Every skill we teach. Every grade we touch. 190+ skills mapped across six math and English
disciplines, Grade 3 through 12. Each skill carries its grade
coverage, its development tier, and the contests it prepares for —
so you can see exactly what is taught and
where it leads.
∑ ◆ △ ◎ # ✦ 190+ SKILLS ✦ 190+ distinct skills, individually mapped ◆ 20 disciplines spanning math & English ★ 50 olympiad-grade techniques ⚐ 12 global contests the skills point at
All grades
Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8
All tiers
◯ Foundation ◐ Core ● Contest Prep ★ Olympiad
◯ Fractions G3–G8 ◯ Decimals G4–G8 ◯ Percentage G5–G8 ◐ Algebraic Expressions G3–G8 ◐ Rational Numbers G6–G8 ◐ Financial Literacy (taxes, profit, interest) G3 G5–G8 ◐ Sequences & Series G6–G8 ◐ Algebraic Equations G6–G8 ◐ Statistics (Data Analysis & Management) G4–G8 ◐ Inequalities G3–G8 ◐ Irrational Numbers G8 ● Counting Rectangles G3–G6 ● Counting Triangles G3–G5 ● Number Combinations G3–G5 ● Counting Paths G3–G5 G7 ● Permutations & Combinations G6–G8 ● Drawing Random Numbers G3–G6 ● Pigeonhole Principle G6–G8 ◯ Length, Perimeter & Area G3–G5 ◯ Polygons — Faces, Edges & Vertices G3–G5 ◐ Triangles G6–G8 ◐ Angles G5–G8 ◐ Quadrilaterals G6–G8 ◐ Circles G7–G8 ◐ 3D — Surface Area & Volume G6–G8 ● 3D Visualization G3–G5 ◐ Analytic Geometry G6–G8 ● Chickens & Rabbits G3–G7 ● Age Problems G3–G6 ◯ Ratios & Rates G3–G8 ● Calendar Problems G3–G5 ◯ Patterns G3–G5 ◐ Speed, Distance & Time G5–G8 ● Optimization G5–G8 ◯ Number Sense / Divisibility G3–G8 ◯ Multiples G3–G5 ◐ Prime Factoring (LCM / GCD) G4–G8 ● Modular Arithmetic G3 G5–G8 ◐ Exponents G6–G8 ◐ NT Problem Solving (word problems) G3–G8 ● Cryptarithmetic G3–G5 ✦ Problem-Solving Techniques 7 ● Intervals & Gaps G3–G5 ◯ Order of Operations G5–G6 ● Working Backward G3–G6 ● Application of Gauss’s Discovery G5–G7 ● Venn Diagrams G6–G8 ● Fibonacci Numbers G3–G5 ● Excess-and-Shortage Problems G3–G7 ● Advanced Algebraic Manipulation ● Sequences & Series (deeper) ● Inequalities (intro) ★ Functional thinking ◆ Combinatorics & Counting 4 ● Permutations & Combinations ● Pigeonhole Principle ★ Inclusion–Exclusion (intro) ★ Constructive Counting ◐ Triangle Properties ★ Cyclic Quadrilaterals (intro) ★ Area Method ● 3D Visualization ● Modular Arithmetic ◐ Prime Factorization ◐ Divisibility Tests ◐ Exponents ◐ Algebraic Identities & Manipulations ◐ Factorizations ● Rational Expressions & Partial Fractions ● Telescopic Sums & Products ◐ Equations & Systems of Equations ◐ Functions & Function Transformations ◐ Radical Functions ◐ Polynomial Functions ◐ Remainder & Factor Theorems ◐ Equations and Graphs of Polynomials ◐ Exponents & Logarithms ◐ Exponential Functions & Equations ◐ Logarithmic Functions ◐ Logarithmic & Exponential Equations ◐ Rational Functions ◐ Function Operations ◐ Composite Functions ◐ Congruent & Similar Triangles ◐ Area & Area Method ◐ Circle — Geometric Approach ◐ Circle Computations ★ Cyclic Quadrilaterals ◐ Trigonometry — Circle, Properties, Functions ◐ Trigonometric Identities ◐ Trigonometric Equations ◐ Law of Sines & Cosines ◐ Coordinate Geometry (1) ◐ Coordinate Geometry (2) ◆ Counting & Combinatorics 2 ◐ Counting Methods — Permutations, Arrangements, Combinations ◐ The Binomial Theorem ★ Divisibility — Number & Sum of Divisors ★ Modular Arithmetic ★ Advanced Algebraic Manipulations ★ Inequalities — AM-GM, Cauchy-Schwarz ★ Polynomials — Vieta’s Formulas, Newton’s Sums ● Polynomials — AMC / AIME Review Problems ★ Functions — Injective, Surjective, Bijective ★ Functional Equations (intro) ◐ Exponent & Logarithm Functions ★ Sequences & Recursions ◐ Arithmetic & Geometric Sequences ★ Complex Numbers — Algebraic