D2.Geo.3.9-12: Analyzing Spatial Patterns at Multiple Scales
In plain English: D2.Geo.3.9-12 is the C3 Framework geography indicator for grades 9-12 that asks students to use geographic data to analyze how spatial patterns of cultural and environmental characteristics vary at multiple scales. Students compare the same pattern across a nation, a group of states and the counties of one state, and test whether a conclusion drawn at one scale still holds at another.
Use geographic data to analyze variations in the spatial patterns of cultural and environmental characteristics at multiple scales.
C3 Framework for Social Studies (NCSS) · Dimension 2: Applying Disciplinary Concepts and Tools · Discipline: Geography · Geographic Representations: Spatial Views of the World · Official standard
Students analyze one cultural characteristic, the share of residents who report Norwegian ancestry, and one environmental characteristic, average annual precipitation, at three scales: the United States as a whole, six Northern states, and the 53 counties of North Dakota. All data are real: the cultural data come from the U.S. Census Bureau's American Community Survey (ACS) 2020-2024 5-year estimates, and the environmental data are 1991-2020 averages from NOAA's National Centers for Environmental Information (Climate at a Glance). Two county maps (Diagrams 1 and 2) were drawn for this page from Census boundary files.
The key idea of D2.Geo.3.9-12 is that variation depends on scale. A pattern that looks clear when states are compared can blur, or even reverse, when the same data are broken into counties. Students compute shares, read choropleth maps, interpret correlation coefficients and margins of error, and then judge two SVHS-written sample interpretations (Source 4) that reach different conclusions from the same data.
Learning Objectives
By the end of this lesson, students will be able to:
Compute and compare shares, counts and averages for a cultural and an environmental characteristic at national, state and county scales.
Describe how the spatial pattern of each characteristic varies at each scale, using numbers and map evidence.
Explain how choices about scale, units and choropleth classes change what a map or statistic appears to show.
Interpret correlation coefficients at two scales without treating a correlation as a cause or an area's average as a fact about individuals.
Evaluate an interpretation of geographic data by testing it at a second scale and naming the further data it needs.
Prior Knowledge Required
Students should already be comfortable with:
Making maps to display and explain spatial patterns of cultural and environmental characteristics D2.Geo.1.9-12
Integrating quantitative analysis, such as charts and research data, with analysis in text RH.9-10.7
Computing percentages and means, and reading a scatter plot
"A news story says, 'This state is one of the rainiest in the country.' Does that mean every town in the state is rainy? What would you need to know to check?"
Collect answers. Students usually see that a state average hides differences inside the state, and that you would need data for smaller places. Name the idea: scale. Today students look at the same two data sets at three scales and test whether a conclusion survives the change of scale.
Direct Instruction20 minutes
Key terms for D2.Geo.3.9-12 (working definitions)
Term
Meaning in this lesson
Geographic scale
The size of the area and of the units being compared: nation, states, counties, neighborhoods. Not the same as map scale (the ratio of map distance to real distance)
Unit of analysis
The area that each number describes, such as one county
Share and count
A share is a percent of an area's population; a count is the number of people. A small county can have a high share and a small count
Ancestry (ACS)
The ethnic origin or descent people report for themselves. People may report one or two ancestries, so shares for different ancestries can add up to more than 100%
Choropleth map
A map that shades each area by its value, using a set of classes (ranges) shown in the legend
Class breaks
The values where one shade ends and the next begins. Different breaks can make the same data look different
Gradient
A steady change in a value across space, such as precipitation rising from west to east
Correlation coefficient (r)
A number from -1 to +1 for how closely two variables move together in a straight-line way: near +1 or -1 is strong, near 0 is weak. It does not show cause
Ecological fallacy
The error of treating a pattern among areas as a fact about the individual people in them
Modifiable areal unit problem (MAUP)
Results can change when the same data are grouped into different units or at a different scale
Margin of error (MOE)
ACS numbers are survey estimates. The MOE gives a 90% range around the estimate; small populations have larger MOEs
Part 1: Three scales, one question. Draw three nested boxes on the board: United States, six Northern states, North Dakota's counties. Under each box, write the unit of analysis. Explain that the question "Where is Norwegian ancestry common, and does it line up with precipitation?" can be asked at each level, and that each level can give a different answer.
