12 STEM-Focused Curriculum Checklist

A comprehensive and ambitious STEM-heavy curriculum roadmap from early childhood through 12th grade, designed to prepare students to become first-principle thinkers and fast continual learners.

Objective

This work-in-progress curriculum checklist will be continually updated; it outlines a rigorous educational pathway that emphasizes Strong mathematical foundations and scientific exploration from the earliest ages.

The goal is not to teach facts, but to build a mind that can learn anything.

By the end of 12th grade, the learner will:

Master the mathematical languages of reality: Calculus, Linear Algebra, Probability & Statistics.
Think from first principles: Deconstruct any problem to its fundamental building blocks and rebuild upward.
Learn anything quickly: Possess robust metacognitive tools, research skills, and the confidence to enter any domain.
Build with their hands: Translate abstract ideas into a physical reality via making, electronics, and fabrication.
Communicate powerfully: Write, speak, and visualize ideas with clarity and persuasion.
Exercise human judgment: Navigate ethics, ambiguity, and value trade-offs.
Create across domains: Synthesize insights from multiple fields into novel solutions.

How to Use This Curriculum

This independent curriculum is best used as a checklist for parents to ensure their child are adequately educated. It is meant as a supplementary checklist - to identify weaknesses and blind spots, allowing for early intervention. Parents can supplement any topics not covered by their kid’s school curriculum. Recommended books and resources are provided for each topic.

About the Author

I am a physician, data scientist, and father of 2 kids. I immigrated to New York City at age 6 and attended NYC public schools from grade 1 to 12. I attended college at Columbia University where I graduated with high honors in Mechanical Engineering. I then obtained my medical degree at NYU, and did my radiology residency at Harvard. While practicing as a radiologist, along the way I also obtained a master of science in Data Science from UT Austin.

📋 Curriculum Overview

Toddler and Pre-School Years (Ages 2-5)

Elementary School (Grades K-5)

Middle School (Grades 6-8)

High School (Grades 9-12)

Ages 2-5: Foundation Building Through Play

This stage of life is mostly about guided discovery and play-based learning. The goal is to build a physical intuition for concepts that will be formalized later.

🗣️ Language

At this stage of life, building strong language skills is most important as it is the foundation for all future learning, STEM or otherwise. This includes reading, writing, and speaking. - [ ] English: Focus on reading and writing alphabets and numbers. - [ ] Letter recognition (ABCs), phonics, and sight words. - [ ] Introduction to basic grammar and punctuation. - [ ] Additional Language is crucial: Exposure to other languages like Chinese through songs, stories, and basic vocabulary.

➗ Mathematics & Logic

Counting & Arithmetic: Rote counting in written and spoken form, one-to-one correspondence, simple addition, subtraction, and multiplication with physical objects.
Geometry: Identifying and describing shapes. Building 3D geometric shapes with blocks. Extending 2D shapes into 3D shapes (e.g. circle and sphere, square and cube). Understanding symmetry and congruence.
Probability & Data: Simple probability concepts (e.g., coin toss and dice (be careful of small parts!), playing cards, chance of pulling a specific color block from a bag). Sorting objects by attributes (color, size, shape).

🔬 Science: Hands-On Exploration

Nature: Plants and Animals, Weather

Observing and identifying common animals and plants.
Understanding life cycles in animal and plants (e.g. caterpillar to butterfly, seed to plant).
Understanding natural cycles (e.g. water cycles, seasons).
Concept of Time: time of the day, days of the week, weeks, months, and years.
Distinguishing natural from human-made objects.

Mechanical

Exploring simple machines with toys: Pulleys, levers, wheels and axles.
Investigating concepts of balance, center of mass, hinges, and joints through building.
Exploring friction by sliding toys on different surfaces.
Experimenting with elastic and inelastic collisions using different types of balls.
Investigating springs and their properties.
Understanding buoyancy through water play.

Electricity and Magnetism

Building simple parallel vs. serial circuits with snap-together kits.
Playing with magnets to understand attraction and repulsion.
Lighting a small light bulb with a battery (be careful!)

Chemical, Biological, & Motor Skills

Simple kitchen chemistry (mixing ingredients, observing reactions like baking soda and vinegar).
Introducing the phases of elements and compounds. Example: Ice, water, steam.
Gross and fine motor skill development through building, drawing, and outdoor play.

Computing

Recognizing letters and typing on the keyboard
Using the mouse
Introducing the proper typing technique

Elementary School: Building a Framework (Grades K-5)

This era focuses on building causal thinking, scientific reasoning, and computational fluency.