Form ★ Complex Numbers — Trigonometric Form ★ Algebraic Trigonometry ◆ Counting & Combinatorics 13 ◐ Counting & Probability Basics (review) ◐ Sets and Logic ★ The Pigeonhole Principle ★ Principle of Inclusion–Exclusion ★ Constructive Counting & 1-1 Correspondences ★ Constructive Expectation ★ Distributions ★ Mathematical Induction ★ Recursion ◐ Conditional Probability ★ Events with States ★ Tables & Chess Boards ★ Challenge Problems ★ Area & Area Method ◐ Trigonometric Ratios in a Right Triangle ★ Geometric Trigonometry — Stewart, Pappus ★ Cyclic Quadrilaterals ★ Circle Computations — Descartes’s Formula ★ Important Circles in a Triangle (Nine-Point) ★ Power of a Point ★ Radical Axis ★ Mass Points (2 sessions) ◐ Coordinate Geometry ★ Prime Numbers, GCD, Bézout, Euclidean Algorithm ★ Gauss’s Lemma ◐ Fundamental Theorem of Arithmetic ★ A Theorem of Legendre & Applications ★ Bertrand’s Postulate ★ Modular Arithmetic ★ Chinese Remainder Theorem ★ Linear Diophantine Equations ★ Nonlinear Diophantine Equations ★ Arithmetic Functions ★ Euler’s Totient Function ★ Fermat, Euler & Wilson’s Theorems ★ p-adic Valuation ◯ Subject – Predicate G4–G5 ◐ Clauses, Types & Structures of Sentences G5–G6 ◐ Sentence Fragments & Run-on Sentences G6 ◯ Parts of Speech (Basic) — Noun, Pronoun, Verb, Adjective, Adverb G4–G6 ◐ Parts of Speech (Advanced) — Gerunds, Tenses, Active/Passive G6 ◐ Other Parts of Speech — Appositives & Appositive Phrases G6 ◯ Reading Strategy — Accuracy & Fluency G4–G5 ◯ Comprehension — Review, Summarize, Predictions, Facts vs Opinions G4–G6 ◐ Comprehension — Inferences, Visualizing, Fact vs Judgement G5–G6 ◯ Techniques — Main Idea, Details, Context Clues G4 ◐ Techniques — Compare & Contrast, Cause & Effect, Sequencing G5–G6 ◐ Literary Genres — Prose, Poetry & Drama G6 ◯ Vocabulary — Definition, Synonyms & Antonyms G4–G5 ◐ Vocabulary — Homophones, Multiple Meaning, Confusing Words G4–G5 ◐ Vocabulary — Crosswords, Puzzles, Word Scrambles G4–G6 ● Verbal Analogies — Word Relations, Pair, Odd One G4–G6 ● Verbal Analogies — Logical Sequencing & Ordering G4–G6 ◯ Writing Process — Steps & Process G4–G6 ◐ Narrative Writing — Basic Structure & Story Elements G4–G5 ● Narrative Writing — Advanced (PoV, Themes, Flashbacks, Foreshadowing) G6 ◐ Expository Writing — Structure, Topic & Evidence G5–G6 ◐ Descriptive Writing — Sensory & Descriptive Details G6 ● Persuasive Writing — Argument Formation & Transitions G5–G6 ◯ Conventions — Punctuation (Basic) & Capitalization G4 ◐ Conventions — Advanced Punctuation G5–G6 ● Advanced — Idiomatic & Figurative Language G5–G6 ◐ Advanced — Visuals, Charts, Graphs & Maps G6 ◯ Public Speaking — Addressing Fear G5–G6 ◐ Public Speaking — Developing Effectiveness G5–G6 ◐ Public Speaking — Interpretive Reading & Storytelling G6 ◐ Speech Types & Structure G5–G6 ● Persuasive Speech Presentation G5–G6 ● Argument Construction Techniques G6 ◐ Long-form essay craft ● Persuasive & argumentative writing (advanced) ● Narrative voice & style ◐ Editing & revision discipline ☞ Rhetoric & Critical Reading 3 ★ Rhetorical analysis ◐ Author intent & literary devices ◐ Comparative reading across genres ⟁ Vocabulary & Verbal Reasoning 3 ◐ Senior vocabulary ★ Etymology & word roots ★ Verbal analogies (advanced) ● CIWC writing prompts & format ● Timed writing under contest conditions ● School-board contest coaching (where applicable) Curriculum questions? Talk to a coach about placement, pace, or a custom plan. Every CKSTEM course can flex by a grade in either direction — we evaluate readiness, not age. Book a free assessment and we'll help you pick the right starting point.
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