Part 2: Reading a choropleth. Walk through the legend of Diagram 1. Point out that the classes are 10 percentage points wide and that each county gets one shade, however many people live in it. Then show the worked examples.
National scale: computing a share
The ACS estimates that 3,920,371 of the 334,922,499 people in the United States report Norwegian ancestry. What share is that?
Result: 3,920,371 / 334,922,499 = 0.0117, so about 1.2% of U.S. residents. This one number is the national-scale value in Source 1.
County scale: share versus count
Burleigh County (home of Bismarck) has 13,648 residents who report Norwegian ancestry, 13.6% of its people. Divide County has 923, which is 42.6%. Which county would stand out on a share map, and which on a count map?
Result: On a share map, Divide stands out (42.6% against 13.6%). On a count map, Burleigh does, with 13,648 / 923 = about 15 times as many people. The two maps answer different questions.
Choropleth classes: how breaks shape a map
On Diagram 1, Cass (24.7%) and Richland (21.2%) share a shade. Pembina County, in the northeast corner, is 18.2% and gets a lighter shade than Richland.
Result: Cass and Richland differ by 24.7 - 21.2 = 3.5 points but look the same; Richland and Pembina differ by 21.2 - 18.2 = 3.0 points but look different. The break at 20% creates a visible edge that the data alone do not.
Reading a correlation coefficient
Source 3 reports r = -0.33 for German ancestry share and Norwegian ancestry share across the 53 counties. What does it mean?
Result: A weak negative relationship: counties with higher German shares tend, loosely, to have lower Norwegian shares. It does not say why, and it says nothing about any one family, since people can report both ancestries.
Teacher tip. Students often read r = +0.27 as "27% related." Correct this early: r is not a percent, and a value this close to 0 means the points are widely scattered around any straight line.
Guided Practice15 minutes
The state scale. Source 1 compares the nation with six Northern states. Work through it together.
Source 1: Norwegian ancestry and precipitation, nation and six states
Area
Population
Norwegian ancestry (% of residents)
Mean annual precipitation, 1991-2020 (inches)
United States
334,922,499
1.2
31.3 (contiguous U.S.)
North Dakota
784,841
20.3
18.8
Minnesota
5,739,445
12.1
28.6
South Dakota
907,428
10.4
21.2
Montana
1,116,875
7.5
18.9
Wisconsin
5,914,872
6.1
34.1
Iowa
3,210,507
4.2
35.5
Source 1: U.S. Census Bureau, American Community Survey 2020-2024 5-year estimates, tables B04006 and B01003; NOAA National Centers for Environmental Information, Climate at a Glance, statewide and national January-December precipitation, mean of 1991-2020. Percents and inches rounded to one decimal place.
Compare with the nation. Prompt: Minnesota's share is how many times the national share? Teacher note: 12.1 / 1.2 = 10.1, so about 10 times.
Rank the environment. Prompt: which of the six states get less precipitation than the contiguous U.S. average of 31.3 inches? Teacher note: North Dakota, Minnesota, South Dakota and Montana; Wisconsin and Iowa get more.
Name the unit. Prompt: what does one row of Source 1 describe? Teacher note: a whole state. Every resident of a state is summarized in one number, so differences inside a state are invisible at this scale.
Check the sample. Prompt: who chose these six states, and why might that matter? Teacher note: SVHS chose them as Northern states with notable Norwegian-ancestry shares. A different set of states could show a different relationship.
Independent Practice20 minutes
The county scale. Diagrams 1 and 2 map all 53 North Dakota counties. Source 2 lists 12 of them, the labeled counties, and Source 3 gives correlation coefficients that SVHS computed from the same data.