Kindergarten: Mathematical Foundations & Scientific Wonder

➗ Mathematics: Number Sense & Basic Operations

Counting & Number Recognition

Rote Counting: Count to 100 by 1s, 2s, 5s, and 10s
Number Writing: Write numerals 0-20 clearly and accurately
Number Relationships: Understand “greater than,” “less than,” “equal to”
Place Value: Recognize that teen numbers are composed of ten and some ones

Addition & Subtraction Foundations

Conceptual Understanding: Use manipulatives to model addition/subtraction
Fact Fluency: Master addition/subtraction facts to 10
Word Problems: Solve simple join, separate, and compare problems
Number Bonds: Understand all the ways to make numbers 5-10

Geometry & Measurement

2D Shapes: Identify and describe circles, triangles, squares, rectangles, etc.
3D Shapes: Recognize spheres, cubes, cylinders, cones, etc.
Spatial Reasoning: Build with blocks, complete puzzles, follow patterns.
Measurement: Compare length, weight, capacity using non-standard units.

Data & Probability

Sorting & Classifying: Group objects by multiple attributes.
Simple Graphs: Create and interpret picture graphs and bar graphs.
Probability Language: Use words like “always,” “sometimes,” “never”.

🔬 Science: Observation & Wonder

Living Things

Animal Characteristics: Group animals by observable features (fur, feathers, scales).
Plant Parts: Identify roots, stems, leaves, flowers and their functions
Life Cycles: Compare life cycles of butterflies, frogs, and plants
Habitats: Match animals to their habitats and explain why

Earth & Sky

Weather Patterns: Observe and record daily weather, seasonal changes
Day & Night: Understand the sun’s apparent movement across the sky
Earth Materials: Classify rocks, soil, sand, and water
Reduce, Reuse, Recycle: Basic environmental responsibility

Physical Science

Properties of Objects: Describe objects by color, size, shape, texture, weight
Motion: Investigate how things move (push, pull, roll, slide)
Sound: Explore how sounds are made and how they travel
Light: Observe shadows and how light affects what we see

💻 Technology & Engineering

Simple Machines: Explore ramps, levers, and wheels through play
Building Challenges: Design structures with blocks to solve problems
Digital Tools: Use age-appropriate educational software and tablets

Grade 1: Building Number Fluency & Scientific Thinking

🗣️ Communication

Write 3–5 sentence paragraphs.
Keep a “science journal” with drawings and labels.
Give a 1-minute presentation to family.

➗ Mathematics: Addition/Subtraction Mastery

Number Concepts

Counting: Count to 120, starting from any number
Place Value: Understand 10 ones equal 1 ten, work with numbers to 100
Number Comparison: Use <, >, = symbols correctly
Skip Counting: Count by 2s, 5s, and 10s to prepare for multiplication

Addition & Subtraction

Fact Fluency: Master all addition/subtraction facts to 20
Mental Math Strategies: Make 10, doubles, near doubles, counting on
Two-Digit Addition: Add/subtract multiples of 10, simple two-digit problems
Word Problems: Solve result unknown, change unknown, and compare problems

Geometry & Measurement

Shape Analysis: Identify defining vs. non-defining attributes of shapes
Compose Shapes: Create larger shapes from smaller shapes
Measurement: Measure length using standard and non-standard units
Time: Tell time to the hour and half-hour

Data Analysis

Data Collection: Ask questions, collect data, organize results
Graph Interpretation: Read and create picture graphs, bar graphs, tally charts

🔬 Science: Patterns in Nature

Plants & Animals

Animal Structures: How body parts help animals survive (beaks, feet, tails)
Plant Structures: How plant parts help them survive and grow
Parent & Offspring: Compare adult animals with their young
Animal Behavior: How animals use their senses and communicate

Light & Sound

Light Sources: Natural vs. artificial light sources
Materials & Light: Transparent, translucent, and opaque materials
Sound Vibrations: Investigate how vibrating materials make sound
Sound Volume: Explore loud vs. soft sounds and distance

Space Systems

Sun’s Path: Track the sun’s position throughout the day
Seasonal Changes: Observe how daylight hours change through seasons
Moon Observation: Notice the moon’s changing appearance

💻 Technology & Engineering

Engineering Design: Ask, imagine, plan, create, improve
Material Properties: Test materials for strength, flexibility, absorbency
Digital Research: Use kid-friendly search engines with supervision

Grade 2: Advancing Operations & Deeper Investigation

🗣️ Communication

Write short informational paragraphs.
Create labeled diagrams for science observations.
Explain an experiment step-by-step to a listener.

