Write an explanatory text that manages a complex idea with extended definitions, a table, analogy and domain-specific vocabulary

Learning goal: Write informative/explanatory texts to examine and convey complex ideas, concepts and information clearly and accurately through the effective selection, organization and analysis of content. Establish a clear and thorough thesis to present and explain information; introduce a topic and organize complex ideas so that each new element builds on that which precedes it to create a unified whole, including formatting such as headings, graphics such as tables, and multimedia when they aid comprehension; develop the topic with the most significant and relevant facts, extended definitions, concrete details, quotations and examples appropriate to the audience's knowledge; use appropriate and varied transitions and syntax to link sections and clarify relationships among complex ideas; use precise language, domain-specific vocabulary, and techniques such as metaphor, simile and analogy to manage the complexity of the topic; keep a formal style and objective tone; and conclude by articulating implications or the significance of the topic.

What makes an idea complex. A complex idea has parts that depend on one another, so a reader who misunderstands the first part misreads the rest. Explaining it is different from arguing about it: an explanatory text does not ask the reader to take a side. It asks the reader to understand. The writer's analysis shows up in selection (which facts matter), in organization (which idea must come first) and in the relationships the writer states between ideas.

A clear and thorough thesis for explanation. An explanatory thesis states what the reader will understand and how the parts relate. "This essay is about costs" is a topic, not a thesis. "Two economic ideas, opportunity cost and sunk cost, explain why a good decision looks only at what can still change: opportunity cost adds a hidden cost to every choice, and sunk cost removes a cost that feels real but cannot be recovered" is thorough: it names both concepts, says what each does and states the relationship.

Organizing so each new element builds on the one before. Order matters most in complex explanation. Some order is fixed and some is chosen. The section Using both at once must come after both definitions, because it uses both. Placing opportunity cost before sunk cost is a choice the writer can justify (a sunk cost is easiest to see as a cost with no choice left attached to it) but not the only workable order. Headings let a reader see that order: The cost you do not see, The cost you cannot recover, Using both at once. A table can hold a comparison the prose would make tangled. Multimedia, such as a short interactive calculator in a digital version, belongs only when it aids comprehension; a decorative image does not.

Extended definitions, not dictionary definitions. An extended definition gives the term, its category, the conditions under which it applies, an example, and a non-example. Opportunity cost is a kind of cost: the value of the best alternative given up when a choice is made. Condition: it counts only the best alternative, not every alternative. Example: a student who works a four-hour Saturday shift at 12 dollars an hour instead of studying gives up the study time; a student who instead spends those four hours studying gives up 48 dollars of wages, and, if working is her best alternative and the options differ only in pay, that 48 dollars is the opportunity cost of studying. Non-example: the sum of all her alternatives (48 dollars of wages plus 42 of babysitting) is not the opportunity cost, because she could take only one. Opportunity cost is not limited to hidden costs: money actually spent also has an opportunity cost, the best other use of that money. Here the forgone wages are the implicit part. Sunk cost is a cost already paid that cannot be recovered whatever is decided next. Condition: it must truly be unrecoverable; a refundable deposit is not sunk.

Selecting facts appropriate to the audience's knowledge. The audience for the model is juniors and seniors who have not taken economics. They need concrete, everyday examples before any vocabulary, and the domain-specific words (explicit cost, marginal, recoverable) should each be defined at first use. A reader who already knows economics would need fewer definitions and a harder case.

Metaphor, simile and analogy to manage complexity. These techniques are tools for understanding, not ornaments. An analogy maps the structure of a familiar thing onto an unfamiliar one: "A sunk cost is like the fare for a train that has already left the station; the ticket in your hand does not change which train you should take next." The analogy works because the ticket, like a sunk cost, is paid and gone (take it to be a ticket that cannot be refunded or exchanged), and the decision now concerns only future trains. A simile makes a brief comparison with like or as; a metaphor makes it without them ("opportunity cost is the shadow of every choice"). Every comparison has a breaking point, and a careful writer states it: the train analogy suggests the past is always irrelevant, but information learned from past spending can still matter, even though the money cannot be recovered. The analogy also depends on its condition: a fare that could be refunded or exchanged is not sunk.

Transitions and syntax that clarify relationships. Varied transitions name exact relationships: by contrast, which is why, this depends on, the two ideas meet when. Syntax carries relationships too: a sentence built as "Not X, but Y" states a correction; a colon introduces the item that explains what precedes it.

