Geometric classification, measurement of area and volume, and the study of transformations and rigid motions. Builds toward complex proofs, trigonometry for general triangles, and the algebraic representation of conic sections.
A comprehensive math intervention sequence for 6th-grade students, focusing on four key domains: Numbers & Operations, Algebraic Thinking, Measurement & Data, and Geometry. This sequence uses high-leverage strategies from the All Learners Network (ALN) and aligns with i-Ready prerequisite modules to bridge conceptual gaps.
A math sequence for 5th graders focused on identifying and classifying 3D figures in the real world by analyzing their properties such as faces, edges, and vertices.
A beginner's introduction to geometry focusing on identifying angles as a measure of turn using real-world objects. Students explore the classroom to find 'turns' and 'corners', classifying them as small or large.
A math sequence for 4th graders focused on mastering the perimeter formula for squares, specifically applying multi-digit multiplication in real-world contexts.
This sequence uses geometric area models (algebra tiles and the box method) to provide a concrete foundation for polynomial arithmetic and factoring, specifically designed for students needing academic support.
This sequence explores the geometric logic of polygons, focusing on the relationship between sides and angles. Students will derive formulas for interior and exterior angles and apply this knowledge to determine which shapes can tessellate a plane, culminating in the creation of original geometric art.
This sequence investigates the mathematical properties of polygons and their structural applications in engineering and architecture. Students explore interior and exterior angles, the unique attributes of regular polygons, and the fundamental reasons why triangles provide structural rigidity where other polygons fail.
A comprehensive 10th-grade physics and geometry sequence exploring symmetry, transformations, and their applications in engineering, crystallography, and design. Students progress from 2D reflectional symmetry to 3D spatial reasoning and professional design synthesis.
A 10th-grade physics and geometry sequence exploring the transition from 2D planar representations to 3D solids, focusing on polyhedra, curved surfaces, and engineering design through Euler's Formula and net construction.
A 7th-grade geometry sequence exploring the mathematical constraints of triangles, from side length inequalities to angle sums and uniqueness conditions. Students progress from hands-on experimentation to formalizing geometric rules and applying them to engineering scenarios.
This hands-on sequence focuses on spatial visualization, specifically the relationship between three-dimensional solids and two-dimensional figures. Students explore how slicing 3D objects creates 2D cross-sections, progressing from basic classification to complex angled cuts and orthographic projections.
A comprehensive geometry sequence for 9th-grade students focusing on the classification, properties, and algebraic analysis of polygons. Students progress from basic definitions to complex hierarchical relationships and angle sum derivations.
A comprehensive 9th-grade physics and geometry sequence where students transition from 2D components to 3D modeling, covering Euler's Formula, nets, solids of revolution, and cross-sections.
A game-based sequence for 2nd grade focusing on the logical categorization of geometric figures and the quadrilateral family. Students explore defining versus non-defining attributes through sorting games, riddles, and a culminating museum curation project.
A 5-lesson inquiry-based sequence for 2nd grade focusing on the physical properties and geometric attributes of three-dimensional solids. Students explore how the form of a shape determines its movement and function in the real world through hands-on labs, building challenges, and scavenger hunts.
This sequence introduces 2nd-grade students to the fundamental properties of two-dimensional polygons, moving from identifying open/closed figures to classifying and drawing shapes based on their attributes. Students will learn to recognize triangles, quadrilaterals, pentagons, and hexagons by counting sides and vertices, regardless of size or orientation.
A comprehensive geometry and engineering sequence where 6th-grade students explore the relationship between 2D nets and 3D solids. Students progress from identifying geometric parts to calculating surface area for prisms and pyramids, culminating in a real-world packaging design challenge.
This sequence introduces 6th-grade students to the coordinate plane as a tool for geometric modeling, moving from basic point plotting to calculating area, perimeter, and distance of complex polygons within all four quadrants.
This sequence guides 6th-grade students through the rigorous classification of two-dimensional figures based on their defining attributes, moving from basic identification to complex hierarchical logic. Students explore triangles, quadrilaterals, regular polygons, and symmetry through hands-on investigations and deductive reasoning.
This 3rd-grade sequence guides students from recognizing basic shapes to analyzing their defining attributes, such as sides and vertices. Students explore polygons, distinguish between defining and non-defining attributes, and culminate their learning in a 'Geometry Gallery' project.
A series of lessons focused on geometry and spatial reasoning, where students explore the properties of 2D shapes, symmetry, and patterns.
A comprehensive unit exploring circle geometry, vocabulary, arcs, angles, and properties through visual and hands-on investigation.
This sequence teaches 10th-grade students with academic support needs how to translate complex geometric text descriptions into accurate, solvable visual representations. It covers geometric vocabulary, 2D blueprints from word problems, 3D nets/transformations, and similarity modeling, culminating in a synthesis project.
A multi-disciplinary unit exploring line symmetry and reflection through folding, mirrors, nature observation, and artistic creation. Students bridge mathematics and science to understand how balance and congruence appear in the world around them.
A Pre-K sequence introducing symmetry and patterns through hands-on exploration with mirrors, art, nature, and shape manipulatives. Students learn to identify balanced halves and predict sequences.
An engineering-focused sequence where 3rd Grade students explore the relationship between 2D shapes and 3D solids. Students investigate physical properties like rolling and stacking, analyze geometric features, and apply their knowledge to structural engineering challenges.
This sequence introduces Pre-K students to 2D shapes (circles, squares, rectangles, triangles) through sensory play, physical movement, and environmental exploration. Students will learn to distinguish shapes by their attributes like sides and corners.
A 5th-grade geometry sequence exploring line and rotational symmetry, spatial patterns, and tessellations through the lens of a drafting studio. Students analyze symmetry in nature, art, and design while developing precision in geometric transformations.
A 1st-grade sequence exploring the concept of line symmetry through mirrors, paper folding, grid drawing, and natural observations. Students move from identifying simple mirror lines to creating complex symmetrical patterns using geometric shapes.
A 1st-grade sequence exploring spatial relationships and coordinate geometry through positional language. Students progress from physical movement to map-making, grid navigation, and basic algorithmic thinking.
