Statistics & Probability

A diverse collection of high-quality math resources spanning Algebra, Geometry, Statistics, and Pre-Calculus.

A comprehensive practice session for the TSIA2 Math exam, focusing on quantitative reasoning, algebraic reasoning, geometry, and statistics.

A comprehensive introduction to the normal distribution, focusing on the empirical rule and calculating probabilities using z-score tables. Students will learn to visualize data distributions and find areas under the curve.

A summative assessment evaluating mastery of the Data Decoder sequence. Students apply their skills to a final case study involving complex data analysis and interpretation.

A deep dive into distinguishing between correlation and causation. Students analyze the correlation coefficient (r) and explore how external factors can influence perceived relationships between variables.

Explores bivariate data through scatter plots, trend lines, and the basics of linear regression. Students learn to use technology or manual methods to find the line of best fit and interpret the slope and intercept.

Instruction on organizing and interpreting categorical data using two-way frequency tables. Students calculate joint, marginal, and conditional relative frequencies to find associations between variables.

Guided practice in comparing two or more datasets using visual displays and summary statistics. Students analyze differences in shape, center, and spread to draw meaningful conclusions.

Introduces measures of center (mean, median) and spread (range, interquartile range, standard deviation basics). Students learn how to calculate these values and understand what they represent in the context of a dataset.

Focuses on constructing and interpreting visual data displays including histograms, box plots, and dot plots. Students learn to identify the most appropriate display for different data types and describe the shape of distributions.

A baseline assessment designed to identify student gaps in data interpretation, display construction, and statistical reasoning. Includes a variety of item types to gauge prior knowledge of histograms, box plots, and measures of center.

A lesson focused on calculating the mean, variance, and standard deviation of binomial probability distributions in real-world contexts.

A lesson on constructing and analyzing probability distributions for discrete random variables based on collected samples or simulations, aligned with TEKS S.5(C).

A Tier 2 intervention lesson focused on using simulation to estimate population parameters and determine the margin of error, aligned with Colorado standard HS.S-IC.B.4. Students engage in hands-on data collection and visual analysis of sampling distributions.

A Tier 2 intervention lesson focusing on the conceptual understanding of sampling variability and the margin of error using simulation models. Students transition from individual samples to distributions of many samples to estimate population parameters.

This Tier 2 intervention lesson focuses on the normal distribution, teaching students how to use the mean and standard deviation to estimate population percentages using the Empirical Rule and technology. It provides scaffolded support for students who need additional practice with statistical modeling and standard scores.

A targeted small-group lesson on fitting data to a normal distribution, applying the Empirical Rule, and estimating population percentages in real-world contexts.

A Tier 2 intervention lesson designed for small groups to master fitting data to a normal distribution and estimating percentages using the Empirical Rule. This lesson features visual 'blueprint' models to help students scaffold their understanding of the normal curve.

A targeted intervention lesson for high school students focusing on how outliers influence the shape, center, and spread of data distributions, featuring concrete manipulative-based activities.

A targeted Tier 2 intervention lesson focusing on choosing the correct measures of center and spread based on data distribution shape to compare datasets. Includes scaffolded matching activities and real-world contexts like social media and sports.

A foundational ACT/SAT prep lesson focusing on high-frequency algebra, geometry, and data questions for students looking to move past the 15-20 score range. Includes strategies for time management and a diagnostic assessment.

A comprehensive practice session for the TSIA2 Math exam, focusing on quantitative reasoning, algebraic reasoning, geometry, and statistics.

A comprehensive 20-question practice test covering all four TSIA2 Math domains: Quantitative Reasoning, Algebraic Reasoning, Geometry, and Probability and Statistics.

A comprehensive introduction to the normal distribution, focusing on the empirical rule and calculating probabilities using z-score tables. Students will learn to visualize data distributions and find areas under the curve.

A strategic masterclass for the ACT Science section, focusing on speed-reading data sets, identifying experimental variables, and decoding scientific logic. This lesson emphasizes the 'Straight to the Data' approach to maximize score in the 35-minute time limit.

An introductory exploration of calculus-adjacent concepts tested on the ACT, focusing on limits, instantaneous rates of change, and function optimization. Students will master the Limit Blueprint and apply rate-of-change logic to complex algebraic scenarios.

