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 detailed answer key for the adjusted TSIA2 Math practice test, featuring the new distribution of quantitative, algebraic, geometric, and statistical questions.
A 20-question multiple-choice practice test for the TSIA2 Mathematics assessment, with a specific distribution of quantitative (6), algebraic (7), geometric (3), and statistical (4) questions.
A teacher-facing facilitation guide for the 'Keyword Detective' lesson. Includes pacing, discussion prompts, strategies for addressing common misconceptions, and differentiation tips for various learner levels.
Detailed answer key for the Keyword Detective worksheet. Includes step-by-step mathematical solutions using permutation and combination formulas, along with annotated keywords for each word problem case.
A professional facilitation guide for the Math Club instructor, featuring a pacing guide, discussion prompts, common misconceptions, and a complete answer key for the Pascal's Triangle activity.
A visual presentation for teaching the difference between permutations and combinations. Features embedded video instructions, a breakdown of 'specific tasks' vs 'general tasks', and a walk-through of a complex multi-step word problem.
A comprehensive student activity worksheet featuring a Pascal's Triangle template, space for combination calculations, and investigation prompts to discover the link between combinations and the triangle's structure.
A 'Keyword Detective' themed worksheet where students analyze word problems to distinguish between permutations and combinations by identifying specific keywords. Includes a field guide, warm-up exercises, and mixed problems ranging in difficulty.
A vibrant and professional slide deck for High School Math Club that guides students through the discovery of the relationship between Pascal's Triangle and Combinations. Includes video embedding and guided discussion prompts.
A comprehensive teacher guide and answer key for the Pascal's Architect lesson, including a lesson schedule, full triangle values, and worksheet answers.
A blank Pascal's Triangle (up to Row 7) for student investigation. It includes dedicated space for students to fill in values, shade specific hidden patterns, and record their mathematical observations.
A visual presentation for instruction including the warm-up, video embed, symmetry concept visualization, and activity instructions.
A visual presentation deck for the Pascal Pattern Hunters lesson. It includes a warm-up challenge, embedded video segments, activity instructions for the Pattern Hunter investigation, and closing reflection prompts.
A visual presentation for teaching path permutations using Pascal's Triangle. Includes the embedded YouTube video, activity instructions, and a final challenge problem.
An exit ticket asking students to reproduce Row 5 of Pascal's Triangle and explain its symmetry using combination logic.
A visually striking anchor chart summarizing the key properties of Pascal's Triangle, including the additive rule, row sums, path permutations, and binomial expansion coefficients. It serves as a classroom reference for the Pattern Hunter activity.
A set of 6 discussion cards for small group prompts regarding Pascal's Triangle, symmetry, and path permutations. Designed to be printed and cut.
An instructional anchor chart illustrating the construction rules and symmetry principles of Pascal's Triangle, featuring the additive rule and the nCr coordinate system.
A professional rubric for evaluating group presentations on Pascal's Triangle, featuring criteria for accuracy, concept application, and collaboration.
A design-focused worksheet where students simplify fractions, recap the video problem, design their own closet inventory, and challenge a partner with three probability questions.
A 4-point grading rubric for the "House Always Wins" lesson, assessing simulation execution, data analysis, conceptual understanding, and the final synthesis reflection.
A comprehensive teacher's guide for the "House Always Wins" lesson. It includes a time-stamped instructional sequence, specific pause-and-discuss points for the video, materials checklist, and a discussion guide focused on the Law of Large Numbers.
A 7-slide presentation deck covering the basketball hook, embedded YouTube video on experimental probability, definitions of key terms, simulation instructions, and the final connection to casino economics and the Law of Large Numbers.
A 2-page student worksheet for a probability simulation lab. It includes space for predictions, video notes, a structured data table for 10/100/1000 trials, a graphing area to visualize variance, and reflection questions on the Law of Large Numbers and casino economics.
A group activity worksheet where students must determine the minimum combination of letter grades across five specific courses to achieve a target GPA of 3.5.
A concise assessment for students to demonstrate their ability to calculate a weighted GPA and justify their answer using logical reasoning.
A specialized student worksheet designed for use during the video tutorial, featuring structured calculation tables for two practice problems and dedicated space for long division and GPA logic checks.
