A complete 12th grade homeschool curriculum

1. Unit 1: Tragic Form and the Question of FaultThis is the whole year's foundation, built on one play: Oedipus Rex. Your child learns the vocabulary of Greek tragedy, hamartia (the flaw or error that leads to downfall), hubris, the chorus, catharsis, dramatic irony, and the shape of the plot itself (setup, complication, the turn, the disaster). The big idea: how Sophocles arranges what the audience knows versus what Oedipus knows is itself an argument about how much of the disaster is really his fault.9 skills ▸close ▾

   • Hamartia versus accident or villainyGiven a definition and two contrasting scenarios, distinguish hamartia from a simple accidental mistake and from deliberate villainy.
   • The chorus and audience distanceExplain how the chorus's odes function structurally to control audience emotional distance from Oedipus, rather than merely commenting on the action.
   • Dramatic irony and the knowledge gapClassify specific moments in Oedipus Rex as dramatic irony, verbal irony, or no irony, based on the gap between audience and character knowledge.
   • Timing the shepherd's testimonyInfer, from the play's sequencing of revelations, why Sophocles places the shepherd's testimony where he does rather than earlier or later.
   • Two views of catharsisCompare two rival claims about the purpose of catharsis (relief/purgation versus moral instruction) and evaluate which better accounts for a specific scene in the play.
   • Assigning blame for Oedipus's fallGenerate a specific, defensible thesis allocating responsibility for the catastrophe between Oedipus's choices and forces outside his control, using structural features as evidence.
   • Using hamartia beyond Greek tragedyApply the concept of hamartia to a character in a text never discussed in class (e.g., a short story or news profile of a real downfall) to determine whether hamartia is a defensible lens for that case.
   • Plot evidence versus structure evidenceCritique a peer's or a provided sample thesis for whether it treats plot events (what happened) as if they were structural evidence (how the text is built), and justify the judgment.
   • Tragic structure as an argumentGeneralize, beyond Oedipus Rex, a working definition of 'tragic structure as argument' that could predict what claim a DIFFERENT unread tragic structure is likely making about fault, based on where it places knowledge-gaps and reversals.
2. Unit 2: The Architecture of Argument: Ethos, Logos, Pathos, and the CounterargumentThis unit turns 'name the rhetorical appeal' from a worksheet exercise into something closer to real persuasion: why does the same appeal work on one audience and flop on another? Students read 4-6 real speeches and essays and learn to state a claim, its evidence, and the unstated assumption connecting them (the warrant), then build a counterargument-and-rebuttal paragraph where the opposing view has to be stated at full strength before it gets answered.9 skills ▸close ▾

   • Ethos, logos, and pathosGiven a short excerpt and its stated audience, identify which appeal (ethos, logos, or pathos) is doing the primary work and cite the textual feature that signals it.
   • The same appeal, different audiencesExplain why the same rhetorical appeal (e.g., an appeal to shared religious values) would succeed with one named historical audience and fail or backfire with a different named audience, citing specific features of each audience's values or knowledge.
   • Claim, evidence, and warrantDeconstruct a written argument into its claim, evidence, and warrant, and state the warrant explicitly when the text leaves it unstated.
   • Counterargument and rebuttal paragraphsConstruct a two-paragraph counterargument-and-rebuttal sequence for a claim of the student's own, in which the counterargument is stated in its strongest form (not a weakened version) before the rebuttal engages it.
   • Straw man, false dilemma, ad hominemGiven a paragraph containing a straw man, false dilemma, or ad hominem move, name the fallacy and explain specifically how it misrepresents or substitutes for the opposing position rather than engaging it.
   • Testing a counterargument's strengthCritique a classmate's draft counterargument paragraph by identifying whether it represents the objection in its strongest form and pointing to the specific phrase that weakens it, if any.
   • Analyzing an unfamiliar controversyAnalyze an unfamiliar contested claim and its opposing position (neither discussed in class) to determine which appeal each side is primarily relying on and evaluate which side's counterargument-handling is more rhetorically complete.
   • Argument structure in any genreGeneralize the claim-evidence-warrant-counterargument schema to evaluate a piece of persuasive writing from a domain not covered in this unit (e.g., an advertisement, a scientific op-ed, a legal brief excerpt) and justify why the schema does or does not transfer cleanly to that domain.
   • Core rhetoric vocabularyRecall the definitions of ethos, logos, and pathos and the terms claim, evidence, warrant, counterargument, and rebuttal with sufficient precision to use them correctly in analytic writing.
3. Unit 3: Shakespearean Tragedy: Interiority and Persuasion on StageSatire says one thing and means another, and the reader has to close the gap. This unit teaches that gap directly, literal claim versus real claim, how harsh the tone is (Juvenalian) versus how gentle (Horatian), the 'follow the premise to its absurd conclusion' move (reductio ad absurdum), and how to figure out the argument a satire never states outright. It also asks a separate question the humor can distract from: who is this joke actually aimed at, and who pays for it?9 skills ▸close ▾

   • Soliloquy and the Greek chorusGiven a soliloquy and the chorus's function from Antigone, state how each performs the structural job of revealing information the other characters do not have access to.
   • Tragic terms applied to HamletIdentify hamartia, dramatic irony, and catastrophe within a act of Hamlet using the definitions built in Unit 1.
   • Hamlet's hamartia inside his mindExplain how Hamlet's hamartia is reframed as a psychological trait (indecision, overthinking, corrosive doubt) rather than a single circumstantial error, using at least two soliloquies as evidence.
   • Dramatic irony in manipulation scenesClassify moments of dramatic irony in a persuasive scene by whether the audience's superior knowledge is about a fact, a motive, or an outcome.
   • Appeals in Antony's funeral speechAnalyze Antony's funeral oration to identify how ethos, logos, and pathos are sequenced to reverse a hostile crowd's position, citing specific lines for each appeal.
   • Admire or distrust Antony's rhetoricEvaluate whether the audience is meant to admire or distrust Antony's rhetoric, using textual evidence for both readings before committing to a position.
   • What an unseen soliloquy doesGiven an unfamiliar Shakespearean soliloquy not covered in class, determine whether it functions primarily to reveal hamartia, advance dramatic irony, or foreshadow catastrophe, and justify the choice with structural evidence.
   • Ordering appeals in a new speechGiven a persuasive speech from a play not studied in this unit (e.g., a monologue from Othello or Richard III), construct an argument for how its appeals are sequenced for its specific in-play audience, without teacher-provided appeal labels.
   • Soliloquy, speech, and what characters hideCompose a comparative essay arguing how the contrast between one soliloquy and one persuasive speech in the same play makes a claim about the gap between what a character knows and what they perform, anticipating and answering the strongest counter-reading.
4. Unit 4: Satire: Weaponized IronyThe same ethos/counterargument tools from Unit 2 now get applied to serious, high-stakes, non-ironic writing: the Declaration of Independence, Thoreau's 'Civil Disobedience,' and King's 'Letter from Birmingham Jail.' The question underneath: when a writer appeals to 'natural rights' or 'conscience,' is that an argument, or is it a premise being smuggled in as if it needs no defense? And is going to jail for breaking a law part of the argument itself, not just a consequence of it?9 skills ▸close ▾

   • Literal and actual claims in satireGiven a short satirical excerpt not previously seen in class, state the literal claim and the actual (ironic) claim in separate sentences and name the specific textual signal that marks the gap between them.
   • Three steps for analyzing ironyFollowing the teacher's complete worked example, identify the literal claim, actual claim, and textual signal in a short satirical excerpt using the same three-part structure just demonstrated.
   • Juvenalian and Horatian satire spectrumSort a set of six paired satirical excerpts along a Juvenalian-Horatian spectrum and justify each placement using tone-toward-target and severity-of-target's-real-world-harm as criteria, not the mere presence of exaggeration.
   • Reductio ad absurdum in satireTrace a reductio ad absurdum move in a satirical text by identifying the opponent's premise the text adopts, the logical step(s) it exaggerates, and the absurd conclusion it arrives at.
   • The counterargument hidden in satireGiven an unfamiliar satirical text and no prior discussion of it, reconstruct the implicit counterargument the text is building against its target's real-world defenders, before being shown the formal 'counterargument in satire' framework.
   • Power and target choice in satireGiven a satirical text's target choice, identify who holds power relative to that target and evaluate whether the satire's real object of attack is the powerful or the vulnerable, using textual evidence rather than personal reaction.
   • Analyzing a completely new satireAnalyze a satirical text unrelated to any text studied in this unit (a genuinely new author, era, and target) and explain how its irony and exaggeration build an implicit counterargument, applying the unit's analytic routine with no cue as to which concept applies.
   • Writing a full satire analysis essayWrite a rhetorical analysis essay that identifies a satirical text's literal claim versus actual claim, classifies its position on the Juvenalian-Horatian spectrum, traces its reductio move, and explains how it builds an implicit counterargument against its target's real-world defenders, integrating textual evidence throughout.
   • When exaggeration weakens satire's pointExplain how a satirical text's use of exaggeration could plausibly reduce a real audience's willingness to take the underlying real-world problem seriously, as a counter-consideration to the unit's claim that satire builds effective implicit argument.
5. Unit 5: The Rhetoric of Principle: Rights, Conscience, and Civil DisobedienceOne novel, usually Camus's The Stranger, becomes the meeting point for three questions the year has been building: fate versus choice (Unit 1), being real versus performing for others (Unit 3), and what you owe to something other than society (Unit 5). Before touching the novel, your child spends about a week learning four abstract terms (existence precedes essence, the absurd, bad faith, authenticity) using made-up, non-book examples first, this is deliberate; abstract philosophy lands better when it's explained plainly before it's applied to a hard text.9 skills ▸close ▾

   • Premise, evidence, conclusion in the DeclarationGiven a passage from the Declaration of Independence, identify which sentences function as premise (natural rights claims), which function as evidence (the list of grievances), and which function as the conclusion (the right and duty to alter or abolish government).
   • How the Declaration builds ethosExplain how the Declaration of Independence builds ethos in its opening paragraphs by appealing to self-evident truths and the 'opinions of mankind' rather than to the authors' personal authority.
   • Conscience versus higher lawCompare Thoreau's appeal to individual conscience with King's appeal to a moral 'higher law' that supersedes unjust human law, identifying what work each concept is doing that the other is not.
   • What critics actually said to KingReconstruct the strongest real historical objection to King's argument that was actually raised against him (by the white clergymen he addresses, or by contemporaries advocating patience/gradualism) rather than a manufactured strawman.
   • Testing King's answer about waitingEvaluate whether King's rebuttal to the 'wait/be patient' objection actually answers the objection on its own terms or reframes/evades it, citing specific textual evidence for the judgment.
   • Reading a new argument for resistanceGiven an unfamiliar short op-ed arguing for a specific act of civil disobedience or resistance not covered in class, identify the writer's central premise about rights or conscience, locate the strongest counterargument the writer addresses, and judge whether the rebuttal succeeds.
   • Argue for or against modern disobedienceGenerate an original argument for or against a specific, real, contemporary instance of civil disobedience, building ethos appropriate to the audience and constructing a rebuttal to that audience's most likely real objection.
   • Declaration and King on legal channelsCompare how the Declaration of Independence and King's Letter each handle the objection that the disobedient party should instead work within existing legal/political channels, explaining what each writer's choice of rebuttal reveals about their differing theories of when law loses legitimacy.
   • Choosing a thesis after weighing evidencePlan and draft a comparative essay establishing which of two textual comparisons (Declaration/Thoreau, Declaration/King, or Thoreau/King) best supports a defensible claim about how ethos and counterargument-handling differ, before committing to a thesis.
6. Unit 6: Existentialism and the Absurd: When No Authority HoldsFor the first time this year, your child runs the whole research process solo: pick a real contested issue, write a working research question, find at least five sources they chose (not handed to them) covering different views, judge those sources' credibility themselves, and be willing to change their thesis when a real counter-source pushes back on it. It ends with a research paper, a log of the objections they went looking for, and an oral defense where they have to say, out loud, where their own argument is weakest.8 skills ▸close ▾

