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 two-week intensive spiral review of 4th-grade math standards designed for 5th-grade RSP students to bridge foundational gaps through short, focused daily practice.
A comprehensive framework for K-5 RSP math instruction, including a California Common Core aligned scope and sequence of power standards and a leveled placement diagnostic.
A series of official Grade 4 PEP-style assessments and teacher resources designed to prepare students for the Jamaican Primary Exit Profile, covering all key mathematical domains from the National Standards Curriculum.
A series of materials designed to evaluate and document first-grade students' mastery of year-long mathematical standards in preparation for second grade.
A series of assessment resources for foundational mathematics based on the Massachusetts Curriculum Frameworks, spanning Pre-K and early elementary grades.
A comprehensive unit plan for 2nd Grade Mathematics based on Illustrative Mathematics Units 5-8, integrated with Building Thinking Classrooms (BTC) pedagogy. Each section includes a sequence of six 'thin-sliced' tasks designed to build conceptual rigor through collaborative problem-solving on vertical surfaces.
A comprehensive geometry unit for 2nd-grade special education students, focusing on 2D and 3D shape identification, attributes, and composition through visual and hands-on activities.
A series of lessons designed to build fluency in mathematical notation and operations through visual and tactile learning.
A comprehensive unit on lines of symmetry, exploring identification, drawing, and real-world applications through geometric and organic forms. Students will develop a deep understanding of balance and reflection.
A Dr. Seuss-themed unit focusing on 'Wacky Wednesday' with a focus on counting, size sorting, prepositions, and creative expression for Pre-K and Kindergarten students.
A comprehensive unit where students become architects in the 'Pattern Palace', learning to identify, extend, and create complex shape and number patterns. Students develop algebraic thinking through hands-on tiling activities, visual challenges, and numerical sequences.
A comprehensive multi-grade longitudinal analysis of MCAS Math data (Grades 3-4) for 2023-2025. This sequence provides diagnostic reporting, visual aids, and instructional intervention strategies based on identified categorical trends.
A comprehensive Tier 2 intervention sequence for 3rd-grade students struggling with fraction concepts. This unit covers partitioning shapes, understanding fractions as numbers on a line, comparing unit fractions, and introducing equivalency through a construction and blueprint theme.
A Tier 2 intervention sequence focused on modeling real-world objects using geometric shapes, measures, and properties. Designed for small group instruction to support students in mastering Colorado High School Geometry standard HS.G-MG.A.1.
A targeted Tier 2 intervention sequence focused on helping Kindergarten students master the composition of geometric shapes using tangrams and guided discovery.
A 12-lesson series focused on understanding fractions as numbers, partitioning shapes and number lines, and exploring equivalence through a 'Blueprint Builder' architectural theme. Students progress from naming parts of a whole to locating fractions greater than 1 on number lines.
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 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 unit exploring the properties of exponents, scientific notation, and exponential functions.
A 3-day project-based learning experience where students design, budget, and run their own food truck business, integrating fractions, geometry, operations, and data analysis.
A 5-day self-paced unit explicitly aligned to Arizona Mathematics Standard 3.G.A.2. Students partition shapes into equal areas and express the parts as unit fractions (1/b). The 'Fraction Factory' theme provides a real-world engineering context for geometry and spatial reasoning.
A collection of modified math scope and sequence documents for 3rd grade, tailored for Tier 2 and Tier 3 intervention pathways. These documents adapt grade-level standards into accessible, functional, and scaffolded learning goals.
Un programme d'entraînement complet pour le concours Kangourou (niveau 4ème), couvrant la géométrie, la logique pure et les stratégies de résolution rapide.
Une séquence de 8 séances conçue pour préparer les élèves de 4ème au concours Kangourou des Mathématiques, mettant l'accent sur la logique, la géométrie et le raisonnement, avec une séance finale innovante pour une inspection.
A multi-day math unit on complex rectilinear figures, progressing from finding area with all labels to identifying missing side lengths and solving multi-step problems.
A four-day intensive unit on decomposing rectilinear figures to find total area, progressing from basic strategies to complex real-world architectural challenges. Students act as 'Blueprint Builders' to master vertical cuts, horizontal cuts, and additive/subtractive methods.
A targeted intervention sequence for Grade 4 students to master the classification of 2D figures using properties of lines and angles. The theme of a 'Shape Detective Agency' provides an engaging context for rigorous attribute analysis and evidence-based justification.
A Tier 2 intervention sequence for Grade 1 students focusing on partitioning circles and rectangles into halves and fourths using a concrete folding approach. Includes instructional slides, teacher guidance, printable manipulatives, and progress monitoring.