A comprehensive visual reference for students outlining the step-by-step process of calculating GPA, including the point system, quality point multiplication, and the final division formula.
A professional instructional presentation for calculating college GPAs, featuring a comparative hook, vocabulary definitions, embedded tutorial video with pause points, and instructions for a group challenge activity.
A teacher guide for facilitating the Human Box Plot activity, including pacing, material lists, and tips for handling even/odd data sets.
A visual presentation for the Human Box Plot lesson, including the YouTube video embed and step-by-step activity instructions.
A student worksheet for recording class heights, calculating the five-number summary, and sketching the resulting box-and-whisker plot.
Comprehensive teacher reference containing sorted dataset, completed stem and leaf plot, correct statistical measures (median, mode, range), exit ticket answer, and pedagogical tips for addressing common misconceptions.
Final assessment task for the lesson. Students must demonstrate their understanding of keys by creating a specific key that translates a stem of 4 and leaf of 3 into the decimal value 4.3.
Student activity worksheet for organizing bowling scores into a stem and leaf plot. Includes dedicated sections for sorting raw data, constructing the plot with multi-digit stems, defining a key, and calculating statistical measures (range, median, mode).
A clear, formatted dataset of 20 bowling scores ranging from 72 to 148. Designed as a reference sheet for students to use during the main activity.
Visual presentation for the lesson including a warm-up mystery plot, embedded instructional video, key concept refreshers, and activity instructions. Features a bowling theme and clear visual aids for large number stems.
This comprehensive answer key provides the solutions for the 'Salary Cap Worksheet'. It includes the ordered dataset, calculated mean and median (both with and without the outlier), 5-number summary, outlier boundary calculations, and suggested responses for the discussion and conclusion questions.
Guide de correction complet pour les exercices sur la loi normale, détaillant les calculs de scores Z et l'application de la règle empirique.
Feuille d'exercices sur la loi normale, incluant le calcul de scores Z, la conversion de scores en valeurs réelles et l'application de la règle empirique.
Présentation de la loi normale, des propriétés de la courbe en cloche, de la règle empirique (68-95-99.7) et du calcul du score Z pour la standardisation.
Guide de correction pour l'atelier de visualisation, illustrant le tracé de l'histogramme et fournissant les justifications analytiques pour l'interprétation des boîtes à moustaches.
Atelier de tracé d'un histogramme à partir de données groupées et d'analyse comparative de boîtes à moustaches pour identifier les performances et les valeurs aberrantes.
Support visuel présentant les principes de visualisation de données : choix du graphique, structure de l'histogramme et anatomie d'une boîte à moustaches.
Guide de correction détaillé pour les calculs de tendance centrale et de dispersion, incluant les calculs intermédiaires et les interprétations conceptuelles.
Feuille de travail axée sur le calcul de la moyenne, médiane, mode et écart-type à partir de jeux de données réels, avec une section sur l'interprétation de la dispersion.
Présentation sur les mesures de tendance centrale (moyenne, médiane, mode) et de dispersion (variance, écart-type), incluant l'interprétation de la forme d'une distribution.
Guide de correction pour le Lab de Classification, incluant les justifications pour les types de variables et les échelles de mesure.
Feuille d'exercices pratique pour identifier les populations/échantillons et classer divers types de variables selon leur nature et leur échelle de mesure.
Support de présentation visuel introduisant les concepts de population vs échantillon, ainsi que la classification des variables et les échelles de mesure.
A visual presentation for the Data Detectives lesson, featuring embedded video, pause point discussion prompts, and clear activity instructions for students.
A comprehensive teacher guide for the Data Detectives lesson, including learning objectives, a timed lesson flow, video pause points, and vocabulary definitions.
A set of guidelines and a workspace for students to design an intentionally biased poll about a school issue, including a section for peer review.
A worksheet for students to complete while watching the Crash Course video on public opinion and polling, focusing on key statistical concepts like sampling error and selection bias.
Printable paper die templates, evidence labels for 'rigging' dice, and case file tags for organizing classroom materials.
A professional teacher guide providing a detailed lesson walkthrough, pacing advice, discussion prompts, and key vocabulary for the Theory vs Reality probability lesson.
