Does one city-size pattern explain every city’s internal layout?
Your task: Plot city size against rank, then sketch the separate employment map. Choose a model for each scale and identify a place where its assumptions fail.
Read counts with their units. A percentage divides a part by its named whole and multiplies by 100. A model assumption is not an observed fact.
Urban hierarchy
An ordering of settlements by size, functions or service roles within a wider system.
Assumption
A condition accepted for a model or argument; it needs justification before applying the result elsewhere.
01 · TRY
Does one city-size pattern explain every city’s internal layout?
Plot city size against rank, then sketch the separate employment map. Choose a model for each scale and identify a place where its assumptions fail.
Plot city size against rank, then sketch the separate employment map. Choose a model for each scale and identify a place where its assumptions fail. Use the supplied records and show one intermediate step.
Make a provisional claim
Loading saved evidence…
Inspect evidence and test an explanation
The investigation controls appear when your local evidence is ready.
04 · UNDERSTAND
Connect evidence and mechanism
Compare urban hierarchy with neighborhood models
Question and record
Does one city-size pattern explain every city’s internal layout?
A fictional region has cities with populations 1000000, 500000, 333000 and 250000. A separate city map shows a central employment district, rail-linked manufacturing corridors and several suburban job centers.
The opening city examples and their worked graph use fictional teaching quantities, not observed policy outcomes. The separate published Census comparison later on this page uses observed 2020 counts, with source definitions supplied in the activity.
Mechanism and worked calculation
Rank-size and primate-city patterns describe urban systems, while concentric-zone, sector and multiple-nuclei models propose different internal spatial arrangements. Central-place ideas connect service thresholds and market ranges to settlement hierarchy. These models are analytical lenses, not universal stages or a license to erase regional histories.
Under a rank-size approximation P(r)=P(1)/r, the first region’s fourth city is predicted at250000, matching the table. The second region’s top-to-second ratio is6, unlike the ratio2 in the first. Neither ratio identifies its neighborhood pattern.
Challenge the interpretation
A second region has one city of 1800000 and a second of 300000. A neighborhood map includes informal housing and colonial infrastructure that do not match an idealized concentric pattern. Regional city size and internal land use are different scales.
Your evidence task
Plot city size against rank, then sketch the separate employment map. Choose a model for each scale and identify a place where its assumptions fail.
Revise your answer to “Does one city-size pattern explain every city’s internal layout?” using both source IDs. Separate the checked calculation from a judgment, and identify evidence that could reverse your judgment.
Vocabulary
Urban hierarchy: An ordering of settlements by size, functions or service roles within a wider system.
Assumption: A condition accepted for a model or argument; it needs justification before applying the result elsewhere.
Observed urban hierarchy: what are we ranking?
These are the complete ten entries in each Census-published national top-ten population table, not a hand-picked set and not every settlement. Both use April 1, 2020 population counts. City boundaries and Census urban-area boundaries include different people.
Predict: New York City has 8,804,190 residents and Los Angeles city has 3,898,747. Is the second city half the first? Would a comparison of densely developed urban areas necessarily give the same ratio? Record a reason before changing the geographic unit.
This worksheet is temporary and clears on reload/navigation. Copy the JSON report to retain it. Existing lesson progress and saved responses are unchanged.
The first list contains city populations within municipal boundaries. Governance and annexation can affect which residents are included. These top-ten cities are not the same units as the named urban areas. Changing this control changes the geographic definition and ranking; it is not a time-series comparison.
Reference assumption: take the first-ranked population and divide by rank: Preference(r) = P1 ÷ r. Here r is position in this published list, P1 is its first entry’s population, and the result is a reference count—not a forecast, fitted estimate or law.
On a narrow screen, focus this chart and use the arrow keys or swipe to inspect its full width. The values also appear in the table below.
Fixed scales across both geographic definitions. Observations are discrete circles; the dashed reference is an assumption. No observed line is interpolated. A first-rank match is guaranteed by the formula and is not evidence of fit.
Percentage deviation = 100 × difference ÷ reference = -11.43%. Positive means above this reference; negative means below it. This is not population growth or a causal effect.
First/second population ratio = 8,804,190 ÷ 3,898,747 = 2.2582. The reference ratio is 2. One ratio alone does not establish political importance, regional dominance or a primate-city classification.
Inspect all ten observed and reference values
City populations (published top ten) — people, April 1, 2020
The source’s city-table heading uses “urban places”; this does not mean the separate Census urban-area unit. See the Census geographic glossary and 2020 urban-area criteria. Legal boundaries reflect municipal organization; statistical urban boundaries answer a settlement-pattern question. Neither is inherently the right unit for every question.
Only attributed factual names, ranks and population counts are reproduced. Local record IDs are extract identifiers, not Census geographic codes. Matching similar names across these lists would not establish identical boundaries or prove that an entire city lies within an urban area. Do not add both lists together: their populations overlap.
Top-ten selection omits smaller places and cannot establish a national distribution’s full shape. No sample uncertainty, model fit test or causal identification is supplied. Differences could reflect many processes; this activity does not isolate any one explanation.
Worked interpretation: second rank
Los Angeles city is about 11.43% below the city-list reference of 4,402,095 people. Los Angeles–Long Beach–Anaheim urban area is about 25.99% above the urban-list reference of 9,713,224.5. Both the observed count and the anchor changed. This is evidence that the geographic definition matters, not that Los Angeles grew between the observations.
Apply to a changed rank and unit
Before loading the changed case, predict whether fourth-ranked Houston city and fourth-ranked Miami–Fort Lauderdale urban area refer to the same place. Inspect the names and calculate each deviation. Explain why subtracting these two observed populations would not measure growth or an annexation effect.
Keep the initial prediction. State the definition and rank in your revision; changing controls preserves writing but changes the current report rows. For a further check, choose rank 10 and explain why this different deviation does not prove that one entire list fits a universal model. These are practice tasks, not calibrated independent assessment.
Copy your analysis report
Copy to save separately; this is not a course-progress import format.
Independent extension
Independently extend the investigation “Compare urban hierarchy with neighborhood models” with a documented real dataset or scholarly source. Preserve definitions, recreate one calculation or evidence table, and compare a rival explanation. Distinguish the opening fictional examples from the observed Census counts; explain why neither a toy match nor one observed population ratio establishes a universal model or a causal conclusion.
Opening fictional example: worked graph
Discrete points are not interpolated. Table labels provide a non-color way to identify every series. Axes begin at zero.
Series
City rank
Population (thousands)
Fictional region
1
1000
Fictional region
2
500
Fictional region
3
333
Fictional region
4
250
Worked example
Under a rank-size approximation P(r)=P(1)/r, the first region’s fourth city is predicted at250000, matching the table. The second region’s top-to-second ratio is6, unlike the ratio2 in the first. Neither ratio identifies its neighborhood pattern.
