Reading change, authority, and hidden work in The Clockroom
Trace a narrator’s changed judgment through repeated objects, precise evidence and ordered analogies.
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Lessons with worked examples, practice questions and a study plan.
Updated October 2, 2026
73 lessons connect the ideas, worked examples and practice for each authored problem family. Use the question bank to get more practice.
Verbal Reasoning
close reading · inference · argument
Reading selection, representation, and qualified conclusions in The Road on the Map
Distinguish accurate detail from fair representation, and support qualified interpretations of a restrained ending.
Start lessonReading collaboration and changing perception in The Night Cloth
Connect material details, audience participation and a narrator’s changing relationship with another person.
Start lessonReading experiments, data, and limits in Collecting the Night
Interpret controlled comparisons, data units, causal limits and the evidence needed for broader reliability claims.
Start lessonReading measurement, purpose, and uncertainty in the seed-library study
Evaluate provisional evidence by matching the observation period and outcome measure to the intended goal.
Start lessonReading detection errors and controlled evidence in the harbor study
Separate detection errors, broader inferences and independent checks when evaluating a research tool.
Start lessonReading moral distinctions in The Gift Ledger
Read an ethical argument by preserving its distinctions between records, obligations, motives and authority.
Start lessonReading qualified definitions in Patience and Decision
Distinguish purposeful inquiry from avoidance and explain why responsible choices can remain revisable.
Start lessonReading competing values in The Repaired Bowl
Analyze tradeoffs in preservation and distinguish accountable explanation from automatic justification.
Start lessonComparing participation and representation in Speaking for the City
Compare shared principles across different institutions and test whether a proposed mechanism preserves public judgment.
Start lessonComparing principled flexibility and public standards in The Rule and the Case
Compare case-sensitive judgment with prospective standards while testing the limits on personal favoritism.
Start lessonComparing habits and institutions in Learning to Be Citizens
Connect intellectual standards, inherited beliefs and public access while distinguishing opportunity from guaranteed wisdom.
Start lessonGrammar & Writing
sentence structure · usage · editing
Editing a historical profile: responsibility made visible
Edit subjects, modifiers, parallel clauses and paragraph decisions while preserving the difference between a traceable correction procedure and a guarantee of truth.
Start lessonEditing an explanation of useful limits
Use grammatical structure, punctuation, precise wording and a purposeful conclusion to explain a map’s usefulness without overstating access or certainty.
Start lessonEditing a profile with two kinds of authority
Connect sentence structure and paragraph order to the distinction between keeping accurate time and deciding the town’s public schedule.
Start lessonEditing an argument about public value
Repair sentence relationships and evaluate revisions against a public bench proposal’s purpose, evidence and practical qualifications.
Start lessonEditing an argument about learning through decisions
Resolve embedded pronoun case, compare complete costs and trace an argument that distinguishes repairing an object from learning to make a sound repair decision.
Start lessonEditing an argument about criteria and judgment
Use parallelism, punctuation and precise evaluative language to distinguish shared judging criteria from identical preferences or unanimous agreement.
Start lessonEditing a model without overstating its conclusions
Edit a classroom model’s procedure, comparisons and recommendations so that grammatical clarity preserves the limits of its evidence.
Start lessonEditing an account of comparison and analogy
Clarify clauses, comparisons and paragraph bridges while keeping individual observations, experimental patterns and the limits of an analogy distinct.
Start lessonEditing an explanation before choosing a solution
Use agreement, pronoun case and explanatory order to distinguish hearing a voice from understanding its words and diagnosis from choosing equipment.
Start lessonEditing an argument about continuing responsibility
Interpret counterfactual time, restrictive clauses and rhetorical bridges while preserving the responsibilities that can continue after a justified change of plan.
Start lessonEditing a discussion of freedom and limits
Connect grammar, transitions and organization to an argument that balances a host’s limits with a guest’s freedom to respond honestly.
Start lessonEditing an argument that leaves room for revision
Edit parallel reasoning, sentence boundaries and conclusions to preserve both openness to revision and the need for reasons grounded in the work.
Start lessonQuantitative Reasoning
algebra · geometry · data reasoning
Divisibility as a set of constraints
Use parity, prime powers and residues to identify exactly which integers satisfy a condition.
Start lessonAbsolute value, intervals and the number of solutions
Translate absolute values into distances and sign cases before counting or solving.
Start lessonSee the structure inside powers and radicals
Use equivalent forms to simplify roots and turn exponential equations into familiar algebra.
Start lessonFollow the rule, then locate the term
Distinguish constant differences, constant ratios and recurring cycles before using an index.
Start lessonBuild the right sample space before counting
Count equally likely outcomes and rebuild the denominator when a condition is supplied.
Start lessonPreserve meaning while transforming expressions
Use identities, definitions and remainders without losing restrictions or changing the target.
Start lessonSolve inequalities while preserving their boundaries
Track direction, intersections and exceptional parameter values rather than treating every equation alike.
Start lessonCombine equations with a purpose
Use elimination and proportionality to obtain a target and recognize when equations describe the same line.