Formal style, objective tone and disciplinary norms. Explanation in economics defines terms precisely, uses consistent numbers, and does not tell the reader what to value.

A conclusion that articulates implications or significance. The conclusion answers "so what?": what the reader can now do or notice because of the explanation.

Original model explanatory text — The Cost You Do Not See and the Cost You Cannot Recover.

Introduction. Every choice costs something, but the costs that most distort decisions are the ones people either overlook or cannot let go. Two economic ideas, opportunity cost and sunk cost, explain why a good decision looks only at what can still change.

The cost you do not see. Opportunity cost is the value of the best alternative given up when you choose. Suppose Maya can work a four-hour Saturday shift at 12 dollars an hour or spend those hours preparing for an exam. If she studies, the opportunity cost is the 48 dollars she did not earn. No money leaves her wallet, which is why the cost is easy to ignore; it is, in effect, the shadow cast by the choice not made.

The cost you cannot recover. A sunk cost is already paid and cannot be recovered. Suppose Maya bought a 30-dollar concert ticket that can be neither refunded nor resold, and on the night she has a fever. The 30 dollars is gone whether she goes or stays home, so it should not decide the question. Only the future matters: an evening at a concert while ill against an evening of rest. A sunk cost is like the fare for a train that has already left.

Using both at once. The two ideas meet whenever someone asks, "But I've already spent so much." The answer is to set aside what is sunk and compare the opportunity costs of the choices still open. The analogy has a limit: past spending can still teach something, even when the money cannot be recovered.

Conclusion. The significance is practical. A student deciding whether to stay in a course, a city deciding whether to finish a costly project, and a family deciding whether to repair an old car all face the same test: ignore what cannot be recovered, and count what will be given up.

Worked extended definition: Term: sunk cost. Category: a cost. Distinguishing feature: already paid and unrecoverable whatever is decided next. Condition: it must be truly unrecoverable; if a 30-dollar ticket could be resold for 20 dollars, only 10 dollars is sunk, and the 20 dollars of resale value becomes part of the opportunity cost of attending. Example: a ticket that can be neither refunded nor resold. Non-example: a refundable deposit. The condition is what makes the definition extended rather than a one-line gloss.

Worked opportunity-cost arithmetic: Maya's shift is 4 hours at 12 dollars an hour, so the wages given up by studying are 4 times 12, or 48 dollars. If she had a second alternative, babysitting for 3 hours at 14 dollars (42 dollars), the opportunity cost of studying is still 48 dollars, because opportunity cost counts only the best alternative given up, not the sum of all alternatives. This assumes the two jobs cannot both be done, differ only in pay and carry no costs of their own; a bus fare to work, for example, would lower the value of working and could change which alternative is best.

Worked analogy test: Analogy: "A sunk cost is like the fare for a train that has already left." Mapping: fare to money already spent; departed train to the choice that can no longer be changed; the next train to the decision still open. Where it holds: the fare, on a ticket that cannot be refunded or exchanged, does not change which train to take next. Where it breaks: a traveler may learn from missing the train, just as past spending can carry information. A writer who states the breaking point uses the analogy to manage complexity without introducing a new error.

Worked organization decision: Which order is required and which is chosen? The synthesis section's instruction, "compare the opportunity costs of the choices still open", depends on both terms, so it must come last; placing it earlier would use terms before defining them. The two definition sections could appear in either order. The writer puts opportunity cost first because the sunk-cost example (fever against concert) is itself a comparison of the choices still open, so a reader who already knows opportunity cost sees that comparison more quickly.

Representation record: Choose a complex idea from another course (for example, feedback loops in biology, checks and balances in government, or compound interest in mathematics). Build a four-column table: element, extended definition (category, conditions, example, non-example), what earlier element it depends on, and one metaphor, simile or analogy with its breaking point. Number the rows in the order a reader must learn them.

Independent performance: Write a 700-900-word explanatory text for classmates who have not studied the idea. Success criteria: a clear and thorough thesis that names the parts and their relationship; an organization in which each section builds on the one before, shown with at least two headings; one table or figure that aids comprehension; at least two extended definitions with conditions; facts, concrete details, a quotation or examples selected for the audience's knowledge; varied transitions and syntax that state relationships; domain-specific vocabulary defined at first use; at least one analogy with its limit stated; formal style and objective tone; a conclusion that articulates implications or significance. Every fact must be accurate; if you cite a figure, name its source.