➗ Mathematics: Multi-Digit Operations

Place Value & Number Systems

Three-Digit Numbers: Read, write, and represent numbers to 1,000
Place Value Understanding: Hundreds, tens, ones with base-10 blocks
Number Comparison: Compare three-digit numbers using <, >, =
Rounding: Round to nearest 10 and 100

Addition & Subtraction

Algorithm Development: Add/subtract two-digit numbers with regrouping
Mental Math: Add/subtract 10 or 100 mentally
Estimation: Estimate sums and differences to check reasonableness
Word Problem Strategies: Identify key information and choose operations

Multiplication & Division Foundations

Equal Groups: Use objects and drawings to represent multiplication
Arrays: Create and interpret rectangular arrays
Skip Counting: Count by 3s, 4s, 6s, 7s, 8s, 9s
Division as Sharing: Divide objects into equal groups

Geometry & Measurement

Quadrilaterals: Recognize squares, rectangles, rhombuses, trapezoids
Partitioning Shapes: Divide circles and rectangles into equal parts
Standard Measurement: Measure in inches, feet, centimeters, meters
Time & Money: Tell time to 5 minutes, count coin combinations

Data & Graphs

Line Plots: Create and interpret line plots with whole numbers
Survey Data: Collect, organize, and display survey results

🔬 Science: Matter & Its Interactions

Properties of Materials

Observable Properties: Color, texture, hardness, flexibility, absorbency
Material Classification: Sort materials by properties
Heating & Cooling: Investigate how heating/cooling changes materials
Reversible vs. Irreversible: Identify changes that can/cannot be undone

Plant & Animal Diversity

Habitat Requirements: How plants and animals need different environments
Seed Dispersal: Ways plants spread their seeds
Pollination: How animals help plants reproduce
Adaptation Examples: Specific examples of animal and plant adaptations

Earth’s Systems

Landforms: Identify mountains, valleys, plains, hills, rivers, lakes
Maps: Use simple maps to locate landforms and bodies of water
Natural Resources: Identify renewable vs. non-renewable resources
Human Impact: How humans change the land (farming, building, pollution)

💻 Technology & Engineering

Design Process: Define problems, generate solutions, test and refine
Simple Programming: Introduction to coding concepts through block-based programming
Digital Citizenship: Safe and responsible technology use

Grade 3: Multiplication/Division & Scientific Method

🗣️ Communication

Write multi-paragraph essays with topic sentences.
Create data presentations with graphs and explanations.
Debate a scientific question with evidence.

➗ Mathematics: Multiplicative Thinking

Multiplication & Division

Multiplication Concepts: Equal groups, arrays, area models
Multiplication Facts: Fluency with facts through 12 × 12
Division Concepts: Sharing and grouping models
Division Facts: Related to multiplication facts, fact families
Word Problems: Multi-step problems with all four operations

Fractions

Fraction Concepts: Unit fractions, fractions as parts of a whole
Equivalent Fractions: Use visual models to find equivalent fractions
Comparing Fractions: Compare fractions with same numerator or denominator
Fractions on Number Line: Place fractions on number line

Multi-Digit Operations

Addition/Subtraction: Three-digit numbers with regrouping
Rounding: Round to nearest 10 and 100, use for estimation
Mental Math: Multiplication by 10 and 100

Geometry & Measurement

Polygon Classification: Identify polygons by number of sides
Area & Perimeter: Find area and perimeter of rectangles
Measurement Precision: Choose appropriate units and tools
Time Intervals: Calculate elapsed time, solve time problems

Data Analysis

Scaled Graphs: Create and interpret bar graphs with scales
Data Interpretation: Draw conclusions from data displays

🔬 Science: Forces & Motion

Balanced & Unbalanced Forces

Force Effects: How forces change object motion (speed, direction).
Friction: Investigate how surface texture affects motion.
Magnetism: Explore magnetic and non-magnetic materials.
Patterns in Motion: Predict motion based on patterns observed.

Life Cycles & Inheritance

Animal Life Cycles: Compare life cycles of different animal groups.
Plant Life Cycles: Detailed study of flowering plant reproduction.
Inherited Traits: Characteristics passed from parents to offspring.
Environmental Influences: How environment affects organism growth.

Weather & Climate

Weather vs. Climate: Distinguish between daily weather and climate patterns
Climate Data: Analyze and interpret climate data from different regions
Weather Prediction: Use weather data to make simple predictions
Weather Safety: Prepare for and respond to severe weather

💻 Technology & Engineering

Engineering Design Cycle: Systematic problem-solving approach
Force & Motion Engineering: Design solutions using magnetic forces
Data Collection Tools: Use digital tools to collect and analyze data
Beginning Spreadsheets: Enter data and create simple charts

Grade 4: Advanced Operations & Systems Thinking

🗣️ Communication

Write research reports with citations.
Present findings using slides or posters.
Peer review: give constructive feedback on others’ work.