   • Hamartia and bad faith comparedGiven the tragic concept of hamartia and the existentialist concept of bad faith applied to the same event, state what each position claims is responsible for a character's downfall.
   • Four key existentialist termsDefine 'existence precedes essence,' 'the absurd,' 'bad faith,' and 'authenticity' using the course's own worked examples (not the novel) and distinguish 'the absurd' from nihilism.
   • Authenticity and bad faith in actionClassify a character's action in a given passage of the novel as an instance of authenticity or bad faith, citing the specific textual signal for the choice.
   • The protagonist and authority over timeTrack how the protagonist's stance toward one specific authority (society, reason, religion, or the self) changes across three or more points in the novel, explaining what event or realization produces each change.
   • Telling nihilism from absurdismGiven an unfamiliar short absurdist text not read in class, identify whether it treats meaninglessness as nihilism or as absurdism-in-Camus's-sense and justify the identification from the text's own language.
   • Does the ending settle the conflictArgue whether the novel's ending resolves or refuses to resolve the individual-vs-authority tension, using evidence from at least two points in the novel and addressing the strongest counterreading.
   • Applying the four terms to new storiesGiven a new absurdist or existentialist narrative excerpt outside the course text set, predict which of the four core terms an analyst would most likely apply to a described character action and explain the reasoning.
   • Individual versus authority across the courseExplain how the course's individual-vs-authority question, first raised by the chorus in Unit 1 and reframed by civil disobedience in Unit 5, is answered differently by existentialism.
7. Unit 7: The Research Seminar: Building a Defensible PositionThe last unit teaches nothing new. A full contemporary novel is read alongside real-world speeches, op-eds, and at least one video or image-based argument, all on the novel's central real issue. The whole demand is deciding, on the fly and without being told, whether a given passage calls for structural analysis, rhetorical analysis, or counterargument-testing, and often more than one at once, then writing an essay that keeps all three straight and defending it out loud.10 skills ▸close ▾

   • Research questions versus debate promptsGiven a self-selected contested issue, generate a working research question and explain what evidence would count as an answer, distinguishing a researchable question from a yes/no opinion prompt.
   • Credibility checklist on a clear sourceGiven a source whose author, publishing body, and publication date are clearly and explicitly stated on the page (a scaffolded case matching the classroom worked examples), apply the four-part credibility checklist step by step to arrive at a strong / usable-with-caveats / unusable classification.
   • Credibility checklist on your own sourceApply a credibility-evaluation checklist (authorship, evidence base, funding/affiliation, currency) to a self-found source and classify it as strong, usable-with-caveats, or unusable for the paper.
   • Good sources can disagree with youExplain why a source that agrees with the student's initial claim can still be a weak source, and why a source that disagrees can still be a strong one, using two contrasting examples from their own search.
   • Hunting for the strongest objectionGiven their own working thesis, plan and execute a targeted search whose explicit goal is to find the strongest available objection to that thesis, not a source that supports it.
   • Synthesis versus summary of sourcesDistinguish synthesis, an account of how multiple disagreeing sources bear on one another and on the thesis, from summary-by-accumulation, in a paragraph that must use at least two sources that conflict.
   • Revising a thesis without giving upRevise a working thesis in response to a specific piece of counter-evidence and produce a written rationale explaining what changed and why the change is a strengthening rather than an abandonment of the argument.
   • Citing five kinds of sourcesCorrectly execute in-text citation and a Works Cited/References entry for at least five source types (book, periodical article, website, government/organization report, and one additional type) in a consistent citation style.
   • Planning research on a new claimGiven a novel contested claim never discussed in class (e.g., a local policy issue specific to the school or town), plan a five-source research strategy specifying what kind of source would be needed to establish credibility, find agreement, and find the strongest objection, without executing the search.
   • Naming your argument's weakest pointDuring an oral defense, respond to a question about the paper's weakest point by identifying it accurately and explaining what additional evidence would change the argument, rather than defending the paper as already complete.
8. Unit 8: Synthesis: The Novel in Public Argument9 skills ▸close ▾

   • Structural, rhetorical, or thematic readingGiven an unmarked passage from the course novel, identify whether the primary interpretive demand is structural (form-as-argument), rhetorical (appeal-based), or thematic (individual-vs-authority), and justify the choice.
   • How structure argues about responsibilityExplain how the novel's structural choice (e.g., unreliable narration, nonlinear timeline, frame narrative) advances a specific claim about who or what is responsible for the central conflict, using textual evidence.
   • Persuasive appeals in public argumentsClassify the dominant rhetorical appeal(s) in a public-argument text on the novel's central issue, cite the textual feature that signals it, and judge whether the appeal actually succeeds or undermines itself.
   • Novel and public argument comparedCompare how the novel and a public-argument text each frame responsibility for the same real-world issue, identifying where their claims agree, conflict, or talk past each other.
   • Writing a counterargument and rebuttalConstruct a counterargument-and-rebuttal paragraph that anticipates the strongest objection to a synthesis claim about the novel's ambiguity, using evidence from both the novel and a public-argument source.
   • Is the novel's ambiguity a strengthEvaluate whether the novel's refusal to resolve its central ambiguity strengthens or weakens its contribution to the public conversation on the issue, defending the judgment against a posed counterargument in real time.
   • Three lenses on a new pairingGiven a novel and public-argument pairing on an issue never discussed in class, apply the same three-lens routine (structural, rhetorical, thematic) independently to produce a defensible claim.
   • Key vocabulary from the whole courseRecall and correctly define at least 12 course-vocabulary terms (spanning tragedy, rhetoric, satire, existentialism) when cued by a mixed, non-blocked list.
   • Organizing a multi-source synthesis essayOrganize evidence from the novel and multiple public-argument sources into a single essay structure that keeps literary analysis, rhetorical analysis, and counterargument distinct yet mutually supporting.

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1. Unit 1: Functions as a Family of StructuresThis unit doesn't teach any new function type -- your child already met linear, quadratic, exponential, rational, and log functions in Algebra II. What's new is the skill of choosing among them: given a table of numbers or a real situation described in words, figuring out which family actually fits, by testing the underlying assumption (constant add, constant multiply, limited number of turning points, or a value that breaks the function) rather than just eyeballing the shape.9 skills ▸close ▾

   • Four tests for function familiesGiven a table, graph, or equation for an unfamiliar data set, execute the correct family-specific move (compute first differences, compute ratios, count roots, or check for a vertical asymptote) fluently and correctly on request.
   • Classifying messy data tablesClassify a data set presented as a table with unevenly spaced or noisy values into its most likely function family by selecting and running the appropriate structural test.
   • Telling look-alike graphs apartExplain, using two contrasted data sets that produce visually similar graphs over a limited window, which structural assumption (constant rate vs. constant ratio vs. bounded root count) each data set actually satisfies and why the other family's assumption fails it.
   • Matching stories to function familiesGiven a real-world scenario described only in words (no equation, table, or graph provided), infer which function family's structural assumption plausibly matches the described process and justify the inference by naming the real-world condition that corresponds to the mathematical assumption.
   • End behavior and real-world limitsState, for a given function family and a stated real-world domain restriction (e.g., time cannot be negative, population cannot be negative), what the family's end behavior predicts about the modeled quantity, and judge whether that prediction is physically plausible.
   • Undoing a process in wordsGiven a verbal description of a real multi-step process (e.g., a unit conversion or a multi-stage pricing rule), construct in words the sequence of steps that undoes the process in the correct reverse order, before writing any symbolic inverse.
   • Building an inverse functionGiven a novel two-step real process not used in instruction, construct the symbolic inverse function and verify it undoes a specific numeric example correctly.
   • Choosing and defending a function familyGiven three unfamiliar real data sets, select a function family for each, justify the choice by naming the structural assumption the data satisfies, identify a specific alternative family that was considered and rejected, and state what future data would falsify the chosen model.
   • Comparing how function families growCompare two function families' rate-of-change behavior (constant, linearly increasing, or multiplicatively increasing) by summarizing how each family's output changes as input increases across equal intervals.
2. Unit 2: Polynomial and Rational Functions: Structure and BehaviorThis unit takes the factoring and rational-expression skills your child already has and turns them into a prediction tool: given just the equation of a polynomial or rational function, predict the entire graph -- every zero, every asymptote, every hole -- before plotting a single point. Division of polynomials and the remainder theorem show up here as tools for finding zeros, not as separate arithmetic drills.10 skills ▸close ▾

   • Zeros that cross or bounceGiven a polynomial in factored form, state the multiplicity of each zero and predict whether the graph crosses or bounces at that zero.
   • End behavior from the leading termGiven the leading term of a polynomial (degree and sign of leading coefficient), state the end behavior of the function using correct limit-style notation (as x approaches +/- infinity).
   • Synthetic division and the remainder theoremApply synthetic division and the remainder theorem to determine whether a given linear expression is a factor of a polynomial and to find remaining factors.
   • Finding all zeros and sketchingGiven a higher-degree polynomial and one or more known rational zeros, find all remaining real zeros by successive division and factoring, then use those zeros and their multiplicities to sketch a complete graph without a calculator.
   • Why vertical asymptotes happenExplain, using the behavior of 1/(x-a) numerically for x-values approaching a from both sides, why division by an expression approaching zero produces unbounded output, and connect this to the definition of a vertical asymptote.
   • Holes versus vertical asymptotesGiven a rational function, factor numerator and denominator, cancel common factors, and correctly classify each remaining zero of the denominator as a vertical asymptote and each canceled factor's zero as a removable discontinuity (hole), including finding the hole's coordinates.
   • Horizontal asymptotes from degreesDetermine the horizontal asymptote (or absence of one) of a rational function by comparing the degrees of numerator and denominator and reasoning about end behavior via substitution of large x-values, rather than by rote application of a memorized rule.
   • Predicting a graph from its equationGiven only a function's algebraic equation (polynomial or rational, in a form not previously encountered), predict its complete graphical behavior, zeros with crossing/bounce behavior, end behavior, and any asymptotes/holes, entirely from structure, without graphing or a calculator, and justify each prediction using the specific structural feature that produces it.
   • Building rational functions from graph featuresConstruct a rational function equation that satisfies a specified combination of structural constraints (e.g., exactly one hole at a given x-value, one vertical asymptote, a specified horizontal asymptote), reasoning backward from graphical behavior to algebraic structure.
   • Naming function families in new settingsRetrieve and correctly classify a function's family (polynomial, rational, exponential, or other, based on Unit 1 vocabulary) when given an equation or graph, distinguishing it from the polynomial/rational structural features taught this unit.
3. Unit 3: Exponential and Logarithmic Functions: Growth, Decay, and InversionThis unit nails down the difference between constant-rate growth (polynomial) and constant-ratio growth (exponential), then builds the logarithm as the function that undoes an exponential. Your child already knows exponent rules and probably saw logs briefly before; the new work is deriving log properties from exponent rules instead of memorizing them, solving equations with the unknown in the exponent, and understanding where the number e comes from.11 skills ▸close ▾

   • Constant rate or constant ratioGiven a table of values, determine whether the underlying process has a constant additive rate (linear/polynomial) or a constant multiplicative ratio (exponential) and justify the classification using the table structure.
   • Why percent growth is exponentialExplain why a percent-growth context (e.g., population, investment) produces an exponential function rather than a linear one, referencing the constant-ratio structure.
   • Rewriting exponentials with new ratesExecute the algorithm for rewriting an exponential expression a·b^(ct) into an equivalent form revealing a different (e.g., monthly rather than annual) percent rate, using exponent rules.
   • The inverse of an exponentialGiven the graph and rule of an exponential function, construct its inverse function's graph and rule and explain why the inverse cannot be expressed using previously known algebraic operations (roots, polynomials, rational expressions).
   • Defining logarithms and changing formsRecall the definition of log_b(x) as the exponent to which b must be raised to produce x, and convert fluently between exponential and logarithmic form.
   • Where log properties come fromDerive the product, quotient, and power properties of logarithms from the corresponding exponent rules, rather than merely applying them.
   • Solving exponential and logarithmic equationsExecute multi-step procedures to solve exponential equations (unknown in exponent) using logarithms, and logarithmic equations using exponentiation, including checking for extraneous solutions.
   • Combining logs to solve equationsSolve exponential/logarithmic equations that require first combining multiple terms using log properties before isolating the variable, selecting the correct property sequence.
   • Continuous compounding and the number eExplain why continuous compounding produces the constant e, comparing discrete compounding at increasing frequency to the continuous limit.
   • Choosing exponential, logarithmic, or polynomial modelsGiven a real-world scenario never discussed in class (e.g., radioactive contamination spreading through an untaught decay-rate context, or a novel financial instrument), determine whether an exponential, logarithmic, or polynomial model applies and justify the choice using structural features of the data, not surface vocabulary.
   • Testing claimed logarithm shortcutsConstruct a counterexample or valid proof to evaluate a peer's or textbook's claimed logarithm 'shortcut' (e.g., log(a+b) = log a + log b) and generalize what structural feature of logs makes such shortcuts invalid.
4. Unit 4: The Unit Circle and Trigonometric FunctionsRight-triangle trig only works for angles between 0 and 90 degrees. This unit extends the idea using a circle: an angle becomes a rotation, and the point where that rotation lands gives you (cos θ, sin θ) directly as coordinates. That single move explains why sine and cosine can be negative, why they repeat, and why their graphs are smooth waves. From there your child builds sine, cosine, and tangent graphs from the circle itself, learns to shift and stretch them, and defines arcsine, arccosine, and arctangent as true inverse functions.11 skills ▸close ▾