This sequence introduces 1st-grade students to spatial reasoning through the composition and decomposition of geometric figures. Students explore how shapes can be combined and divided using pattern blocks, tangrams, and paper-folding activities, building a foundation for understanding area and fractions.
A math sequence focused on understanding and calculating the perimeter of irregular quadrilaterals through real-world scenarios like fencing a farm.
A comprehensive 7th-grade math lesson on identifying and calculating complementary and supplementary angles. The sequence covers basic definitions, linear pairs, and connects geometric concepts to algebraic problem-solving.
This 8th Grade Math sequence explores the properties of triangles, focusing on the Triangle Angle Sum Theorem and its applications in algebraic problem-solving. Students progress from hands-on measurement to complex multi-step relay challenges.
A mathematics sequence focusing on geometry, circles, and the calculation of circumference and area for middle school students.
This sequence bridges geometry and physics, investigating the structural properties of 2D and 3D shapes. Students analyze rigidity, tessellation, and surface area-to-volume ratios to understand how geometric attributes influence physical performance in engineering and nature.
A game-based exploration of polygons on the coordinate plane. Students learn to plot, calculate distance, reflect shapes, and deduce geometric properties using coordinate data in all four quadrants.
A mastery-based sequence focusing on the logical hierarchy of geometric shapes, addressing complex classifications and property-based definitions through Venn diagrams and logic puzzles.
A 4th-grade geometry unit focused on identifying and classifying lines, angles, and polygons, and exploring concepts of symmetry through hands-on investigation and artistic application.
A 12-lesson Tier 2 intervention sequence for 6th-grade students focused on computational fluency with decimals and the system of rational numbers. The sequence follows the All Learner Network High Leverage Concepts, moving from multi-digit decimal operations to complex coordinate plane navigation.
A comprehensive geometry unit focused on rigid transformations: translations, reflections, and rotations. Students explore how shapes move across the coordinate plane while maintaining their size and shape.
A series of activities for 2nd graders to master spatial relationships (over, under, in front, behind) and temporal sequencing (first, next, last, before, after). Students will use hands-on exploration and logical ordering to understand how things exist in space and time.
A series of geometry lessons focused on points of concurrency and their real-world applications in urban planning and design.
A Pre-Algebra unit focused on understanding the nature of linear equations and their solutions. Students explore how the structure of an equation determines whether it has one, none, or infinite solutions, connecting algebraic results to geometric representations.
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 lesson sequence focusing on the geometric properties of quadratic functions, specifically using symmetry to locate key features like the vertex and axis of symmetry.
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 specialized geometry sequence for 11th-grade students focusing on visual representation strategies. Students learn to deconstruct composite shapes, create 2D nets from 3D objects, sketch trigonometric scenarios, and visualize cross-sections, culminating in a real-world blueprint design project.
This sequence applies coordinate geometry to the classification of polygons, moving students from visual estimation to mathematical proof using distance and slope formulas. Students act as geometric investigators, verifying the properties of triangles and quadrilaterals through rigorous calculation.
A 10th-grade sequence focusing on the cognitive skill of spatial visualization. Students explore 3D objects through 2D cross-sections and conceptualize how 2D shapes create 3D forms when rotated around an axis, bridging geometry and engineering.
A Pre-K sequence focused on developing spatial awareness and positional vocabulary through physical movement, object manipulation, and classroom mapping. students explore terms like in, out, over, under, next to, and between.
This inquiry-driven sequence guides 5th-grade students through the logical hierarchy of two-dimensional figures, focusing on triangles and quadrilaterals. Students investigate properties, construct Venn diagrams, and defend geometric definitions through argumentation and debate.
A 1st-grade physics sequence exploring 3D solids, their properties (rolling, stacking, sliding), and their relationship to 2D faces through hands-on inquiry and engineering challenges.
A comprehensive first-grade geometry unit focusing on the defining attributes of 2D shapes, including sides, vertices, and closure, while distinguishing them from non-defining attributes like size and color.
A Kindergarten sequence focusing on higher-level critical thinking skills by asking students to classify, sort, and analyze shapes based on defining versus non-defining attributes. Students explore why color and size do not change a shape's name, while the number of sides and vertices do, and conclude with a mystery analysis challenge.
This 8th-grade sequence focuses on visual strategies to deconstruct geometry and systems of equations, helping students manage cognitive load through sketching, color-coding, and decomposition of complex problems.
A comprehensive 8th-grade geometry sequence exploring translations, reflections, rotations, and dilations on the coordinate plane. Students move from rigid transformations to similarity through inquiry-based activities and design challenges.
Students explore symmetry and rigid transformations (reflections, rotations, translations) through simulations, coordinate mapping, and creative projects. The unit culminates in the design of complex tessellations using transformation composition.
A game-based introduction to coordinate geometry where students learn to navigate grids, plot points, and transform shapes within a space exploration theme. Students transition from basic location-finding to complex mapping and translations.
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.
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 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.
A comprehensive exploration of the polar coordinate system, covering point plotting, coordinate conversion, and the analysis of complex polar curves including rose curves, limacons, and spirals. Students move from basic radial positioning to deep geometric analysis of symmetry and periodicity.
This sequence establishes the rigorous mathematical underpinnings necessary for advanced optimization work, moving beyond procedural calculus to analysis-based proofs. Students explore the intersection of topology, set theory, and multivariate calculus to determine the existence and uniqueness of optimal solutions.
A comprehensive 9th-grade math sequence exploring the geometric transformations of parent functions. Students move from basic translations to complex dilations and reflections, culminating in a creative design project using transformed functions.
This sequence explores the geometric interpretation of matrices, treating them as operators that transform space. Students move from calculation to visual application, using matrices to represent coordinates, perform translations/dilations, and apply rotations/reflections via matrix multiplication.
A comprehensive undergraduate sequence on the metric properties of circles, focusing on the Power of a Point as a unifying concept. Students progress from basic segment products to advanced topics like radical axes, radical centers, and geometric inversion.
A 12-lesson Tier 2 intervention sequence focused on developing conceptual understanding of area and volume for 6th-grade students. Using the All Learners Network High Leverage Concepts, students move from concrete tiling to decomposing shapes and finally calculating volume with fractional edges and surface area with nets.
