Mapping relationships through notation, algebraic representations, and growth rate comparisons. Equips learners to transform functions, model contextual data, and solve exponential equations.
A focused sequence on distinguishing between additive and multiplicative numerical patterns, specifically targeting TEKS 5.4D and 5.4C for 5th-grade students.
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 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 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 10-week preparation sequence designed to get students ready for the Algebra I Regents exam by May 15th, featuring bi-weekly 30-minute practice sessions and visual anchor charts.
Une séquence de deux séances pour introduire les bases des fonctions en 3ème : vocabulaire (image, antécédent), notation f(x) et représentation graphique, en utilisant des méthodes de pédagogie coopérative.
A 10-day intensive review sequence for the Texas Algebra I EOC exam, focusing on two high-stakes vocabulary terms each day with definitions, visual samples, and practice problems.
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 6-part homework series designed to prepare 7th-grade students for their math interim assessments. Each sheet covers specific standards from Expressions and Equations, Ratios and Proportional Relationships, and Rational Number operations, mirroring the format and rigor of the assessment.
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 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 Tier 2 intervention sequence for 8th-grade students focused on mastering the concept of functions and interpreting linear equations in the form y = mx + b. This unit provides scaffolded instruction on identifying functions, calculating slope, and connecting multiple representations.
A foundational math sequence for special education students (grades 5-6) focusing on algebraic thinking and spatial reasoning through highly visual, themed units.
A targeted intervention sequence focused on helping high school students master arithmetic and geometric sequences through visual patterns, number lines, and real-world modeling. This sequence aligns with Colorado standard HS.F-BF.A.2.
A targeted intervention sequence for High School students to master interpreting initial values and rates of change or growth factors in linear and exponential contexts, aligned with Colorado standard HS.F-LE.B.5.
A targeted intervention sequence for high school statistics students focusing on fitting linear functions to scatter plots. It moves from conceptual understanding of 'balance' in data to the procedural steps of calculating lines of best fit.
A targeted intervention series focused on helping students compare key features of functions across various representations including graphs, tables, and equations.
A targeted intervention sequence focused on Grade 8 linear modeling, helping students construct functions from verbal descriptions, tables, and graphs while interpreting rate of change and initial value in context.
A Tier 2 intervention unit focused on comparing linear functions across different representations (tables, graphs, equations, and verbal descriptions) using real-world contexts.
A targeted intervention sequence for 8th-grade students to master linear functions, focusing on interpreting y=mx+b, constant rates of change, and distinguishing linear from nonlinear relationships.
A sequence exploring radical functions, focusing on solving radical equations through algebraic manipulation and function notation.
Ce module introduit les concepts fondamentaux des relations linéaires pour les élèves de CM2/Grade 5 en utilisant l'analogie de la machine à transformer les nombres.
A comprehensive grade recovery packet for 9th Grade Algebra 1 students, covering exponent laws, exponential functions, polynomial operations, and factoring techniques.
A comprehensive 3-day review sequence for the Algebra I Regents examination, focusing on foundations, systems, and polynomial operations. Each 75-minute lesson provides a balance of guided instruction and independent practice with problems modeled after the NYS Interim Assessment.
A series of five high-stakes review rounds designed to prepare students for the Algebra I NYS Regents exam, focusing on expressions, equations, inequalities, and functions.
A targeted Tier 2 intervention sequence for high school students struggling with quadratic expressions and equations. This unit focuses on building procedural fluency through scaffolded instruction, visual models, and step-by-step factoring and solving techniques aligned with Colorado Standard 2.
A comprehensive Tier 2 intervention sequence designed for high school students to master interpreting functions, including domain, range, key features, and real-world applications. The sequence uses a 'Blueprint' aesthetic to provide high-clarity, professional visuals that support conceptual understanding through scaffolded tasks.
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 Tier 2 intervention sequence focused on interpreting linear and exponential parameters in contextual problems, aligned with Colorado standard HS.F-LE.B.5. Students learn to decode slope, initial value, and growth factors using a navigation-inspired theme.
A high school Tier 2 intervention unit focused on comparing linear, quadratic, and exponential growth rates using tables and graphs to demonstrate the eventual dominance of exponential functions.