   • Radians and arc lengthGiven an angle measure in degrees, convert to radians and vice versa, and explain radian measure as arc length on a unit circle.
   • Exact trig values without a calculatorState the exact sine, cosine, and tangent values for all unit circle angles that are multiples of π/6 and π/4, without a calculator.
   • Right triangles meet the unit circleExplain why the unit-circle definitions of sine and cosine agree with right-triangle definitions for acute angles but extend to angles beyond 0-90 degrees and to negative angles.
   • Reference angles and quadrant signsGiven an angle's reference angle and quadrant, determine the sign and exact value of its sine, cosine, or tangent using symmetry of the unit circle.
   • Building sine and cosine graphsSketch the graph of y = sin x or y = cos x directly from unit-circle coordinates, identifying period, midline, and key points without plotting from a table of decimal values.
   • Transforming sine and cosine graphsGiven values for amplitude, period, phase shift, and vertical shift, write and graph a transformed sine or cosine function, and given a graph, determine those four parameters.
   • Why tangent has asymptotesExplain why the tangent function has vertical asymptotes and a period of π, in terms of the ratio sin θ / cos θ on the unit circle.
   • Inverse trig functions and restricted domainsRestrict the domain of sine, cosine, and tangent to define arcsine, arccosine, and arctangent as functions, and evaluate them at exact values.
   • Modeling cycles with sine and cosineGiven a real-world periodic scenario (tide height, Ferris wheel height, sound wave) with a partial data description, construct a sine or cosine model and justify parameter choices against the context.
   • Matching functions to unfamiliar patternsGiven a novel periodic pattern in an unfamiliar context (e.g. a rotating machine part's coordinate over time, or an angle-vs-shadow-length relationship not resembling a standard textbook Ferris wheel), determine whether a sine, cosine, or non-periodic function best models it, and defend the choice using structural features rather than surface similarity.
   • Supplementary angles and circle symmetryDetermine algebraically why sin(π − x) = sin x and cos(π − x) = −cos x hold for every real x, using unit circle symmetry rather than checking specific numeric cases.
5. Unit 5: Trigonometric Identities and EquationsUnit 4 was about finding a trig value. This unit is about proving two trig expressions are secretly the same function (an identity), and separately, solving trig equations that are only true for specific angles. The identity-manipulation work reuses the same moves as simplifying rational expressions in Unit 2, now with sin, cos, and tan instead of polynomials.10 skills ▸close ▾

   • Using the Pythagorean identityGiven a value of sin θ (or cos θ) and the quadrant of θ, find the remaining trig function values by applying the Pythagorean identity sin^2θ + cos^2θ = 1.
   • Simplifying trig expressions with identitiesSimplify a given trigonometric expression (e.g., (1-cos^2x)/sin x) to a single term by substituting an equivalent Pythagorean or reciprocal identity, using the same expression-manipulation moves as simplifying rational expressions in Unit 2.
   • Proving identities versus solving equationsExplain why a valid identity-verification proof may only transform one side of the equation using known-equal substitutions, while a valid equation-solving proof may perform the same operation to both sides, and identify which situation a given problem is.
   • Verifying trig identities step by stepVerify a given trigonometric identity by producing a chain of algebraically equivalent expressions from one side to the other, using sum/difference, double-angle, or Pythagorean identities as needed, and justify each substitution step.
   • Double angle identities from sum formulasDerive the double-angle formula for cosine in the three equivalent forms (in terms of cos only, sin only, or both) starting from the sum formula cos(A+B), by substituting A = B.
   • Solving trig equations on an intervalSolve a trigonometric equation of the form a·trig(bx)=c over a specified restricted domain (e.g., [0, 2π)), finding all solutions.
   • General solutions to trig equationsSolve a trigonometric equation over all real numbers, expressing the complete solution set using the correct period-based general-solution notation (+2πk or +πk).
   • Using identities to solve mixed equationsGiven an unfamiliar trigonometric equation involving a squared term (e.g., 2sin^2x - cos x - 1 = 0), decide and justify which identity substitution transforms it into a solvable algebraic form, in a context not explicitly modeled in class.
   • Testing whether trig expressions are equalGiven two trigonometric expressions that are claimed to be equivalent, determine whether the claim is a true identity or false by testing strategically chosen values and, if true, construct a proof; if false, produce a counterexample.
   • Deriving half-angle identities from double anglesDerive the half-angle formulas for sine and cosine from the double-angle cosine identity by solving for cos^2(x) or sin^2(x) and substituting x/2, and determine the correct sign from the quadrant of the half-angle.
6. Unit 6: Vectors and Matrices: Representing Multi-Part QuantitiesTwo new ways to hold more than one number in a single object. Vectors carry a magnitude and a direction (used for velocity, force); matrices carry organized rows and columns of data. Vectors literally reuse the (cos θ, sin θ) coordinates from Unit 4 as their x- and y-parts. Matrices extend the 2-equation, 2-unknown systems your child already solved in Algebra II into a compact notation.11 skills ▸close ▾

   • Vectors as magnitude and directionGiven a directed line segment or a real-world description (velocity, force), state the vector's magnitude and direction and represent it with correct vector notation.
   • Vector components with sine and cosineResolve a vector given as magnitude and direction into horizontal and vertical (x, y) components using cos θ and sin θ.
   • Adding vectors and their magnitudesAdd two or more vectors both graphically (tip-to-tail) and algebraically (component-wise), and explain why the magnitude of the sum is generally not the sum of the magnitudes.
   • Finding the resultant force or velocityGiven a real-world scenario with two or more forces or velocities acting on an object (e.g., wind and airspeed, current and rowing), construct a vector model, compute the resultant, and interpret its magnitude and direction in context.
   • When a quantity needs a vectorGiven a completely novel multi-part-quantity scenario never framed as vectors during instruction (e.g., a recipe-scaling or ranking context with no direction language at all), determine whether a vector representation is appropriate and justify the decision using the definition of a vector.
   • Organizing data in matricesOrganize a multi-category data set (e.g., inventory across stores, scores across categories) into a matrix and identify entries by row and column position.
   • Matrix addition, subtraction, and scalingAdd, subtract, and scalar-multiply matrices, and compare these operations to the equivalent operations on vectors and real numbers to identify what stays the same and what changes.
   • Matrix multiplication and why order mattersMultiply two matrices where defined, and explain, using a constructed counterexample, why matrix multiplication is not commutative in general.
   • Determinants and invertible matricesCompute the determinant of a 2x2 and 3x3 matrix and use it to determine whether the matrix has a multiplicative inverse.
   • Solving linear systems with matricesSet up and solve a system of two or three linear equations using matrix methods (inverse-matrix or row-reduction), and verify the solution satisfies all original equations.
   • Turning new problems into matrix equationsGiven an unfamiliar multi-constraint scenario (e.g., a network of three interdependent prices/quantities never modeled during instruction), translate it into a matrix equation, solve it, and justify why a matrix approach was more efficient than solving the constraints one at a time.
7. Unit 7: Polar Coordinates and Parametric EquationsTwo more ways to describe the same curve. Polar coordinates locate a point by distance and angle from a center instead of by x and y. Parametric equations describe x and y as both depending on a hidden third variable, usually called t, often standing for time. This unit is as much about combining Units 4 and 6 as it is about new material -- the conversion formulas are literally the unit-circle coordinates, and motion problems use the vector-direction idea directly.8 skills ▸close ▾

   • Converting between rectangular and polar pointsGiven a point in rectangular coordinates, compute its polar coordinates (r, θ) using r = sqrt(x^2+y^2) and tan θ = y/x, and given a point in polar coordinates, compute its rectangular coordinates using x = r cos θ, y = r sin θ.
   • Many polar names for one pointExplain why a single point can be represented by more than one valid polar coordinate pair, using the periodicity of angle measurement and the meaning of negative r.
   • Reading polar equations to predict graphsGiven the equation of a common polar curve (circle, cardioid, or rose r = a cos(nθ)), predict qualitative features of its graph (does it pass through the pole, how many petals, symmetry) from the equation's coefficients without plotting every point.
   • Graphing curves from parametric equationsGiven a parametric pair x(t), y(t), generate a table of (t, x, y) values and use it to sketch the resulting curve, indicating direction of motion as t increases.
   • Choosing how to eliminate the parameterEliminate the parameter from a parametric pair to produce a rectangular equation, selecting substitution when one equation is invertible and the Pythagorean identity when the pair involves sine and cosine of the same argument.
   • Writing parametric equations for steady motionGiven a real-world description of motion with an initial position, direction, and constant rate (e.g. a plane's displacement), write a parametric model x(t), y(t) using vector-direction components from Unit 6.
   • Choosing polar or parametric formGiven two representations of the same curve, one polar, one parametric, both unfamiliar in exact form, decide and justify which representation is more efficient to convert to rectangular form or graph directly, based on the algebraic structure of each equation.
   • Switching equations between polar and rectangularConvert a simple rectangular equation of a line or circle (e.g. x^2+y^2=9, or y=x) into its polar equation form and vice versa, using substitution of the conversion identities.
8. Unit 8: Conics and an Introduction to LimitsThe last unit does two things that turn out to share an idea. First, conic sections (circles, parabolas, ellipses, hyperbolas) get defined by distance rules -- an ellipse is every point where the distance to two fixed points adds up to the same total -- rather than by a formula to memorize. Second, limits ask what a function's output approaches as the input gets closer and closer to some value, even if the function is never actually defined there. Both ideas are 'defined by approaching or relating, not by a formula you just plug into.'11 skills ▸close ▾

   • Circle equations and completing the squareGiven the center and radius of a circle, derive its standard-form equation using the distance formula/Pythagorean theorem, and given an equation in expanded form, complete the square to find center and radius.
   • Conic sections from slicing a coneExplain why every conic section (circle, ellipse, parabola, hyperbola) can be produced as a planar cross-section of a double cone, connecting the cross-section angle to which curve results.
   • Parabolas from a focus and directrixDerive the standard-form equation of a parabola from its focus-directrix definition (the set of points equidistant from a fixed point and a fixed line).
   • Ellipses and hyperbolas from two fociDerive the standard-form equation of an ellipse and of a hyperbola from their distance-sum / distance-difference definitions given the foci, and identify foci, vertices, and axes from a standard-form equation.
   • Eccentricity and the shape of conicsGiven eccentricity values and defining parameters, classify a conic by type and explain how eccentricity controls the shape's elongation, ranging continuously from circle through ellipse to parabola to hyperbola.
   • Conics in unfamiliar real situationsGiven a conic equation in a real-world modeling context not previously encountered (e.g. a satellite orbit, a whispering gallery, a comet's path), identify the conic type, extract relevant parameters, and answer a question about the physical situation.
   • Estimating limits with tables and graphsEstimate the value a function's output approaches as the input approaches a given value or infinity, using a table of successive values and using a graph, and represent that value using limit notation.
   • Limit versus actual function valueDistinguish between a function's limit at a point and its actual value at that point, and identify from a graph or table cases where a limit exists but the function is undefined or defined differently there (removable discontinuity).
   • Types of discontinuities and limitsGiven a novel piecewise or rational function not previously seen, determine algebraically or graphically whether a limit exists at a specified point, and if the function is discontinuous there, classify the discontinuity as removable or non-removable and justify the classification.
   • Rates of change over shrinking intervalsCompute the average rate of change of a function over progressively smaller intervals around a point and explain how this sequence of average rates is used to estimate an instantaneous rate of change as a limit.
   • Choosing conics or limits to modelGiven a real-world scenario described only verbally (e.g., a quantity whose behavior involves both a distance-defined boundary curve and a described rate of change near a critical moment), decide whether a conic model, a limit/rate argument, or both are needed, and justify the choice of representation.