A concise exit ticket for students to define theoretical and experimental probability and reflect on the impact of sample size. Includes two tickets per page for easy printing.
A comprehensive teacher guide for facilitating 'The Rigged Case Files'. Includes instructions for rigging dice, video pause prompts, and guidance on explaining statistical significance to 9th graders.
A student worksheet styled as a detective case file, where students analyze three specific instances of data manipulation involving misleading graphs, correlation vs. causation, and source bias.
A dynamic slide deck for instruction on data manipulation, featuring visual examples of misleading graphs, correlation vs. causation, and source credibility.
A comprehensive teacher guide for a 45-minute lesson on data manipulation, including a timed pacing guide, key discussion questions, and differentiation strategies.
A student worksheet for the Data Detectives lesson, featuring chart labeling exercises and practical interpretation questions based on budgeting and savings scenarios.
A comprehensive facilitator guide for the Data Detectives lesson, including learning objectives, pacing suggestions, discussion prompts, and answer keys.
A 7-slide introductory presentation for Life Skills students on reading and interpreting bar and pie charts, featuring real-world budgeting examples and clear visual anatomy of charts. Revised for improved readability, font scaling, and uniform answer styling.
Work Sample 10: A circle graph showing chores with distinct vibrant colors and direct labels. Questions cover identification, quantitative comparisons, and calculating totals. tracking box included.
Work Sample 9: A bar graph showing sunny days with grid lines and grounded bars. Questions cover identification and quantitative comparisons. Includes tracking box.
Work Sample 8: A circle graph showing favorite subjects with distinct colors and direct slice labels for maximum independence. Questions cover ties and comparisons. tracking box included.
Work Sample 7: A bar graph showing books read with grounded bars and unit grid lines. Questions cover monthly comparisons and totals. tracking box included.
Work Sample 6: A circle graph showing color preferences with distinct vibrant colors and direct slice labels. Questions focus on popular colors and comparisons. Includes tracking box.
Work Sample 5: A bar graph showing sports preferences with grid lines and grounded bars. Questions cover player counts and quantitative comparisons. Includes tracking box.
Work Sample 4: A circle graph showing lunch choices with distinct colors and direct slice labels. Questions focus on popularity and comparisons. tracking box included.
Work Sample 3: A bar graph showing ice cream flavor preferences with grid lines and grounded bars. Questions focus on popularity, comparisons, and total counts. tracking box included.
Work Sample 2: A circle graph showing favorite fruit with distinct vibrant colors using SVG path elements for maximum print reliability. Labels and values are directly on the slices. tracking box included.
Work Sample 1: A bar graph showing favorite pets with bars seated directly on the axis and unit-level grid lines. Questions focus on identification, comparisons, and totals. tracking box included.
A detailed answer key for the Algebra Arsenal and Geometry Grid worksheets, providing not just correct answers but step-by-step strategy insights and explanations for teachers or self-grading students.
A targeted practice worksheet covering ACT Geometry, Trigonometry, and Statistics, featuring diagrams, circle equations, probability, and average problems with designated space for student work.
A targeted practice worksheet focusing on ACT Algebra and Functions, including linear equations, substitution, system of equations, exponent rules, and inequalities with designated space for student work.
A comprehensive 2-page study guide summarizing the most critical ACT Math concepts, including Algebra, Geometry, Statistics, and Trigonometry, along with rapid-fire testing strategies.
A set of 8 essential ACT Math formula flashcards covering Algebra, Geometry, and Trigonometry, designed for easy printing and cutting.
A visual presentation covering ACT Math structure, time management strategies (the 20-20-20 rule), problem-solving techniques like PIN and PITA, and common test traps to avoid.
A structured worksheet for students to record answers to presentation missions and conduct independent research on a math-related career of their choice.
A comprehensive guide for teachers to facilitate the Math Careers Exploration lesson, including slide-by-slide talking points, answer keys, and differentiation strategies.
A vibrant and engaging slide deck introducing 5th-grade students to careers that use mathematics, featuring real-world missions and interactive questions.
A comprehensive teacher guide for the 'Data of Disparity' lesson, including pacing, detailed mathematical answer keys, and pedagogical strategies for facilitating the data visualization lab.