An intensive masterclass on advanced trigonometric identities, the unit circle, and non-right triangle laws. Students will master the Pythagorean identities, Law of Sines/Cosines, and the specific ACT-style unit circle coordinates required for top-tier scores.

A specialized deep dive into advanced geometry concepts including circle equations, 3D volume/surface area of complex shapes, and coordinate geometry involving perpendicularity and distance. Students will master completing the square for circles and visualizing 3D cross-sections.

A specialized deep dive into trigonometric functions, mastering the critical distinction between period and frequency. Students will apply the 2π/b blueprint to decode sine and cosine graphs and solve high-difficulty periodic motion problems.

A focused deep dive into imaginary and complex numbers. Students will master powers of i, arithmetic with complex conjugates, and solving quadratic equations with complex roots—all through the lens of ACT-style 'Final Ten' questions.

A comprehensive lesson focused on high-level ACT Math topics including matrices, complex functions, trigonometry, and advanced statistics. The lesson emphasizes identifying common 'traps' and applying architectural-style problem-solving strategies.

A lesson focused on calculating the mean, variance, and standard deviation of binomial probability distributions in real-world contexts.

A lesson on constructing and analyzing probability distributions for discrete random variables based on collected samples or simulations, aligned with TEKS S.5(C).

A Tier 2 intervention lesson focusing on using probability to design and evaluate fair decision-making procedures. Students learn to use tools like random number generators and drawing lots to ensure equal opportunity.

A scaffolded intervention lesson where students analyze the effectiveness of medical tests and strategic decisions using tree diagrams and expected value. Focused on High School Statistics standard HS.S-MD.B.7 with a heavy emphasis on visual logic and false positive/negative reasoning.

A scaffolded lesson where students test various random selection methods (drawing lots, dice, RNG) to determine if they are fair and use probability to justify their findings.

Students define random variables, create probability distributions, and calculate the expected value (mean) of a game of chance. The lesson concludes with a multi-trial experiment to see how experimental results converge on theoretical expectations.

A targeted Tier 2 intervention lesson focusing on evaluating model consistency through simulations, designed for small group support in High School Statistics.

A Tier 2 intervention lesson focused on calculating expected payoffs for games of chance using a vintage carnival theme. Students use probability distributions to determine if carnival games are 'fair' through scaffolded, hands-on simulations.

A Tier 2 intervention lesson focusing on creating probability distributions and calculating expected values through the lens of guessing on multiple-choice tests. Includes scaffolded instruction, visual models, and progress monitoring.

A comprehensive practice session for the TSIA2 Math exam, focusing on quantitative reasoning, algebraic reasoning, geometry, and statistics.

An introductory exploration of calculus-adjacent concepts tested on the ACT, focusing on limits, instantaneous rates of change, and function optimization. Students will master the Limit Blueprint and apply rate-of-change logic to complex algebraic scenarios.

An intensive masterclass on advanced trigonometric identities, the unit circle, and non-right triangle laws. Students will master the Pythagorean identities, Law of Sines/Cosines, and the specific ACT-style unit circle coordinates required for top-tier scores.

A specialized deep dive into advanced geometry concepts including circle equations, 3D volume/surface area of complex shapes, and coordinate geometry involving perpendicularity and distance. Students will master completing the square for circles and visualizing 3D cross-sections.

A specialized deep dive into trigonometric functions, mastering the critical distinction between period and frequency. Students will apply the 2π/b blueprint to decode sine and cosine graphs and solve high-difficulty periodic motion problems.

A focused deep dive into imaginary and complex numbers. Students will master powers of i, arithmetic with complex conjugates, and solving quadratic equations with complex roots—all through the lens of ACT-style 'Final Ten' questions.

A comprehensive lesson focused on high-level ACT Math topics including matrices, complex functions, trigonometry, and advanced statistics. The lesson emphasizes identifying common 'traps' and applying architectural-style problem-solving strategies.

A targeted Tier 2 intervention lesson focusing on distinguishing between permutations and combinations to solve probability problems, featuring scaffolded sorting tasks and decision flowcharts.

A Tier 2 intervention lesson focusing on distinguishing between permutations and combinations to calculate probabilities in real-world contexts like lotteries and committees. Includes scaffolded calculator support and outcome-based reasoning.

A Tier 2 intervention lesson focusing on the General Multiplication Rule for probability, specifically comparing independent and dependent events through scaffolded practice and interpretation.