A 7th-grade math lesson focused on the distinction between exact values in terms of Pi and decimal approximations using circumference calculations from the 'Circumference Song'.
A high school geometry and algebra sequence focused on applying 3D geometry formulas to real-world optimization problems, specifically focusing on cones.
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.
An engineering-focused unit where 8th-grade students analyze 3D solids through nets, volume formulas, and surface area optimization. The sequence culminates in a design project to create efficient packaging using geometric principles.
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 mathematical physics sequence explores the coordinate systems necessary for solving problems involving complex shapes, moving beyond Cartesian coordinates to General Curvilinear systems. Students derive scale factors, volume elements, and differential operators, culminating in solving Laplace's equation and understanding metric tensors.
This sequence guides 6th-grade students through the conceptual and procedural aspects of calculating the volume of rectangular prisms. Starting with unit cubes and moving through fractional edge lengths and composite figures, students develop a deep understanding of 3D space measurement.
This sequence connects geometry to physical space by exploring volume and the attributes of solid figures. Students progress from packing unit cubes to deriving and applying the standard volume formulas (V = l x w x h and V = B x h) to real-world engineering challenges.
A 7th-grade project-based sequence exploring scale drawings, proportional reasoning, and the geometric properties of dilation. Students progress from basic scale factors to designing a professional tiny house blueprint.
A mastery-based algebra sequence for 9th graders focusing on the structural properties of rational exponents and radicals. Students analyze, compare, and defend mathematical forms to deepen conceptual understanding beyond rote calculation.
This sequence introduces students to parametric equations as a tool for modeling dynamic systems. Students explore the relationship between independent components, algebraic conversion to Cartesian form, and real-world applications like projectile motion and cycloids.
This sequence explores the intersection of calculus and geometry through infinite series and fractals. Students investigate convergence and divergence using visual area models, fractal dimensions, and physical simulations like block stacking.
A project-based sequence exploring infinite geometric series through Zeno's paradox, algebraic proofs of convergence, and fractal geometry. Students investigate how infinite additions can result in finite sums and apply these concepts to real-world paradoxes and self-similar shapes.
A 12th-grade inquiry into complex numbers through the lens of geometry and vector operations. Students transition from algebraic rules to visual intuition, exploring rotations, dilations, and translations in the complex plane.
A comprehensive exploration of complex numbers through a geometric lens, bridging algebraic arithmetic with vector transformations and polynomial theory for undergraduate students.
This sequence explores matrices as geometric transformations of vectors. Students learn to visualize and calculate how matrices stretch, rotate, reflect, and shear space, culminating in a project where they design a computer graphics animation sequence.
A project-based sequence for 12th Grade students exploring linear transformations through the lens of computer graphics. Students learn to use 2x2 matrices to scale, reflect, shear, and rotate vectors, culminating in a retro video game animation project.
This mastery-based sequence focuses on the properties of transformations (translations, reflections, rotations, and dilations) and how they preserve or change geometric relationships. Students build arguments for congruence and similarity by analyzing parallelism, orientation, and angle preservation.
A game-based exploration of composite geometric transformations where students act as navigators, programming shapes through coordinate mazes and investigating how the order of transformations affects final positions.
A comprehensive 8th-grade geometry sequence focusing on the algebraic notation of geometric transformations. Students transition from visual graphing to using coordinate rules like (x, y) -> (x+a, y+b) to predict the position of images.
A comprehensive 8th-grade geometry unit that explores rigid transformations (translations, reflections, rotations) through inquiry-based activities and coordinate plane analysis to define congruence. Students move from physical manipulatives to algebraic rules, culminating in proving congruence through sequences of transformations.
A project-based geometry sequence for 10th graders focusing on the intersection of art and mathematics through composite transformations, symmetry, and procedural design. Students transition from analyzing complex patterns in the world to synthesizing their own designs using algebraic coordinate rules.
A comprehensive 10th-grade geometry unit exploring dilations as non-rigid transformations. Students investigate scale factors, coordinate rules, and the formal definition of similarity, culminating in complex problem-solving and forensic modeling applications.
A comprehensive 10th-grade geometry sequence on rigid transformations, covering translations, reflections, rotations, and compositions to define and prove congruence in the coordinate plane.
A project-based sequence exploring rigid and non-rigid transformations through the lenses of art, architecture, and digital animation. Students transition from identifying patterns in Escher prints to engineering their own geometric designs and animations using precise coordinate rules.
An inquiry-driven 8th-grade geometry sequence where students discover the logical foundations of angle relationships through data collection, deductive puzzles, and argumentative proof-building.
This 8th-grade sequence bridges the gap between geometry and algebra by using angle relationships to build and solve linear equations. Students progress from basic measurement to solving complex multi-step geometric puzzles involving unknown variables.
A high school geometry sequence focused on the logical derivation and formal proof of circle angle relationships, moving from basic inscribed angles to complex multi-step proofs.
A 10th-grade geometry unit that bridges algebra and geometry by using coordinate methods (slope, distance, and midpoint formulas) to classify polygons and write formal coordinate proofs. Students progress from verifying specific shapes to generalizing geometric properties using variables.
This sequence explores the fundamental theorems of circle geometry, from inscribed angles and semicircles to cyclic quadrilaterals and tangent properties. Students use inquiry-based methods and formal proofs to master the relationships between angles, arcs, and line segments in circles.
This inquiry-driven sequence guides students from intuitive shape recognition to formal deductive reasoning about quadrilaterals. Students investigate properties of parallelograms, special quadrilaterals, and trapezoids, culminating in the construction of a logical hierarchy based on geometric attributes.
A rigorous undergraduate-level exploration of circle geometry, focusing on axiomatic proofs, inscribed angles, tangency, cyclic quadrilaterals, and advanced Euclidean theorems. Students transition from intuitive understanding to formal deductive reasoning.
This inquiry-based sequence guides students through the discovery and formalization of angle relationships within and around circles. Students progress from central and inscribed angles to cyclic quadrilaterals and intersections involving chords, secants, and tangents.
A comprehensive 9th-grade geometry unit focused on the logical classification of quadrilaterals and the verification of geometric properties using coordinate geometry. Students move from intuitive definitions to rigorous proofs, exploring hierarchical relationships and using algebraic tools to defend mathematical claims.