A revised 6-slide presentation for guiding the lesson, ensuring all text meets the minimum 24px requirement for accessibility and impact, including updated layouts for clarity.
A comprehensive 2-page lab worksheet for students to record results from a probability warm-up, gather data from the video, and create three distinct infographics based on calculated ratio disparities.
An anchor chart for high school statistics classrooms that defines equal likelihood, disproportionality, and ratio disparity, featuring a visual comparison of the 1:100 crack vs. powder cocaine sentencing ratio.
Comprehensive teacher facilitator guide for the Pearl Prospectors lesson, featuring setup instructions for the simulation, instructional pacing, and guiding questions.
Student worksheet for tracking the Pearl Hunt simulation, featuring a tally chart, bar graph section, and reflection questions on rarity and fractions.
Visual presentation for the Pearl Prospectors lesson, including the SciShow Kids video embed, activity instructions, and discussion prompts on rarity and probability.
A sleek, card-style exit ticket for students to demonstrate their understanding by creating and categorizing their own permutation or combination scenarios.
A tiered Algebra 1 worksheet covering correlation and linear regression with instructional mini lessons before each section. It includes three levels of difficulty: Pattern Recognition (Tier 1), Data Modeling with technology (Tier 2), and Contextual Interpretation (Tier 3).
The complete answer key for the Trend Trackers Worksheet, providing solutions for all three levels of difficulty (Tiers 1, 2, and 3). All explanations and data points are perfectly aligned with the worksheet content.
A tiered Algebra 1 worksheet covering correlation and linear regression with instructional mini lessons. Layout optimized for printing by compressing headers and using CSS to prevent orphaned content.
A comprehensive teacher resource containing lesson timing, answer keys, discussion prompts for the video, and troubleshooting tips for the main activity.
A specialized graphing sheet designed for students to plot their researched data points, featuring custom axis labels and a slope interpretation area.
A presentation deck for a 9th-grade algebra lesson on modeling real-world data with point-slope form, featuring video integration and prediction activities.
A comprehensive worksheet for 9th-grade algebra students to practice calculating slope, using point-slope form, and predicting real-world statistics based on researched data.
A comprehensive teacher guide for the 'Zero Hour' lesson, including pacing, facilitation notes for the video challenge, and a complete answer key for the student worksheet.
A student activity sheet for the 'Zero Hour' lesson. It includes a video-based challenge, two real-world data sets for graphing and slope calculation (CD sales and landline usage), and reflection questions on the limits of linear modeling.
A set of interactive slides for the Zero Hour lesson, including a hook activity, video-based calculations, and instructions for the main data extrapolation activity.
A quick assessment tool for the end of the Body Blueprint lesson. Asks students to define bivariate data, identify a correlation, and explain the importance of outliers.
A comprehensive lesson plan for teachers, including a timeline, discussion prompts, 'Teaching Moments' from the video, and a full answer key for the 'Case Files' activity.
A sheet of printable data point markers for students to cut and paste onto the class scatter plot. Styled with a blueprint aesthetic.
A comprehensive reference sheet for students summarizing the four types of data representations. It includes use cases, whether individual data points are visible, and key features to look for.
A large printable grid for creating the class-wide scatter plot. Includes clear axis labels for Arm Span and Total Height, and a blueprint-themed design.
A teacher guide and answer key for the Lottery Logic lesson. Includes pacing suggestions, detailed calculation steps for the lottery activity, and instructional tips for addressing common student misconceptions.
A presentation slide deck for teaching the combination formula. Includes factorial warm-ups, embedded YouTube instructional video, visual formula derivations, and a class lottery activity.
A student worksheet for a 10th-grade statistics lesson on combinations, featuring factorial warm-ups, video analysis prompts for the 'crossing out' visual, and a lottery-themed application activity.
A comprehensive student reference sheet summarizing conditional probability, the funnel metaphor, independent/dependent events, and the Gambler's Fallacy.
Visual presentation slides to guide the Gambler's Fallacy lesson, including the video embed, the funnel metaphor for conditional probability, and experiment instructions.