A comprehensive ACT Math preparation program focusing on essential strategies, high-yield Algebra and Geometry concepts, and realistic practice to boost scores.
A series of lessons exploring exponential functions, their components, graphs, and real-world applications in Algebra 1.
A lesson sequence focusing on the nuances of exponential decay, specifically distinguishing between annual rates and those occurring over non-standard time intervals like months or half-lives.
A lesson sequence focused on understanding the relationships between variables, specifically direct and inverse variation, and translating verbal descriptions into algebraic equations.
A comprehensive lesson for 8th-grade math students to distinguish between arithmetic and geometric sequences through interactive sorting and video-based analysis.
A lesson sequence focused on the critical thinking skills required to verify mathematical patterns, using geometric sequences as the primary vehicle for exploration. Students learn that initial data points can be deceptive and that rigorous verification is essential for mathematical proof and real-world predictions.
A series of targeted review lessons designed to prepare students for the Texas Algebra 1 End-of-Course (EOC) assessment, focusing on high-stakes TEKS.
A targeted Tier 2 intervention sequence focused on helping high school students master quadratic transformations through factoring and completing the square using visual algebra tile models.
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 comprehensive 5-lesson unit on linear relationships, focusing on conceptual understanding of slope as a rate of change through real-world scenarios, multiple representations, and error analysis.
A Tier 2 intervention program for high school Algebra students focusing on linear equations and inequalities, featuring high-scaffolding, error analysis, and real-world modeling.
A 4-lesson intervention sequence focused on the fundamentals of the coordinate plane, specifically the first quadrant. Students progress from identifying axes to plotting patterns from numerical rules using a consistent 'Run then Jump' protocol.
A 6-lesson Tier 2 intervention designed to help students master the relationship between numerical patterns, converting them into ordered pairs, and graphing them on a coordinate plane using a cartography and exploration theme.
A series of high-level enrichment activities for 6th-grade students to master expressions and equations through logic puzzles and real-world modeling.
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 3-day math sequence for 3rd graders focused on multiplication comparisons and identifying patterns in tables using a fun Toy Factory theme.
A specialized intervention sequence designed for Algebra I students to master TEKS A2A and A6A, focusing on the domain and range of linear and quadratic functions through tiered small-group instruction.
A targeted intervention sequence focusing on the derivation and application of the geometric series sum formula for high school algebra students requiring Tier 2 support.
A Tier 2 intervention sequence focused on helping 8th-grade students master the construction and interpretation of linear functions ($y = mx + b$) from various representations. The sequence emphasizes scaffolding, contextual meaning, and procedural fluency with rate of change and initial values.
A comprehensive unit where students act as data scientists to model real-world environmental phenomena using trigonometric functions. They progress from visual estimation to precise algebraic modeling and technological regression to predict future environmental conditions.
This sequence explores real-world applications of rational exponents across biology, astronomy, music, finance, and physics. Students transition from abstract algebraic manipulation to applying fractional powers to model complex natural and human-made systems.
A graduate-level exploration of non-linear bivariate analysis, moving from the limitations of linear correlation to rank-based methods, local regression, and information-theoretic metrics. Students develop the skills to quantify complex dependencies in biological, financial, and environmental systems where standard assumptions fail.
A graduate-level project-based sequence focused on the rigorous comparison and selection of mathematical models. Students progress from strategy definition and candidate generation to statistical benchmarking and stability analysis, culminating in a professional-grade technical defense.
A technical workshop sequence for 11th-grade students focusing on cross-validation techniques, including train-test splits, MSE calculation, and K-Fold validation to assess and select robust mathematical models.
This sequence guides undergraduate students through the transition from descriptive statistics to predictive modeling. It covers hypothesis testing, linear and multiple regression, model evaluation, and logistic classification, emphasizing both mathematical foundations and practical coding implementation.
This sequence moves beyond simple error metrics to explore sophisticated selection criteria that penalize complexity, specifically AIC and BIC. Students learn to balance model fit with parsimony through real-world datasets and comparative analysis.
An advanced 12th-grade mathematics sequence focusing on model evaluation and selection. Students explore the bias-variance trade-off, information criteria (AIC/BIC), and cross-validation to select optimal predictive models.