A high school geometry sequence that bridges the gap between concrete angle measurement and abstract algebraic reasoning. Students move from measuring physical angles to modeling relationships with equations and justifying their logic through formal geometric theorems.
An inquiry-based exploration of circular geometry, focusing on the relationships between angles and arcs. Students move from basic inscribed angles to complex intersections of secants and tangents through a celestial cartography theme.
A rigorous exploration of geometric classification, focusing on logical hierarchies of quadrilaterals, properties of diagonals, 3D polyhedra attributes via Euler's Formula, and the visualization of cross-sections. Students move from visual identification to formal geometric reasoning and proof construction.
A sequence designed for 11th-grade students requiring academic support to break down complex mathematical problems using visual modeling, color-coding, and flowcharting. This approach reduces cognitive load and bypasses working memory deficits by externalizing abstract relationships into concrete visual structures.
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 geometry sequence for 9th-grade students exploring the SSA ambiguous case in trigonometry. Through a mix of visual simulation, algebraic calculation of altitudes, and real-world context, students master why certain geometric constraints lead to zero, one, or two possible triangles.
This sequence explores the metric relationships of circles, focusing on the Power of a Point theorems (chords, secants, and tangents) and their applications in engineering and geometry. Students will derive these relationships using similarity and apply them to solve complex algebraic problems, including common tangents in pulley systems.
A rigorous undergraduate exploration of similarity theory, proportionality, and their applications in proving the Pythagorean Theorem and circle properties. Students move from dynamic exploration to formal proofs.
This sequence explores the geometric foundations of similarity, connecting dilations on the coordinate plane to the Angle-Angle criterion. Students will prove the constancy of slope using similar right triangles and apply these theorems to solve real-world indirect measurement problems.
A 10th-grade geometry unit exploring similarity, proportionality, and dilations through transformations, proofs, and real-world indirect measurement. Students move from abstract coordinate plane dilations to physical field measurements of unreachable heights.
A comprehensive geometry unit exploring similarity, dilations, and proportionality theorems. Students progress from intuitive transformations to formal proofs and real-world applications of geometric ratios.
A high school geometry sequence that moves students from the fundamental proofs of the Pythagorean Theorem to advanced applications in coordinate geometry, similarity, and the equation of a circle. Students will explore visual proofs, classify triangles using the converse, and derive the distance and circle formulas.
This undergraduate geometry sequence bridges classical Euclidean similarity with modern fractal theory. Students progress from formal proofs of homothety to calculating the Hausdorff dimension of self-similar sets, exploring how scaling laws govern both biological structures and infinite recursive shapes.
This undergraduate sequence bridges classical geometry and modern algebra by exploring similarity through the lens of complex numbers and linear algebra. Students will master spiral similarities, matrix representations of conformal mappings, and iterative fractal generation.
An advanced exploration of similarity and proportionality in Euclidean geometry, focusing on Menelaus' and Ceva's Theorems, homothety, and the Euler Line. Students move from directed segments and area ratios to complex proofs of collinearity and concurrence suitable for undergraduate mathematics.
This undergraduate geometry sequence rigorously explores the axiomatic foundations of similarity, bridging the gap between transformational geometry and Euclidean proofs. Students move from the formal definition of dilations to proving major theorems like the Fundamental Theorem of Similarity, AA/SAS/SSS criteria, and advanced circle applications like Ptolemy's Theorem.
This geometry sequence for 9th-grade students explores proportionality theorems involving triangles and parallel lines. Starting with inquiry-based exploration and moving through formal proofs of the Side-Splitter Theorem, its converse, and the Midsegment Theorem, the unit concludes with real-world applications of parallel lines in urban planning and perspective.
This 9th-grade geometry sequence focuses on mastering similarity proofs in complex, overlapping, and non-standard geometric configurations. Students transition from identifying basic similarity to analyzing, critiquing, and constructing multi-step logical arguments, culminating in a Socratic seminar on proof efficiency.
This sequence explores the geometric relationships within right triangles when an altitude is drawn to the hypotenuse. Students will discover triangle similarity, derive geometric mean theorems, and ultimately prove the Pythagorean Theorem using similarity ratios.
A project-based geometry sequence where 9th-grade students apply similarity theorems and proportions to measure inaccessible heights using shadow and mirror methods, culminating in a formal geometric proof and field report.
A comprehensive geometry sequence for 9th-grade students focused on proving triangle similarity. Students progress from understanding transformations and dilations to constructing formal flowchart and two-column proofs using AA, SAS, and SSS criteria.
A 10th-grade geometry project where students apply similarity theorems to measure inaccessible heights using historical methods (Thales' shadows) and modern tools (clinometers). The unit blends historical context, hands-on construction, field data collection, and rigorous mathematical proof.
A comprehensive 5-lesson geometry sequence exploring the unique similarity relationships in right triangles, culminating in a formal similarity-based proof of the Pythagorean Theorem. Students move from hands-on discovery to algebraic derivation and multi-step mastery.
A project-based unit exploring non-rigid transformations. Students learn to apply scale factors, perform dilations on the coordinate plane, and distinguish between similarity and congruence, culminating in a logo design scaling project.
This sequence introduces non-rigid transformations, specifically focusing on dilations and the concept of similarity. Students explore how dilations change size while preserving shape, investigating the roles of the center of dilation and the scale factor.
A comprehensive 9th Grade Geometry sequence on rigid transformations, focusing on composition, mapping congruence, and symmetry using a transformational approach.
An 8th-grade geometry unit exploring congruence through the lens of rigid transformations. Students define congruence by mapping figures via translations, rotations, and reflections, building up to formal triangle congruence criteria and their applications in real-world problem-solving.
A comprehensive geometry unit for 9th-grade students focusing on triangle congruence criteria. Students progress from rigid motion definitions to multi-step formal proofs using SSS, SAS, ASA, AAS, and HL, culminating in the application of CPCTC and the analysis of complex overlapping figures.
This sequence bridges the gap between physical rigid motions and formal geometric proof. Students explore how pinning down specific parts of a triangle (SAS, SSS, ASA) creates a rigid structure that forces congruence, while other combinations (SSA) fail.