A Tier 2 intervention lesson focusing on the general Multiplication Rule of probability. Students use tree diagrams to visualize dependent events and interpret joint probabilities in real-world contexts.

A scaffolded intervention lesson where students map sample spaces to random variables, build probability distributions, and calculate expected values using tree diagrams.

A targeted small group intervention for high school students focusing on the General Multiplication Rule for probability using hands-on simulations of drawing without replacement. Students will calculate P(A and B) and interpret results in context.

A Tier 2 small group intervention focused on defining sample spaces and describing events as subsets using unions, intersections, and complements through hands-on dice and card activities.

A targeted intervention lesson for high school students to master the Addition Rule of probability through visual Venn diagrams and step-by-step modeling to avoid double-counting.

A targeted Tier 2 intervention lesson focusing on permutations and combinations. Students move from physical counting and organized lists to using formulas to calculate probabilities in real-world 'code-breaking' scenarios.

A Tier 2 intervention lesson focusing on the Addition Rule of Probability, emphasizing the visual 'double counting' of overlapping events and error analysis. Students move from concrete Venn diagrams to abstract calculations and contextual interpretations.

A small-group intervention lesson teaching students to identify independent events using the product rule and structured decision-making tools.

A targeted Tier 2 intervention lesson focusing on the mathematical definition of independence using the multiplication rule. Students use simulations with coins and cards to collect data, verify probabilities, and apply the formula P(A and B) = P(A) * P(B) to determine if events are independent.

A Tier 2 intervention lesson focusing on describing events as subsets, unions, intersections, and complements within a sample space using everyday scenarios and visual Venn diagrams.

A diverse collection of high-quality math resources spanning Algebra, Geometry, Statistics, and Pre-Calculus.

A comprehensive practice session for the TSIA2 Math exam, focusing on quantitative reasoning, algebraic reasoning, geometry, and statistics.

A summative assessment evaluating mastery of the Data Decoder sequence. Students apply their skills to a final case study involving complex data analysis and interpretation.

A deep dive into distinguishing between correlation and causation. Students analyze the correlation coefficient (r) and explore how external factors can influence perceived relationships between variables.

Explores bivariate data through scatter plots, trend lines, and the basics of linear regression. Students learn to use technology or manual methods to find the line of best fit and interpret the slope and intercept.

Instruction on organizing and interpreting categorical data using two-way frequency tables. Students calculate joint, marginal, and conditional relative frequencies to find associations between variables.

Guided practice in comparing two or more datasets using visual displays and summary statistics. Students analyze differences in shape, center, and spread to draw meaningful conclusions.

Introduces measures of center (mean, median) and spread (range, interquartile range, standard deviation basics). Students learn how to calculate these values and understand what they represent in the context of a dataset.

Focuses on constructing and interpreting visual data displays including histograms, box plots, and dot plots. Students learn to identify the most appropriate display for different data types and describe the shape of distributions.

A baseline assessment designed to identify student gaps in data interpretation, display construction, and statistical reasoning. Includes a variety of item types to gauge prior knowledge of histograms, box plots, and measures of center.

A lesson on constructing and analyzing probability distributions for discrete random variables based on collected samples or simulations, aligned with TEKS S.5(C).

A targeted intervention lesson where students build a probability distribution from empirical data sets (household surveys) and calculate the expected value of a random variable.

A targeted Tier 2 intervention lesson focusing on constructing two-way frequency tables, calculating conditional probabilities, and testing for independence using a color-coded blueprint approach.

A Tier 2 intervention lesson for high school statistics focused on using simulations to determine if experimental results are consistent with a theoretical model. Students use coin flips and dice rolls to understand the boundary between 'random chance' and 'likely rigged' outcomes.

A Tier 2 intervention lesson focused on defining random variables and graphing probability distributions using concrete coin and dice experiments. Includes scaffolded tasks and progress monitoring tools for small group instruction.

A Tier 2 intervention lesson for high school statistics focused on two-way frequency tables, conditional probability, and the mathematical test for independence using expected vs. observed frequencies.

A Tier 2 intervention lesson focusing on the conceptual understanding of sampling variability and the margin of error using simulation models. Students transition from individual samples to distributions of many samples to estimate population parameters.

