Differentiation of interdependent variables with respect to time using the chain rule. Connects geometric formulas with algebraic manipulation to solve problems involving moving objects, fluid flow, and changing dimensions.
This advanced sequence explores related rates through the lens of geometric similarity and trigonometry, focusing on shadows and angular motion. Students move from linear proportions to complex angular derivatives, culminating in a mastery-based problem-solving seminar.
This sequence explores the calculus of related rates through the lens of 3D geometry and fluid dynamics. Students progress from simple spherical expansion to complex conical substitution and industrial net-flow applications.
A comprehensive exploration of Related Rates using Pythagorean geometry, moving from basic ladder problems to complex multi-object motion. Students master the calculus of moving triangles through inquiry, digital modeling, and skill-building workshops.
A foundational sequence for 11th-grade students on Related Rates in Calculus. Students move from static derivatives to dynamic, time-dependent rates of change, establishing a rigorous 4-step problem-solving protocol.
A calculus sequence for undergraduate students exploring related rates through environmental, engineering, and mechanical lenses. Students analyze dynamic systems like oil spills, reservoir drainage, and piston mechanics to understand the physical significance of time-dependent derivatives.
A systematic workshop-style approach to mastering related rates in Calculus. Students progress from foundational implicit differentiation to complex geometric modeling involving Pythagorean theorem, volume expansion, conical constraints, and trigonometric rates.