A comprehensive 8th-grade geometry sequence exploring angle relationships in transversals and triangles, moving from empirical discovery to algebraic application and formal proof. Students investigate parallel lines, prove triangle theorems, and solve complex multi-step geometric puzzles.
This sequence bridges Euclidean geometry with abstract algebra, investigating the field of constructible numbers and the Gauss-Wantzel Theorem to determine which regular polygons can be constructed using a ruler and compass.
This sequence explores geometric congruence and similarity through the lens of linear algebra. Students learn to represent and manipulate shapes using matrices, homogeneous coordinates, and composite transformations, bridging the gap between abstract geometry and computer graphics.
This sequence explores the abstraction of similarity into fractal geometry and iterated function systems (IFS). Undergraduate students will investigate contraction mappings, calculate fractal dimensions using logarithms, and apply the Banach Contraction Principle to understand why these self-similar structures converge to unique attractors.
A focused unit on mastering the volume of cones, specifically identifying and correcting common calculation errors like the 'diameter trap'.
A 5-lesson sequence for 5th Grade students focusing on the conceptual development of volume using unit cubes, specifically designed for academic support. Students progress from physical building and counting to discovering the multiplicative formula and applying it to composite shapes and real-world design challenges.
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 hands-on geometry sequence for 1st graders to explore 3D shapes, capacity, and volume using 'Shape Lab' investigations. Students progress from distinguishing 2D from 3D to measuring volume with unit cubes and exploring capacity through liquid displacement and estimation.
A project-based calculus sequence where students use optimization to design efficient packaging. They transition from physical modeling to algebraic functions and derivative-based solutions to maximize volume and minimize material costs.
A project-based unit exploring the relationship between 2D shapes and 3D solids through cross-sections, rotations, volume principles, and real-world modeling. Students move from visualization to optimization, culminating in a container design challenge.
This sequence bridges the gap between theoretical calculus operations and applied problem-solving by focusing on optimization in real-world contexts. Students begin by mastering the 'modeling process'—translating verbal constraints into mathematical objective functions. Over five lessons, they progress from simple geometric maximization to complex economic minimization and physical efficiency problems. By the end, students will demonstrate proficiency in using the First and Second Derivative Tests to justify absolute extrema in manufacturing and design scenarios.
A comprehensive calculus sequence for undergraduate students focused on the rigorous application of derivatives to industrial, geometric, and economic optimization problems. Students progress from basic modeling to multi-constraint capstone analysis.
This graduate-level sequence bridges univariate statistics and multivariate geometry, exploring how variability manifests in high-dimensional spaces through covariance matrices, generalized variance, and principal component analysis.
A sequence focused on breaking down complex geometric shapes into manageable parts. Students use color-coding, physical manipulation, and organized calculations to solve 2D area and 3D volume problems, culminating in a design challenge.
A project-based calculus unit where students apply curve sketching and derivative tests to real-world optimization problems, moving from modeling constraints to defending optimized designs.
A comprehensive 11th Grade Calculus sequence covering applications of integration including arc length, surface area of revolution, centroids, and the theorems of Pappus. Students explore the geometric properties of curves and regions using analytical methods.
This 10th-grade geometry sequence explores the metric relationships of chords, secants, and tangents within circles. Students will move from internal chord intersections to complex external secant/tangent theorems, culminating in a real-world architectural design project.
This sequence explores the metric relationships of segments in circles, including chords, secants, and tangents. Students progress from basic tangent properties to complex 'Power of a Point' theorems, culminating in a real-world modeling project.
This sequence explores the metric relationships of segments in circles, covering tangent-radius orthogonality, the 'Ice Cream Cone' theorem, and the Power of a Point theorems for chords, secants, and tangents. Students apply these geometric principles to solve algebraic problems and model real-world scenarios like horizon distance and GPS trilateration.
This sequence explores the metric properties of circles, specifically segment lengths formed by tangents, chords, and secants. Students progress from basic tangent properties to complex 'Power of a Point' theorems, culminating in a real-world archaeological reconstruction project.
This inquiry-based sequence explores transcendental numbers like Pi and Euler's number (e) to connect irrationality with real-world phenomena and geometry. Students investigate historical methods of approximation and modern infinite series.
This sequence explores the geometric and algebraic properties of circles. Students progress from defining a circle as a locus of points to deriving its standard equation, converting between forms by completing the square, and solving complex coordinate geometry problems involving tangents and geofencing.
This sequence explores the three famous problems of antiquity (squaring the circle, doubling the cube, trisecting the angle) and the alternative construction methods that solve them. Students analyze why standard tools fail and experiment with 'Neusis' constructions, Origami (paper folding) axioms, and conic sections. It highlights how changing the axioms changes the solvable universe.
This undergraduate-level sequence explores the axiomatic foundations of Euclidean constructions. Students move from basic operations to complex theorems like the Nine-Point Circle, emphasizing formal proof and logical dependency over mechanical procedure.
This Kindergarten sequence explores the intersection of geometry and engineering. Students learn to compose and decompose 2D shapes before applying those principles to 3D structural stability, culminating in a collaborative project to design a geometric city.
A Kindergarten physics sequence exploring the physical properties of 3D solids. Students compare flat and solid shapes, investigate movement (rolling, sliding, stacking), and identify geometric solids in the real world.
A Kindergarten sequence focused on the fundamental properties of 2D shapes, starting with the distinction between curves and straight lines and progressing to identifying triangles, quadrilaterals, circles, and hexagons by their attributes.
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 calculus in the polar coordinate system, focusing on differentiation and integration. Students will master finding slopes of tangent lines, calculating areas of polar regions and intersection areas, and determining arc lengths of polar curves.
A foundational unit on geometric measurement where 1st Grade students learn to measure area by tiling with square units, focusing on precision (no gaps or overlaps) and comparison.
An 8th-grade geometry sequence focused on the derivation and application of polygon angle properties. Students progress from the Triangle Sum Theorem to general formulas for interior and exterior angles of any polygon, ultimately applying these properties to solve complex algebraic problems.
A 5-lesson unit for 3rd graders exploring the additive nature of angles. Students move from kinesthetic turns to calculating missing measurements in complementary, supplementary, and complex angle diagrams.