A structured data tracking sheet for students to record 50 coin flips, identify streaks, and calculate conditional probabilities to test the Gambler's Fallacy.
A comprehensive lesson plan for 11th-grade statistics focusing on the Gambler's Fallacy. Includes lesson timing, objectives, discussion prompts, and instructional steps for a coin-flip experiment.
Problem set for graduate students to practice implementing Monte Carlo simulations, calculating standard error, and understanding variance reduction techniques.
Graduate-level slides covering Monte Carlo methods, Geometric Brownian Motion paths, and the Law of Large Numbers applied to derivative pricing.
Problem set for graduate students to practice calculating VaR and Expected Shortfall, analyzing the impact of non-normal distributions on risk metrics.
Graduate-level slides covering VaR, Expected Shortfall, tail risk metrics, and the limitations of normal distributions.
Problem set for graduate students to price European options using the binomial model and calculate delta-hedging portfolios.
Graduate-level slides covering risk-neutral measures, the fundamental theorem of asset pricing, and the derivation of the binomial model.
Problem set for graduate students to compute portfolio expected returns and variance using matrix algebra, and derive the Minimum Variance Portfolio.
Graduate-level slides covering portfolio expected returns, covariance matrices, and the formulation of the Markowitz mean-variance optimization problem.
Problem set for graduate students to practice calculating expected utility, risk premiums, and deriving risk aversion measures.
Graduate-level slides covering the St. Petersburg Paradox, vNM Utility functions, and risk premiums in quantitative finance.
A comprehensive teacher key for the Bistro Battle simulation, providing cleaned counts, condition verifications, and full mathematical trace for the p-value calculation.
A teacher key for Lesson 5, containing the calculated values for the Bistro Battle simulation including pooled proportions, SE, Z-statistic, and p-value.
A comprehensive grading and peer-review rubric for the final consultant simulation, assessing model choice, condition checks, and interpretation.
A detective-themed data collection sheet for students to record 50 die rolls, calculate experimental probability, and determine if their die is fair or rigged.
A detective-themed presentation for teaching experimental vs. theoretical probability. Includes embedded video, discussion prompts for specific timestamps, and activity instructions for "The Unfair Game."
A professional teacher-facing guide including a pacing guide, answer keys for the warm-up and video problems, and a comprehensive master solution for the Willow Creek Census activity.
A detailed answer key for the 'Branching Out' worksheet. It provides solutions for the coin-flip warm-up, step-by-step calculations for the video's marble problem, and a complete sample scenario for the creative student activity.
A teacher-facing answer key and instructional guide for the 'Order Matters' problem set. It provides step-by-step logic for categorization and the resulting probability calculations, including specific notes on sampling without replacement.
Visual presentation slides for the 'Probability Without Replacement' lesson, including embedded video segments, interactive discussion prompts, and clear definitions of independent vs dependent events.
A comprehensive teacher facilitation guide for the 'Branching Out' lesson. It includes a detailed 50-minute pacing plan, specific video pause points, common student pitfalls, and differentiation strategies for varying skill levels.
Final assessment exit ticket requiring students to solve an "at least one" probability problem using the complement rule. Includes two copies per page for efficient printing.
A visual presentation deck supporting the lesson. It includes a warm-up discussion about locker locks, instructions for viewing specific segments of the provided YouTube video, and conceptual slides clarifying the difference between 'Order Matters' (single branch) and 'Order Doesn't Matter' (multiple branches).
A student-facing packet containing the lesson warm-up, video note-taking space, fictional demographic data for the Willow Creek Census, and graph paper for constructing a probability tree diagram.
Student group activity worksheet focusing on the application and efficiency of the probability complement rule across different multi-stage scenarios.
A 9-slide presentation for the 'Branching Out' probability lesson. It features high-contrast visuals, a built-in YouTube embed for the marble problem, clear objective slides, and detailed activity instructions with helpful math tips.
A student worksheet for practicing probability without replacement, featuring a warm-up observation log and a multi-step 'Raffle Draw' scenario requiring a tree diagram.
Slide presentation for the probability complement rule lesson, featuring the 10-coin challenge hook, the complement formula, and the embedded instructional video.