A comprehensive diagnostic suite for grades 2-5 designed to identify specific skill gaps in foundational math domains aligned to the Iowa Core standards. This series helps educators pinpoint exactly where students have discrepancies in place value, arithmetic, and early rational numbers.
A growing 180-day morning work volume for 3rd grade. Month 1: Basic ops & 2-8x facts. Month 2: 0,1,9,11x facts & intro fractions. Month 3: Equiv. fractions, perimeter, & 12x facts. Month 4: Area basics, 2-step word problems, and self-awareness.
A comprehensive unit on foundational fraction concepts for 3rd grade, focusing on partitioning shapes into equal parts, understanding unit fractions, and naming parts through eighths.
Un parcours complet sur les angles, les droites parallèles et les polygones, mettant l'accent sur l'identification, le calcul et la justification géométrique.
A deep dive into geometric transformations, starting with the foundational concepts of symmetry and reflection through hands-on exploration and visual practice.
A comprehensive 5-day self-paced packet for remedial Algebra 1 students focusing on the fundamentals of graphing, from basic coordinate planes to finding slope.
A comprehensive Geometry unit on quadrilateral proofs, covering parallelograms, special quadrilaterals, trapezoids, kites, and coordinate geometry through various proof methods.
A comprehensive prep sequence for the most challenging questions on the ACT Math and Science sections. It focuses on high-level conceptual blueprints for math topics like complex numbers and matrices, alongside speed-reading and data-interpretation strategies for the Science section.
A foundational math sequence for special education students (grades 5-6) focusing on algebraic thinking and spatial reasoning through highly visual, themed units.
A specialized geometry intervention sequence focused on applying geometric principles to real-world design challenges, specifically tailored for Tier 2 high school learners. The sequence emphasizes modeling, optimization, and structural integrity through hands-on design tasks.
A targeted intervention sequence for high school geometry students focusing on partitioning line segments in given ratios. This unit breaks down the section formula through visual supports, number line bridging, and scaffolded coordinate plane practice.
A targeted intervention sequence focused on helping students master the process of partitioning directed line segments in specific ratios. This sequence provides high-scaffold support, visual aids, and step-by-step procedures to ensure student success.
A targeted intervention sequence focused on helping students master triangle congruence and similarity criteria through scaffolded logic and collaborative problem-solving.
A targeted intervention sequence focused on verifying triangle congruence through rigid motions and corresponding parts, specifically designed for Tier 2 small group support.
A series of intensive intervention lessons focused on foundational geometry concepts through hands-on construction and formal definitions. This sequence supports Tier 2 learners in mastering transformations and proofs.
A series of lessons using a pixel-art theme to help 2nd grade students master place value (hundreds, tens, and ones) and foundational fractions using visual grids and money.
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 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.
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 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 high-level coordinate geometry sequence where students apply coordinate algebra formulas to identify and verify the properties of quadrilaterals and other polygons on the coordinate plane.
A two-week enrichment project where students act as architects to research, design, and calculate the geometry of a modern structure. The project covers points, lines, angles, and 2D shape classification through real-world application and creative design.
A Tier 2 intervention unit focused on the hierarchical classification of two-dimensional figures, helping students understand that subcategories inherit the attributes of their parent categories.
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 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.
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.
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.
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.
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 targeted intervention sequence for high school geometry students to master circle similarity through transformations and coordinate proofs.
A targeted Tier 2 intervention sequence focused on geometric transformations. It utilizes a Concrete-Representational-Abstract (CRA) approach, guiding struggling learners from physical manipulation with tracing paper to coordinate-based abstract rules.
A targeted intervention sequence focused on understanding triangle congruence (SSS, SAS, ASA) through the lens of rigid motions, specifically designed for Tier 2 small group support.
A targeted intervention sequence for high school geometry students focusing on mastering rigid transformations and sequences of motions to map figures. This unit provides scaffolded support for translation, reflection, and rotation, aligned with Colorado standard HS.G-CO.A.5.
A targeted intervention sequence focused on formalizing geometric transformations using precise language and fundamental constructions. This sequence helps students move from intuitive 'sliding, flipping, turning' to formal mathematical definitions.
A Tier 2 small group intervention focused on similarity and transformation sequences. Students explore dilation, proportional reasoning, and coordinate-based transformations to understand how shapes relate across the plane.
A targeted intervention sequence for 8th-grade students focusing on the geometric properties of angles in triangles and parallel lines. The lessons use informal arguments and visual proofs to build conceptual understanding of angle sums, exterior angles, and similarity.
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.
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.
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 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 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.
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 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.