This Tier 2 intervention lesson focuses on the normal distribution, teaching students how to use the mean and standard deviation to estimate population percentages using the Empirical Rule and technology. It provides scaffolded support for students who need additional practice with statistical modeling and standard scores.

A targeted small-group lesson on fitting data to a normal distribution, applying the Empirical Rule, and estimating population percentages in real-world contexts.

A targeted Tier 2 intervention lesson focusing on constructing two-way tables, calculating conditional probabilities, and testing for independence using student-collected survey data.

An introductory exploration of calculus-adjacent concepts tested on the ACT, focusing on limits, instantaneous rates of change, and function optimization. Students will master the Limit Blueprint and apply rate-of-change logic to complex algebraic scenarios.

An intensive masterclass on advanced trigonometric identities, the unit circle, and non-right triangle laws. Students will master the Pythagorean identities, Law of Sines/Cosines, and the specific ACT-style unit circle coordinates required for top-tier scores.

A specialized deep dive into advanced geometry concepts including circle equations, 3D volume/surface area of complex shapes, and coordinate geometry involving perpendicularity and distance. Students will master completing the square for circles and visualizing 3D cross-sections.

A specialized deep dive into trigonometric functions, mastering the critical distinction between period and frequency. Students will apply the 2π/b blueprint to decode sine and cosine graphs and solve high-difficulty periodic motion problems.

A focused deep dive into imaginary and complex numbers. Students will master powers of i, arithmetic with complex conjugates, and solving quadratic equations with complex roots—all through the lens of ACT-style 'Final Ten' questions.

A comprehensive lesson focused on high-level ACT Math topics including matrices, complex functions, trigonometry, and advanced statistics. The lesson emphasizes identifying common 'traps' and applying architectural-style problem-solving strategies.

A Tier 2 intervention lesson focusing on using probability to design and evaluate fair decision-making procedures. Students learn to use tools like random number generators and drawing lots to ensure equal opportunity.

A scaffolded intervention lesson where students analyze the effectiveness of medical tests and strategic decisions using tree diagrams and expected value. Focused on High School Statistics standard HS.S-MD.B.7 with a heavy emphasis on visual logic and false positive/negative reasoning.

A scaffolded lesson where students test various random selection methods (drawing lots, dice, RNG) to determine if they are fair and use probability to justify their findings.

A targeted Tier 2 intervention lesson focusing on evaluating model consistency through simulations, designed for small group support in High School Statistics.

A Tier 2 intervention lesson focused on calculating expected payoffs for games of chance using a vintage carnival theme. Students use probability distributions to determine if carnival games are 'fair' through scaffolded, hands-on simulations.

A Tier 2 intervention lesson focusing on using probability and expected value to analyze real-world decisions in medical testing, product quality, and sports strategy. Students use decision trees and justification templates to move from calculations to reasoned arguments.

A targeted Tier 2 intervention lesson focused on calculating and comparing expected values to make informed decisions in sports and business contexts. Students will learn to evaluate competing strategies through scaffolded practice and peer justification.

A targeted small group intervention lesson focused on using probability to make and analyze real-world decisions in sports and medicine. Students will use expected value and tree diagrams to justify strategies like pulling a hockey goalie or interpreting medical tests.

A Tier 2 intervention lesson designed for small groups to master calculating and interpreting expected value through scaffolded practice with real-world scenarios like smartphone insurance and carnival games.

A targeted intervention lesson for high school students to master calculating expected values for decision-making. Includes guided practice with payoff tables and scaffolded comparisons of multiple options.

A targeted Tier 2 intervention lesson designed to help high school students evaluate and compare different strategies using expected value calculations and decision-making frameworks.

A targeted intervention lesson for high school students to master the calculation of expected value in games of chance, focusing on defining random variables and determining game fairness.

A Tier 2 intervention lesson focused on using probability to create and evaluate fair decision-making systems in school and community contexts. Students move from identifying unfairness to architecting their own fair systems using tools like random number generators and drawing lots.

A targeted intervention lesson focused on calculating expected value through game design. Students learn to weigh outcomes by multiplying payoff values by their probabilities to make data-driven decisions.

A comprehensive lesson focused on performing and interpreting linear regression analysis using real-world UN population and surface area data. Students will learn to identify variables, evaluate the impact of outliers, and draw conclusions based on correlation coefficients.