A project-based exploration of stochastic modeling, focusing on Queueing Theory and Monte Carlo simulations. Students design and build computational models to optimize real-world systems like traffic flow and service lines.
A project-based unit where students apply polynomial calculus concepts to real-world scenarios like business profits, projectile motion, and engineering design. Students transition from abstract solving to modeling data and optimizing outcomes using regression, intercepts, and extrema.
An advanced graduate-level sequence exploring the mathematical foundations of model selection, including bias-variance decomposition, information criteria (AIC/BIC), resampling methods, and high-dimensional diagnostic strategies.
This sequence guides undergraduate students through model comparison and selection, covering the bias-variance tradeoff, cross-validation methods, and information criteria (AIC/BIC). Students will learn to balance model complexity with generalization ability to select the most robust models for prediction and inference.
This sequence guides undergraduate students through the rigorous process of mathematical modeling, from identifying function families via rates of change to validating complex models using residual analysis. Students explore linear, exponential, logistic, sinusoidal, and piecewise models in real-world contexts.
A 10th-grade mathematics sequence focusing on modeling real-world environmental data using linear, exponential, and piecewise functions. Students progress from identifying variables to performing complex regression analysis and presenting predictive models.
A Tier 2 intervention sequence focused on helping high school students master the conversion between recursive and explicit formulas for arithmetic and geometric sequences through scaffolded side-by-side organizers.
A targeted intervention sequence designed to help students bridge the gap between sequences and function notation, focusing on domain and recursive definitions.
A 2-lesson intervention sequence focused on mastering the first quadrant of the coordinate plane through hands-on exploration and pattern-based plotting. Students develop a strong foundation in the 'over, then up' protocol to bridge the gap between basic graphing and algebraic patterns.
A lesson sequence focusing on the transition from expanded ellipsis notation to formal Sigma notation within the context of arithmetic series proofs. Students analyze a standard proof and reformulate it using summation properties.
A high-level Honors Algebra lesson focused on complex recursive sequences where students analyze notation, explore the Fibonacci sequence, and engage in a 'Sequence Maker' activity to reverse-engineer formulas.
A comprehensive 9th-grade algebra unit exploring the patterns, formulas, and real-world applications of arithmetic and geometric sequences. Students progress from recursive logic to explicit modeling.
A Tier 2 intervention sequence focused on the conceptual and algebraic foundations of inverse functions. Students move from reversing input-output tables to solving algebraic equations to find inverse expressions.
A specialized unit focused on identifying and correcting algebraic misconceptions in function transformations, specifically reflections. Students develop critical analysis skills by acting as "Error Doctors" to diagnose and treat common mathematical pitfalls.
A comprehensive pre-calculus unit focused on the algebraic and geometric properties of inverse functions, including composition-based verification and domain restrictions.
A lesson sequence focusing on analyzing and manipulating exponential functions to reveal true growth rates, using real-world financial contexts and exponent rules.
A comprehensive math lesson focusing on identifying and representing relationships between numerical patterns using input/output tables and equations.
A 10th-grade trigonometry unit where students model circular motion using Ferris wheels, translating physical dimensions like radius, hub height, and speed into sine and cosine functions.
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.
An advanced look at rational exponents through the lens of mathematical proof, equivalence, and error analysis for 10th grade students. Students act as mathematical investigators to justify transformations and identify logical fallacies.
This sequence explores the relationship between rational exponents and the geometric behavior of power functions. Students analyze how numerators and denominators dictate domain, range, shape, and growth rates through inquiry and visual sketching.
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 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.
A math sequence for 11th Grade Special Education focusing on visual representations of functions. Students learn to interpret graphs as narratives, moving from qualitative sketches to precise quantitative analysis of slope, intersections, and non-linear trends.
A comprehensive exploration of linear recurrence relations, from first-order foundations to complex second-order systems and real-world predator-prey modeling. Undergraduate students transition from recursive thinking to closed-form solutions, applying discrete math to algorithm analysis and biology.
A comprehensive unit for undergraduate students on arithmetic and geometric sequences, moving from basic pattern recognition to complex financial and biological modeling. Students will explore linear and exponential growth through real-world applications like simple interest, depreciation, compound growth, and annuities.
