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Content knowledge
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Students will be able to calculate theoretical and experimental probabilities for simple and compound events using sample spaces and trial data to determine likelihood. - calculate
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- I can calculate theoretical probabilities for simple events using a correctly defined sample space and list outcomes that match the event I am asked about.
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- I can calculate theoretical and experimental probabilities by running trials, recording results, and computing experimental frequencies, then comparing them to my theoretical probabilities for simple events.
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- I can calculate theoretical and experimental probabilities for compound events using appropriate event notation (such as “and/or” or complements) and expanded sample spaces, then use my trial data to check whether outcomes align with theory.
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- I can independently model and compute theoretical vs
- experimental probabilities for compound events using trial data robustly (including enough trials to justify estimates), and I can justify discrepancies by explaining how my sampling or assumptions affect likelihood.
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Content knowledge
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Students will be able to develop probability distributions for a random variable in a current-issue scenario to represent possible outcomes and their chances. - develop
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- I can define the random variable for my current-issue scenario and list the possible values it can take from a given sample space (e.g., outcomes I will model)
- I can assign theoretical probabilities to each outcome using clear rules from the scenario.
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- I can build a probability distribution for my random variable (table/graph/list) that matches my sample space, with each value paired to its theoretical probability
- I can check that my distribution is complete and that the probabilities are consistent with the scenario.
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- I can use my probability distribution to calculate and interpret expected value for a decision connected to my current issue (using an organized computation)
- I can explain how each probability influences the outcomes in my distribution and what the expected value means for making a choice.
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- I can develop and justify an accurate probability distribution for my random variable and refine my model when assumptions or evidence change
- I can compare results (e.g., expected value and alternative models) to support a fair, well-reasoned decision and clearly communicate how the distribution represents possible outcomes and their chances.
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Skill
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Students will be able to compute and interpret expected value from a probability distribution to evaluate decisions in a real-world context. - compute and interpret
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- I can compute expected value from a simple probability distribution by multiplying each outcome value by its theoretical probability and summing the results to reach one expected value.
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- I can compute expected value from a full probability distribution and explain what the expected value means in context (e.g., the long-run average or typical payoff for a random decision).
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- I can use expected value to compare at least two real-world decision options by calculating each option’s expected value from its probability model and interpreting which option is more favorable based on those values.
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- I can justify a recommendation using expected value by linking my probability distribution, calculations, and interpretation, and I can revise my decision after comparing my theoretical expected value to experimental results or updated evidence.
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Skill
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Students will be able to analyze fairness and strategy in decision situations using probability evidence to justify a recommendation. - analyze and justify
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- I can use a probability model to compare likely outcomes of two or more choices in a familiar scenario and make a basic recommendation based on which outcome is more probable
- I can show the theoretical probabilities (or frequencies from a small experiment) and connect them to my choice in my work.
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- I can analyze a decision situation by calculating probabilities for relevant outcomes and using expected value (or a comparable probability-based metric) to justify which strategy is fair and/or yields better results
- I can explain how my probabilities support my recommendation and revise my choice when the evidence changes.
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- I can compare competing strategies in a more complex decision context by building a probability distribution, calculating expected value, and analyzing trade-offs (risk vs
- reward) using probability evidence
- I can justify fairness by explaining how the model represents the random process and supports a recommendation that others could evaluate.
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- I can independently design and defend a probability-based recommendation for a current issue by selecting an appropriate random model, justifying assumptions, and using expected value and/or decision analysis to evaluate multiple strategies
- I can clearly communicate why the decision is fair, anticipate counterarguments about assumptions or uncertainty, and adjust my conclusion based on new evidence or feedback.
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Disposition
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Students will be able to select and defend a probability method that fits a current issue investigation by explaining why the method matches the question. - select and defend
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- I can choose a probability method that matches my current-issue question and explain the basic reasoning for my choice using one clear probability idea (such as randomness, sample space, or likelihood)
- I can show how my method connects to the outcomes I want to predict.
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- I can select a probability method for my current-issue investigation and defend it by linking the method to my specific question and the outcomes being modeled
- I can explain, with evidence from my calculations or models, why this method is appropriate for estimating or comparing probabilities.
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- I can justify my chosen probability method by explaining how it supports fair decision-making or strategy analysis for my current issue
- I can connect my model to theoretical and/or experimental probabilities and describe how it helps answer what is most likely and what expected outcomes suggest.
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- I can independently select and strongly defend a probability method that best fits my current-issue investigation, including why alternative methods would be less suitable
- I can clearly explain the assumptions behind my model, use expected value/decision logic to support my prediction, and revise or refine my method as my evidence changes.
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Disposition
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Students will be able to document anomalies, limitations, and revisions in their probability investigation to improve the honesty and quality of their conclusions. - document and revise
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- I can record when my experimental results do not match my theoretical probabilities by naming the specific anomalies and listing the possible reasons I notice from my lab process.
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- I can document limitations in my probability investigation (like small sample size or assumptions about outcomes) and explain how those limitations could affect the match between my predicted and observed probabilities.
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- I can revise my model and prediction using evidence by updating calculations, re-specifying assumptions, and describing exactly how my anomalies or limitations led to a change in my conclusion.
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- I can clearly justify my final conclusions by comparing theoretical vs
- experimental results, quantifying the impact of limitations, and explaining how my revisions improved the honesty, fairness, and credibility of my probability-based decision.
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