Source 2: Twelve North Dakota counties (ACS 2020-2024; NOAA 1991-2020)
County
Population
Norwegian ancestry (%)
German ancestry (%)
Precipitation (in)
Longitude of center (degrees W)
Divide
2,167
42.6
16.8
16.1
103.5
Williams
39,555
16.1
17.5
15.4
103.5
McKenzie
14,321
15.9
16.4
15.9
103.4
Slope
766
21.5
47.7
15.6
103.5
Stark
33,302
8.2
41.8
16.4
102.7
Rolette
11,924
7.3
6.6
18.7
99.8
Burleigh
100,600
13.6
43.8
18.5
100.5
McIntosh
2,497
4.5
57.6
20.8
99.4
Nelson
3,016
43.2
29.3
20.8
98.2
Griggs
2,245
38.6
28.1
21.0
98.2
Cass
193,400
24.7
35.1
22.8
97.2
Richland
16,584
21.2
42.8
24.2
96.9
Source 3: Correlation coefficients computed by SVHS from Sources 1 and 2 and the full 53-county data
Units compared
Variables
r
6 states in Source 1
Norwegian ancestry share and annual precipitation
-0.64
53 North Dakota counties
Norwegian ancestry share and annual precipitation
+0.27
53 North Dakota counties
Annual precipitation and longitude of the county's center (east is higher)
+0.95
53 North Dakota counties
German ancestry share and Norwegian ancestry share
-0.33
Source 2: U.S. Census Bureau, ACS 2020-2024 5-year estimates (B04006, B01003); NOAA NCEI Climate at a Glance, county January-December precipitation, mean of 1991-2020; county centers (area centroids) from Census 2023 cartographic boundary files. Each share is a survey estimate with a 90% margin of error, which is widest in the smallest counties: Divide is 42.6% plus or minus about 7.5 points, against about 1.2 points for Cass. Source 3: Pearson correlation computed by SVHS from these values, rounded to two decimal places.
Task (pairs). Complete a three-column organizer (Nation, States, Counties). In each column, write (1) what one data value describes, (2) how much the Norwegian-ancestry share varies, (3) how much precipitation varies and (4) what the two patterns look like together. Use at least two numbers per column.
Look for: the unit of analysis named correctly in each column; ranges given as low and high values with the place names; the direction of each gradient on the maps described in compass terms; and statements that compare patterns without saying that one causes the other.
Closure10 minutes
Two interpretations. Source 4 gives two SVHS-written sample interpretations of the same data. Students read it now and use it in the quiz and homework.
1Sample interpretation A (SVHS-written). I compared six Northern states using Source 1. North Dakota has the highest share of residents who report Norwegian ancestry, 20.3 percent, and it is also the driest of the six states, with 18.8 inches of precipitation in an average year. Iowa has the lowest share, 4.2 percent, and it is the wettest, with 35.5 inches.
2Across the six states, the pattern holds fairly well: the drier the state, the higher the share tends to be. My conclusion is that people of Norwegian ancestry chose dry places to live, so precipitation explains where this cultural characteristic is found.
3Sample interpretation B (SVHS-written). I looked one scale closer, at North Dakota's 53 counties in Diagrams 1 and 2. Precipitation changes smoothly across the state, from about 15 inches a year in the northwest to about 24 inches in the southeast. Norwegian ancestry does not follow that gradient. Divide County, in the dry northwest corner, has one of the highest shares in the state, 42.6 percent, but its even drier neighbor, Williams County, has only 16.1 percent, and Nelson County, which gets almost 5 inches more precipitation a year than Divide, has 43.2 percent.
4A pattern that appears at one scale can weaken, vanish or even reverse at another. Six states are also a small, hand-picked group. Before I said that precipitation explains the pattern, I would want historical data, such as where immigrants from Norway first settled and when, and I would test the idea again at more than one scale.
SVHS (sample interpretations written for this page), Two Sample Interpretations of One Pattern (Source 4: SVHS-written sample interpretations). Original passage written for this page.
Exit ticket: "One thing that looked true at the state scale but not at the county scale was ... One thing I would need to know before explaining the pattern is ..."
Teacher note on the data: ACS ancestry is self-reported, and a person may report two ancestries, so it measures identity and heritage, not birthplace. The Norwegian shares are estimates with margins of error, and the margins are widest in the counties with the fewest people. Precipitation values are 30-year averages, so any single year can be much wetter or drier. Source 4 is not real student work; it was written for this page to model two lines of reasoning.
