Data representation, distributions, and statistical variability using sampling and inference techniques. Integrates probability models, compound events, bivariate patterns, and linear models to guide data-driven decision making.
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 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 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 math sequence focused on statistical analysis, data collection, and visualization through the lens of a detective agency. Students learn to create frequency tables and line plots using real-world data.
Une exploration mathématique de l'impact des coefficients sur les moyennes, utilisant des cas pratiques concrets pour comprendre la pondération et les moyennes pondérées.
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 complète sur les statistiques en 3ème, abordant la collecte, le traitement et l'interprétation de données avec des outils numériques.
A collection of Valentine's Day math packets at two different levels (Level 1 and Quest), covering budgeting, graphing, measurement, time, and word problems.
A Tier 2 intervention sequence focused on building concrete understanding of data representations including dot plots, histograms, and box plots for high school statistics students.
A targeted intervention sequence for 6th-grade students to master the construction and interpretation of dot plots, histograms, and box plots through hands-on data collection and analysis.
A targeted Tier 2 intervention lesson designed for Grade 2 students to master measuring length to the nearest whole inch and representing that data on line plots. The sequence focuses on hands-on measurement and concrete-to-abstract transitions for data visualization.
An interdisciplinary unit for 7th and 8th graders that transforms students into 'Data Detectives'. They learn to collect, analyze, and visualize real-world data to uncover trends and communicate findings effectively.
A comprehensive ACT Math preparation program focusing on essential strategies, high-yield Algebra and Geometry concepts, and realistic practice to boost scores.
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 hands-on introduction to probability and chance for early elementary students using the concepts of will, won't, and might.
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 unit where students act as data scientists to model real-world environmental phenomena using trigonometric functions. They progress from visual estimation to precise algebraic modeling and technological regression to predict future environmental conditions.
A Kindergarten math sequence introducing tally marks as a method for recording data. Students progress from simple vertical marks to groups of five, culminating in real-world data collection and interpretation.
A project-based sequence where 5th-grade students act as data analysts to investigate school-wide questions, moving from question formulation to data collection, organization, visualization, and final presentation.
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 two-day sequence for 5th graders to master finding the mean (average) using engaging data from the worlds of professional sports and wildlife.
A unit focused on statistics and data analysis, teaching students how to interpret, compare, and draw conclusions from various data sets.
A comprehensive collection of mathematical vocabulary resources covering number systems, algebraic expressions, and statistical analysis. This unit focuses on building precise mathematical language for foundational concepts.
Une série de ressources éducatives couvrant divers concepts mathématiques essentiels comme les statistiques et la trigonométrie.
A comprehensive Tier 2 intervention sequence for high school students focused on summarizing, representing, and interpreting data, aligned with Colorado Standard 3. The program uses a 'Data Forensics' theme to engage students in uncovering insights from real-world datasets through scaffolded analysis and visual interpretation.
A Tier 2 intervention sequence focused on helping students master the Normal Distribution and the Empirical Rule through real-world applications and scaffolded practice.
A targeted Tier 2 intervention for High School Statistics focusing on comparing data distributions (shape, center, spread) and understanding the impact of outliers. Includes scaffolded instruction, guided practice with sentence frames, and progress monitoring tools.
A targeted intervention sequence focused on helping students use measures of center and variability to compare two different populations from sample data. Students engage in scaffolded calculations and collaborative projects to build statistical reasoning.
A specialized intervention sequence focused on data analysis and informal inferences, helping students bridge the gap between calculating statistics and interpreting their real-world meaning through comparative analysis.
A specialized intervention sequence focused on understanding how multiple samples provide a clearer picture of a population and how variability affects predictions. Students engage in hands-on simulations and visual data analysis to master seventh-grade sampling standards.
A 4th-grade chemistry and engineering sequence focusing on the analysis and manipulation of measurement data. Students explore metric and customary conversions, benchmark comparisons, and data accuracy through a project-based blueprint scaling challenge.
A comprehensive 12th-grade statistics sequence focused on identifying, analyzing, and performing inference on paired data designs to reduce variability and compare population means.
A targeted Tier 2 intervention sequence designed to help high school students master the fundamental concepts of statistical inference, moving from population parameters to sample statistics and back again through real-world applications.
