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.
Une introduction complète aux statistiques universitaires, couvrant la classification des données, les mesures descriptives, la visualisation et les fondements de la loi normale. L'approche est axée sur l'analyse de données réelles et la compréhension conceptuelle.
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.
An 11th-grade mathematics sequence focused on analyzing linear-quadratic systems through algebraic and geometric lenses, specifically utilizing the discriminant to predict intersection counts.
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 foundational sequence for 11th Grade Pre-Calculus focusing on the essential building blocks of functions, their graphs, and their behavior. Students develop the ability to recognize, sketch, and analyze parent functions which serves as the basis for all future transformation and modeling work.
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 lesson on rationalizing binomial denominators using complex conjugates for 11th Grade Pre-Calculus students. The sequence focuses on the algebraic logic behind conjugates and their relationship to the difference of squares.
A comprehensive lesson sequence for Undergraduate College Algebra focused on synthesizing and selecting the most efficient strategies for solving exponential equations, utilizing common bases, logarithms, and quadratic forms.
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 scaffolded sequence for 10th-grade academic support, focusing on using two-color counters and algebra tiles to master integer operations and transition to algebraic reasoning. This sequence moves from concrete manipulation to representational drawing and finally to abstract procedural fluency.
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 math sequence for 11th-grade students focusing on practical fraction operations and ratios through the lens of construction and design. Students move from basic measurement precision to complex scaling tasks using physical manipulatives like tape measures and Cuisenaire rods.
A sequence designed for 11th-grade academic support students to master integer operations and linear equations using two-color counters and algebra tiles. This tactile approach builds conceptual understanding through zero pairs and balance models, eventually transitioning students to abstract algebraic notation.
A specialized math sequence for 9th-grade academic support, focusing on fraction mastery through concrete manipulatives and visual models. It follows the CRA framework to bridge gaps in foundational understanding for high school success.
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 specialized math sequence for 11th-grade students focusing on visual strategies like flowcharts and decision trees to support executive functioning and procedural memory. Students transition from following provided visual guides to designing their own logical maps for complex algebraic operations.
A math sequence for 11th Grade Special Education focusing on visual representations of functions. Students learn to interpret graphs as narratives, moving from qualitative sketches to precise quantitative analysis of slope, intersections, and non-linear trends.