Differentiation Strategies
For Struggling Students
Give the organizer with the unit of analysis already filled in for each column.
Before Source 3, have students sort five printed scatter plots from strong positive to strong negative, so r has a picture.
Pair each county in Source 2 with its label on both maps before students describe any pattern.
For Advanced Students
Ask them to download the same ACS table for the counties of South Dakota from data.census.gov and compare its county pattern with North Dakota's.
Ask them to compute a population-weighted mean of the 12 county shares in Source 2 and explain why it differs from the simple mean.
Assessment Guidance
What to Look For
Strong work names the scale and the unit of analysis, describes each pattern with correct numbers from the sources, notes how class breaks and margins of error affect what a map seems to show, and refuses to turn a correlation among areas into a claim about cause or about individuals. Watch for answers that treat r as a percent, that mix up shares and counts, or that read a state average as true of every county.
02
Classroom Activities
3 Activities
1
Zoom In, Zoom Out
15 minGroups of 3
Each group gets three scale cards: Nation, Six States and North Dakota Counties. Each card repeats the same question: "Where is Norwegian ancestry common, and does it line up with precipitation?"
Predict
Before looking at the data, each student writes a one-sentence prediction for each card. Predictions stay on the cards.
Check
Each student takes one card and answers it from the matching source: Source 1 (first row) for Nation, Source 1 for Six States, and Diagrams 1 and 2 with Source 2 for Counties. Each answer must quote at least two numbers and name the unit of analysis.
Compare
The group lines up the three cards and writes one "scale statement" that begins: "When we zoomed in from ... to ..., the pattern ..." Groups share their statements; the class looks for statements that mention both a cultural and an environmental characteristic.
2
Correlation Lab
20 minPairs
Pairs build two scatter plots in a spreadsheet from Source 2 and compute the correlation themselves, then compare their result with the 53-county value in Source 3.
Build
Enter the 12 counties of Source 2: county, Norwegian share, precipitation and longitude.
Make Scatter Plot A: precipitation across, Norwegian share up. Label every point with its county.
Use =CORREL on the two columns. With the rounded values in Source 2, the result is r = 0.16.
Make Scatter Plot B: longitude across (enter it as a negative number, so east is to the right), precipitation up.
Discuss
Compare r = 0.16 for 12 counties with r = 0.27 for all 53 counties in Source 3. Both are weak, and the value moved when more counties were added. Ask: Which two counties sit farthest above the cloud of points in Plot A? Which plot shows a near-straight line, and what does that say about the environmental pattern?
3
Same Data, Different Breaks
20 minPairs
Pairs color the 12 Source 2 counties on two blank North Dakota county outline maps, using different class breaks, and compare the stories the maps tell.
Map A
Use Diagram 1's four classes: under 10%, 10% to 19.9%, 20% to 29.9% and 30% or more. Leave the other 41 counties uncolored and write "no data on this map" in the legend.
Map B
Use two classes split at the median of the 12 shares. Sort the shares first: the median is halfway between the 6th and 7th values, (16.1 + 21.2) / 2 = 18.65%. Color counties at or above 18.65% dark and the rest light.
Compare
On Map B, six counties are dark: Richland, Slope, Cass, Griggs, Divide and Nelson. Ask: Which counties look alike on Map B but different on Map A? Which map makes North Dakota look more divided, and which choice of breaks would a careful geographer report, and why?
Variation: digital
Pairs with a GIS or web-map tool load the county layer, join the Source 2 values and switch between equal-interval and quantile classes, recording how many counties change shade.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Norwegian Ancestry by County, North Dakota
Choropleth map of the share of residents in each of North Dakota's 53 counties who report Norwegian ancestry (U.S. Census Bureau, ACS 2020-2024 5-year estimates, tables B04006 and B01003). Classes are 10 percentage points wide. Labeled counties are the 12 in Source 2. County outlines: Census 2023 cartographic boundary files.