Une introduction complète aux statistiques universitaires, couvrant la classification des données, les mesures descriptives, la visualisation et les fondements de la loi normale. L'approche est axée sur l'analyse de données réelles et la compréhension conceptuelle.
A project-based unit where 12th-grade students design and execute an original statistical study comparing two populations. Students move from research design and ethical data collection to exploratory data analysis and formal inferential testing, culminating in a professional research presentation.
Students build a conceptual understanding of comparing two proportions through simulation before formalizing the math. They learn to conduct and interpret 2-sample z-tests and confidence intervals for differences in proportions in real-world contexts like marketing and public opinion.
A comprehensive unit for 11th-grade statistics focusing on the comparison of proportions between two independent populations. Students transition from simulation-based inquiry to formal z-tests and confidence intervals, culminating in a real-world sociological data analysis project.
A comprehensive undergraduate statistics sequence on comparing two population proportions and rates. Students move from the theoretical sampling distribution to practical A/B testing, clinical risk assessment, and project-based experimental design.
This advanced sequence for undergraduate students explores the critical distinction between statistical significance and practical importance. Students move beyond p-values to master effect size measures like Cohen's d and the principles of statistical power, culminating in a critical analysis of the replication crisis and the role of rigorous study design in scientific integrity.
This sequence explores the distinction between independent and paired samples in statistics. Students learn to identify matched-pair designs, calculate paired differences, conduct hypothesis tests for means of differences, and understand how pairing increases statistical power by reducing variability.
A project-based unit where 10th-grade students design surveys, collect categorical data, and use 2-proportion z-tests and confidence intervals to determine if meaningful differences exist between two populations. Students apply statistical rigor to real-world questions like demographic opinion gaps and school-wide trends.
A 5-lesson sequence for 7th graders exploring the relationship between theoretical probability and experimental results, culminating in Bayesian-style predictive updates and simulations. Students move from simple dice rolls to complex forecasting scenarios.
An advanced graduate-level module on statistical sampling techniques focusing on the mathematical correction of data after collection. Topics include probability weights, non-response adjustment through raking, imputation of missing values, and computational variance estimation via Bootstrap and Jackknife methods.
This graduate-level sequence covers advanced statistical sampling techniques, focusing on the optimization of stratified, cluster, and multi-stage designs. Students learn to navigate the trade-offs between precision and cost, calculate design effects, and mitigate biases like periodicity.
This graduate-level sequence covers the theoretical foundations and practical applications of power analysis. Students will learn to determine necessary sample sizes for various statistical models, conduct sensitivity analyses, and write robust justifications for research protocols.
A rigorous graduate-level examination of probability sampling theory, focusing on the mathematical properties of estimators, the mechanics of selection bias, and the use of Monte Carlo simulations to validate sampling designs. Students explore simple random sampling, sampling frame errors, and the 'Big Data Paradox' through proofs and simulation logic.
A graduate-level sequence exploring computational resampling methods (Bootstrap, Jackknife, Permutation) to estimate the variability and uncertainty of dispersion statistics when parametric assumptions fail.
A collection of sports-themed instructional materials that use real-world events to teach logic, statistics, and organizational skills.
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 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 Tier 2 intervention sequence focused on using probability to analyze decisions, specifically targeting medical testing (false positives/negatives) and game-time strategies. Students learn to use tree diagrams and contingency tables to navigate complex conditional probability scenarios.
A comprehensive unit focused on practical applications of probability for high school students, emphasizing decision-making, fairness, and risk assessment.
A small group intervention sequence focused on understanding and applying probability to ensure fair decision-making, specifically designed for students needing extra support in High School Statistics.
A Tier 2 statistics intervention focusing on calculating and interpreting expected values in games of chance. Students transition from intuitive guesses to formal probability distributions and compare experimental data to theoretical outcomes.
A targeted Tier 2 intervention sequence focused on conditional probability and independence for high school students. This sequence emphasizes visual models like tree diagrams and area models to bridge conceptual understanding to formal notation.
A Tier 2 intervention sequence focused on helping students develop empirical probability distributions and calculate expected values using real-world household data. This sequence provides high-scaffolding and structured practice for small group instruction.
