LabPathAdvanced math course path

Statistics LabPath

A replacement-grade Statistics path where students design studies, simulate uncertainty, detect bias, infer responsibly, and communicate evidence.

Start first mission Assign to class

10/10operating gate

10units

30missions

8simulator modes

Day 1

Teach the idea, run the model, defend the evidence.

Students start with a visual walkthrough, then use one clean control change to produce evidence they can explain, revise, defend, and transfer.

statsphere

Data, Variables, And Displays: Explore

Explore variable type using data, variables, and displays.

Open mission

Student loop

One visible mathematical consequence per mission.

Learn the structure with a visual walkthrough.
Predict which control will change the model.
Run one clean test and inspect the consequence.
Explain the evidence in words, symbols, and context.
Revise, defend, and transfer to a new situation.

Representative missions

Course depth with simulator-backed evidence.

statsphere

Data, Variables, And Displays: Explore

Display choices can reveal patterns or distort them, changing the evidence story.

Try it

wordproblemengine

Sampling And Bias: Test

Biased sampling can create stable-looking estimates that are still wrong.

Try it

proofbuilder

Experimental Design: Defend

Randomization and control reduce confounding and strengthen causal interpretation.

Try it

statsphere

Random Variables And Distributions: Explore

Wrong distribution assumptions produce predictions that diverge from simulated evidence.

Try it

graphverse

Sampling Distributions And Confidence: Test

Increasing sample size narrows intervals while confidence level changes coverage.

Try it

bizcase

Hypothesis Tests: Defend

Changing alpha changes false alarm and missed signal risk, not the truth of the claim.

Try it

Course map

10 units with daily evidence loops.

Unit 1

Data, Variables, And Displays

How do we turn messy observations into useful, honest displays?

Data, Variables, And Displays: ExploreExplore variable type using data, variables, and displays.Data, Variables, And Displays: TestTest data display using data, variables, and displays.Data, Variables, And Displays: DefendDefend misleading scale using data, variables, and displays.

Mastery gate: Student chooses variables, display type, scale, and summary with clear justification.

Unit 2

Sampling And Bias

What makes data trustworthy before any calculation happens?

Sampling And Bias: ExploreExplore sampling method using sampling and bias.Sampling And Bias: TestTest selection bias using sampling and bias.Sampling And Bias: DefendDefend generalization using sampling and bias.

Mastery gate: Student identifies sampling method, bias risk, and generalizability limits.

Unit 3

Experimental Design

How does design allow stronger causal claims?

Experimental Design: ExploreExplore random assignment using experimental design.Experimental Design: TestTest control group using experimental design.Experimental Design: DefendDefend confounding using experimental design.

Mastery gate: Student designs treatment, control, random assignment, blocking, and blinding with causal limits.

Unit 4

Probability Models

How do probability rules model uncertainty without pretending to predict individuals?

Probability Models: ExploreExplore conditional probability using probability models.Probability Models: TestTest independence using probability models.Probability Models: DefendDefend simulation using probability models.

Mastery gate: Student uses probability rules, conditional probability, and simulation to defend uncertainty claims.

Unit 5

Random Variables And Distributions

How do distributions summarize possible outcomes and long-run behavior?

Random Variables And Distributions: ExploreExplore expected value using random variables and distributions.Random Variables And Distributions: TestTest binomial conditions using random variables and distributions.Random Variables And Distributions: DefendDefend normal model using random variables and distributions.

Mastery gate: Student chooses a distribution, interprets expected value, and checks assumptions.

Unit 6

Sampling Distributions And Confidence

How can samples vary but still support a reliable interval estimate?

Sampling Distributions And Confidence: ExploreExplore sampling distribution using sampling distributions and confidence.Sampling Distributions And Confidence: TestTest margin of error using sampling distributions and confidence.Sampling Distributions And Confidence: DefendDefend confidence interval using sampling distributions and confidence.

Mastery gate: Student explains sampling distribution, margin of error, confidence level, and interval interpretation.

Unit 7

Hypothesis Tests

How do we decide whether evidence is surprising under a null model?

Hypothesis Tests: ExploreExplore null model using hypothesis tests.Hypothesis Tests: TestTest p-value using hypothesis tests.Hypothesis Tests: DefendDefend Type I/II error using hypothesis tests.

Mastery gate: Student states hypotheses, checks conditions, interprets p-value, and makes a contextual decision.

Unit 8

Regression, Communication, And Ethics

How do statistical models become responsible decisions?

Regression, Communication, And Ethics: ExploreExplore regression using regression, communication, and ethics.Regression, Communication, And Ethics: TestTest residuals using regression, communication, and ethics.Regression, Communication, And Ethics: DefendDefend ethical inference using regression, communication, and ethics.

Mastery gate: Student interprets regression, residuals, limitations, uncertainty, and ethical communication.

Unit 9

Bayesian Updating And Decision Risk

How should beliefs change when new evidence arrives?

Bayesian Updating And Decision Risk: ExploreExplore prior belief using bayesian updating and decision risk.Bayesian Updating And Decision Risk: TestTest likelihood using bayesian updating and decision risk.Bayesian Updating And Decision Risk: DefendDefend posterior decision using bayesian updating and decision risk.

Mastery gate: Student updates prior belief with evidence, explains likelihood, and defends a decision under risk.

Unit 10

Multivariable Models And Responsible Prediction

How do we build useful predictive models without overclaiming what they prove?

Multivariable Models And Responsible Prediction: ExploreExplore multiple regression using multivariable models and responsible prediction.Multivariable Models And Responsible Prediction: TestTest validation using multivariable models and responsible prediction.Multivariable Models And Responsible Prediction: DefendDefend fairness limits using multivariable models and responsible prediction.

Mastery gate: Student compares predictors, interactions, residuals, validation split, and fairness/equity limits.

TeacherOS

Evidence becomes action.

Assign the next course mission to a class or misconception cluster.
Inspect TeacherOS evidence by concept, representation, and transfer.
Launch TeachProof practice for the hardest teaching move.
Share readable parent/district evidence without reducing learning to completion.

Family and district

Progress without reducing learning to completion.

What Statistics concept the student can explain
Where the student is confusing structure, procedure, or interpretation
The next best practice mission
Statistics mastery by unit
Misconception resolution time