A comprehensive problem set where students must categorize probability word problems as 'Order Matters' or 'Order Doesn't Matter' before solving them. It includes space for tree diagrams and calculations for both independent and dependent events.
A comprehensive slide deck for the Census Circuit lesson, featuring learning objectives, a math warm-up, an embedded probability video, and instructions for the main census activity.
A structured student worksheet for the 'Branching Out' probability lesson. It includes a coin-flip warm-up, a dedicated section for video notes on independent events, and a creative 'Design Your Own Tree' activity space with room for calculations and reflection.
A comprehensive teacher guide for the 'Probability Without Replacement' lesson, featuring a scripted candy bag demo, video discussion prompts, and a complete answer key for the student worksheet.
Teacher facilitation guide for the probability complement rule lesson, including learning objectives, pacing, and answer keys.
A set of six discussion cards for a 5-minute warm-up activity. These cards present real-world scenarios to help students distinguish between situations where the order of events changes the outcome (permutations) and where it does not (combinations).
A teacher-facing answer key and reference sheet for the Marble Madness lesson, featuring step-by-step solutions for the video examples and lab expectations.
An answer key for the Marble Lab Student Journal. Includes the correct denominator shifts, group practice calculations, and sample reflection answers for teacher use.
Teacher reference guide containing learning objectives, pacing, instructional tips, and a full answer key for the battery brand data analysis.
Scaffolded writing template for students to draft their final recommendation. Uses the CER (Claim, Evidence, Reasoning) framework to help students articulate their statistical arguments.
Worksheet for student calculations and graphing. Includes dedicated spaces for 5-number summaries, outlier checks, and a large number line for constructing stacked box plots.
Reference sheet containing battery life data (in hours) for two competing brands, Alpha and Omega, with distinct statistical profiles for comparison.
Visual presentation for the 'Double Plot Duel' lesson, including a sports-themed warm-up, the YouTube video embed, activity instructions, and a closing discussion prompt.
A set of six colorful discussion cards designed for student pairs. Each card provides a specific analytical prompt to help students compare the two line plots, focusing on concepts like frequency, range, and data distribution.
A student worksheet featuring two side-by-side line plots representing rainfall data for May and June. Students are prompted to analyze the distributions and write three comparative statements based on the data.
A visual presentation for the Data Duel lesson. Includes a thematic hook, embedded instructional video on line plots with fractions, guided discussion prompts for data analysis, and clear activity instructions.
A comprehensive teacher guide for the Data Duel lesson, including learning objectives, a detailed step-by-step facilitation plan, discussion prompts, and an answer key for the student activities.
A teacher guide and answer key for the Court Side Comparisons lesson. Includes calculated values for the student activity, sample responses for discussion, and common student misconceptions to address during the lesson.
A student worksheet and exit ticket for comparing basketball player data using Box-and-Whisker plots. Includes a section for 5-number summary calculation, a comparative graphing template on a shared number line, and an analysis section.
A slide deck for a 7th-grade math lesson comparing basketball players using Box-and-Whisker plots. Features a scout/basketball theme, embedded video, and data comparison for two players, Jordan and Alex.
Review worksheet for selecting the appropriate statistical procedure among paired means, independent means, and proportions.
Answer key for the Decision Danger Exit Ticket, including error classification and conclusion writing.
Exit ticket assessment for identifying Type I and Type II errors and writing statistical conclusions in non-technical language.
Answer key and exemplar for the Medical Treatment Efficacy Case Study, including full 4-step hypothesis testing and interval calculation.
Slide deck explaining Type I and Type II errors and how to communicate statistical conclusions in non-technical language.
Introductory slides for the Taste Test Challenge experiment, explaining experimental design, randomization, and blinding.
Worksheet for performing a complete statistical analysis of the Nexalin-B clinical trial data, including hypothesis testing and confidence intervals.
A comprehensive project rubric for teachers and students to assess the comparative statistics project across design, ethics, analysis, and communication.
Student worksheet for Lesson 5, focusing on manual random walk simulations and the mathematical application of the stochastic price equation.
Teacher facilitation guide for Lesson 5, detailing the introduction to stochastic sequences, the drift/volatility model, and the concept of Monte Carlo simulations.