A targeted intervention sequence focused on foundational probability concepts, specifically defining random variables and constructing probability distributions for high school statistics students.
A targeted intervention sequence focused on helping High School students master the calculation and interpretation of expected value using concrete game scenarios and scaffolded table methods.
A targeted intervention sequence focused on foundational probability concepts, specifically developing discrete probability distributions and calculating expected values through visual scaffolds like tree diagrams and organized counting.
A Tier 2 intervention sequence focused on mastering conditional probability through visual filters and fractional reasoning. Students learn to restrict their sample space to the 'given' condition using Venn diagrams and tables.
A targeted intervention sequence focused on understanding and calculating the independence of events through structured reasoning and decision trees.
A targeted Tier 2 intervention unit focused on understanding and calculating the independence of two events using the multiplication rule. This sequence uses concrete manipulative-based experiments to bridge the gap between intuition and formal probability notation.
A targeted intervention sequence focused on compound probability, designed for small groups to master sample space construction and simulations.
A targeted intervention sequence focused on understanding probability through experimental data, recording frequencies, and observing how relative frequency stabilizes over many trials.
A Tier 2 intervention sequence focused on uniform and non-uniform probability models. Students use fair and weighted dice to compare theoretical models with experimental data, developing a deep understanding of why discrepancies occur.
A 5-day series of morning work activities for 7th graders designed to sharpen critical thinking through error analysis, logic puzzles, open-ended problems, and real-world tasks.
A Tier 2 intervention sequence focused on analyzing bivariate data. Students learn to use technology to create scatter plots and develop a precise vocabulary for describing relationships between quantitative variables.
A comprehensive unit on adding and subtracting integers for grades 5-7, focusing on visual supports, mnemonic rules, and scaffolded practice for students with diverse learning needs.
A lesson sequence focusing on compound probability, specifically analyzing events where order matters versus where it doesn't, using marble jar scenarios and tree diagrams.
A sequence for 12th-grade students focusing on selecting and using visual organizers like Venn diagrams, tree diagrams, flowcharts, and logic grids to solve complex logic and probability problems. Students move from guided practice to independent metacognitive selection of the best tool for the job.
This sequence explores conditional probability and the reliability of tests using frequency trees and area models. Students investigate 'false positives' and 'false negatives' in real-world contexts like medical testing and spam filters, ultimately debating the ethical implications of screening policies.
An 8th-grade mathematics unit focused on using probability trees to model and solve complex decision-making problems. Students progress from simple compound events to weighted averages and backward induction in real-world business and logistics scenarios.
This sequence guides students through the visualization and calculation of compound probabilities using tree diagrams. Students progress from basic branching to analyzing complex real-world decisions involving dependent and independent events.
A comprehensive 7th-grade unit exploring probability through game design, where students move from understanding basic likelihood to analyzing mathematical fairness and building their own chance-based simulations.
A 12th-grade mathematics sequence exploring compound probability through the lens of engineering reliability. Students learn to model series and parallel systems, use complement rules for redundancy, and optimize system designs within budgetary constraints.
A rigorous, theoretical approach to compound event probabilities for 12th-grade students. This sequence covers set notation, formal definitions of independence, the general addition and multiplication rules, and the distinction between mutually exclusive and independent events.
A 12th-grade mathematics unit exploring compound probability through the lens of casino games, lotteries, and game design, focusing on the distinction between independent and dependent events.
A comprehensive 12th-grade probability unit focusing on visualizing multi-stage experiments, distinguishing between independent and dependent events, and applying formal multiplication rules to solve complex compound scenarios.
This 11th-grade sequence explores conditional probability and compound events through professional lenses like medicine, law, and engineering. Students move beyond dice and cards to analyze real-world data, calculating risk, diagnostic accuracy, and system reliability to make informed decisions under uncertainty.
This 11th-grade sequence explores compound probability through the lens of game design and analysis. Students move from analyzing existing games of chance to engineering their own balanced systems using the multiplication rule, expected value, and area models.