A project-based unit where 3rd-grade students learn to construct angles and geometric figures using protractors and straightedges. The sequence culminates in an 'Angle Art' project where students apply their precision drawing skills to create a labeled masterpiece.
This workshop-style sequence transitions students from visual estimation to precise measurement using a protractor. Students learn the logic behind the 360-degree circle and how to align a protractor correctly to read measurements.
A hands-on geometry sequence where students explore the building blocks of angles, identify right angles in their environment, and classify angles as acute, obtuse, or straight through inquiry and shape analysis.
This sequence bridges algebra and geometry by applying coordinate methods to the classification of geometric figures. Students use distance, midpoint, and slope formulas to verify properties of triangles and quadrilaterals, preparing them for vector physics and computer-aided design.
This sequence guides third graders through the hierarchical classification of quadrilaterals. Students move from basic sorting to understanding complex relationships, such as why a square is both a rectangle and a rhombus, using hands-on sorting, Venn diagrams, and a final design project.
An 8th-grade geometry sequence focused on the logical classification of shapes using necessary and sufficient conditions, hierarchies, and diagonal properties. Students transition from simple identification to rigorous logical reasoning and set theory.
A comprehensive geometry sequence for 7th grade focusing on the mathematical rules of shape existence, including the Triangle Inequality Theorem, angle sums, unique vs. ambiguous constructions, and quadrilateral hierarchies. Students act as geometric architects, analyzing constraints to determine if shapes can exist and if they are unique.
A project-based sequence where 12th-grade students explore the coordinate geometry of circles to model GPS triangulation and search-and-rescue operations. Students transition from algebraic derivations to complex multi-circle intersection problems.
An advanced exploration of the general second-degree equation, focusing on identifying, rotating, and graphing conics with cross-product terms using both trigonometric and matrix methods.
A project-based exploration of analytic geometry focusing on the physics and engineering applications of conic sections, including reflection properties, navigation, and optical systems.
A rigorous undergraduate-level exploration of conic sections unified through the eccentricity parameter and polar coordinate systems. Students transition from traditional Cartesian definitions to a singular focus-directrix approach, concluding with the elegant 3D proof of Dandelin Spheres.
This sequence explores the geometric and algebraic foundations of ellipses and hyperbolas. Students move from locus definitions and dynamic simulations to rigorous algebraic derivations, parameter analysis, and comparative studies of central conics.
This sequence bridges the gap between geometric locus definitions and algebraic representations of circles and parabolas. Students will move from physical distance constraints to rigorous derivations, mastering the standard forms and their properties through an 'analytic architecture' lens.
A 12th-grade advanced geometry sequence exploring the unified nature of conic sections through eccentricity, focus-directrix definitions, polar coordinates, and rotation. Students use dynamic software to visualize how algebraic parameters shift geometric reality.
An advanced 12th-grade geometry sequence exploring conic sections through the lens of orbital mechanics. Students act as mission specialists analyzing elliptical orbits, parabolic escape trajectories, and hyperbolic gravity assists to determine the paths of celestial bodies.
A project-based sequence for 12th-grade students exploring the real-world applications of conic sections in engineering, physics, and medicine. Students transition from geometric definitions to algebraic equations while solving practical problems involving satellite dishes, whispering galleries, and navigation systems.
A mastery-focused sequence on converting general second-degree equations into standard conic forms through completing the square. Students reveal geometric properties like centers, foci, and vertices from complex algebraic expressions.
Students explore conic sections as geometric loci, deriving standard equations from distance-based definitions through inquiry, physical construction, and algebraic proof.
This mastery-based sequence focuses on the synthesis of all conic sections. Students learn to manipulate the General Second-Degree Equation to classify curves and transform them into standard forms.
This sequence explores the ellipse as a geometric locus where the sum of distances to two foci is constant. Students move from hands-on construction to algebraic derivation and real-world applications in acoustics and astronomy.
This 10th-grade geometry sequence explores hyperbolas through their geometric definition as a constant difference of distances. Students transition from visual conceptualization using sonic booms to algebraic mastery of standard equations and asymptotic graphing, culminating in a real-world LORAN navigation simulation.
This sequence explores the geometric definition of parabolas through focus and directrix, moving from hands-on construction to algebraic derivation and real-world reflective applications. Students will learn to translate between geometric descriptions and algebraic equations while exploring the physical properties of parabolic curves.
This inquiry-based sequence bridges the gap between the geometric concept of a locus of points and algebraic equations, specifically focusing on circles. Students begin by exploring the definition of a circle using the distance formula, rather than just memorizing the standard equation. Through guided investigation, they derive (x-h)^2 + (y-k)^2 = r^2 and learn to manipulate it. The sequence culminates in applying this understanding to solving problems involving regions of coverage, such as cellular signals or earthquake epicenters.
This sequence guides 11th-grade students through the transition from visualizing conic sections as physical cross-sections of a double-napped cone to mastering the algebraic manipulation of the general second-degree equation. Students will learn to classify equations by inspection, transform them through completing the square, and identify unique 'degenerate' cases.
A comprehensive sequence exploring hyperbolas through their geometric definition, algebraic derivation, and real-world application in LORAN navigation. Students move from conceptual inquiry to rigorous graphing and complex problem-solving.
A series of lessons focused on the practical applications of linear equations, slope, and geometric relationships in real-world contexts like urban planning and engineering.
This sequence integrates algebra and geometry by using the coordinate plane to verify shape attributes. Students move beyond visual estimation to rigorous verification using the distance formula (Pythagorean Theorem) and slope.
A 9th-grade geometry unit where students use algebraic tools—distance, slope, and midpoint formulas—to rigorously prove and classify the properties of polygons on a coordinate plane.
This advanced geometry sequence guides students through proving the properties of quadrilaterals and using coordinate geometry to verify shape classifications. Students will master formal deductive proofs, explore hierarchical relationships, and apply algebraic methods to geometric reasoning.
This sequence explores the geometric properties of quadrilaterals through formal proofs and coordinate geometry. Students progress from basic parallelogram properties to complex hierarchical classifications and algebraic verifications.
