A lesson sequence focusing on the algebraic and graphical properties of radical equations, bridging the gap between symbolic manipulation and visual intersection points.

A series of higher-level mathematics lessons exploring calculus foundations through engaging, thematic activities and visual demonstrations.

A specialized unit focused on identifying and correcting algebraic misconceptions in function transformations, specifically reflections. Students develop critical analysis skills by acting as "Error Doctors" to diagnose and treat common mathematical pitfalls.

A lesson sequence focusing on the transition from expanded ellipsis notation to formal Sigma notation within the context of arithmetic series proofs. Students analyze a standard proof and reformulate it using summation properties.

A high-level Honors Algebra lesson focused on complex recursive sequences where students analyze notation, explore the Fibonacci sequence, and engage in a 'Sequence Maker' activity to reverse-engineer formulas.

A specialized unit exploring the geometric properties of slope, connecting algebraic rates of change to trigonometric functions and the geometry of inclination.

A high school geometry and algebra sequence focused on applying 3D geometry formulas to real-world optimization problems, specifically focusing on cones.

A comprehensive pre-calculus unit focused on the algebraic and geometric properties of inverse functions, including composition-based verification and domain restrictions.

A unit focused on mastering polynomial operations, from long division to advanced shortcuts like the Remainder and Factor Theorems. Students move from laborious calculation to strategic evaluation.

A comprehensive lesson sequence for 12th Grade Pre-Calculus/Calculus students on solving and visualizing systems of nonlinear equations involving conic sections. Students move from sketching predictions to algebraic verification and creative system design.

A lesson sequence focusing on analyzing and manipulating exponential functions to reveal true growth rates, using real-world financial contexts and exponent rules.

A mastery-based sequence using base-ten blocks and area models to build conceptual understanding of multi-digit multiplication and division for high school students. This sequence bridges the gap between concrete manipulatives and abstract algorithms through the visual scaffold of area.

A specialized sequence for 12th-grade students focusing on math manipulative use and visual modeling to master multi-digit multiplication and division. Students progress from concrete base-ten blocks to representational area models, ending with strategy efficiency and real-world application.

A math sequence for 12th-grade students in special education, focusing on practical fraction mastery through measurement, construction, and home maintenance scenarios. Students use manipulatives like fraction tiles and rulers to build conceptual understanding and operational fluency.

A sequence for 12th-grade students focusing on selecting and using visual organizers like Venn diagrams, tree diagrams, flowcharts, and logic grids to solve complex logic and probability problems. Students move from guided practice to independent metacognitive selection of the best tool for the job.

A specialized sequence for 12th-grade students needing academic support, focusing on translating word problems into visual models. This unit bridges language processing and algebraic reasoning through sketching, geometric modeling, and diagramming.

This sequence explores spatial visualization through the study of cross-sections and solids of revolution. Students learn to translate between 2D and 3D representations, a critical skill for engineering, physics, and advanced mathematics.

This sequence explores the intersection of geometry and engineering, focusing on 3D visualization, technical drawing, and the optimization of physical forms. Students develop spatial reasoning skills through orthographic and isometric sketching and apply geometric modeling to solve real-world design constraints.

A high school geometry unit that integrates algebra and geometry by using coordinate systems to verify geometric properties. Students use distance, midpoint, and slope formulas to classify shapes and prove properties with algebraic rigor.

This sequence explores numerical analysis through the lens of sequences, focusing on iterative methods to approximate solutions to complex equations. Students investigate fixed-point iteration, Newton's method, convergence rates, and the transition into chaotic behavior.

An 11th-grade mathematics sequence that bridges the gap between abstract sequences and real-world applications in finance and physics. Students explore arithmetic and geometric models through interest, depreciation, projectile rebounds, and loan amortization.

This sequence explores arithmetic and geometric sequences through inquiry, algebraic modeling, and real-world applications. Students transition from pattern recognition to formalizing recursive and explicit formulas to predict outcomes in linear and exponential systems.

A high school trigonometry sequence that uses the physics of sound waves to teach modeling with trigonometric functions. Students explore pitch as frequency, volume as amplitude, and the superposition of waves to create harmonies and digital tones.

A comprehensive unit on modeling real-world periodic phenomena using trigonometric functions across physics, biology, and astronomy. Students master identifying amplitude, midline, and period from contextual data to build and solve predictive equations.

