Mathematics
I see a continuous path from Grade 1 arithmetic to precalculus: numbers become relationships, relationships become functions, and functions lead us to calculus.
Grade 3Multiplication, division, fractions, and the meaning of a unit.
Grade 4Place value, larger numbers, equivalent fractions, and shapes.
Grade 5Fraction operations, decimals, volume, and coordinate patterns.
Grade 6Ratios, rates, negative numbers, and expressions—the bridge to algebra.
Pre-AlgebraProportions, equations, and graphs: turning number sense into relationships.
Algebra IEquations and functions: connect known quantities with unknowns.
GeometryShape, measurement, and proof: explain why a relationship must hold.
Algebra IIPolynomial, exponential, and logarithmic functions: compare how quantities change.
PrecalculusFunctions, trigonometry, and limits: prepare to describe continuous change.
AP Calculus AB / BCDerivatives, integrals, and their connection: study change and accumulation.
WHERE THE IDEAS MEET
Change. Accumulation. Calculus.
Derivative — what happens next?
A slope tells us how one quantity changes with another. A derivative gives that rate at a moment, helping us estimate what happens next—locally, while the model holds.
Integral — what does it add up to?
An integral gathers small contributions into a total. Add up a changing velocity over time to find displacement; add up a flow rate to find how much has passed through.
These two ideas connect the mathematics learned along the way—and reach into physics, engineering, economics, biology, and many other fields.
AP Physics 1 — Mechanics
AP Physics 2 — Fields, Light & Modern Physics
AP Physics C — Calculus-Based Physics


SAT Math
ACT Math