Diagram 2: Mean Annual Precipitation by County, North Dakota
Choropleth map of mean January-December precipitation, 1991-2020, for the same 53 counties (NOAA National Centers for Environmental Information, Climate at a Glance). Classes are 2 inches wide, with open-ended top and bottom classes. Counties are classed by their value rounded to one decimal place.
04
Homework Assignment
~30 min
D2.Geo.3.9-12 Homework: Testing the Pattern in Minnesota
Directions: Use Source 5 below, Sources 1-4 and Diagrams 1-2. A spreadsheet is allowed. Source 5, eight Minnesota counties from west to east (ACS 2020-2024 5-year estimates; NOAA mean annual precipitation 1991-2020; longitude of the county's center): Clay: 66,059 residents, 17,860 reporting Norwegian ancestry, 25.0 in, 96.49 degrees W; Norman: 6,367 residents, 2,704 reporting Norwegian ancestry, 24.0 in, 96.46 degrees W; Polk: 30,705 residents, 10,296 reporting Norwegian ancestry, 23.2 in, 96.40 degrees W; Otter Tail: 60,475 residents, 15,611 reporting Norwegian ancestry, 26.7 in, 95.71 degrees W; Stearns: 160,865 residents, 11,609 reporting Norwegian ancestry, 29.3 in, 94.61 degrees W; Hennepin: 1,269,496 residents, 126,553 reporting Norwegian ancestry, 31.9 in, 93.48 degrees W; Ramsey: 542,945 residents, 44,756 reporting Norwegian ancestry, 32.5 in, 93.10 degrees W; Houston: 18,653 residents, 4,058 reporting Norwegian ancestry, 37.2 in, 91.49 degrees W. Show your work for every number.
Part 1: Compute and Classify (Problems 1-3)
Compute the Norwegian-ancestry share for every county in Source 5, to one decimal place. Which county has the most residents of Norwegian ancestry, and which has the highest share? Explain why they are not the same county.
Place each of the eight counties in one of Diagram 1's four classes. Then sketch a simple choropleth: draw the eight counties as boxes in west-to-east order and shade each by its class, with a legend.
Describe the precipitation pattern in Source 5 with the lowest and highest values and their counties. Compare its range with the range of the 12 North Dakota counties in Source 2.
Part 2: Analyze Across Scales (Problems 4-6)
Compute r for Norwegian share and precipitation across the eight Minnesota counties, using your shares from Problem 1 and the precipitation values in Source 5 (round r to two decimal places). Compare it with the two r values for Norwegian share and precipitation in Source 3.
Give two reasons, drawn from the key terms of this lesson, why the r values for six states, 53 North Dakota counties and eight Minnesota counties could differ so much.
Write a 150-200 word evaluation of Interpretation A in Source 4 (paragraphs 1-2). Use evidence from at least two scales, say whether the evidence supports A's conclusion, and describe one further data set, at any scale, that would test the idea more fairly.
Rubric
Criterion
3: Strong
2: Developing
1: Beginning
Computation
Shares, ranges and r are correct and shown step by step
One or two small errors
Several errors or no work shown
Map and classes
Every county in the right class; legend complete; order west to east
One county misclassed or legend incomplete
Classes or legend missing
Scale reasoning
Explains differences with scale, units of analysis, sample choice and the ecological fallacy, using the lesson's terms
Names one reason with some support
No reasoning about scale
Evaluation
Judges A with evidence from two or more scales and proposes a fitting data set
Judges A with evidence from one scale
Gives an opinion without evidence
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Questions 1, 9, 10 and 13 use Source 1 (Guided Practice). Questions 2, 4, 7, 8, 11 and 15-16 use Sources 2 and 3 and Diagrams 1-2 (Independent Practice). Questions 5, 6, 17 and 18 use Source 4, the two sample interpretations in Closure. Choose an answer to see whether it is right; for short-answer questions, write your answer before opening the model answer.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
Use Source 1. North Dakota's Norwegian-ancestry share is about how many times the national share?
Answer: B
B is right: 20.3 / 1.2 = 16.9, about 17 times (the unrounded counts give 17.3). C subtracts instead of dividing (20.3 - 1.2 = 19.1 points). A uses Minnesota's share (12.1 / 1.2 = 10.1). D compares North Dakota with Minnesota (20.3 / 12.1 = 1.7), not with the nation.