A comprehensive unit where students act as data scientists to model real-world environmental phenomena using trigonometric functions. They progress from visual estimation to precise algebraic modeling and technological regression to predict future environmental conditions.

A comprehensive unit on trigonometric transformations, focusing on how parameters A, B, C, and D modify the parent sine and cosine functions. Students progress from simple vertical shifts to complex multi-parameter modeling.

An advanced exploration of vector-valued functions and their applications in modeling 2D motion and force, preparing students for multivariable calculus.

A comprehensive unit for 12th Grade Calculus students focusing on the integration of polar functions to find area, arc length, and surface area. Students transition from Cartesian thinking to radial accumulation, mastering the geometry of circular sectors and polar coordinate transformations.

A comprehensive unit for 12th Grade Calculus students focusing on the derivation and application of derivatives in polar coordinates. Students transition from Cartesian slope to polar slope, analyze horizontal and vertical tangency, investigate behavior at the pole, and solve optimization problems involving polar curves.

Students transition from Cartesian to polar coordinates, exploring the geometry of circular grids and the equations that define complex curves like roses and lima\u00e7ons. The unit covers plotting, conversion, and advanced graphing analysis with a focus on symmetry and intersection.

A comprehensive unit on parametric equations and their applications in modeling motion. Students move from the basics of parametric curves to advanced calculus concepts like derivatives, concavity, vectors, and arc length.

A gamified approach to mastering rational exponents through competition, collaboration, and high-stakes simulations. Students move from basic radical conversions to complex multi-variable simplification in a fast-paced 'Power Play' environment.

This sequence explores the relationship between rational exponents and the geometric behavior of power functions. Students analyze how numerators and denominators dictate domain, range, shape, and growth rates through inquiry and visual sketching.

This sequence explores real-world applications of rational exponents across biology, astronomy, music, finance, and physics. Students transition from abstract algebraic manipulation to applying fractional powers to model complex natural and human-made systems.

A comprehensive unit for 12th-grade algebra focusing on solving equations with rational exponents, investigating extraneous solutions, and visualizing intersections graphically.

This sequence investigates real-world applications of rational exponents in biology, finance, music, and physics. Students explore how fractional powers model growth, scaling, and harmonic relationships, culminating in a data-modeling project.

An advanced, rigorous exploration of rational exponents and radical manipulation for 12th-grade students. This sequence focuses on the technical facility required for calculus, including factoring fractional exponents, handling nested radicals, rationalizing higher-order roots, and solving equations reducible to quadratic forms.

An advanced 11th-grade Calculus unit focusing on the integration of parametric and polar coordinate systems. Students analyze motion, calculate complex areas, perform error analysis, and complete a final synthesis project based on particle kinematics.

This sequence bridges the gap between radical notation and exponential notation, establishing a unified system for algebraic manipulation. Students begin by defining rational exponents through the lens of roots and powers, then systematically apply the laws of exponents to simplify expressions containing fractional powers.

This calculus sequence guides 11th-grade students through the integration techniques required to calculate area and arc length within polar coordinate systems. From the geometric derivation of the polar sector formula to complex multi-curve regions and boundary measurements, students apply integral calculus to circular geometries.

This sequence explores the calculus of polar functions, focusing on differentiation techniques. Students will learn to calculate slopes of tangent lines, identify horizontal and vertical tangents, analyze behavior at the pole, and apply optimization to find maximum and minimum distances from the origin.

A comprehensive unit on polar coordinates and functions, moving from basic plotting to complex intersections and symmetry. Students explore the geometric beauty of curves like roses and lima\u00e7ons while mastering the algebraic conversions between rectangular and polar systems.

This sequence introduces students to parametric equations through the lens of particle motion and physics simulations. Students progress from basic plotting and parameter elimination to advanced calculus applications involving derivatives, vectors, and arc length.

This sequence explores the practical application of rational exponents and power functions in biology, physics, and finance. Students will progress from evaluating existing models like Kleiber's Law and Kepler's Third Law to constructing their own mathematical models from empirical data.

This sequence establishes the theoretical foundation linking radical notation to rational exponents. Students move from conceptual inquiry to rigorous algebraic application, covering translation, evaluation, domain analysis, and formal justification of exponent properties for rational numbers.

An intensive procedural fluency module for undergraduate students focusing on the systematic simplification of algebraic expressions with rational exponents. The sequence progresses from basic operations to advanced factoring techniques required for higher-level calculus and engineering mathematics.