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1. Unit 1: Describing Data: One Variable at a TimeThis is where all the vocabulary for the rest of the year gets built: distribution, shape, center, spread, standard deviation. Your child moves from just describing a plot in words to computing mean, median, mode, range, IQR, and standard deviation by hand, then z-scores and boxplots, then finally the same statistics in a spreadsheet on a bigger, real dataset. The big idea underneath all of it: every summary number throws away information, and choosing which one to report is a choice about what to hide.9 skills ▸close ▾

   • Mean, median, and mode by handGiven an ordered list of 8-10 numeric values, compute the mean, median, and mode by hand and state which, if any, are equal.
   • Range, IQR, and standard deviationGiven a raw dataset of 8-10 values, compute the range, interquartile range, and standard deviation by hand, showing the deviation-from-mean step explicitly.
   • How skew pulls the meanExplain why the mean and median diverge in a skewed distribution and which one is being pulled by which feature of the data.
   • Deciding whether to remove outliersClassify a given value in a dataset as an outlier or not, using a stated numeric or contextual criterion, and justify whether it should be reported or removed for a specific analytic purpose.
   • Using z scores to find positionCompute a z-score for a given value and interpret what it says about that value's position relative to the rest of the distribution, in the units of the original variable.
   • Why matching statistics can misleadGiven two datasets with identical mean and range but different shape, determine which additional statistic (median, IQR, or SD) reveals the difference and justify why the matching statistics failed to.
   • Describing an unfamiliar real datasetGiven a real public-dataset variable never encountered in class (e.g., a CDC BRFSS or ACS variable), select and compute an appropriate set of summary statistics, describe the distribution's shape/center/spread in writing, and defend the choice of statistics used.
   • Reading distribution shape from graphsClassify a given histogram, dotplot, or boxplot by shape (symmetric, skewed left, skewed right, uniform, bimodal) using visual features alone.
   • Building a boxplot by handConstruct a boxplot by hand from a five-number summary computed from raw data, correctly placing whiskers and the box relative to Q1, median, and Q3.
2. Unit 2: Relationships Between Two VariablesNow your child moves from describing one variable to describing how two variables move together, scatterplots, the correlation coefficient r, and a regression line, all computed by hand first. The unit's real teaching moment is a set of datasets (Anscombe-style) that all have the identical r but look completely different when plotted, proof that a single number can hide a lot.9 skills ▸close ▾

   • Describing associations in scatterplotsGiven a scatterplot of paired numeric data, describe the association using direction, form, and strength in words.
   • Computing the correlation coefficient rCompute the correlation coefficient r by hand on a small paired dataset (n=8-10) using the deviation-product formula.
   • Why r alone can misleadExplain why two datasets can share an identical correlation coefficient while representing very different underlying relationships (e.g., one linear and consistent, one driven by a single outlier, one curved).
   • Fitting and interpreting a regression lineFit a least-squares regression line by hand to a small paired dataset and interpret the slope and intercept in the context of the variables.
   • Interpolation versus extrapolation in predictionsGiven a regression equation and a new x-value, calculate and evaluate a prediction, classifying it as interpolation or extrapolation and stating the confidence warranted by that classification.
   • Checking linearity with residual plotsConstruct a residual plot from a regression line's residuals and use its pattern (or lack of pattern) to judge whether a linear model is appropriate for the data.
   • What r squared tells usInterpret the coefficient of determination (r-squared) as the proportion of variability in the response variable accounted for by the linear model, in the context of a specific pair of variables.
   • Judging linearity before calculating anythingGiven a completely unfamiliar pair of real-world variables and a scatterplot with no accompanying r or regression statistics, judge whether a linear model would be appropriate before any computation is performed, and justify the judgment from the shape of the cloud of points alone.
   • Analyzing real data and its limitsUsing a real, previously unseen paired dataset (e.g., a World Bank indicator pair not used in class) accessed via spreadsheet software, compute r, the regression line, and r-squared, and write an interpretation that names at least one thing the summary statistics conceal about the relationship.
3. Unit 3: Study Design: What a Result Does and Does Not License You to ClaimThis unit is a turn in the road: instead of asking 'how do I compute this,' it asks 'am I even allowed to conclude this, given how the data was collected.' It covers population vs. sample, the four sampling methods and the specific bias each one causes, observational studies vs. experiments, confounding variables, and why random assignment is the one thing that actually licenses a cause-and-effect claim.9 skills ▸close ▾

   • Population, sample, parameter, and statisticGiven a written research scenario, state whether the group described is the population or a sample, and identify the corresponding number described as a parameter or a statistic.
   • Spotting sampling methods from cue wordsGiven a sampling scenario that uses the same structural cue words practiced in the Day 3-4 worked examples (e.g., 'names drawn from a hat' for SRS, 'divided by grade level first, then randomly selected within each' for stratified, 'entire classrooms selected' for cluster, 'surveys whoever happens to walk by' for convenience), correctly apply the taught classification routine to label the method as simple random, stratified, cluster, or convenience.
   • Sampling methods and their biasesClassify a described sampling procedure as simple random, stratified, cluster, or convenience, and name the specific bias (if any) that procedure introduces.
   • Random assignment and causal claimsGiven two study summaries reporting the same correlation but differing in whether treatment was randomly assigned, explain why only one licenses a causal claim, connecting the presence or absence of random assignment to the possibility of confounding.
   • Finding confounding variables in studiesFor a described observational study, generate a specific confounding variable (not previously discussed in class) and justify why it plausibly affects both the explanatory and response variable.
   • How wording changes survey answersCompare two survey vignettes that ask 'the same' question with different wording and identify the specific wording feature responsible for the differing response patterns.
   • Finding the study behind the headlineGiven a real, previously unseen news article reporting a causal claim from data, determine from the body text whether the underlying study was observational or experimental, even when the headline's language implies causation regardless of design.
   • What a study really provesWrite a critique of a real news article's causal claim that states precisely what claim the study's actual design licenses, distinct from what the headline claims, integrating sampling method, study design, and at least one specific unresolved confounder into a single coherent judgment.
   • Sampling and assignment are separateGiven a scenario describing both the sampling method and the assignment method of a study, evaluate separately what the sampling method licenses (generalizability to the population) and what the assignment method licenses (a causal claim), rather than forming one combined judgment about whether the study is 'good.'
4. Unit 4: Probability as a Model for UncertaintyProbability here isn't formulas to memorize, it's a model for describing patterns in random processes over the long run. Your child moves from listing outcomes and applying addition/multiplication rules, to conditional probability and independence on real two-way tables, to random variables and their expected value, ending with simulation as a way to check theoretical probability against what actually happens when you run something many times.9 skills ▸close ▾

   • Sample spaces and eventsGiven a description of a random process (e.g., drawing two cards, rolling two dice), list the sample space and identify a specified event as a subset of it.
   • Probability of A or BCompute P(A or B) using the addition rule, correctly determining first whether A and B are mutually exclusive from a given scenario.
   • Checking independence with tablesDetermine whether two events described by a real two-way table are independent by comparing P(A) to P(A|B), and explain in writing what the comparison shows.
   • Expected value of a random variableGiven a probability distribution table for a discrete random variable, compute the expected value E(X) using summation notation and interpret it as a long-run average.
   • Standard deviation of a random variableCompute the standard deviation of a discrete random variable by hand and explain what a large versus small SD(X) implies about the variable's real-world behavior.
   • Estimating probability by simulationDesign and run a hand or spreadsheet simulation (using random digits or RAND) to estimate the probability of a compound event, and compare the simulated relative frequency to the theoretical probability computed by rule.
   • Independence with three or more variablesGiven a completely novel real-world scenario involving three or more categorical variables (not two-way, not modeled in class), determine what additional information would be required to assess whether any pair of variables is independent, without being told which variables to compare.
   • What probability says about one trialCritique a media or textbook claim that treats a single trial's outcome as evidence against (or for) a stated long-run probability (e.g., 'the model said 70% chance and it didn't happen, so the model was wrong'), using the distinction between single-trial outcomes and long-run relative frequency.
   • The definition of independent eventsRecall the definition of independent events (P(A and B) = P(A)·P(B), equivalently P(A|B) = P(A)) from memory without reference to a specific scenario.
5. Unit 5: Modeling Randomness: Binomial and Normal DistributionsTwo specific, reusable models, plus the judgment to know which one (if either) fits a given situation. The first third builds the binomial distribution by hand for small numbers of trials. The rest builds the normal distribution as a model for continuous measurements, reusing Unit 1's z-scores and standard deviation, working up through the 68-95-99.7 rule to spreadsheet tools (NORM.DIST) for any proportion, and ending with the harder skill of checking whether a normal model even fits a given dataset in the first place.10 skills ▸close ▾

   • The four binomial conditionsGiven a description of a random process, state whether it meets the four binomial conditions (fixed number of trials, two outcomes, constant probability of success, independent trials) and identify which condition fails when it does not.
   • The binomial probability formulaCompute the probability of exactly k successes in n binomial trials by hand using the binomial probability formula, for n ≤ 6.
   • Binomial mean and standard deviationCalculate the mean (np) and standard deviation (√(np(1-p))) of a binomial random variable and explain what each measures in terms of repeated trials of the process.
   • Why many trials make bell shapesExplain, using the shape of overlaid binomial histograms for increasing n, why a sum of many small independent random effects tends toward a bell shape regardless of the shape of the individual trials.
   • The empirical rule for normal curvesApply the 68-95-99.7 rule to estimate the percentage of a normally distributed population falling within 1, 2, or 3 standard deviations of the mean, or between two given values that fall exactly on those boundaries.
   • Standardizing values into z scoresStandardize a raw score from an approximately normal distribution into a z-score and interpret it as a distance in standard deviations from the mean, including for values that do not fall on the 68-95-99.7 boundaries.
   • Normal proportions using tables and spreadsheetsUse a standard normal table or the spreadsheet function NORM.DIST to find the proportion of a normal distribution above, below, or between arbitrary values, and use NORM.INV (or table lookup in reverse) to find a value corresponding to a given proportion.
   • Judging when a normal model fitsGiven a real, unfamiliar dataset's histogram and summary statistics, judge whether a normal model is an appropriate simplification, and justify the judgment by citing specific features of the shape (symmetry, tails, number of modes, outliers) that support or undermine the fit.
   • Binomial, normal, or neitherGiven a short scenario, decide whether a binomial model, a normal model, or neither is the appropriate model, and justify the choice by naming which defining feature of the scenario drove the decision.
   • Normal model uses and limitsGiven a novel measurement context outside any taught example (e.g., a manufacturing tolerance, a biological measurement), design a plan for whether and how a normal model would be used to answer a specific question, and state what additional information would be needed before trusting that plan.
6. Unit 6: Sampling Distributions: The Hinge of InferenceThis is the unit everything else in the second half of the course depends on. Your child first generates, by hand and in a spreadsheet, the fact that a sample statistic (like an average) changes from sample to sample and that this variation has its own shape, before the Central Limit Theorem is even named. Only after they've seen it happen is the rule stated. The unit also uses a side-by-side comparison of a genuinely random simulation and a deliberately biased one to nail down that more data reduces spread but never fixes bias.9 skills ▸close ▾

   • Sample means from a small populationGiven a small finite population (4-6 values) and a fixed sample size, list every possible simple random sample of that size, compute the sample mean for each, and state how many distinct samples produce each possible mean value.
   • Population versus sampling distributionsExplain why a sample statistic computed from a random sample is itself a random variable with its own distribution, distinguishing this distribution from the distribution of the original population data.
   • Predicting how sample means pile upPredict, before instruction, what will happen to the shape, center, and spread of an accumulating dot-plot of sample means as the number of simulation trials and the sample size per trial both increase, and revise the prediction using evidence from the simulation.
   • Central Limit Theorem and conditionsState the Central Limit Theorem in words, specifying the two conditions (large enough n; independent random samples) under which the sampling distribution of a sample mean is approximately normal regardless of population shape.
   • Standard error for means and proportionsCompute the standard error of a sample mean given a population standard deviation and sample size, and of a sample proportion given a population proportion and sample size, using the square-root-of-n formulas.
   • When the Central Limit Theorem appliesGiven a description of a real sampling scenario, judge whether a reported statistic's sampling distribution can be assumed approximately normal, and identify what additional information (n, population shape, independence) would be needed to justify that judgment.
   • Bias versus variabilityExplain, using a specific biased-versus-unbiased sampling comparison, why increasing sample size reduces the spread of a sampling distribution but does not correct a sampling method's bias.
   • Classifying real sampling flawsGiven a novel real-world scenario (e.g., a nonresponse-heavy online poll, or a convenience-sample health study reported in the news) never discussed in class, identify whether the described flaw would primarily inflate the sampling distribution's spread, shift its center, or both, and justify the classification.
   • Building a sampling distribution in spreadsheetsDesign and run a spreadsheet simulation that draws repeated random samples of a specified size from a real dataset treated as a population, computes the sample statistic each time, and produces an empirical sampling distribution to compare against the CLT's shape/center/spread predictions.
7. Unit 7: Inference for One and Two GroupsThis is where sampling variability (Unit 6) becomes the actual machinery of drawing conclusions. Your child builds confidence intervals and hypothesis tests for one and two groups, by hand on small data first, then by spreadsheet. The core idea running through the whole unit: a p-value or confidence interval tells you how surprising your data would be under an assumed model, it is not a verdict on truth, and mixing those two up is an error professionals make constantly, not just students.10 skills ▸close ▾