A graduate-level exploration of discrete dynamical systems, moving from linear growth models to the complex, chaotic behavior of the logistic map. Students apply recursive sequences to model biological and economic phenomena, emphasizing stability analysis and bifurcation theory.
This sequence bridges the gap between discrete mathematics and quantitative finance, focusing on the application of geometric series to asset valuation, loan amortization, and risk management. Graduate students will develop the mathematical foundations for pricing complex financial instruments and understanding market dynamics.
A rigorous graduate-level exploration of real-valued sequences, bridging computational calculus and formal real analysis through epsilon-N proofs, Cauchy sequences, and topological theorems.
An 11th-grade mathematics sequence that bridges the gap between abstract sequences and real-world applications in finance and physics. Students explore arithmetic and geometric models through interest, depreciation, projectile rebounds, and loan amortization.
This sequence explores arithmetic and geometric sequences through inquiry, algebraic modeling, and real-world applications. Students transition from pattern recognition to formalizing recursive and explicit formulas to predict outcomes in linear and exponential systems.
This sequence investigates real-world applications of rational exponents in biology, finance, music, and physics. Students explore how fractional powers model growth, scaling, and harmonic relationships, culminating in a data-modeling project.
A sequence for undergraduate students bridging pre-calculus and calculus by focusing on the analytical properties of functions with rational exponents. Students explore graphing, algebraic rewriting, rationalizing for limits, and growth comparison.
This sequence explores the practical application of rational exponents and power functions in biology, physics, and finance. Students will progress from evaluating existing models like Kleiber's Law and Kepler's Third Law to constructing their own mathematical models from empirical data.
A 9th-grade algebra project-based sequence exploring rational exponents through real-world biological scaling (allometry) and physical laws. Students transition from evaluating fractional powers in Kleiber's Law to creating and presenting their own mathematical models.
This advanced sequence introduces powerful tools for analyzing series with factorials and powers, leading to the concept of power series. Students master the Ratio and Root tests, explore absolute versus conditional convergence, and conclude by connecting series to functions through Taylor polynomials.
A targeted intervention sequence focused on mastering trigonometric equations through inverse functions, visual symmetry, and contextual application. This sequence provides Tier 2 support for students needing scaffolded paths to find both principal and secondary solutions.
A comprehensive unit for 12th-grade algebra focusing on solving equations with rational exponents, investigating extraneous solutions, and visualizing intersections graphically.
A comprehensive unit for undergraduate students focusing on the algebraic techniques and logical pitfalls involved in solving equations with variables raised to rational exponents. Students progress from basic isolation to quadratic-form structures and non-linear systems.
This sequence introduces undergraduate students to first-order differential equations through geometric visualization, analytical solving techniques (separation, integrating factors), and real-world modeling of thermal, biological, and electrical systems.
This sequence for undergraduate students focuses on complex algebraic structures involving exponentials, including quadratic forms, distinct bases, inequalities, systems, and transcendental limitations. It prepares students for higher-level calculus and engineering mathematics through rigorous analytical techniques.
A comprehensive exploration of exponential modeling across finance, biology, and physics, focusing on the algebraic techniques required to solve for time and rate variables in real-world growth and decay scenarios.
This sequence establishes foundational algebraic techniques for solving exponential equations, moving from common base matching to logarithmic inversion. It emphasizes the concept of inverse functions as the primary mechanism for variable isolation, preparing students for calculus and scientific applications.
A 9th-grade algebra sequence focused on modeling and solving exponential equations in real-world contexts like finance, biology, and archaeology. Students learn to construct models and solve for time using algebraic and graphical methods.
This sequence guides students through the algebraic methods for solving exponential equations, from the foundational skill of base rewriting to the introduction and application of logarithms. Students build structural recognition to handle both matchable and non-matchable bases.
This sequence guides 11th-grade students through algebraic techniques for solving exponential equations. It starts with base manipulation, introduces logarithms as inverse operations, and concludes with complex quadratic forms and the natural base e.
A comprehensive 11th-grade unit where students apply logarithmic solving techniques to real-world exponential growth and decay scenarios. Students act as financial planners, archaeologists, ecologists, and forensic scientists to solve for the time variable in complex equations.
This sequence explores exponential equations through real-world modeling, moving from identifying growth/decay parameters to solving for time using logarithms in financial, biological, and forensic contexts.