Start lessonUse roots, factors and domains together
Translate between a quadratic and its roots, then reject candidates that fail the original equation.
Start lessonKeep real and imaginary structure visible
Use conjugates to solve quadratics and reconstruct real-coefficient polynomials.
Start lessonRead a line through change and position
Separate slope from intercept and distinguish parallel, perpendicular and vertical lines.
Start lessonCompose transformations in the stated order
Track points, centers and line intercepts through reflections, rotations and dilations.
Start lessonTurn angle relationships into equations
Identify the geometric relationship before using a sum, ratio or equality.
Start lessonMove correctly between length, area and volume
Use one linear scale factor, then apply its square or cube to the appropriate measurement.
Start lessonCreate the right triangle inside the figure
Use congruence, symmetry and similarity to uncover lengths before calculating area or perimeter.
Start lessonConnect radii, chords, arcs and coordinates
Use the center to organize circle measurements and distinguish full-circle quantities from fractions.
Start lessonAccount for area without losing the geometry
Add, subtract or compare regions using perpendicular heights and the correct dimensions.
Start lessonChoose between surface, volume and a route
Model three-dimensional objects with the measurement and movement restrictions the problem actually gives.
Start lessonRead a trigonometric ratio relative to its angle
Identify opposite, adjacent and hypotenuse, then use the ratio and sign information the problem gives.
Start lessonSimplify trigonometric equations without erasing their domains
Use identities to reveal algebraic structure, then reject values excluded by the original expression.
Start lessonUse magnitude and signs to locate an angle
Combine reference angles, coordinates and extra conditions instead of relying on one trigonometric value.
Start lessonSeparate vertical changes from horizontal timing
Read amplitude and range from outputs, then solve for every allowed maximum location.
Start lessonCount a complete set while respecting overlapping rules
Use organized enumeration and inclusion-exclusion to combine restrictions without double subtraction.
Start lessonSeparate what is necessary from what is merely possible
Translate rules into implications, test alternatives and count only orders satisfying every condition.
Start lessonDisprove a claim by satisfying its premise
Find a case that meets every stated assumption and then makes the proposed conclusion false.
Start lessonNarrow integer possibilities with every condition
Use digits, residues and divisor structure to reduce a search and prove that it is complete.
Start lessonCount the structure hidden in a diagram
Translate shared edges, borders, painted faces and forbidden vertices into precise counting models.
Start lessonChoose the correct total and the correct units
Model ratios and motion using the quantities that remain fixed and the time the problem includes.
Start lessonKeep track of the base behind every percentage
Use multipliers for successive changes and distinguish revenue, profit and percentage points.
Start lessonTrack the ingredient amount before the concentration
Use conservation and retention factors to model combining, diluting and replacing a mixture.
Start lessonAdd rates, then account for the time each rate operates
Express work in fractions of a job and separate stages when workers join, leave or change speed.
Start lessonOptimize the model on its allowed domain
Distinguish a vertex from a feasible maximum and separate a return event from a peak.
Start lessonTranslate physical space into a precise model
Match units and distinguish usable packing, closed boundaries and straight-line distance.
Start lessonUse totals for means and order for medians
Distinguish averages from positions and prove an extremum with both a bound and an example.
Start lessonOptional in-school essay
argument · organization
Promises and changed knowledge
Build a principled argument about promises by separating genuine new evidence from a convenient excuse.
Start lessonPatience and discovery
Explain how preparation and insight contribute different kinds of work to a discovery.
Start lessonTruth and persuasion
Distinguish the accuracy of a claim from the choices that help an audience understand it.
Start lessonCooperation and individual credit
Develop a fair rule for credit that accounts for exceptional work and less visible contributions.
Start lessonRules and mercy
Evaluate exceptions by the purpose of a rule and by a principle that could apply to unfamiliar people.
Start lessonUsefulness and beauty
Distinguish kinds of value so an argument about beauty does not succeed by redefining every benefit as practical use.
Start lessonCustom and reflection
Evaluate an inherited practice by what it preserves, whom it burdens and whether those reasons survive examination.
Start lessonExpertise and public judgment
Build an argument for informed trust by distinguishing technical verification from the evaluation of reasons and accountability.
Start lessonMemory and written records
Compare trustworthiness by the kind of claim being checked and by how each account was produced.
Start lessonAmbition and limits
Show how recognizing a present limitation can change a method without deciding the worth of a goal.
Start lessonLearning without reward
Defend a course of study by explaining its value and opportunity cost, even when immediate rewards are absent.
Start lessonForgiveness and trust
Separate a response to past wrongdoing from a prediction about future reliability.
Start lessonSpeed and deliberation
Compare the cost of waiting with the cost of error, and explain how reversibility changes the decision.
Start lessonTranslation and understanding
Evaluate a translation by its purpose while accounting for meaning, connotation and features it cannot fully preserve.
Start lessonSolitude and service
Trace private reflection or practice to a concrete contribution, and distinguish preparation from avoidance.
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