   • Writing null and alternative hypothesesState, from a written research question, the correct null and alternative hypotheses in symbols and in words.
   • Confidence intervals for proportions and meansCompute a one-sample confidence interval for a proportion or a mean by hand from raw data (n=8-12), then reproduce the same interval using spreadsheet functions.
   • What changes the margin of errorExplain how each of confidence level, sample size, and sample variability changes the margin of error, holding the other two fixed.
   • What a confidence interval really meansGiven a confidence interval and its stated confidence level, distinguish a correct long-run interpretation of the interval from a common incorrect probability-of-the-parameter interpretation.
   • Running a full hypothesis testCarry out a complete one-sample or two-sample hypothesis test (t-test or proportion z-test) on small raw data, including stating hypotheses, checking conditions, computing the test statistic and p-value, and stating a conclusion in context.
   • Choosing a proportion or mean testGiven a new research context not matched to any lesson by date or label, decide whether the appropriate procedure is a one- or two-sample, proportion or mean test, and justify the choice from the structure of the variables and design.
   • Type I and Type II errorsExplain, in a specific scenario, what a Type I error and a Type II error would each look like in context, and why lowering one generally raises the other for a fixed sample size.
   • Misreading p-values and confidence intervalsGiven a student-written or media statement interpreting a p-value or confidence interval, identify which specific documented misinterpretation it commits and rewrite it correctly.
   • Comparing two groups with real dataAnalyze a real two-group dataset (e.g., a GSS attitude comparison) to determine whether an observed difference is statistically significant, whether it is practically important, and what the result does and does not establish about causation.
   • The shared formula behind every testRecall the defining formula elements (test statistic = (statistic - null value) / standard error) common to every hypothesis test in the unit.
8. Unit 8: Extending Inference and the Capstone StudyThe last new technique of the course, the chi-square test for categorical data, plus a framework for choosing among every inference tool met since Unit 6. Then, for the last two and a half weeks, the capstone: your child designs an original study or pulls together real public data, collects or retrieves it, picks and justifies a procedure, computes part of it by hand and the rest by spreadsheet, and writes and defends a report on what the results do and don't prove.8 skills ▸close ▾

   • Computing the chi-square statisticGiven a two-way frequency table of observed counts, compute expected counts under independence and a chi-square test statistic by hand, matching the row-total-times-column-total-over-grand-total formula.
   • Independence versus goodness of fitExplain why the chi-square test for independence and the chi-square goodness-of-fit test answer different questions (association between two categorical variables vs. fit of one categorical variable to a hypothesized distribution), using the same test statistic formula for both.
   • Choosing among all inference proceduresGiven an unfamiliar research scenario with a data structure (one sample vs. two, categorical vs. quantitative, one variable vs. two), select and justify the single correct inference procedure from the full set met in Units 6-8 using a decision framework.
   • Significant results and causal claimsGiven a novel, real public-health or social-science report (not used in instruction) that presents a statistically significant result, identify what the reported statistic does and does not license the reader to claim about causation, generalizability, and practical importance.
   • Designing your own studyFormulate an original, testable research question and a data-collection or dataset-selection plan that names the sampling or experimental design and at least one specific safeguard against a bias named in Unit 3 (e.g., confounding, non-response, voluntary-response sampling).
   • Analyzing your own study dataExecute the full inference procedure appropriate to their own capstone data (compute by hand for a representative subset, then reproduce for the complete dataset using spreadsheet functions), matching the hand and spreadsheet results within rounding error.
   • Limits of your own studyWrite an explicit, specific statement of the limitations of their own capstone conclusion, identifying at least one threat to the validity of their causal or generalizability claim that is particular to their own study design (not a generic disclaimer).
   • Degrees of freedom for chi-squareGiven a two-way table already set up with observed and expected counts, recall which row of a chi-square distribution table (which degrees of freedom) applies, using the (rows-1)(columns-1) rule.

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1. Unit 1: Systems, Energy Flow, and Biogeochemical CyclesThis unit is the quantitative backbone of the whole year. Your child learns that energy moves through a food web in one direction and mostly dissipates as heat at each step (roughly 90% lost per level), while matter cycles endlessly through living things, rock, water, and air. They move from naming things (producer, consumer, decomposer) to actually measuring them, estimating real biomass in a plot outside and predicting energy available higher up the food chain.8 skills ▸close ▾

   • The 10% energy ruleGiven a food chain with population counts or biomass at each level, calculate the energy or biomass available at the next trophic level using the 10% transfer rule.
   • Why energy is lost between levelsExplain why approximately 90% of energy is lost, rather than passed on, at each trophic transfer, citing metabolism, movement, and heat loss as mechanisms.
   • Biomass pyramids and energy pyramidsDifferentiate biomass pyramids from energy pyramids, identifying the specific ecosystem condition (e.g., aquatic systems with fast-turnover producers) under which a biomass pyramid can appear inverted while the energy pyramid does not.
   • Estimating biomass from field samplesGiven real or simulated plot-sampling data (plant counts, dry mass estimates by species/area), estimate total producer biomass per square meter and identify sources of sampling error.
   • Mapping a cycle and its bottleneckConstruct a labeled diagram of the carbon or nitrogen cycle that connects at least four reservoirs and processes and explains one bottleneck (a process that limits flow rate) as a causal constraint on the whole cycle, not just a labeled stage.
   • Comparing GPP and NPPCompare gross primary productivity (GPP) and net primary productivity (NPP) for two ecosystems with different respiration rates, and infer which ecosystem has more energy available to higher trophic levels.
   • Applying energy rules to new systemsGiven a novel biome or engineered system never discussed in class (e.g., an aquaponics tank or a Martian greenhouse habitat design), predict where the energy-transfer and matter-cycling constraints taught in this unit would create the tightest bottleneck, and justify the prediction using the 10% rule and cycle mechanisms.
   • Testing a food web claimCritique a claim such as 'a food web can support one more predator species with no other change' by evaluating whether the claim is consistent with the 10% rule and available biomass data.
2. Unit 2: Population, Consumption, and Carrying CapacityThis unit takes Unit 1's idea that ecosystems have real limits and turns it into math that predicts when a population will outgrow what its system can support. Then it complicates that picture: your child learns that a bigger population doesn't automatically mean bigger environmental impact, consumption per person matters just as much, sometimes more.8 skills ▸close ▾

   • Spotting exponential and logistic growthGiven a dataset of population counts over time for an unfamiliar species, determine whether the data follow an exponential or logistic pattern and identify the specific data point where growth rate changes, if any.
   • Calculating exponential growthExecute the exponential growth calculation (N_t = N_0 * e^(rt)) to predict a future population size given an initial population, growth rate, and time interval.
   • Why growth slows near capacityExplain why a population's growth rate slows as it approaches carrying capacity, using the concept of density-dependent limiting factors.
   • Population and consumption togetherGiven population and per-capita consumption data for two contrasting regions (one high-population/low-consumption, one lower-population/high-consumption), compare their total environmental impact and identify which variable, population or affluence/technology, is doing more work in each case.
   • The IPAT impact equationImplement the IPAT identity (Impact = Population x Affluence x Technology) to calculate and compare total environmental impact across two or more regions or scenarios with different population, affluence, and technology values.
   • What ecological footprint leaves outCritique a published claim that cites ecological footprint or a similar single-number sustainability metric, identifying at least two categories of environmental impact the metric does not capture.
   • Applying capacity and IPAT to resourcesGiven a completely unfamiliar resource-consuming system outside of population ecology (e.g., a groundwater aquifer under municipal withdrawal, or a fishery under harvest quotas), apply the logistic growth/carrying-capacity model and the IPAT-style decomposition to argue whether the system is approaching, at, or in overshoot of its capacity, and whether the larger driver is extraction rate or number of users.
   • Arguing from growth, limits, and impactGiven a real regional dataset (the summative task), construct a written argument integrating a fitted growth curve, an identified limiting factor, and an IPAT-based claim about whether population or consumption is the larger driver of impact in that specific region.
3. Unit 3: The Greenhouse Effect and the Carbon Cycle PerturbedThis unit explains the greenhouse effect as an actual physical mechanism, specific gas molecules absorbing and re-emitting infrared radiation, instead of the vague 'trapping heat like a blanket' version most people carry around. Then it uses that mechanism to make sense of two real datasets: the Keeling curve (CO2 rising over decades) and ice-core records going back 800,000 years.10 skills ▸close ▾

   • Incoming and outgoing radiation bandsGiven a diagram of the electromagnetic spectrum labeled with wavelength bands, identify which band corresponds to incoming solar radiation and which corresponds to outgoing radiation from Earth's surface.
   • Why greenhouse gases absorb infraredExplain why CO2, CH4, and H2O vapor absorb outgoing infrared radiation while N2 and O2 do not, using molecular structure as the mechanism.
   • Why Earth is warmer than predictedUsing the contrasting cases of a bare-rock planet with no atmosphere versus Earth's actual measured surface temperature, infer that an additional energy-retaining mechanism must be operating on Earth.
   • Keeling curve seasons and trendRead the Keeling curve to distinguish the annual seasonal oscillation (biological carbon uptake/release) from the multi-decade upward trend (net atmospheric accumulation).
   • Ice cores and the Keeling curveCompare the ice-core CO2/temperature record with the Keeling curve to determine which time periods in the combined record show natural variation and which show a post-industrial pattern inconsistent with the prior 800,000-year range.
   • Positive and negative climate feedbacksGiven a description of a specific feedback process (ice-albedo, water-vapor, or cloud feedback), classify it as amplifying (positive) or dampening (negative) the initial warming and state the boundary condition under which the loop changes or stops.
   • From fossil fuels to warmingConstruct a mechanistic causal chain connecting fossil fuel combustion, atmospheric CO2 concentration, radiative forcing, and measured global temperature, explicitly stating what physical relationship connects each pair of steps.
   • What would disprove the CO2 mechanismState a specific, measurable observation in atmospheric or paleoclimate data that would falsify the claim that rising CO2 causes the observed warming, and explain why that observation would contradict the mechanism rather than merely fail to support it.
   • Greenhouse effect on a new planetGiven an unfamiliar planetary scenario (e.g., a planet with a much thicker or thinner CO2 atmosphere than Earth, or one with no water vapor feedback), predict the qualitative direction and reason about the relative magnitude of its greenhouse effect compared to Earth's.
   • Mechanism claims and policy claimsDistinguish a scientific claim about mechanism ('CO2 causes warming because it absorbs and re-emits infrared radiation') from a claim about magnitude or policy ('we must cut emissions by X% by Y date'), recognizing that disputing the second does not require disputing the first.
4. Unit 4: Evidence, Attribution, and Climate DataThis unit is about method, not new climate facts. It teaches the actual four-part test scientists use before saying 'this specific event was caused by human-driven warming': a stated mechanism, confounders considered and ruled out, at least two independent lines of evidence, and a confidence level that matches how specific the claim is.9 skills ▸close ▾

