Unit 12 · 2 Weeks · 7 Lessons
Probability, Distributions & Statistical Inference
How do counting, probability models, distributions, and sampling support responsible conclusions under uncertainty?
Complete instructional sequence
Detailed Lessons
Lessons include objectives, formulas, concept development, worked examples, guided and independent practice, differentiated pathways, application, misconception analysis, mastery evidence, reflection, and local completion.
Fundamental Counting Principle, Permutations & Combinations
Use permutations when order matters and combinations when order does not. The Fundamental Counting Principle multiplies independent stage choices.
Open detailed lesson
Lesson 02Probability Rules, Complements & Unions
Complements, unions, intersections, and mutually exclusive events organize probability calculations. Probabilities must remain between 0 and 1.
Open detailed lesson
Lesson 03Conditional Probability, Independence & Bayes Reasoning
Conditional probability updates the sample space after information is known. Independence means P(A|B)=P(A), not merely that events are different.
Open detailed lesson
Lesson 04Binomial Experiments & Expected Value
A binomial model requires fixed n, two outcomes, constant p, and independent trials. Mean is np and standard deviation is √[np(1−p)].
Open detailed lesson
Lesson 05Normal Distributions, z-Scores & Percentiles
The normal model describes symmetric bell-shaped distributions. z-scores standardize distance from the mean, enabling percentile comparisons.
Open detailed lesson
Lesson 06Sampling, Bias, Margin of Error & Study Design
Sampling design, randomization, sample size, and response quality affect inference. Larger random samples reduce sampling variability but do not automatically remove systematic bias.
Open detailed lesson
Lesson 07Evaluating Statistical Claims & Communicating Uncertainty
Responsible statistical communication distinguishes observational studies from randomized experiments, reports uncertainty, and avoids misleading scales or selective summaries.
Open detailed lesson
Practice and evidence
Unit Resources
Foundation Practice
Prerequisite support, smaller steps, representation aids, and correction prompts.
Core Practice
Complete standards-level definitive-answer practice and explanation.
Extended Practice
Generalization, proof, parameter analysis, technology, and deeper modelling.
Unit Mastery Check
Fresh randomized questions with scoring and explanations.
Probability & Statistical Evidence Audit
Applied investigation with evidence, validation, limitations, and defense.
Family Guide
Plain-language overview, support questions, and evidence expectations.
Teacher Guide
Pacing, differentiation, assessment, misconceptions, and records.
Vocabulary Data
Core English terms with Spanish, French, Arabic, and Portuguese support.
Standards Map
Unit concepts and broad national/international alignment categories.