A high-level probability sequence for 11th grade students focusing on translating complex word problems into symbolic notation and solving multi-stage compound events. The sequence utilizes a flipped classroom model to prioritize collaborative problem-solving and mastery of advanced concepts like the complement rule and asymmetric probability trees.
This 11th-grade statistics sequence builds a deep understanding of compound probability, from visualizing sample spaces to applying the General Multiplication Rule. Students progress through independent and dependent events, conditional probability, and complex multi-stage scenarios including the 'at least one' rule.
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 graduate-level exploration of expected value through the lens of measure theory, covering Lebesgue integration, fundamental inequalities, convergence theorems, and conditional expectation using Sigma-algebras.
A graduate-level sequence exploring the gradient vector as the foundational tool for modern optimization. Students move from the geometric interpretation of multivariate derivatives to the implementation of stochastic algorithms used in machine learning.
An advanced graduate-level exploration of stochastic processes, covering discrete and continuous-time Markov chains, Poisson processes, and queueing theory. The sequence bridges theoretical rigor with computational application through simulations and real-world modeling.
An advanced graduate-level sequence exploring the mathematical foundations and computational applications of stochastic processes, from discrete-time Markov chains to Monte Carlo simulations.
A comprehensive introduction to Time Series Analysis for 12th-grade students, focusing on random processes, autocorrelation, stationarity, and smoothing techniques. Students move from basic random walks to understanding complex dependencies in temporal data.
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 12th-grade statistics sequence exploring Poisson processes, transitioning from discrete counts to continuous time intervals and waiting times. Students will investigate arrival rates, the exponential distribution, and the unique memoryless property through inquiry and simulation.
A high-level exploration of stochastic processes, focusing on how random systems reach equilibrium. Students will master Markov chains, steady-state algebra, and real-world applications like Google's PageRank algorithm.
A comprehensive sequence for 12th-grade students on discrete-time Markov chains, covering state diagrams, transition matrices, and n-step probability calculations using matrix algebra.
A graduate-level sequence exploring continuous-time stochastic processes through the lens of computational simulation. Students transition from discrete to continuous time models, focusing on Poisson processes, CTMCs, and queuing theory with a strong emphasis on empirical validation and theoretical rigor.
A graduate-level exploration of the mathematical foundations of discrete-time Markov chains, focusing on state classification, limiting behavior, and time reversibility. This sequence emphasizes formal derivation, proofs, and the application of linear algebra to stochastic systems.
A comprehensive sequence on stochastic processes, stationarity, autocorrelation, and ergodicity, designed for undergraduate statistics and engineering students. The sequence moves from basic definitions of ensemble averages to the complex relationship between time and statistical averages.
An undergraduate-level sequence exploring Poisson processes as continuous-time counting models, covering derivations, inter-arrival times, superposition, order statistics, and non-homogeneous variations.
An undergraduate-level introduction to Discrete-Time Markov Chains, covering state classification, transition matrices, n-step probabilities, and stationary distributions. Students will apply linear algebra and probability theory to model stochastic systems and solve classic problems like Gambler's Ruin.
An advanced statistics sequence for 10th graders focusing on the nuance of hypothesis testing. Students move beyond calculations to explore P-values, Type I/II errors, practical significance, and effect size through real-world case studies and a culminating funding simulation.
This sequence explores probability-based decision making through the lens of financial literacy. Students apply expected value and risk assessment to evaluate insurance, extended warranties, and the mathematical trade-off between known costs and unknown risks.
A comprehensive 12th-grade sequence exploring conditional probability through high-stakes real-world applications in medicine, forensics, and public safety. Students move from tabular data analysis to Bayesian reasoning, learning to navigate the counter-intuitive nature of false positives and the logical pitfalls of legal evidence.
An advanced exploration of statistical power, error types, and effect sizes in the context of comparing two populations, teaching students to look beyond p-values to evaluate the practical importance and reliability of scientific findings.
A comprehensive unit on comparing means from two independent populations. Students move from the theoretical foundations of sampling distributions to practical applications in clinical trials, mastering two-sample t-procedures, degrees of freedom, and robustness analysis.
A comprehensive 11th-grade statistics sequence focusing on the distinction between independent samples and matched pairs. Students learn to identify, analyze, and conduct inference on paired data through hands-on labs, case studies, and experimental design projects.