This workshop-style sequence bridges algebra and geometry by verifying geometric classifications through coordinate proofs. Students apply the distance formula to verify congruency and the slope formula to verify parallel and perpendicular relationships to classify triangles and quadrilaterals.
This undergraduate-level sequence explores the application of coordinate geometry in spatial design, surveying, and structural engineering. Students learn to translate physical spaces into algebraic models, use coordinate proofs to verify geometric properties, and optimize locations using distance-based functions.
This undergraduate-level sequence focuses on the transition from numerical to algebraic coordinate geometry. Students learn to define shapes using variable coordinates, manipulate symbolic expressions to prove universal theorems, and handle complex concurrency proofs using literal systems of equations.
A rigorous undergraduate-level sequence exploring the algebraic classification of quadrilaterals using coordinate geometry. Students apply slope, distance, and midpoint formulas to prove properties of parallelograms, rectangles, rhombi, and squares.
This sequence guides undergraduate students through the algebraic verification of geometric theorems using coordinate geometry. Starting with the strategic placement of figures, students progress through the Triangle Midsegment Theorem, classification of special triangles, and the properties of centroids.
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 related rates in calculus through geometric modeling of 3D systems, including fluid dynamics and shadow propagation. Students progress from 2D similar triangle models to complex 3D variable elimination in conical tanks.
A rigorous graduate-level sequence exploring the algebraic and topological foundations of vector quantities, transitioning from Euclidean geometry to abstract Banach and Hilbert spaces.
A project-based 8th-grade sequence where students act as structural engineers and architects. They apply angle concepts (complementary, supplementary, vertical, adjacent) to design and verify the structural integrity of bridges and trusses.
This sequence explores the 'Ambiguous Case' (SSA) of the Law of Sines through visualization, algebraic proof, and real-world application. Students move from physical constructions to systematic classification and problem-solving.
A project-based sequence for 12th-grade students exploring the spatial and structural applications of irrational constants like the Square Roots, Phi, Pi, and Euler's Number. Students connect geometric construction, probability, and continuous growth models to real-world design and natural phenomena.
A 10th-grade mathematics unit exploring the geometric origins and logical proofs of irrational numbers. Students move from physical constructions of radicals using the Spiral of Theodorus to formal algebraic proofs by contradiction.
This advanced geometry sequence explores the algebraic structure of the Euclidean Group, focusing on reflections as generators and the classification of all plane isometries. Students will move from geometric constructions to formal group theory, culminating in the Three Reflections Theorem and non-commutative properties.
This sequence explores the intersection of geometry, art, and architecture. Students master compass and straightedge constructions to recreate historical designs from Gothic cathedrals and Islamic tilings while understanding the underlying mathematical principles of root rectangles and aperiodic tilings.
This sequence utilizes Dynamic Geometry Systems (DGS) to modernize the study of constructions, shifting focus from physical precision to logical robustness. Students explore dependencies, loci, transformations, and complex mechanical linkages through the 'drag test' methodology.
This advanced geometry sequence explores the points of concurrency in triangles through geometric constructions. Students use physical and digital tools to construct and analyze the circumcenter, incenter, centroid, and orthocenter, culminating in the discovery of the Euler Line.
This sequence explores the intersection of art and geometry through inscribed regular polygons. Students use compass and straightedge techniques to construct triangles, hexagons, squares, and pentagons, culminating in a geometric mandala project.
This geometry sequence guides 10th-grade students through the precision and logic of geometric constructions. Focusing on perpendicular and parallel relationships, students move from basic line interactions to complex grid systems using only a compass and straightedge.
This sequence introduces 10th-grade students to the core skills of Euclidean geometry using a compass and straightedge. Students progress from basic segment and angle duplication to complex bisecting techniques, culminating in a multi-step construction challenge.
A 4th-grade geometry sequence where students use a compass and straightedge to construct regular polygons (triangles, hexagons, and squares) inscribed in circles, culminating in a creative tile design project.
A 4th-grade geometry sequence exploring the intersection of math and art. Students master compass and straightedge constructions, moving from basic overlapping circles to complex geometric patterns and optical illusions.
A 4th-grade geometry sequence focusing on the art and science of geometric constructions. Students move from estimating angles to using compasses and straightedges to copy, bisect, and construct specific angles, culminating in a radially symmetrical art project.
Students explore geometric constructions focusing on parallel and perpendicular relationships using tools and folding techniques, culminating in a city grid design project.
A comprehensive introduction to geometric constructions for 4th graders, focusing on tool mastery, segment copying, and the fundamental properties of circles using a compass and straightedge.
A 6-lesson intervention sequence for 6th-grade students focusing on multi-digit decimal operations and rational number concepts on the number line and coordinate plane. Designed for small-group instruction using High Leverage Concepts.
A series of lessons focused on spatial reasoning, map skills, and coordinate logic for elementary students.
A sequence focused on visualizing linear functions through physical movement and spatial reasoning, designed for middle school students to master slope-intercept form.
A foundational algebra sequence focused on linear relationships, starting with the calculation of slope and graphing equations in slope-intercept form. Students progress from conceptual understanding to procedural fluency using visual and kinesthetic activities.
This sequence introduces 3rd-grade students to coordinate geometry and spatial reasoning. Students progress from using relative positional vocabulary to navigating absolute alpha-numeric grids, culminating in mapping and city planning projects.
This inquiry-driven sequence connects the geometric definitions of the unit circle to algebraic trigonometric identities. Students derive Pythagorean, reciprocal, and quotient identities through visualization and algebraic proof to foster deep conceptual understanding.
A comprehensive introduction to vector analysis for 11th-grade students, moving from geometric representations to algebraic components and real-world mechanical applications. Students master vector addition, scalar multiplication, the dot product, and force decomposition.
This sequence introduces students to the imaginary unit i through an inquiry-based approach, moving from the limitations of the real number system to the visualization of the complex plane and calculation of the modulus. Students transition from solving unsolvable quadratics to representing numbers in a 2D coordinate system.
This sequence introduces 12th-grade students to vectors, covering geometric representations, algebraic operations in component form, and real-world applications in physics and navigation. Students will progress from visual concepts to complex analytical modeling of velocity and force.