➗ Mathematics: Multi-Digit Mastery

Multi-Digit Operations

Multiplication Algorithm: 2-digit × 2-digit multiplication
Division Algorithm: Long division with remainders
Estimation Strategies: Use rounding and compatible numbers
Order of Operations: Solve expressions with multiple operations

Fractions & Decimals

Equivalent Fractions: Generate equivalent fractions systematically
Adding/Subtracting Fractions: Same denominators, mixed numbers
Fraction × Whole Number: Multiply fractions by whole numbers
Decimal Notation: Read, write, and compare decimals to hundredths
Decimal-Fraction Connection: Convert between fractions and decimals

Geometry

Angle Measurement: Use protractors to measure and draw angles
Triangle Classification: By angles (acute, obtuse, right) and sides
Line Relationships: Parallel, perpendicular, and intersecting lines
Symmetry: Identify line symmetry in 2D shapes

Measurement

Metric System: Convert within metric units (mm, cm, m, km)
Customary System: Convert within customary units (in, ft, yd, mi)
Area & Perimeter: Calculate for complex shapes
Volume: Understand volume as filling space with unit cubes

Data & Probability

Line Plots: Display and interpret fractional measurement data
Probability: Express probability as fractions

🔬 Science: Energy & Ecosystems

Energy Transfer

Energy Forms: Kinetic, potential, thermal, light, sound energy
Energy Transfer: How energy moves from place to place
Collisions: Energy transfer in collisions
Wave Properties: Waves carry energy (amplitude, wavelength, frequency)

Structure & Function

Plant Structures: How structures support growth, reproduction, survival
Animal Structures: Internal and external structures and their functions
Sensory Systems: How animals process sensory information
Information Processing: How animals use information to survive

Earth’s Features

Weathering & Erosion: How water, wind, and ice change landforms
Natural Hazards: Earthquakes, volcanoes, floods, hurricanes
Hazard Mitigation: Engineering solutions to reduce hazard impacts
Rock Formation: How different types of rocks form

💻 Technology & Engineering

Advanced Programming: Loops, conditionals in block-based programming
Engineering Solutions: Design solutions for energy transfer problems
Data Analysis: Use spreadsheets for calculations and graphing
Digital Presentations: Create multimedia presentations of findings

Grade 5: Pre-Algebra Readiness & Integrated Science

🗣️ Communication

Write persuasive essays with evidence.
Create video explanations of scientific concepts.
Lead a group discussion with Socratic questioning.

➗ Mathematics: Rational Number Operations

Advanced Operations

Multi-Digit Multiplication: 3-digit × 2-digit fluently
Multi-Digit Division: 4-digit ÷ 2-digit with remainders
Decimal Operations: Add, subtract, multiply, divide decimals to hundredths
Mental Math Mastery: Quick computation strategies for all operations

Fraction Operations

Adding/Subtracting: Unlike denominators using equivalent fractions
Multiplying Fractions: Fraction × fraction, mixed number operations
Dividing Fractions: Divide unit fractions by whole numbers and vice versa
Real-World Applications: Solve complex word problems with fractions

Algebraic Thinking

Expressions: Write and interpret expressions with variables
Patterns: Identify rules in numerical and geometric patterns
Coordinate Plane: Plot points, identify patterns in coordinate pairs
Function Tables: Complete tables showing relationships between variables

Advanced Geometry

Coordinate Geometry: Plot shapes, calculate areas using coordinates
Volume Formulas: V = l × w × h for rectangular prisms
Surface Area: Calculate surface area of rectangular prisms
Scale Drawings: Understand scale and proportional relationships

Statistics & Probability

Data Distribution: Understand spread, clusters, gaps in data
Mean, Median, Mode: Calculate and interpret measures of center
Probability Experiments: Design and conduct probability experiments
Sample Spaces: List all possible outcomes for simple events

🔬 Science: Matter & Earth Systems

Matter & Chemical Reactions

Particle Model: Matter is made of particles too small to see
Conservation of Matter: Matter is conserved in chemical reactions
Chemical vs. Physical: Distinguish between chemical and physical changes
Mixtures & Solutions: Separate mixtures based on properties

Ecosystems & Environment

Food Webs: Model energy flow in ecosystems
Population Dynamics: Factors affecting animal and plant populations
Human Impact: How humans affect ecosystems positively and negatively
Conservation: Strategies for protecting ecosystems and biodiversity

Earth Systems Interactions

Water Cycle: How water moves through Earth’s systems
Weather Systems: How uneven heating creates weather patterns
Climate Patterns: How latitude and geography affect climate
Natural Resources: Formation and distribution of Earth’s resources