   • How the greenhouse effect worksState the physical mechanism of the greenhouse effect (radiative forcing) taught in Unit 3, without re-derivation.
   • Weather versus climateDifferentiate a weather observation from a climate observation given a described event (e.g., 'record cold week in Chicago' vs. '30-year warming trend in Chicago').
   • Proxy data as indirect evidenceExplain how a proxy dataset (ice core, tree ring, or coral record) provides indirect evidence of past temperature, identifying the physical or biological relationship the proxy depends on.
   • Testing climate models against historyEvaluate whether a climate model has been adequately validated by comparing its hindcast output to the historical instrument record and calculating the size of the residual.
   • Causation versus correlation in climateGiven two attribution claims about the same general phenomenon (one well-supported by multiple independent lines of evidence, one supported by a single correlation), identify what specific additional evidence separates the defensible claim from the merely plausible one.
   • Building a climate attribution argumentConstruct a complete attribution argument for a specific observed climate-related event, stating the proposed mechanism, at least one confounder considered and how it was ruled out, and at least two independent lines of evidence.
   • Confidence language for climate claimsAssign and justify an appropriate confidence level (using IPCC-style likelihood language) to a specific attribution claim, distinguishing the confidence appropriate to the general phenomenon from the confidence appropriate to a specific regional or single-event claim.
   • Judging a new attribution claimGiven a contested real-world attribution claim never discussed in class (e.g., a specific claim about a named recent extreme-weather event not covered in the unit), write an evidence-based argument rating confidence and citing at least two independent data sources, applying the full attribution framework without a provided graphic organizer.
   • Critiquing an attribution argumentCritique a peer's or a published source's attribution argument by identifying which required structural element (mechanism, confounder ruled out, independent evidence, or proportionate confidence level) is missing or weak, and explain why its absence weakens the argument's defensibility.
5. Unit 5: Biodiversity Loss and Ecosystem StabilityThis unit looks at how ecosystems absorb damage up to a point, and what happens past that point, one species disappearing can cascade through the energy pathways from Unit 1. Your child uses Unit 4's attribution method to figure out, given a real local decline, which of several competing stressors (habitat loss, climate, invasive species) actually explains it.9 skills ▸close ▾

   • Trophic cascades after keystone removalStudents trace the direct sequence of population changes across trophic levels that follows the removal of a keystone predator from a given food web diagram.
   • Why keystone species matter so muchStudents explain why removing a keystone species produces disproportionate ecosystem change while removing a redundant mid-level species does not, citing the structural difference between the two cases.
   • Tipping points in stress graphsGiven a graph of an ecological indicator against increasing stress with a nonlinear, delayed decline, students identify the region representing an undetected approach to a threshold and state what an early-warning indicator would need to show.
   • Fragmentation, climate, or invasive speciesStudents distinguish habitat fragmentation, climate stress, and invasive species as competing candidate explanations for a described population decline, identifying which observed evidence is consistent with each.
   • Quadrat and point count surveysStudents collect a species-count dataset from a local site using quadrat sampling or point-count method, correctly following the standardized procedure.
   • Arguing which stressor caused declineStudents construct a written argument identifying which of 2-3 candidate stressors best explains an observed local species decline, naming a mechanism and explicitly ruling out the less-supported alternatives using timing and evidence.
   • Comparing local counts to baselinesStudents compare their local species-count data to regional historical baseline data to determine whether an observed count constitutes a meaningful decline, an increase, or is within normal fluctuation.
   • Judging a new conservation planStudents evaluate whether a novel proposed conservation intervention (not discussed in class) would plausibly restore resilience to a described degraded ecosystem, given its cascade structure and threshold position.
   • Background extinction rate versus todayStudents recall the definition of background extinction rate and state how current estimated extinction rates compare to it in order of magnitude.
6. Unit 6: Water and Land: Pollution PathwaysThis unit treats pollution as a disruption of the water and nitrogen cycles from Unit 1, pollutants travel along traceable paths, not appear from nowhere. Your child learns to trace contamination using a source-pathway-receptor model, understands eutrophication (nutrient overload in water) as a threshold problem with a delay before visible symptoms, and runs a real water-quality test on a local water source.9 skills ▸close ▾

   • The nitrogen cycle in a watershedGiven a watershed diagram with a labeled fertilizer application area, storm drain, and downstream pond, students correctly identify which cycle process (fixation, nitrification, runoff, denitrification) each stage represents, matching the labels used in the Unit 1 nitrogen cycle diagram.
   • Point source versus nonpoint pollutionStudents classify a set of 8-10 real-world pollution scenarios (a factory discharge pipe, agricultural runoff from multiple farms, a leaking septic tank, urban street runoff, a wastewater treatment outfall) as point source or nonpoint source, justifying each classification by whether a single identifiable discharge location exists.
   • Tracing a new contamination scenarioGiven a new, previously unseen contamination scenario (e.g., a chemical spill upstream of a municipal water intake), students construct a complete source-pathway-receptor chain, explaining the mechanism by which the pollutant travels from source to receptor and citing what would need to be true for that pathway to actually connect them.
   • Why eutrophication shows up lateStudents explain why a lake showing no visible algal bloom in year 1 of a nutrient-loading dataset can still cross a eutrophication threshold by year 4, using the concept of a limiting nutrient and cumulative loading, without relying on visible symptoms as the only evidence of change.
   • Bioaccumulation versus biomagnificationGiven paired data on a single fish's tissue mercury concentration over its lifetime and a four-level food chain's mercury concentration at one point in time, students differentiate which case is bioaccumulation and which is biomagnification, identifying which axis (time vs. trophic position) distinguishes them.
   • Same water result, different limitsStudents interpret a single numeric water-quality result (e.g., nitrate at 8 mg/L) against two different stated reference thresholds (EPA drinking water MCL and a documented ecological eutrophication threshold) and determine which threshold is relevant given a stated receptor, explaining why the same number yields different verdicts.
   • Testing pH, turbidity, and nitrateStudents correctly execute pH, turbidity, and nitrate test-strip procedures on a water sample, recording results with correct units and comparing their technique against the manufacturer's reference color chart.
   • Tracing and fixing water pollutionUsing their own collected water-quality data and a locally plausible geographic context, students construct and justify a complete, connected source-pathway-receptor argument for any anomalous reading, and propose one remediation action along with at least one cost it would impose and on whom.
   • Causal chains versus lists of factsStudents critique a peer's draft source-pathway-receptor chain, identifying whether each link is a genuine causal connection or a restated fact, and write one specific revision suggestion referencing the missing or weak link.
7. Unit 7: Air Quality, Toxicology, and Distributed HarmThis unit takes the source-pathway-receptor model from Unit 6 and moves it into the air, where wind and temperature layers (inversions) change who actually breathes a pollutant, and where individual differences (age, indoor time) change how much harm the same dose does. It ends with a comparative case using real public air-sensor data for two nearby locations.8 skills ▸close ▾

   • Primary and secondary air pollutantsClassify a given air pollutant scenario as primary or secondary based on whether it is emitted directly or formed through atmospheric reaction.
   • How inversion layers trap pollutantsExplain how an inversion layer changes pollutant concentration at ground level compared to normal atmospheric mixing conditions.
   • Threshold and linear dose response modelsInterpret a dose-response curve to determine whether it better fits a threshold or a no-threshold (linear) model for a given pollutant-outcome pair.
   • Comparing dose response curvesCompare two dose-response curves for different pollutants to explain why the same numeric exposure level can carry different levels of risk.
   • Tracing air pollution with sensor dataConstruct a causal chain (source to pathway to receptor) for a real air pollutant using public sensor data for a specific, previously unexamined location.
   • Does dose response evidence prove harmEvaluate whether a stated health-outcome claim about a pollutant is supported by the available dose-response evidence or relies on correlation alone.
   • Pollution exposure across different groupsAnalyze public sensor and demographic data for two locations to identify whether exposure to a pollutant is distributed disproportionately across groups.
   • Writing a full pollution case briefGenerate a written case brief that connects pollutant transport pathway, dose-response evidence, and disproportionate exposure into a single causal argument for two real, previously unexamined locations.
8. Unit 8: Capstone: Energy Systems and Tradeoff AnalysisThis closing unit asks your child to combine four things they've built all year, energy-return math from Unit 1, carbon intensity and confidence levels from Units 3/4, demand forecasting from Unit 2, and who-bears-the-cost thinking from Units 6/7, into one real project: comparing three or more actual energy sources for a real local or regional decision. Almost nothing here is brand-new content; it's mostly research, drafting, peer review, and a final presentation.10 skills ▸close ▾

   • Energy return on energy investedGiven a fuel source's energy output and the energy cost of extracting/processing/delivering it, calculate its EROEI and correctly identify which value belongs in the numerator versus denominator.
   • From nameplate capacity to energy outputGiven a fuel source's nameplate capacity and its published capacity factor, calculate expected annual energy output and identify the value's units correctly (MWh, not MW).
   • Why no single metric winsCompare three energy sources' EROEI, carbon intensity, and LCOE data presented side by side and explain why ranking by one metric alone produces a different 'best' choice than ranking by another.
   • Evidence claims versus value judgmentsClassify a given statement about an energy tradeoff as an evidence claim (checkable against a data source) or a value judgment (a stated priority), applying a consistent test across at least six varied example statements.
   • Forecasting energy demand and grid capacityGiven demand-growth data for a hypothetical or real region, forecast future energy demand using exponential or logistic growth math and identify which existing energy mix would fail to meet that forecast without additional capacity.
   • Building your own energy tradeoff analysisSelect a real local or regional energy-decision scenario and construct an original comparative tradeoff analysis integrating EROEI, carbon intensity, and distributed cost-benefit data across at least three energy sources not covered in the class's worked examples.
   • Finding why energy recommendations disagreeGiven a completed case study (not their own), identify whether a stated disagreement between two possible recommendations stems from a factual/data dispute or a difference in value-weighting, and justify the distinction using specific text from the case study.
   • Why energy output has a limitExplain, using a specific energy source as the case, why a system's measurable output cannot exceed what its energy inputs and internal conversion losses allow.
   • Defining carbon intensity and its unitsRecall the definition and units of carbon intensity (grams CO2-equivalent per kWh) without reference support.
   • Presenting your energy tradeoff analysisDeliver a case-study presentation that explicitly separates evidence claims from value judgments and states a reasoned recommendation, responding to at least one clarifying question from the audience about a specific data source used.

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1. Unit 1: Constitutional Design: Power, Limits, and FederalismThis is where all the vocabulary for the whole semester gets built: separation of powers, checks and balances, the three kinds of governmental power (enumerated, implied, reserved), and federalism. It's taught slowly and directly at first, using the actual constitutional text, because these are not ideas your kid already has a rough version of, they're genuinely new categories.9 skills ▸close ▾

   • Separation of powers and checksGiven a short excerpt from Article I, II, or III of the Constitution, students classify the specific governmental action described as belonging exclusively to one branch or requiring interference from another branch.
   • Enumerated, implied, and reserved powersStudents recall the definitions of enumerated, implied, and reserved powers and identify which constitutional clause (Article I Section 8, Necessary and Proper Clause, Tenth Amendment) establishes each category.
   • Classifying a brand new powerGiven a governmental power never discussed in class (e.g., regulating drone delivery airspace, or a state's authority over a new form of currency), students classify it as enumerated, implied, or reserved and justify the classification by citing the relevant constitutional clause.
   • National uniformity versus state independenceStudents explain why federalism creates a specific tension between national uniformity and state autonomy, using a contrasting pair of state-vs-federal conflict cases presented in class.
   • Settling a state versus federal conflictGiven a novel, previously unseen state-federal policy conflict (e.g., a hypothetical dispute in a policy area not discussed in class), students determine which level of government has authority and construct an argument using the Supremacy Clause and Tenth Amendment.
   • Originalism and living constitutionalismStudents compare an originalist and a living-constitutionalist reading of the same constitutional clause applied to a modern, previously undiscussed circumstance, and evaluate which reading is better supported by the clause's text and purpose.
   • Arguing over one design featureStudents summarize the core argument of a designated Federalist paper excerpt and a designated Anti-Federalist paper excerpt addressing the same design feature, stating each author's central claim in one sentence.
   • How design choices reflect tradeoffsUsing excerpts from the Constitution and one Federalist and one Anti-Federalist paper, students construct a written argument explaining how a specific design choice reflects a tradeoff the framers faced, connecting textual evidence from all three sources to that tradeoff.
   • Popular sovereignty and constitutionalismStudents recognize the terms popular sovereignty and constitutionalism when defined in context and match each to a corresponding phrase in the Preamble or a designated constitutional excerpt.
2. Unit 2: The Three Branches in Practice: Institutions and Power in ActionYour kid already knows the stories, Marbury v. Madison, presidents sending troops without a declared war, bills dying in Congress. This unit takes those stories, which they know as plot, and turns them into evidence: which branch actually won this fight, and what in the Constitution let them win it.10 skills ▸close ▾