A summative assessment evaluating mastery of the Data Decoder sequence. Students apply their skills to a final case study involving complex data analysis and interpretation.

A deep dive into distinguishing between correlation and causation. Students analyze the correlation coefficient (r) and explore how external factors can influence perceived relationships between variables.

Explores bivariate data through scatter plots, trend lines, and the basics of linear regression. Students learn to use technology or manual methods to find the line of best fit and interpret the slope and intercept.

Instruction on organizing and interpreting categorical data using two-way frequency tables. Students calculate joint, marginal, and conditional relative frequencies to find associations between variables.

Guided practice in comparing two or more datasets using visual displays and summary statistics. Students analyze differences in shape, center, and spread to draw meaningful conclusions.

Introduces measures of center (mean, median) and spread (range, interquartile range, standard deviation basics). Students learn how to calculate these values and understand what they represent in the context of a dataset.

Focuses on constructing and interpreting visual data displays including histograms, box plots, and dot plots. Students learn to identify the most appropriate display for different data types and describe the shape of distributions.

A baseline assessment designed to identify student gaps in data interpretation, display construction, and statistical reasoning. Includes a variety of item types to gauge prior knowledge of histograms, box plots, and measures of center.

This lesson focuses on the informal and formal methods of fitting a linear function to a scatter plot. Students learn to visually balance points and use two-point slope-intercept form to define the line.

A targeted Tier 2 intervention lesson for high school students focusing on fitting linear functions to scatter plots. This lesson uses a 'Data Detective' theme to engage students in real-world prediction tasks with scaffolded support and sentence starters.

A Tier 2 intervention lesson focused on decoding linear models. Students learn to use structured sentence frames to interpret the slope and y-intercept of regression lines within real-world contexts like phone battery life and career earnings.

A small-group intervention lesson focused on the relationship between variables, the scale of the correlation coefficient, and using technology to find 'r'.

A targeted Tier 2 intervention lesson focusing on interpreting the components of linear models. Students will master the language used to describe slope (rate of change) and the y-intercept (constant term) through scaffolded sentence frames and interactive sorting activities.

A targeted intervention lesson on interpreting the slope and intercept of linear models. Students use sentence frames and peer feedback to master contextual explanations.

A targeted Tier 2 intervention lesson focused on distinguishing between correlation and causation through investigative scenarios, lurking variable identification, and sorting activities.

A targeted Tier 2 intervention lesson focusing on informally assessing function fit using residual plots, designed for small group instruction with scaffolded support and technology integration.

A targeted Tier 2 intervention lesson focusing on computing and interpreting the correlation coefficient (r). Students will use technology to find r, interpret its meaning in real-world contexts, and collaborate to analyze the strength and direction of linear relationships.

A Tier 2 small group intervention lesson focused on visual estimation, calculation, and interpretation of the correlation coefficient (r). Students progress from sorting scatter plots by eye to using technology for precise analysis.

A Tier 2 intervention lesson focused on calculating, plotting, and interpreting residuals to assess the fit of linear models. Students will move from visual estimation to mathematical analysis of prediction errors.

This lesson focuses on the statistical inference process, helping students distinguish between populations and samples, and parameters and statistics. It is designed for Tier 2 intervention, utilizing scaffolded vocabulary activities and scenario-based sorting to build conceptual understanding.

A Tier 2 intervention lesson focusing on the core logic of statistical inference. Students move from physical sampling to conceptual understanding of how samples represent populations.

A Tier 2 intervention lesson focusing on using sample data to estimate population parameters. Students use simulations to develop and interpret margin of error in real-world polling contexts.

A Tier 2 intervention lesson focused on using simulation to estimate population parameters and determine the margin of error, aligned with Colorado standard HS.S-IC.B.4. Students engage in hands-on data collection and visual analysis of sampling distributions.

A Tier 2 intervention lesson focusing on randomized experiments and simulation-based significance testing. Students learn to determine if observed differences between two treatments are statistically significant using a hands-on shuffling simulation approach.

A targeted Tier 2 intervention lesson where students act as 'Study Architects' to master the design of sample surveys, experiments, and observational studies. The lesson emphasizes the critical role of randomization in each design type through collaborative mini-study planning and peer critique.

A Tier 2 intervention lesson focusing on the conceptual understanding of sampling variability and the margin of error using simulation models. Students transition from individual samples to distributions of many samples to estimate population parameters.