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Expected Values

Mathematical foundations for calculating the long-term average of random variables across multiple trials. Addresses discrete probability distributions and applications in game theory and financial forecasting.

MathNumbers & CountingCounting ObjectsNumber NamesComparing NumbersNumber OperationsCounting SequenceNumbers 0-10Place Value Understanding and SystemAdd and Subtract Within 20Addition and Subtraction ConceptsAddition and Subtraction EquationsAddition and Subtraction ProblemsFoundations for MultiplicationMultiplication and Division PropertiesMultiply and Divide Within 100Multiplication and Division ProblemsFactors and MultiplesProperties of OperationsPatterns and RelationshipsGenerate and Analyze PatternsMulti-Digit ArithmeticPlace Value OperationsMulti-Digit and Decimal OperationsNumerical ExpressionsFour Operations and PatternsFour Operations Problem SolvingMeasurement & DataMeasurable AttributesMeasuring LengthsMeasure and Estimate Lengths in Standard UnitsRelate Addition and Subtraction to LengthClassifying and Counting ObjectsTime and MoneyArea Concepts and MeasurementPerimeter and Area MeasuresAngle Concepts and MeasurementTime, Volume, and MassMeasurement Unit ConversionsGeometryIdentifying ShapesShapes and AttributesShape Attributes and ReasoningShapes and CompositionClassifying 2D FiguresGeometric Figures and RelationshipsLines, Angles, and ShapesAngle, Area, and VolumeGeometric MeasurementVolume of 3D ShapesCoordinate Plane ApplicationsTransformations in the PlaneCongruence and SimilarityUnderstand congruence in terms of rigid motionsSimilarity and TransformationsProve Theorems Involving SimilarityPythagorean TheoremTrigonometry for General TrianglesMake Geometric ConstructionsProve Geometric TheoremsTheorems About CirclesFind Arc Lengths And Areas of Sectors of CirclesVolume FormulasRelationships Between Two-Dimensional and Three-Dimensional ObjectsProve Simple Geometric Theorems AlgebraicallyTranslate Between Geometric Description and Equation for Conic SectionApply Geometric Concepts in Modeling SituationsFractions & DecimalsFractions as NumbersBuilding FractionsFraction Equivalence and OrderingAdding and Subtracting FractionsMultiplying and Dividing FractionsDividing FractionsDecimal FractionsMulti-Digit Computation and FactorsAdd, Subtract, Multiply, and Divide Rational NumbersRational Number SystemIrrational Numbers and ApproximationsRatiosRatios and ProportionsProportional RelationshipsUnit RateAlgebraAlgebraic ExpressionsGenerate Equivalent ExpressionsQuantitative RelationshipsProportional Relationships and Linear EquationsEquations and InequalitiesEquation Solving and ReasoningLinear Equations and SystemsGraph Equations and InequalitiesSystems of EquationsReal-World Algebraic ProblemsQuantitative Reasoning with UnitsExpression StructureEquivalent Expression FormsRadicals and Integer ExponentsRational ExponentsRational and Irrational NumbersPolynomial OperationsPolynomial IdentitiesPolynomial Zeros and FactorsRational ExpressionsComplex Number OperationsComplex Numbers in PolynomialsComplex Numbers on PlaneStatistics & ProbabilityRepresent and Interpret DataData DistributionsStatistical VariabilityProbability ModelsCompound Event ProbabilitiesStatistical SamplingInterpret Categorical and Quantitative DataBivariate Data PatternsInterpret Linear ModelsComparing Two PopulationsRandom Processes in StatisticsIndependence and Conditional ProbabilityExpected ValuesProbability-Based Decision MakingStatistical Inference and ConclusionsFunctionsFunction Concepts and NotationDefine and Compare FunctionsInterpret Functions in ContextAnalyze Function RepresentationsModel Relationships with FunctionsIdentify Linear vs Exponential GrowthDistinguish Between Function TypesCompare Growth RatesInterpret Function ExpressionsBuild Functions from RelationshipsConstruct and Model FunctionsTransform and Combine FunctionsModel Comparison and SelectionSolve Exponential EquationsTrigonometryTrigonometric Ratios Involving Right TrianglesTrigonometric Functions and Unit CircleModel with Trigonometric FunctionsTrigonometric IdentitiesVectors & MatricesIntroduction to Vectors and MatricesVector QuantitiesVector OperationsMatrix OperationsCalculusLimits and ContinuityDerivative Concepts and NotationDerivative Rules and TechniquesApplications of DerivativesOptimization ProblemsRelated RatesCurve Sketching and AnalysisIntegration Concepts and NotationAntiderivatives and Indefinite IntegralsDefinite Integrals and AreaFundamental Theorem of CalculusIntegration TechniquesApplications of IntegrationDifferential EquationsSequences and SeriesParametric and Polar FunctionsVector-Valued Functions

Sequences

Blueprint Billions Brief

Blueprint Billions

A month-long architectural design and statistical analysis project for high school students, focusing on precision decimal operations through real-world urban planning, budgeting, and data synthesis.

SF

Steven Flint

6
Elite Math Teacher Guide

Advanced ACT Mastery

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.

AL

ava larumbe

29
Odds Architect Slides

Calculating Chance

A high-stakes dive into the mathematics of probability, risk assessment, and expected value, teaching students how to analyze games of chance and skill through a professional lens.

3
Probability Station Cards

The Decision Lab

A two-part, 90-minute sequence designed for French Terminale Section Européenne (Maths in English) students, exploring probability models, expected value, decision trees, and game theory with a strong emphasis on oral communication.

6
Decision Coach Guide

Decision Lab Probability

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.

5
Jackpot Journey Slides

Luck by Numbers

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.

5

Lessons

Probability Power Sheet Reference Sheet

Probability Power Review

A comprehensive lesson covering probability rules, counting principles, discrete random variables, and empirical distributions. Includes a condensed reference sheet and a practice review worksheet.

KB

Kayla Borozny

3
Random Variables Presentation Slides

Random Variables Revealed

An introduction to random variables, distinguishing between discrete and continuous types, graphing probability distributions, and calculating mean and standard deviation.

AC

Anjoe Calamba

3
Binomial Bounds Worksheet Corrected

Binomial Probability Distributions

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

MR

Mahuya Roy Chowdhury

2
Capital and Chance Framework

Curriculum Design

Master planning resources, pacing guides, and curriculum frameworks for advanced high school mathematics courses.

KB

Kayla Borozny

2
Binomial Breakdown Slides

Binomial Breakdown

A focused lesson on the binomial distribution, covering the BINS criteria, identifying parameters, and calculating probabilities using digital spreadsheet tools.

KC

Katelyn Coleman

6
Binomial Battles Assessment

Probability Power

A comprehensive assessment covering discrete random variables, permutations, combinations, and the binomial probability distribution based on real-world statistical data.

AC

Anjoe Calamba

4