Curriculum & Standards
What we teach, and how it stacks up against the world.
Every Rodybee program is benchmarked against the highest international standards — not a national average. Pick a program to explore the standards we follow, the topics we cover by age, and the official sources behind every claim.
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Arithmetic
Counting, addition, subtraction, multiplication, division, and mental shortcuts.
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Fractions
Halves, quarters, thirds; notation a/b on number line; equivalence and comparison; ± × ÷; decimals/percent; bar model word problems.
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Geometry
Shapes, attributes, symmetry, angles, perimeter, area, volume, transformations.
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Reading
From first letters to comprehension: phonics, sight words, fluency, vocabulary, grammar, and reading strategies.
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Pre-Algebra
Integers and rationals, expressions and equations, linear functions and slope, systems, exponents, Pythagoras, and stats/probability — calibrated to CCSS G7-G8 + Singapore Sec 1-2.
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Algebra 1
Linear functions deep, polynomials, factoring, quadratic functions and equations, exponentials, sequences, radicals, rational expressions, and statistics with formal regression — the delta over pre-algebra, calibrated to CCSS HS Algebra/Functions + Singapore Sec 3-4.
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Geometry (Secondary)
Formal proofs (two-column, paragraph, flow), congruence and similarity criteria, right-triangle and oblique trigonometry, advanced circle theorems, analytic geometry, 3D solids and constructions — calibrated to CCSS HS Geometry + Singapore Sec 3-4 + Cambridge IGCSE 0580 Extended.
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Algebra 2
Logarithms, advanced polynomials, rational and radical functions, complete trigonometry (unit circle + identities + equations + graphs), series with sigma and infinite sums, matrices and 3×3 systems, combinatorics with binomial theorem, advanced probability with conditional + Bayes + normal distribution, conics and complex numbers — calibrated to CCSS HS Algebra 2 + IB AA SL Y1 + Cambridge AS 9709 + Singapore JC1 H2.
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Pre-Calculus
Advanced functions (composition, inverse, piecewise), end-behavior with limit notation, advanced trig identities (half-angle, product-to-sum, sum-to-product), 2D + 3D vectors with dot and cross product, parametric and polar curves, complex numbers in polar/Euler form with DeMoivre's theorem and n-th roots, intuitive limits and continuity (IVT, L'Hôpital), sequences and series with telescoping and partial sums, mathematical induction (sum and divisibility), intuitive derivative (tangent, instantaneous rate, velocity) and intuitive integral (Riemann sum, signed area) — calibrated to CCSS HS Functions/Number-CN + IB AA SL Y2 + Cambridge AS/A2 9709 + Singapore JC1-JC2 H2 + Japan SHS Math II/III + Korea KICE 2022 Revised.
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Calculus (Intro)
Formal single-variable calculus: ε-δ definition of limit, classical continuity theorems (IVT formal, EVT, Bolzano, MVT, Rolle), derivative with all rules (power, product, quotient, chain, implicit, logarithmic), derivatives of transcendentals (trig, inverse trig, exp, log, hyperbolic, higher-order), curve analysis (monotonicity, concavity, inflection, full sketching), modeling (optimization, related rates, Newton-Raphson, L'Hôpital formal), antiderivatives + u-substitution + integration by parts, definite integral via Riemann sum + FTC parts I and II, advanced techniques (partial fractions in three forms, trig substitution, trig powers, reduction formulas, improper integrals types I and II), applications (area between curves, volumes by disks/washers/shells, arc length, surface area of revolution, work), separable ODEs (exponential growth formal, Newton's cooling, logistic intro, slope fields), formal sequences and series with all convergence tests (divergence, geometric, p-series, comparison, limit comparison, ratio, root, integral, alternating Leibniz), absolute vs conditional convergence, power series with radius and interval, Taylor and Maclaurin series with Lagrange remainder, classical Maclaurin series (e^x, sin, cos, ln(1+x), 1/(1−x), arctan), binomial series — calibrated to AP Calculus AB+BC + IB AA HL Y2 + Cambridge A2 9709 (Pure 3) + Singapore JC2 H2 + Japan SHS Math III + Korea KICE 2022 Revised Calculus + freshman university (MIT 18.01 / Stanford / UC Berkeley Math 1A-1B / UNAM Cálculo I-II).
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curriculum.programs.calculus_2
Multivariable + vector calculus + ODEs II at the university freshman/sophomore ceiling: 3D vectors with cross product and scalar triple product, lines + planes + quadric surfaces in 3D, vector-valued functions with unit tangent / normal / binormal, curvature and torsion, motion decomposition, multivariable functions with ε-δ limits + path test + Clairaut, partial derivatives + differentiability + tangent planes, multivariable chain rule with tree diagrams, directional derivative + gradient + perpendicular to level surfaces, multivariable extrema with second derivative test 2D + Lagrange multipliers (one and two constraints) + Taylor 2D quadratic, double integrals (rectangular + Type I/II + polar) with applications (volume, mass, centroid), triple integrals (rectangular + cylindrical + spherical) with Jacobians and moments of inertia, vector fields + divergence + curl + conservative fields + potential functions, line integrals (scalar + vector) + path independence + Fundamental Theorem for Line Integrals + Green's theorem (circulation + flux forms), parametrized surfaces + surface integrals (scalar + flux) + Stokes' theorem + divergence theorem + theorem strategy choice. ODEs II: linear first-order with integrating factor, exact ODEs, integrating factors for non-exact, Bernoulli, first-order modeling (mixing, RC circuits); second-order linear with constant coefficients (real distinct, repeated, complex), undetermined coefficients (polynomial, exponential/trig), resonance modification, variation of parameters with Wronskian, reduction of order, mass-spring (unforced, damped, forced + resonance), RLC circuit. Calibrated to MIT 18.02 + 18.03, UC Berkeley Math 53 + 54, Stanford MAT 51 + 53, UNAM Cálculo III + IV, Cambridge Tripos IA Vector Calculus + Differential Equations, Tokyo 解析学 II.