   • What Marbury decided and whyGiven a case summary of Marbury v. Madison, state the holding and identify the constitutional silence it resolved (the Constitution does not explicitly grant the Court power to void a law).
   • Judicial review as an implied powerExplain why judicial review is described as an implied rather than enumerated power, connecting the Unit 1 enumerated/implied distinction to the Court's reasoning in Marbury.
   • How conflicts between branches endGiven three named historical conflicts not covered in class discussion (e.g., Youngstown Sheet & Tube v. Sawyer, the Pentagon Papers case, a recent executive order challenged in court), identify which branch or mechanism ultimately resolved each and justify the resolution using constitutional text.
   • Paper versus practice in war powersCompare the formal war-making powers assigned to Congress with the informal expansion of presidential war power in practice, using at least two named historical episodes.
   • The War Powers Resolution deadlinesGiven the text of the War Powers Resolution and a timeline of a presidential military action, determine whether the statutory reporting and withdrawal requirements were followed.
   • Why political context limits presidentsExplain why the same formal presidential powers (commander-in-chief, executive order authority) produced markedly different levels of practical constraint under different Congresses and Courts, citing at least two examples.
   • Where bills stall in CongressGiven a bill's actual path through Congress (committee, markup, floor vote, conference, veto or signature), sequence the stages correctly and identify where in the sequence the bill in question stalled.
   • Is gridlock design or failureArgue, using the enduring understanding that friction is a design feature, whether a specific instance of legislative gridlock (assigned by the teacher, not previously analyzed in class) represents the system functioning as designed or a failure of representation, and defend the position with constitutional and evidentiary support.
   • Why agencies make rulesExplain why executive agencies exercise delegated authority rather than an independent constitutional grant of power, using the concept of delegation from Congress.
   • Stare decisis and changing precedentGiven a new Supreme Court case description structurally similar to Marbury (a conflict between a statute and constitutional text with no prior ruling on point), predict how the doctrine of stare decisis would apply if a directly relevant precedent existed, and identify what would have to be shown to overturn that precedent.
3. Unit 3: Rights, Liberties, and the Limits of Government PowerThis unit asks a harder question than 'what rights do we have', it asks who gets to decide the limits of a right, and why reasonable people and reasonable courts can land in different places. It leans hard on the federalism split from Unit 1 and judicial review from Unit 2.9 skills ▸close ▾

   • Civil liberties versus civil rightsGiven a scenario, classify whether the situation primarily involves a civil liberty (protection from government action) or a civil right (protection of equal treatment), and justify borderline cases.
   • Selective incorporation over timeExplain why the Bill of Rights did not apply to state governments until the process of selective incorporation, using at least two named incorporation cases and their dates relative to 14th Amendment ratification.
   • Choosing the level of scrutinyGiven a government action that burdens a claimed right, determine which level of scrutiny (rational basis, intermediate, strict) a court would apply based on the classification and right involved, executing the decision-tree procedure taught in class.
   • Choosing the level of scrutinyApply the scrutiny-level decision procedure to a new, previously unseen government-action scenario not used in worked examples, and justify the classification chosen.
   • Why similar cases ended differentlyCompare two Supreme Court cases with conflicting outcomes on a similar right and identify the specific doctrinal test or factual distinction that produced the differing holdings.
   • Spotting the classification in equal protectionGiven equal protection case excerpts, infer which classification (race, gender, or other) the government action targets and what level of scrutiny logically follows, without being told the classification directly.
   • Who should settle new rights conflictsEvaluate, for a current unresolved rights conflict not addressed by existing precedent, which institution (Congress, state legislature, or federal court) is best positioned to resolve it, and justify the choice using the federalism and judicial-review concepts from Units 1-2.
   • Steelmanning a view you disagree withConstruct a steelman argument for an institutional position the student personally disagrees with, regarding who should resolve a rights conflict, before arguing their own position.
   • Due process and equal protectionRecall the definitions of due process (procedural and substantive) and equal protection as established in the 14th Amendment.
4. Unit 4: Civic Participation, Media, and Public PolicyThe last stretch turns from institutions and rights to people, how voting, interest groups, polling, and media coverage actually push on the structure your kid has spent the semester mapping. It ends with a real research project: build the strongest case for two sides of a genuinely contested policy issue.9 skills ▸close ▾

   • Why incumbents start aheadGiven a description of a sitting legislator's voting record and a hypothetical challenger's platform, identify at least three structural (non-performance) advantages the incumbent holds and explain how each lowers the challenger's odds regardless of either candidate's record.
   • Small interest groups beating large onesGiven a short case narrative in which a numerically small, well-funded interest group defeats a numerically larger, diffuse group on a specific bill, explain which resource (concentration, funding, single-issue focus, expertise) substituted for membership size and why collective-action problems make large diffuse groups harder to mobilize.
   • Framing versus factual accuracyGiven two same-event news leads or headlines that are both factually accurate, identify the specific word choice or fact-ordering decision that constitutes the framing difference and distinguish it from any factual claim in the text.
   • Policy process stages and influence pointsRecall the correct sequence of stages in the policy process (agenda-setting, proposal, legislative action, executive/agency action, evaluation) and name what kind of actor (citizen, interest group, media, legislator, agency) has the most leverage at each stage.
   • Why poll wording changes resultsGiven a two-poll comparison on the same issue with different question wording and different topline results, infer which specific wording difference most plausibly produced the different result, and state what claim the polls jointly do and do not support.
   • Which level and branch decidesFor a genuinely contested current policy issue not covered in class, determine which branch and level of government (federal/state, legislative/executive/judicial) has jurisdiction to decide it, citing the specific enumerated, implied, or reserved power or constitutional provision from Units 1-2 that grounds the claim.
   • Steelmanning both sides of an issueConstruct a policy brief presenting the strongest legitimate case for two contested positions on a self-selected current issue, such that a reader could not identify which position the student personally favors from the strength of argument alone.
   • Checking a peer's framing analysisEvaluate whether a peer's media source analysis has identified an actual framing choice versus merely restated a factual claim from the source, using the two-question peer protocol.
   • Key terms of political influenceRecall the definitions of interest group, lobbying, public opinion, agenda-setting, framing, and incumbency accurately enough to use them correctly in original written analysis.

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1. Unit 1: Scarcity, Choice, and Opportunity CostThis is where your child learns the core habit of the whole course: the real cost of anything is the best thing you gave up to get it, not the money you handed over. They'll also build a graph called the production possibilities curve, which is just a picture of 'if I make more of this, I have to make less of that,' and they'll meet a genuine human bias, the sunk cost fallacy, where people keep throwing good time or money after bad because they can't let go of what they already spent.9 skills ▸close ▾

   • Scarcity versus shortageGiven a scenario describing a resource shortage, state whether the situation is an example of scarcity (a permanent condition) or a shortage (a temporary market condition at a given price), and justify the distinction using the definition of each.
   • Opportunity cost and the best alternativeCalculate the opportunity cost of a stated decision by identifying the single best forgone alternative from a list of options, distinguishing it from the sum of all alternatives given up.
   • Opportunity cost versus money costExplain why opportunity cost, not monetary price, is the economically correct measure of cost for a decision, using an example involving a 'free' or already-paid-for good.
   • Drawing a production possibilities curveGiven a two-good production dataset, construct a production possibilities curve, correctly plotting points and connecting them to show the trade-off frontier.
   • Reading a production possibilities graphInterpret a novel, previously unseen PPC graph (including one showing a shift and one showing a point inside/outside the curve) to determine whether an economy is operating efficiently, growing, or facing increasing opportunity costs, and justify the interpretation using features of the curve.
   • The sunk cost fallacyCompare a rational-choice prediction about a sunk cost to the sunk cost fallacy as it actually shows up in a described human decision, identifying which piece of information the decision-maker incorrectly treated as relevant.
   • Marginal benefit equals marginal costApply marginal-benefit/marginal-cost reasoning to determine the optimal quantity of an activity in a scenario providing a table of marginal values, identifying the point where marginal benefit equals marginal cost.
   • Opportunity cost of your own decisionGenerate an original, previously unmodeled real-world or civic decision (not one demonstrated in class) and produce a written opportunity-cost analysis of it that correctly identifies the best forgone alternative and explains why it, rather than another option, is the true cost.
   • Absolute and comparative advantageUsing a simple two-producer, two-good scenario with given output data, distinguish absolute advantage from comparative advantage by identifying which producer has the lower opportunity cost for each good.
2. Unit 2: Markets: Supply, Demand, and the Price SystemThis is the biggest unit and the one the rest of the course leans on hardest. Your child builds the supply-and-demand model from scratch, learns to tell 'the whole curve moved' apart from 'we just moved along the curve because price changed,' calculates how sensitive buyers are to price changes (elasticity), compares competitive markets to monopolies, and finishes with price controls and market failure, the two ways markets can go wrong that the basic model doesn't fix by itself.11 skills ▸close ▾

   • What shifts supply and demandGiven a change in a market condition (e.g., input cost, consumer income, related-good price), state whether the demand curve or the supply curve shifts, and in which direction.
   • Shifts versus movements along curvesDistinguish a shift of an entire supply or demand curve from a movement along a fixed curve, given a scenario describing either a change in price or a change in a non-price determinant.
   • Market equilibrium and price pressureGiven supply and demand schedules or curves for an unfamiliar good, determine the equilibrium price and quantity and explain why a price above or below equilibrium is unsustainable.
   • Calculating price elasticity of demandCalculate price elasticity of demand from percentage-change data and classify a good as elastic, inelastic, or unit elastic based on the resulting coefficient.
   • What makes demand elastic or inelasticPredict, for a good with unfamiliar demand characteristics (novel product, no taught example), whether it is more likely elastic or inelastic based on the presence of substitutes, necessity status, and share of budget, and justify the classification.
   • Perfect competition versus monopolyCompare perfect competition and monopoly on the dimensions of number of firms, barriers to entry, price-setting power, and long-run economic profit.
   • Sorting industries into market structuresClassify a real-world industry example (not used in instruction) as closer to perfect competition or monopoly and justify the classification using at least two structural criteria.
   • Negative externalities and social costExplain why a market with a negative externality (e.g., pollution) produces more than the socially optimal quantity, using the distinction between private cost and social cost.
   • Market shift or market failureGiven an unfamiliar scenario combining a market shock and a possible externality or public-good element, determine whether the situation is best explained by an ordinary equilibrium shift or by a market failure, and identify what evidence in the scenario supports that call.
   • Price ceilings and price floorsPredict the effect of a price ceiling set below equilibrium or a price floor set above equilibrium on quantity supplied, quantity demanded, and the resulting shortage or surplus, using a labeled supply-and-demand diagram.
   • When price controls distort marketsGeneralize, from contrasting cases of a successful price control and a failed one, a rule for predicting when a price control will create a persistent shortage or surplus versus when it will have little effect.
3. Unit 3: The Macroeconomy: Growth, Unemployment, Inflation, and PolicyHere the course zooms out from single markets to the whole economy: GDP, unemployment, inflation, and the two sets of tools, fiscal policy (Congress and the President taxing and spending) and monetary policy (the Federal Reserve managing money and interest rates), used to steer it. The hard idea underneath the whole unit: every big-picture number (GDP, the unemployment rate) is an average that hides real variation, and the tools that fight unemployment often make inflation worse, and vice versa.10 skills ▸close ▾

   • Finding real GDP with a deflatorGiven a table of nominal GDP and a price index for two years, calculate real GDP for each year using the deflator formula.
   • Three types of unemploymentClassify a described worker's job loss as frictional, structural, or cyclical unemployment based on the cause stated in the scenario.
   • Mixed causes of unemploymentCompare a new, previously unseen unemployment vignette (with an ambiguous cause combining automation and a recession-driven layoff) to the three taught categories and justify which type dominates or whether it is mixed.
   • Why GDP can miss local unemploymentExplain why a rising national GDP figure can coexist with a specific region's unemployment rate remaining unchanged, using the concept of aggregation.
   • Judging recovery from conflicting indicatorsGiven a completely novel country-year dataset (GDP growth, disaggregated unemployment by demographic group, and CPI) never used in instruction, determine whether the economy has 'recovered' and identify which population the aggregate numbers likely hide.
   • Who controls fiscal and monetary policyDistinguish which entity (Congress/President vs. the Federal Reserve) controls a described policy action and which broad tool category (fiscal or monetary) it represents.
   • Classifying a new policy actionGiven a new (unpracticed) government action description, infer whether it represents expansionary or contractionary policy and which category (fiscal/monetary) it belongs to.
   • Fighting high unemployment and inflationGiven a scenario describing simultaneously high unemployment and high inflation (stagflation-like conditions never presented in instruction), explain why standard fiscal and monetary tools conflict and propose which priority the student would choose, labeling that choice as a value judgment rather than an empirical claim.
   • Fiscal and monetary policy toolsRecall the definition and one real-world tool for each of fiscal policy and monetary policy.
   • Facts and values in economic argumentsIn a written policy-argument essay, label each claim made as either an empirical claim (testable against data) or a value trade-off (a matter of priorities), and justify each label.
4. Unit 4: Trade, Globalization, and DevelopmentThe course closes by turning Unit 1's opportunity cost into real numbers, this is the theory of comparative advantage, and then asks the harder question: even when trade grows the total pie, who inside a country actually gets more, and who gets less? Tariffs, quotas, and exchange rates come next as the tools that change trade's outcome, and the unit ends with global problems like climate change that no single government can be forced to fix.10 skills ▸close ▾