This sequence moves beyond binary decisions to quantify relationships using confidence intervals and effect sizes. Students explore population overlap, calculate margins of error for means and proportions, and learn to communicate statistical findings to non-technical audiences.
An advanced 11th-grade statistics sequence focusing on the selection, application, and ethical implications of two-population inference tests through a professional consultant simulation.
This sequence covers the comparison of means from two independent groups in quantitative data. Students explore the standard error of the difference, degrees of freedom complexities, hypothesis testing through clinical trials, confidence intervals, and the distinction between statistical and practical significance.
A comprehensive unit for undergraduate statistics students focusing on the identification, calculation, and interpretation of paired (dependent) sample designs. Students explore why controlling for individual variation through matching increases statistical power and narrows confidence intervals.
This sequence covers the theoretical and practical application of comparing means between two independent groups. Students progress from understanding sampling distributions and standard errors to performing pooled and unpooled t-tests, constructing confidence intervals, and verifying statistical assumptions using diagnostic tools.
A comprehensive unit for 10th-grade students on comparing two independent population means. Students move from intuitive simulation-based reasoning to formal hypothesis testing and confidence intervals, focusing on variability and statistical significance.
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 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 Tier 2 intervention sequence focused on computing and interpreting the correlation coefficient (r) using technology, designed for high school statistics students needing targeted support.
This sequence explores the practical application of rational exponents and power functions in biology, physics, and finance. Students will progress from evaluating existing models like Kleiber's Law and Kepler's Third Law to constructing their own mathematical models from empirical data.
This graduate-level sequence bridges the gap between statistical association and causal inference. Students explore pitfalls like Simpson's Paradox and collider bias while learning to use Directed Acyclic Graphs (DAGs) and Instrumental Variables to isolate causal mechanisms in bivariate data.
A graduate-level sequence exploring outlier detection, influence diagnostics, and robust regression techniques. Students will progress from identifying anomalies using leverage and Cook's Distance to implementing robust algorithms like RANSAC and M-estimators.
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 sequence focused on the theoretical derivation of OLS estimators and the rigorous diagnostic procedures required to validate bivariate linear models. Students progress from matrix algebra proofs to advanced residual analysis, transformations, and cross-validation techniques.
This sequence guides 8th-grade students through constructing scatter plots, identifying patterns of association, modeling trends with linear equations, and interpreting data in context while distinguishing correlation from causation.
A graduate-level exploration of probabilistic model selection, focusing on AIC and BIC, their information-theoretic foundations, and practical application in statistical modeling.
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 specialized intervention sequence focusing on the foundational skills of linear modeling in statistics, specifically interpreting slope and intercept in real-world contexts. Designed for small groups requiring Tier 2 support.
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.
A comprehensive 5-lesson unit for 8th-grade students on interpreting linear models. Students progress from drawing lines of best fit to calculating slope and y-intercept in context, culminating in writing full equations and making predictions through interpolation and extrapolation.
A high school statistics intervention sequence focused on decision-making through expected value calculations. Students learn to construct payoff tables, assign probabilities, and compare outcomes in real-world scenarios.
A graduate-level exploration of expected value applications in finance, covering utility theory, portfolio optimization, risk-neutral pricing, and tail risk metrics. Students transition from theoretical foundations to computational implementation using Monte Carlo methods.
A game-based sequence where 8th-grade students explore probability, weighted averages, and expected value to analyze fairness and long-term trends in games of chance.
A 7th-grade math sequence focusing on probability-based decision making and expected value. Students explore risk, reward, and long-term outcomes in insurance, business, and finance.
An undergraduate-level exploration of compound event probabilities through the lens of games of chance, focusing on combinatorics, non-replacement scenarios, and expected value.
A comprehensive module for undergraduate students focusing on visual methods for solving compound probability problems. The sequence progresses from basic tree diagrams and contingency tables to the Law of Total Probability and Bayesian reasoning in medical diagnostics, concluding with decision analysis simulations.
This sequence explores how compound probability and risk assessment are used in professional fields like engineering, medicine, insurance, and law. Students apply the multiplication rule and conditional probability to high-stakes real-world scenarios.