Space Systems

Solar System Model: Relative sizes and distances of planets
Gravity: How gravity affects objects in space and on Earth
Day/Night & Seasons: Earth’s rotation and revolution effects
Moon Phases: How the Moon’s orbit creates phases

💻 Technology & Engineering

Advanced Programming: Functions, parameters in programming
Data Science: Collect, analyze, and present data from investigations
Digital Modeling: Use simulation software to model scientific phenomena
Engineering Design: Complete design projects with multiple constraints

📊 Assessment & Readiness for Grade 6

Mathematical Readiness Indicators

Computational Fluency: Accurate and efficient with all operations
Fraction Mastery: Confident with fraction operations and concepts
Algebraic Thinking: Can work with variables and solve simple equations
Problem-Solving: Can analyze multi-step problems systematically

Scientific Thinking Readiness

Scientific Method: Design and conduct controlled investigations
Data Analysis: Collect, analyze, and interpret quantitative data
Scientific Communication: Present findings clearly with evidence
Systems Thinking: Understand how parts work together in systems

Technology Integration Readiness

Digital Tools: Proficient with spreadsheets, graphing, and presentation software
Programming Logic: Understand sequence, loops, and conditionals
Research Skills: Evaluate online sources for credibility and bias
Digital Citizenship: Understand ethical use of technology and information

Middle School: The Launchpad (Grades 6-8)

Focus shifts to abstract thinking, solidifying algebraic foundations, and formalizing scientific principles.

Grade 6: Advanced Pre-Algebra & Earth Science Foundation

🗣️ Communication

Write lab reports with hypothesis, method, results, conclusion.
Create infographics explaining scientific processes.
Deliver a 5-minute persuasive speech.

➗ Mathematics: Advanced Pre-Algebra

Number Systems & Operations

Rational Numbers: Master operations with positive and negative integers, fractions, and decimals
Order of Operations: Complex multi-step problems with grouping symbols
Prime Factorization: Find GCD and LCM using prime factorization
Exponents: Integer exponents, scientific notation for large and small numbers

Ratios, Rates & Proportions

Unit Rates: Calculate and compare unit rates in real-world contexts
Proportional Relationships: Identify and represent proportional relationships in tables, graphs, and equations
Percent Applications: Percent increase/decrease, simple interest, tax, tips, discounts
Scale Drawings: Create and interpret scale drawings and maps

Algebraic Thinking

Variables & Expressions: Write and evaluate algebraic expressions with one variable
Equations: Solve one-step equations with rational numbers
Inequalities: Write and graph simple inequalities on number lines
Patterns: Identify and extend arithmetic and geometric patterns

Geometry

Area & Volume: Area of triangles, parallelograms, trapezoids; volume of rectangular prisms
Surface Area: Calculate surface area of rectangular and triangular prisms
Coordinate Plane: Plot points, find distances, identify geometric relationships

Statistics & Probability

Data Analysis: Create and interpret histograms, box plots, and dot plots
Measures of Center: Calculate and interpret mean, median, and mode
Probability: Theoretical vs. experimental probability, compound events

🌍 Science: Earth & Space Science

Earth’s Systems

Plate Tectonics: Continental drift, seafloor spreading, types of plate boundaries
Rock Cycle: Formation of igneous, sedimentary, and metamorphic rocks
Weathering & Erosion: Physical and chemical weathering processes
Soil Formation: Factors affecting soil development and composition

Weather & Climate

Atmospheric Layers: Troposphere, stratosphere, mesosphere, thermosphere
Weather Systems: High/low pressure systems, fronts, storms
Climate Factors: Latitude, elevation, proximity to water bodies
Climate Change: Evidence, causes, and potential impacts

Water Systems

Water Cycle: Evaporation, transpiration, condensation, precipitation, runoff
Ocean Currents: Surface and deep currents, thermohaline circulation
Groundwater: Aquifers, water table, wells, springs

Solar System & Universe

Solar System: Characteristics of planets, moons, asteroids, comets
Earth-Moon-Sun System: Seasons, moon phases, eclipses, tides
Stars & Galaxies: Stellar lifecycle, galaxy types, light-years
Space Technology: Telescopes, satellites, space exploration

💻 Technology Integration

Data Collection: Use digital tools to collect and analyze weather data
Modeling: Create computer models of Earth processes (erosion, plate movement)
Research Skills: Evaluate credibility of online scientific sources

Grade 7: Algebra I & Life Science Deep Dive

🗣️ Communication

Write argumentative essays with counterarguments.
Create scientific posters for “conference” presentations.
Record and edit educational videos.