Slide deck for Lesson 5 introducing stochastic sequences, simulations of random walks, and their application to stock price modeling.
Student worksheet for Lesson 4, covering bond price calculations and the derivation of Macaulay and Modified duration to assess interest rate sensitivity.
Teacher facilitation guide for Lesson 4, detailing the bond pricing series derivation and the calculus-based sensitivity analysis (duration).
Slide deck for Lesson 4 exploring bond pricing as a finite series and the derivation of Macaulay duration to measure interest rate risk.
Student worksheet for Lesson 3, covering the pricing of perpetuities and the mathematical derivation/application of the Dividend Discount Model.
Teacher facilitation guide for Lesson 3, outlining the mathematical derivation of perpetuity valuation and the Dividend Discount Model convergence conditions.
Slide deck for Lesson 3 exploring the valuation of perpetuities and the Dividend Discount Model through the lens of infinite geometric series convergence.
Student worksheet for Lesson 2, covering the calculation of future value for savings and the derivation of monthly mortgage payments using finite geometric sums.
Teacher facilitation guide for Lesson 2, outlining the derivation of the annuity formula and providing guidance for the amortization simulation.
Slide deck for Lesson 2 focusing on finite geometric series and their application in calculating annuity values and loan amortization.
Student worksheet for Lesson 1, focusing on modeling interest as a geometric sequence and calculating the effects of different compounding frequencies.
Teacher facilitation guide for Lesson 1, detailing the transition from discrete geometric growth to continuous compounding with lesson delivery steps and answer key highlights.
Introductory slide deck for Lesson 1 covering the derivation of compound interest as a geometric sequence and the limit definition of continuous compounding.
Graduate-level slides for Martingale theory, explaining the fair game concept, filtration, and the Optional Stopping Theorem.
A graduate worksheet on Martingale theory, focusing on the definition of martingales, the Optional Stopping Theorem, and its application to the Gambler's Ruin problem.
Graduate slides on conditional expectation as a projection in Hilbert space and its definition using sub-sigma-algebras.
A graduate worksheet on conditional expectation, covering its measure-theoretic definition, Radon-Nikodym foundation, and the projection property in Hilbert spaces.
Graduate slides covering MCT, Fatou's Lemma, and DCT with visual representations of the convergence requirements.
A reflection journal sheet for students to synthesize their understanding of weighted means, focusing on the conceptual role of volume as a weight and real-world applications.
A structured lab report for students to solve mixture problems using the weighted mean formula. Includes sections for initial predictions, video observations, and multi-scenario calculations.
A visual presentation deck introducing the concept of weighted means in chemistry, including a hook discussion on solution mixing and a video integration section.
A graduate worksheet focusing on Monotone Convergence, Fatou's Lemma, and Dominated Convergence Theorems through rigorous analysis and proof construction.
Slides for Graduate-level probability covering Markov, Chebyshev, Jensen, Hölder, and Minkowski inequalities with proofs and applications.
A workshop-style worksheet for graduate students to practice applying Markov, Chebyshev, Jensen, Hölder, and Minkowski inequalities.
A student measurement lab sheet for the Body Blueprint activity. Includes sections for recording Arm Span and Height, and reflection questions for analyzing the class scatter plot.
A visual presentation for the Body Blueprint lesson, including a video hook, definitions of bivariate data, types of correlation, and outliers. Includes clear instructions for the measurement activity.
A comprehensive teacher facilitation guide for the Body Blueprint lesson, including pacing, material checklists, key vocabulary, and discussion prompts for analyzing scatter plots.
An answer key for the Beyond the Horizon Handout, providing the mathematical solutions for interpolation and extrapolation tasks along with the biological reasoning for model failure.
A student activity handout for the Prediction Pitfalls lesson. It guides students through modeling a bird population dataset, performing interpolation and extrapolation, and analyzing why their exponential model fails when compared to real-world logistic data.
A visual presentation for the Prediction Pitfalls lesson, featuring clear definitions, an embedded case study video, and discussion prompts on the limits of mathematical modeling.
A comprehensive teacher's guide for the Prediction Pitfalls lesson, detailing the instructional sequence, timing, and key discussion prompts for Grade 11 Advanced Algebra.