   • Opportunity cost and comparative advantageGiven a numeric table of resource costs for two countries producing two goods, calculate each country's opportunity cost for each good and identify which country holds the comparative advantage in each good.
   • Absolute versus comparative advantageExplain why a country can gain from trade even when it has an absolute disadvantage in producing every good, using the distinction between absolute and comparative advantage.
   • Specialization and terms of tradeGiven an unfamiliar two-country, two-good numeric scenario with unseen numbers, determine which country should specialize in which good and predict the range within which mutually beneficial terms of trade must fall.
   • Tariffs on a supply and demand graphUsing a supply-and-demand diagram, identify the effect of a tariff on domestic price, quantity, consumer outcomes, producer outcomes, and government revenue.
   • Tariffs, quotas, and trade agreementsCompare the mechanisms and typical uses of tariffs, quotas, and trade agreements as tools that alter the outcome of otherwise free trade.
   • Who gains and loses from tradeGiven a real trade or development policy dataset (GDP growth, sector employment, regional unemployment) covering a case not discussed in class, identify at least one specific group that benefited and one that was harmed, citing the data.
   • Facts and values in trade debatesSort a set of contested statements about trade or development policy into 'empirical claim' (resolvable by evidence) and 'values trade-off' (not resolvable by evidence alone), and justify each sorting decision.
   • Global public goods and market failureExplain why global public goods such as climate stability or pandemic control are underprovided by uncoordinated national markets, using the public-good and externality concepts from Unit 2.
   • Writing a trade policy argumentConstruct an argumentative essay on a contested trade or development policy question that explicitly separates empirical claims from value judgments and supports claims with cited evidence.
   • Comparative advantage meets real dataGiven a novel comparative-advantage numeric problem and an unfamiliar country's trade/GDP/unemployment dataset on the cumulative final, apply opportunity-cost reasoning and macro-aggregate interpretation without any unit-labeled cue as to which method applies.

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1. Unit 1: The Tools of Argument: Validity, Soundness, and FallacyThis is where your child learns the actual vocabulary of logic, not vibes about 'good points,' but a real test for whether an argument's structure holds up, separate from whether you like where it ends up. They'll learn to pull apart premises and conclusions, run a test for validity, add a separate test for truth (soundness), name five common fallacies, and, hardest of all, build the strongest version of an argument they disagree with before they're allowed to criticize it.10 skills ▸close ▾

   • Finding premises and conclusionsGiven a short argumentative passage in ordinary prose whose premises and conclusion appear in the same order and with the same indicator words (because, therefore) used in the Day 1-2 worked examples, the student identifies which sentence functions as the conclusion and which sentences function as premises.
   • Testing validity with a counterexampleGiven a standard-form argument that reproduces the exact structure and content of one already reconstructed together in class (same premises, same conclusion, only surface wording changed), the student correctly reruns the counterexample test taught on Day 4 to state whether it is valid, applying the routine exactly as modeled without needing to adapt it to a new structure.
   • Rewriting arguments in standard formThe student rewrites an argument given in ordinary persuasive prose into numbered standard form (premises listed, conclusion last), preserving the original argument's actual content rather than a simplified version of it.
   • Judging validity and soundness separatelyGiven an argument in standard form, the student judges whether it is valid (would the conclusion have to be true if the premises were true) as a distinct operation from judging whether it is sound (are the premises actually true), producing two separate verdicts rather than one combined judgment.
   • Deductive and inductive argumentsThe student classifies an argument as deductive or inductive based on the relationship the argument itself claims between its premises and conclusion (certainty vs. probability), not based on subject matter or length.
   • Common fallacies and how to test themGiven a flawed argumentative passage, the student identifies which of the six named fallacies (ad hominem, straw man, false dichotomy, affirming the consequent, circular reasoning) is present and explains, using the discriminating test for that fallacy, why the passage fits that test rather than a confusable neighboring fallacy.
   • Why validity and soundness are independentThe student explains, using a specific example, why validity and soundness are logically independent properties of an argument, i.e., why an argument can be valid without being sound, and why no argument can be sound without being valid.
   • Charitable rebuilding of opposing argumentsGiven a real, previously unseen persuasive passage on a contested issue that the student personally disagrees with, the student produces a charitable reconstruction of the position, adding the strongest available missing premise or clarifying an ambiguous term, before writing any critique of it.
   • Modus ponens versus affirming the consequentGiven two structurally similar conditional arguments, one modus ponens (valid) and one affirming the consequent (invalid), presented side by side, the student determines which is valid by constructing a counterexample test (a case where the premises could be true and the conclusion false) rather than by the arguments' surface resemblance.
   • Telling fallacies from fair emphasisGiven a wholly unfamiliar real-world persuasive text (e.g., an advertisement, political cartoon caption, or social-media argument never discussed in class) the student has not seen reconstructed by anyone, the student independently determines whether the persuasive technique used constitutes one of the six named fallacies or is instead non-fallacious rhetorical emphasis, and justifies the call.
2. Unit 2: Knowledge, Belief, and DoubtThis unit asks a genuinely unsettling question: can you ever fully prove you know something, or does every chain of reasons eventually run out, into a circle, an endless chain, or a stopping point you just have to accept without proof? Your child will meet the classic definition of knowledge, the famous case that breaks it, the three ways philosophers have tried to patch the problem, Descartes'-style skeptical arguments, and finally faith-and-reason positions treated as real philosophy, not as a debate to be won.10 skills ▸close ▾

   • Knowledge as justified true beliefState the three components of the justified-true-belief (JTB) definition of knowledge and identify which component is missing in a given short scenario.
   • Gettier cases and lucky true beliefsExplain why a Gettier-style case (true belief, justified, but true only by luck) shows that justification plus truth plus belief is not sufficient for knowledge.
   • The regress problem of justificationReconstruct the regress problem (Agrippa's trilemma) by identifying its three exhaustive outcomes, infinite regress, circularity, and arbitrary stopping point, for a given chain of justification a student produces themselves.
   • Dream and evil demon argumentsFormally reconstruct the dream argument or the evil-demon argument in premise-conclusion form and determine whether it is valid, using the method taught in Unit 1.
   • Foundationalism versus coherentismCompare foundationalism's and coherentism's replies to the isolation/regress objection and explain how each reply follows from what that position treats as needing no further justification.
   • Applying regress responses to new casesGiven a previously unseen skeptical scenario (not the dream argument, not the evil demon), determine which premise a foundationalist, a coherentist, and an infinitist would each be most likely to reject, and justify each attribution from that position's core commitment.
   • Three views on faith and reasonDistinguish fideism, evidentialism, and reformed epistemology by identifying, in a short quotation, which position's core claim about the relationship between faith and evidence it represents.
   • Two distinctions that block bad argumentsExplain the is/ought distinction and the appearance/reality distinction as two separate conceptual moves that block a specific commonly attempted argument (e.g., inferring a moral or metaphysical conclusion directly from a perceptual or factual premise).
   • What regress responses leave unjustifiedGiven two strongest-form responses to the regress problem that a student has not directly compared before (e.g., infinitism versus foundationalism on the arbitrariness objection), generate a novel third position's likely reply by reasoning from the same abstract structure (what must be immune from further justification, and why).
   • Essay comparing two regress responsesWrite a comparative analysis essay presenting two responses to the regress problem, each in its strongest form with its strongest objection, using charitable reconstruction as a graded criterion.
3. Unit 3: Mind, Body, and Personal IdentityThis unit asks whether the mind is just the brain, and it splits that into two separate questions your child has probably never separated before: what a mental state does, and why it feels like something to have one. They'll work through Descartes' argument for a separate mind, physicalist replies, the 'hard problem of consciousness,' philosophical zombies, whether a teleported copy of you is really you, and free will versus determinism, ending in a live oral defense where they have to hold a position under real pushback.11 skills ▸close ▾

   • Descartes' conceivability argument for dualismState Descartes' conceivability argument for substance dualism in premise-conclusion form and identify whether it is valid.
   • Validity versus soundness in DescartesDistinguish the claim that Descartes' argument is valid from the claim that its premises are true, using a case where a student accepts the logical form but rejects premise 1 (conceivability entails possibility).
   • Identity theory and functionalismState the identity theory and functionalist claims about mental states using necessary/sufficient condition language, and explain how the two claims differ.
   • The hard problem of consciousnessExplain why a successful physical/functional account of a mental state's causal role does not by itself resolve the hard problem of consciousness.
   • Philosophical zombies against physicalismConstruct a philosophical zombie thought experiment for a mental state not used in class examples (e.g., regret, boredom) and use it to argue whether physicalism can fully account for that state.
   • Two theories of personal identityRecall the definitions of psychological continuity and bodily continuity as competing criteria for personal identity over time.
   • Personal identity and the teleporterApply the psychological-continuity and bodily-continuity criteria to a teleporter/duplication case not covered in class and determine which criterion, if either, the case satisfies.
   • Three views on free willCompare hard determinism, libertarian free will, and compatibilism on whether moral responsibility requires that choices not be fully caused by prior events.
   • Free will and everyday excusesJudge whether a given real-world excuse ('I was raised that way,' 'it's my brain chemistry') is best explained by hard determinism, libertarian free will, or compatibilism, and defend the judgment against a compatibilist rebuttal.
   • Defending a view on mind and bodyDefend a chosen position on mind (dualism, physicalism, or functionalism) for four minutes and respond to two live objections using validity/soundness and knowledge/belief vocabulary correctly.
   • Evidence and the explanatory gapGeneralize, across dualism, physicalism, and functionalism, what kind of evidence would count as resolving the hard problem, if any evidence could.
4. Unit 4: Ethics: Consequences, Duties, and CharacterThe last unit asks whether three big ethical theories, judge by outcomes, judge by duty, judge by character, are all trying to answer the same question and one of them is simply right, or whether they're actually asking different questions about what makes an action right in the first place. Your child learns to actually run all three frameworks on real cases, then uses the trolley problem to pin down exactly which premise two frameworks disagree on, and closes with a position paper and the question of whether morality is more like a fact or more like an invention.10 skills ▸close ▾

   • How act utilitarians decideGiven a short case description, state the verdict and the single guiding principle (maximize aggregate well-being) that an act utilitarian would use to reach it.
   • Act versus rule utilitarianismDistinguish act utilitarianism from rule utilitarianism by identifying, for a given case, which type of entity each theory evaluates (the individual act vs. the general rule).
   • Kant and the universalizability testApply Kant's categorical imperative test (universalizability and the contradiction-in-conception test) to a new maxim to determine whether it could be willed as universal law.
   • Why Kant's test ignores consequencesExplain why the categorical imperative test evaluates the coherence of willing a maxim as universal law rather than predicting the consequences of universal adoption.
   • Practical wisdom in virtue ethicsApply the virtue-ethics decision procedure (what would a practically wise person, possessing the relevant virtues, perceive and do here) to a new case, naming the specific virtue(s) at stake.
   • Trolley and footbridge across three frameworksGiven the trolley problem and one structural variant (e.g., the footbridge case) not previously analyzed together, reconstruct in standard form the strongest argument each of the three frameworks would make, and identify which specific premise differs between the two frameworks' arguments for the same case.
   • Factual versus moral disagreementGiven a completely unfamiliar moral dilemma never discussed in class (e.g., a resource-allocation case from a different domain than any used in instruction), determine whether two named frameworks' disagreement on the verdict is a disagreement about a fact of the case or a disagreement about what counts as a moral reason, and justify the determination.
   • Arguments for and against moral realismConstruct the strongest available argument for moral realism and the strongest available argument for moral anti-realism, using the unit's three normative frameworks as evidence in the argument, without stating a personal preference.
   • Right act versus good motiveGiven a case where an action produces a good outcome but was performed for a self-interested or accidental reason, separately evaluate the act's rightness (consequentialist question) and the agent's character (virtue-ethics question), and explain why these are not the same question.
   • Position paper on a contested caseProduce a position paper analyzing one contested case through two ethical frameworks, reconstructing each argument in standard form, identifying whether their disagreement is factual or normative, and stating what would have to be true for each side to be right, without declaring a personal winner.

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