➗ Mathematics: Algebra I

Foundations of Algebra

Real Number System: Operations with rational and irrational numbers
Properties of Real Numbers: Commutative, associative, distributive properties
Variable Expressions: Simplify expressions using order of operations
Equation Solving: Multi-step linear equations with variables on both sides

Linear Functions & Graphing

Coordinate Plane: Plot points, identify quadrants, calculate distance
Linear Equations: Slope-intercept form, point-slope form, standard form
Graphing Lines: Graph using slope and y-intercept, x- and y-intercepts
Slope: Calculate slope from graphs, tables, and coordinate points

Systems of Linear Equations

Solving Systems: Graphing, substitution, and elimination methods
Applications: Age problems, mixture problems, distance-rate-time problems
Linear Inequalities: Graph linear inequalities and systems of inequalities

Polynomials & Factoring

Exponent Rules: Product, quotient, power rules with integer exponents
Polynomial Operations: Add, subtract, and multiply polynomials
Factoring: Greatest common factor, difference of squares
Simple Trinomials: Factor trinomials of the form ax² + bx + c

Quadratic Functions (Introduction)

Graphing Parabolas: Vertex form, axis of symmetry, maximum/minimum
Solving Quadratics: Square root method, factoring simple quadratics
Applications: Area problems, projectile motion (basic)

Radical Expressions

Square Roots: Simplify radical expressions, approximate irrational numbers
Pythagorean Theorem: Apply to find missing sides in right triangles
Distance Formula: Calculate distance between coordinate points

🧬 Science: Life Science

Cell Biology & Genetics

Cell Structure: Prokaryotic vs. eukaryotic cells, organelle functions
Cell Processes: Photosynthesis, cellular respiration, mitosis, meiosis
DNA & Heredity: DNA structure, protein synthesis, Mendelian genetics
Mutations: Types of mutations, their causes and effects

Evolution & Classification

Natural Selection: Evidence for evolution, mechanisms of natural selection
Adaptation: Structural, behavioral, and physiological adaptations
Classification: Taxonomic hierarchy, phylogenetic trees
Biodiversity: Factors affecting biodiversity, conservation

Ecology

Ecosystem Dynamics: Energy flow, nutrient cycling, food webs
Population Ecology: Population growth, carrying capacity, limiting factors
Human Impact: Pollution, habitat destruction, climate change effects
Conservation Biology: Strategies for protecting endangered species

Human Biology

Body Systems: Digestive, circulatory, respiratory, nervous, immune systems
Homeostasis: Feedback mechanisms, temperature regulation
Disease: Infectious vs. non-infectious diseases, immune response
Nutrition & Health: Balanced diet, exercise, substance abuse effects

💻 Technology Integration

Bioinformatics: Use online databases to analyze DNA sequences
Data Analysis: Statistical analysis of ecological data using spreadsheets
Virtual Labs: Conduct virtual dissections and microscopy

Grade 8: Geometry & Physical Science

➗ Mathematics: Geometry

Foundations of Geometry

Points, Lines, and Planes: Basic geometric definitions and postulates
Angle Relationships: Vertical, complementary, supplementary, linear pairs
Parallel Lines: Properties when cut by a transversal, alternate interior/exterior angles
Geometric Proofs: Two-column proofs, paragraph proofs, reasoning

Triangles

Triangle Classification: By sides (scalene, isosceles, equilateral) and angles
Triangle Congruence: SSS, SAS, ASA, AAS, HL theorems
Triangle Properties: Angle sum theorem, exterior angle theorem
Special Triangles: Isosceles triangle theorem, 30-60-90, 45-45-90 triangles

Quadrilaterals & Polygons

Quadrilateral Properties: Parallelograms, rectangles, rhombi, squares, trapezoids
Polygon Angle Sums: Interior and exterior angle measures
Regular Polygons: Properties and symmetries

Circles

Circle Properties: Radius, diameter, chord, secant, tangent
Circle Theorems: Inscribed angles, central angles, arc measures
Circle Equations: Standard form (x-h)² + (y-k)² = r²

Area & Volume

2D Area: Triangles, parallelograms, trapezoids, circles, composite figures
3D Volume: Prisms, cylinders, pyramids, cones, spheres
Surface Area: All 3D shapes, including composite solids
Scale Factor: Effect on perimeter, area, and volume

Coordinate Geometry

Distance & Midpoint: Formulas and applications
Slope: Parallel and perpendicular lines
Coordinate Proofs: Prove properties using coordinate methods
Transformations: Translations, reflections, rotations, dilations

Trigonometry Introduction

Right Triangle Ratios: Sine, cosine, tangent
Solving Right Triangles: Find missing sides and angles
Applications: Angle of elevation/depression, real-world problems

⚛️ Science: Physical Science (Chemistry & Physics Introduction)