Une série de micro-leçons de 10 minutes centrée sur l'optimisation de l'espace papier. Les élèves apprennent à mettre à l'échelle une mise en page de 6 photos (format A4) vers le format Raisin (50x65 cm) en minimisant les chutes.
A series of targeted intervention lessons designed to bridge the gap between triangle similarity and basic trigonometry, focusing on conceptual understanding and ratio consistency.
A targeted intervention sequence focused on mastering fundamental angle relationships in triangles and across parallel lines, designed for Grade 8 Tier 2 support.
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.
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 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.
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.
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.
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.
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.
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 project-based learning unit where students apply algebraic equations and inequalities to design and build a scale model of a functional living space. Students must manage budgets, spatial constraints, and material requirements using mathematical modeling.
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 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 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 comprehensive review sequence for Grade 6 Math Unit 7, focusing on rational numbers, absolute value, and the coordinate plane through engaging game-based activities.
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.
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.
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 collection of math challenges focused on operational fluency and geometric measurement.
A 5-day intensive intervention sequence focused on determining area using multiplication (3.6C) and calculating perimeter including missing side lengths (3.7B). The unit uses a 'Boundary Builders' construction theme to make geometric concepts concrete and engaging for small group instruction.
A targeted small group intervention for Grade 7 students focusing on using geometric relationships to solve algebraic equations for unknown angles. The sequence emphasizes scaffolded transitions from visual diagrams to formal algebraic solutions.
A math sequence focused on understanding and calculating the perimeter of irregular quadrilaterals through real-world scenarios like fencing a farm.
A comprehensive unit for 6th graders to master the coordinate plane and line graphs, focusing on plotting points, identifying trends, and representing real-world data.
A comprehensive collection of "Building Thinking Classrooms" (BTC) tasks for Grade 6 Mathematics, Units 5-8. Each unit contains thin-sliced, low-floor high-ceiling tasks designed for collaborative problem-solving on vertical surfaces.
A comprehensive collection of "thin-sliced" math thinking tasks for 5th Grade Illustrative Mathematics Units 5-8, designed using the "Building Thinking Classrooms" framework to promote deep mathematical reasoning and engagement.
A 7-week comprehensive math review sequence designed to prepare 6th-grade students for North Carolina state testing, covering Number Systems, Ratios, Expressions, Geometry, and Statistics.
A unit focused on 5th-grade geometry and measurement standards, specifically coordinate planes and volume calculation. Students apply mathematical concepts to real-world architectural scenarios.
A 2-part unit on the coordinate plane using a baseball theme, moving from first-quadrant basics to full four-quadrant navigation.
A comprehensive math review unit focused on mastering rational numbers, absolute value, and algebraic expressions through structured gameplay and practice.
A comprehensive 4-lesson small group intervention series focused on TEKS 5.4C and 5.8C. Students master generating numerical patterns from rules, plotting ordered pairs in the first quadrant, and solving real-world coordinate plane problems.
A comprehensive unit on the coordinate plane designed for Special Education students, transitioning from the first quadrant to all four quadrants using visual scaffolding and clear navigation-themed guides.
A comprehensive Tier 2 intervention sequence for high school Algebra students focused on solving and graphing linear equations and inequalities. This sequence uses an architectural 'blueprint' theme to help students build conceptual understanding and procedural fluency while addressing common misconceptions.
A specialized Tier 3 intervention sequence for 8th-grade students performing at a 5th-grade level, focusing on bridging foundational arithmetic to high school algebra concepts. This sequence uses concrete-representational-abstract (CRA) methods to explore area modeling, systems of equations, exponential patterns, and inequalities.
A targeted intervention sequence focused on helping High School students master the application of the distance formula to find perimeter and area in the coordinate plane. This unit uses structured calculation templates and scaffolded practice to support Tier 2 learners.
A 6-week curriculum designed to bridge the gap between high school math and real-world financial and practical independence, covering paychecks, budgeting, credit, shopping, housing, and measurement.
A 3-day small group math sequence focused on mastering area concepts (3.MD.C.7a, 7b, 7d) through the lens of architectural design and blueprinting. Students move from tiling and multiplication to finding the area of complex rectilinear figures.
A series of targeted math practice resources designed to reinforce core 6th-grade mathematical concepts including division, decimals, integers, and geometry.
A comprehensive math unit for 3rd grade focusing on area measurement through the context of garden planning, aligned with Arizona standard 3.MD.C.7. Students move from concrete tiling to abstract multiplication.
A 4-day unit on area measurement for 3rd grade students, covering tiling, the relationship between multiplication and addition, and decomposing rectilinear shapes. Designed with a 'Blueprint Builders' architectural theme.