A comprehensive unit on trigonometric substitution in calculus, moving from geometric visualization of radicals to complex integration techniques and algebraic back-substitution. Students learn to map radical expressions onto right triangles and use trigonometric identities to simplify and solve integrals.
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 comprehensive exploration of the unit circle, bridging geometry and trigonometry by scaling triangles, defining radians, and utilizing symmetry to evaluate trigonometric functions.
An advanced geometry sequence focusing on industrial applications of volume, including frustums, partial cylindrical volumes, displacement, and flow rates. Students integrate trigonometry and calculus-adjacent concepts to solve real-world engineering challenges.
This geometry sequence guides 10th-grade students through the concepts of area, starting with fundamental quadrilaterals and progressing to regular polygons, sectors, composite figures, and geometric probability. Students will use decomposition and algebraic derivation to master spatial measurement.
This sequence transitions 12th-grade students from degree-based measurements to radian measure, exploring arc length, sector area, and the physics of rotational motion through the lens of engineering and mechanical systems.
This sequence explores the relationship between angular measurement and spatial geometry, moving from radian-based circle analysis to 3D volume derivation using trigonometry, Cavalieri's Principle, and solids of revolution. Students apply these concepts to high-level engineering and architectural contexts.
An 11th-grade geometry sequence applying arc length and sector area calculations to real-world security and sensor systems. Students analyze camera sweep zones, radar ranges, and wiper blade optimization through engineering-themed simulations.
A high-level geometry sequence for 11th-grade students focusing on decomposing complex circular figures, including annuli, segments, and composite shaded regions. Students apply algebraic and trigonometric techniques to solve advanced area and perimeter problems.
A project-based geometry unit where students act as landscape architects to design a circular park, using arc lengths for paths and sector areas for zones while managing a budget.
A comprehensive 11th-grade geometry sequence exploring the transition from degree-based circular measures to the more natural radian system, covering arc length, sector area, and error analysis.
A logical, inquiry-based progression through the derivation and application of arc length and sector area formulas. Students use proportional reasoning to move from 'parts of a whole' to formal geometric expressions.
A high school geometry unit where students apply arc length and sector area formulas to landscape architecture and urban planning. Students design a public park, calculate material needs, and optimize their designs based on budgetary constraints.
This sequence applies circular geometry to a global scale, introducing students to spherical geometry concepts used in navigation and aviation. Students treat the Earth as a sphere and use arc length formulas to calculate 'Great Circle' distances between cities, concluding with a flight path simulation.
A project-based geometry sequence where 12th-grade students act as mechanical engineers. They apply arc length and sector area formulas to design efficient belt-and-pulley transmission systems, connecting static geometry to dynamic mechanical physics.
A high-level geometry sequence for 12th-grade students focusing on circular segments, composite regions, and their applications in engineering and architecture. Students progress from foundational sector calculations to complex decomposition of architectural forms.
A high-level geometry sequence for 12th-grade students focused on the transition from degree-based measurements to the mathematical efficiency of radians. Students will derive and apply formulas for arc length and sector area, building a foundation for calculus.
A sophisticated sequence for undergraduate students bridging the gap between static geometry (arc length and sector area) and dynamic circular motion. This unit explores linear and angular velocity, Kepler's Second Law, satellite communication footprints, and visual angles.
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.
A graduate-level exploration of the Calculus of Variations, focusing on optimizing functionals. Students derive the Euler-Lagrange equation and apply it to physics and geometry problems like the Brachistochrone and Isoperimetric challenges.
A comprehensive graduate-level exploration of series solutions for differential equations with variable coefficients, focusing on power series, the Method of Frobenius, and the properties of Bessel and Legendre functions within the framework of Sturm-Liouville theory.
An advanced graduate sequence exploring vector calculus from 3D fields to differential forms on manifolds, focusing on fluid dynamics and electromagnetic theory. It moves from parameterizing static fields to understanding global topological constraints on curved surfaces.
A comprehensive geometry unit for 9th grade exploring the transition from 2D shapes to 3D solids through nets, rotations, cross-sections, and Cavalieri's Principle. Students apply spatial reasoning to model and design complex geometric forms.
An inquiry-based exploration of calculus optimization, focusing on real-world efficiency in travel time, infrastructure cost, and business profit. Students progress from geometric shortest-paths to complex rate-based modeling.
A comprehensive undergraduate-level sequence exploring the intrinsic geometry of space curves through the TNB (Tangent, Normal, Binormal) frame, curvature, and torsion. Students move from basic vector functions to advanced structural analysis of curves in 3D space.
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.
A comprehensive 10th-grade sequence on vector quantities, bridging algebraic resolution with real-world physics applications like navigation and static equilibrium. Students master resolving vectors, component arithmetic, and normalizing vectors to solve engineering and navigational challenges.
A comprehensive introduction to vectors through geometric representation, focusing on the distinction between scalars and vectors, visual addition/subtraction, scalar multiplication, and the transition to component form and magnitude calculation.
An undergraduate-level exploration of the roots of unity, connecting algebraic solutions of polynomial equations to geometric symmetry in the complex plane and the fractal nature of complex iteration.
A high-level geometry sequence focused on diagnosing oblique triangles. Students use a medical 'triage' theme to master Law of Sines and Law of Cosines through pattern recognition, algebraic mastery, and mixed practice.
A comprehensive geometry sequence focused on finding the area of oblique triangles using trigonometric ratios and Heron's Formula, culminating in a real-world land surveying project.
A 5-lesson geometry project where students apply the Law of Sines and Law of Cosines to solve real-world navigation and surveying problems, culminating in a search-and-rescue triangulation task.
A 5-lesson geometry sequence where students move from right-triangle trigonometry to general triangles. They derive the Law of Sines and Law of Cosines through inquiry and verify their accuracy via a hands-on measurement lab.
This sequence explores trigonometry through navigation and surveying. Students learn to use bearings, the Law of Sines, and the Law of Cosines to solve real-world problems involving triangulation, course correction, and indirect measurement.
A project-based sequence for 4th graders exploring 3D geometry through the lens of engineering and structural design. Students transition from identifying properties like faces, edges, and vertices to testing structural stability and designing a geometric city block.