Chemistry Foundations

Atomic Structure: Protons, neutrons, electrons, electron configuration
Periodic Table: Trends in atomic radius, ionization energy, electronegativity
Chemical Bonding: Ionic, covalent, and metallic bonding
Chemical Reactions: Balancing equations, types of reactions, conservation of mass

States of Matter & Kinetic Theory

Kinetic Molecular Theory: Relationship between temperature and molecular motion
Phase Changes: Energy changes during melting, boiling, sublimation
Gas Laws: Boyle’s, Charles’s, Gay-Lussac’s laws, combined gas law
Solutions: Concentration, solubility, factors affecting dissolution

Physics Foundations

Motion: Distance vs. displacement, speed vs. velocity, acceleration
Forces: Newton’s three laws, friction, weight vs. mass
Energy: Kinetic and potential energy, conservation of energy
Work & Power: Calculating work done, mechanical advantage

Waves & Electricity

Wave Properties: Frequency, wavelength, amplitude, wave speed equation
Electromagnetic Spectrum: Radio waves through gamma rays, applications
Electricity: Current, voltage, resistance, Ohm’s law
Circuits: Series vs. parallel circuits, electrical power

💻 Technology Integration

Simulations: Use PhET simulations for chemistry and physics concepts
Data Analysis: Graph motion data, analyze trends in experimental results
Programming: Write simple programs to solve physics problems
Laboratory Technology: Use digital sensors and data loggers

📊 Assessment & Mastery Indicators

End-of-Grade 8 Readiness Markers

Algebra Readiness: Score 85%+ on comprehensive Algebra I diagnostic
Scientific Reasoning: Design and conduct independent investigations
Mathematical Modeling: Apply algebraic concepts to real-world problems
Technology Fluency: Use technology tools effectively for learning and problem-solving

High School: The Apex (Grades 9-12)

The goal is to reach mathematical maturity, conduct original inquiry, and build a portfolio of cross-domain projects. The learner becomes the teacher.

Grade 9: The Transition

➗ Mathematics: Algebra II

Advanced Functions

Polynomial Functions: End behavior, zeros, multiplicity
Rational Functions: Asymptotes, holes, domain restrictions
Radical Functions and Equations
Exponential and Logarithmic Functions: Growth/decay, natural log

Complex Numbers

Operations with Complex Numbers
The Complex Plane, Polar Form
Fundamental Theorem of Algebra

Systems & Matrices

Solve Systems of 3+ Variables
Matrix Operations: Addition, multiplication, determinants
Use Matrices to Solve Systems: Gaussian elimination
Linear Algebra Preview

Sequences & Series

Arithmetic and Geometric Sequences
Finite and Infinite Geometric Series
Introduction to Sigma Notation

Conic Sections

Circles, Ellipses, Parabolas, Hyperbolas
Standard and General Forms
Real-World Applications: Orbits, optics

🧬 Science: Honors Biology (Foundation for AP Bio)

Biochemistry: Macromolecules, enzymes, metabolic pathways
Cell Structure and Function: In depth
Genetics: Mendelian, non-Mendelian, molecular
Evolution: Population genetics, speciation
Ecology: Community dynamics, ecosystem energetics
Lab Intensive: Gel electrophoresis, PCR concepts, microscopy, dissection

⚡ Science: AP Physics 1 (Algebra-Based)

Kinematics: 1D and 2D motion
Dynamics: Newton’s laws, friction, circular motion
Energy and Work
Momentum and Collisions
Simple Harmonic Motion, Waves, Sound
Rotational Motion Basics

💻 Technology & Programming

Python Mastery: NumPy, Matplotlib, SciPy for mathematical computation
Data Analysis: Clean, visualize, and analyze real datasets
Version Control: Git and GitHub for project management

Grade 10: Building on Foundations

➗ Mathematics: Pre-Calculus with Trigonometry

Trigonometry Deep Dive

Unit Circle Definitions: Sine, cosine, tangent
Graphing Trig Functions: Amplitude, period, phase shift, vertical shift
Inverse Trig Functions
Trigonometric Identities: Pythagorean, sum/difference, double-angle, half-angle
Solving Trig Equations
Law of Sines, Law of Cosines

Advanced Functions

Piecewise Functions, Absolute Value Functions
Function Composition and Inverses
Parametric Equations
Polar Coordinates and Polar Graphs

Limits & Continuity (Calculus Preview)

Intuitive Understanding of Limits
Evaluating Limits Algebraically
Continuity and Types of Discontinuities
The Squeeze Theorem

Vectors (Linear Algebra Preview)

Vector Operations: Addition, scalar multiplication
Dot Product and Cross Product
Vector Projections
Parametric Lines and Planes in 3D