A targeted intervention sequence for high school geometry students to master the volume of spheres using Cavalieri's Principle through hands-on comparisons and visual proofs.
A targeted intervention sequence for High School Geometry students to master the Laws of Sines and Cosines through scaffolded proofs and practical application. The materials use a blueprint-inspired visual theme to emphasize the structural nature of trigonometry.
A series of geometry lessons focused on points of concurrency and their real-world applications in urban planning and design.
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.
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.
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 targeted intervention sequence focused on geometric constructions, specifically tangent lines from external points to circles, designed for Tier 2 small group support with visual scaffolds and step-by-step mastery.
A specialized intervention sequence for High School Geometry focusing on the logic and execution of formal geometric constructions using compass and straightedge. Designed for Tier 2 small group support with scaffolded steps and targeted practice.
A targeted intervention sequence focusing on geometric constructions related to triangles and circles, specifically designed for Tier 2 support.
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 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 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 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 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 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 targeted Tier 2 intervention for High School Geometry focusing on the derivation of the circle equation and completing the square. Includes scaffolded student worksheets and teacher facilitation guides designed for struggling learners.
A targeted intervention sequence for high school geometry students focusing on circle theorems. The sequence emphasizes visual discovery and scaffolded practice to help Tier 2 learners master inscribed angles and tangent properties.
A comprehensive ACT Math preparation program focusing on essential strategies, high-yield Algebra and Geometry concepts, and realistic practice to boost scores.
A mathematics sequence focusing on geometry, circles, and the calculation of circumference and area for middle school students.
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.
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.
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.
Une série de ressources éducatives couvrant divers concepts mathématiques essentiels comme les statistiques et la trigonométrie.
A specialized intervention sequence designed for high school geometry students to master solving non-right triangles using the Law of Sines and Law of Cosines, with a focus on decision-making and scaffolded practice.
A targeted intervention sequence focused on extending trigonometric functions beyond right triangles using the unit circle. This sequence bridges the gap between basic trigonometry and periodic functions for students needing additional support.
A Tier 2 intervention sequence focused on foundational trigonometry, moving from special right triangles to reference angles on the unit circle. This sequence provides scaffolded support for students struggling with geometric interpretations of sine, cosine, and tangent.
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.
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.
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 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.
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 exploration of the unit circle, bridging geometry and trigonometry by scaling triangles, defining radians, and utilizing symmetry to evaluate trigonometric functions.
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.
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.
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.
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.
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 targeted intervention sequence for high school geometry students to master deriving equations for ellipses and hyperbolas using their geometric definitions.
A small-group algebra intervention sequence focused on solving systems of linear and nonlinear equations. Students learn to identify intersection points graphically and verify them algebraically through substitution.
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.
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.
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.
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.
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 Tier 2 intervention sequence for 5th-grade students focusing on solving complex volume problems. Students act as 'Volume Architects,' using blueprints and unit cubes to master multiplication formulas and the additive property of volume for composite figures.
A comprehensive 12-lesson intervention sequence focused on geometric measurement and volume (5.MD.C). Designed for Tier 2 small groups, it utilizes All Learners Network (ALN) High Leverage Concepts and Illustrative Mathematics (IM) instructional routines to build conceptual understanding from unit cubes to complex additive volume.
A high school geometry and algebra sequence focused on applying 3D geometry formulas to real-world optimization problems, specifically focusing on cones.
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.
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.
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.
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.
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 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 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.
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 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 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 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 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 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 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.
A four-day series of post-testing cooldown activities for 7th graders, featuring math, ELA, logic, and creative tasks with a 'Mission Possible' spy theme.
A Tier 2 intervention sequence focused on foundational circle geometry concepts, specifically arc length proportionality and sector area using similarity reasoning. Students move from concrete measurement to abstract formula derivation.
A Tier 2 intervention sequence focused on foundational trigonometry concepts, specifically the relationship between radian measure and arc length on the unit circle.
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.
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.
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 targeted intervention sequence for 8th-grade students struggling with coordinate distance, focusing on visual scaffolding through right triangle models and the Pythagorean Theorem.
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 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 series of focused prep sessions designed to equip 7th-grade students with the tools and strategies needed for the New York State Math Assessment. This sequence emphasizes reference sheet familiarity, test-taking endurance, and conceptual review.
A focused intervention sequence designed to help students master the relationship between 2D shapes and 3D solids through cross-sections and rotations. This module uses a technical drafting aesthetic to engage students in high-school level geometric visualization.
A comprehensive review for the Grade 7 Math Interim Assessment 3, covering algebraic equations, proportional relationships, rational numbers, and multi-step percent problems.