⚗️ Science: AP Chemistry

Atomic Structure and Periodicity
Chemical Bonding: Lewis structures, VSEPR, hybridization
Stoichiometry, Gas Laws, Thermochemistry
Solutions, Kinetics, Equilibrium
Acids and Bases, Electrochemistry
Lab Intensive: Titrations, calorimetry, spectroscopy, chromatography

💻 Technology & Programming

Python for Science: Simulate chemical kinetics, model physics systems
Web Development: HTML/CSS/JS basics — build a portfolio website
Data Science: Pandas, NumPy, Matplotlib, Seaborn. First machine learning model (scikit-learn)

Grade 11: The AP Push

➗ Mathematics: AP Calculus BC Curriculum

Limits & Continuity

Formal Definition of Limits
Limits at Infinity, Infinite Limits
Squeeze Theorem, Intermediate Value Theorem

Derivatives

Definition of Derivative: Limit of difference quotient
Differentiation Rules: Power, product, quotient, chain
Derivatives of Transcendental Functions: Trig, exponential, log, inverse trig
Implicit Differentiation, Related Rates
Optimization, Curve Sketching, L’Hôpital’s Rule

Integrals

Riemann Sums, Definite Integral as Limit
Fundamental Theorem of Calculus (Both Parts)
Integration Techniques: Substitution, integration by parts, partial fractions
Applications: Area, volume, arc length, work, center of mass

Differential Equations

Slope Fields, Euler’s Method
Separation of Variables
Exponential Growth/Decay, Logistic Growth

Series

Sequences, Series Convergence Tests
Taylor and Maclaurin Series
Power Series, Radius of Convergence
Lagrange Error Bound

Parametric, Polar, Vector Calculus

Derivatives and Integrals in Parametric Form
Polar Area and Arc Length
Vector-Valued Functions, Motion in Space

⚡ Science: AP Physics C: Mechanics (Concurrent with Calculus)

Kinematics, Newton’s Laws, Work/Energy/Power
Systems of Particles, Linear Momentum
Circular Motion and Rotation
Oscillations and Gravitation
All with Calculus: Derivatives for rates, integrals for accumulation

🧬 Science: AP Biology

Chemistry of Life, Cell Structure/Function
Cellular Energetics: Photosynthesis, respiration
Cell Communication, Cell Cycle
Heredity, Gene Expression, Regulation
Natural Selection, Ecology

Grade 12: Collegiate Foundations

➗ Mathematics: Introductory Linear Algebra

Vectors & Vector Spaces

Vectors in Rⁿ, Linear Combinations, Span
Linear Independence, Basis, Dimension
Subspaces, Row Space, Column Space, Null Space

Matrices & Linear Transformations

Matrix Multiplication as Composition of Linear Maps
Matrix Inverses, Elementary Matrices
Determinants and Their Geometric Meaning
Change of Basis

Eigenvalues & Eigenvectors

Characteristic Equation
Diagonalization
Applications: Markov chains, principal component analysis (PCA), dynamical systems

Orthogonality

Orthogonal Projections, Gram-Schmidt Process
Least Squares Approximation
QR Decomposition

📊 Mathematics: Probability & Statistics

Probability Foundations

Sample Spaces, Events, Axioms of Probability
Conditional Probability, Bayes’ Theorem
Random Variables: Discrete and continuous
Probability Distributions: Binomial, Poisson, normal, exponential

Statistical Inference

Sampling Distributions, Central Limit Theorem
Confidence Intervals
Hypothesis Testing: z-tests, t-tests, chi-square
Type I and Type II Errors, Power

Regression & Modeling

Simple and Multiple Linear Regression
Correlation vs. Causation (Revisited with Rigor)
ANOVA Basics
Introduction to Bayesian Statistics

➗ Mathematics: Differential Equations (Introduction)

First-Order ODEs: Separable, linear, exact
Second-Order Linear ODEs: Homogeneous, non-homogeneous
Systems of Linear ODEs: Matrix methods
Applications: Population dynamics, circuits, mechanical vibrations

⚡ Science: AP Physics C: Electricity & Magnetism

Electrostatics: Coulomb’s law, electric fields, Gauss’s law
Electric Potential, Capacitance
Circuits: RC, RL circuits
Magnetism: Biot-Savart, Ampère’s law
Induction: Faraday’s law, Lenz’s law, inductance
Maxwell’s Equations (Integral Form)

💻 Technology & Programming

Advanced Python: Object-oriented design, algorithms, data structures
Data Science Portfolio: End-to-end project — data collection, cleaning, analysis, visualization, modeling, deployment
AI/ML: Deep learning with PyTorch or TensorFlow. Build and train a neural network
Embedded Systems: Raspberry Pi / Arduino advanced projects
Version Control & Collaboration: GitHub portfolio, open-source contribution