Question 2 of 20 · Multiple Choice
Use Source 2. What is the range (highest minus lowest) of Norwegian-ancestry shares among the 12 counties?
Answer: C
C is right: Nelson 43.2% minus McIntosh 4.5% = 38.7 percentage points. A subtracts the state share (43.2 - 20.3 = 22.9). B subtracts the national share (43.2 - 1.2 = 42.0). D adds the two values (43.2 + 4.5 = 47.7) instead of subtracting.
Question 3 of 20 · Multiple Choice
Source 3 gives r = -0.64 for Norwegian share and precipitation across six states, and r = +0.27 across 53 North Dakota counties. What is the best conclusion?
Answer: A
A is right: the same two variables are moderately negative at the state scale and weakly positive at the county scale, which is the scale effect geographers call the modifiable areal unit problem. B treats correlation as cause. C assumes that results must agree across scales. D misreads both values: -0.64 is negative, and +0.27 is weak.
Question 4 of 20 · Multiple Choice
Source 3 gives r = +0.95 for precipitation and the longitude of each North Dakota county's center (east is higher). What does this show?
Answer: C
C is right: an r this close to +1 means precipitation climbs almost in a straight line as you move east, the gradient on Diagram 2. A confuses the two variables: Norwegian share is not part of this correlation. B and D bring in population, which this r does not measure.
Question 5 of 20 · Multiple Choice
In paragraph 2 of Source 4, which reasoning error does Interpretation A make?
Answer: D
D is right. Interpretation A concludes that "people of Norwegian ancestry chose dry places to live" from a pattern among six state averages: that is the ecological fallacy, plus a jump from correlation to cause. Option A is wrong because the interpretation's numbers do match Source 1 (20.3%, 18.8 inches, 4.2%, 35.5 inches). Option C reverses what the interpretation did: it compared states only. Option B is wrong because inches are the units Source 1 uses.
Question 6 of 20 · Multiple Choice
In paragraph 3 of Source 4, what evidence does Interpretation B use against A's conclusion?
Answer: A
A is right: B points to Divide County (42.6 percent) and its "even drier neighbor, Williams County," with only 16.1 percent, and to Nelson County, which is wetter than both yet has 43.2 percent. If dryness explained the pattern, Williams would not be so far below Divide, and Nelson would be lower. B, C and D are not in paragraph 3; B confuses the national scale with the county scale.
Question 7 of 20 · Multiple Choice
Which county in Source 2 falls in the darkest class on both Diagram 1 and Diagram 2?
Answer: D
D is right: Griggs is 38.6% (30% or more) and 21.0 inches (21 inches or more). Divide and Nelson are in the darkest class on Diagram 1 only (Divide gets 16.1 inches; Nelson gets 20.8). Cass is in the darkest class on Diagram 2 only (24.7% Norwegian).
Question 8 of 20 · Multiple Choice
The ACS estimate for Slope County (766 residents) is 21.5% Norwegian, with a margin of error of about 6.7 percentage points; for Cass County (193,400 residents) it is 24.7% with a margin of about 1.2 points. Which statement is best supported?
Answer: C
C is right: survey estimates for small populations are less precise, so Slope's 90% range (about 14.8% to 28.2%) is wide and overlaps Cass's range (about 23.5% to 25.9%). A ignores that overlap. B reverses the relationship between population and precision. D treats overlapping ranges as proof of equal values.
Question 9 of 20 · Multiple Choice
The simple mean of the 53 county shares is 21.1%, but North Dakota's statewide share in Source 1 is 20.3%. Why are they different?
Answer: A
A is right: the statewide share is all reporters divided by all residents, so large counties weigh more; the simple mean gives tiny Slope County the same weight as Cass. B is false: both come from the same ACS table. C is false: every county is included. D goes too far: shares can be averaged, but the method has to be stated.
Question 10 of 20 · Multiple Choice
Cass County has 47,748 residents who report Norwegian ancestry, and North Dakota has 158,982 in all. What share of the state's Norwegian-ancestry residents live in Cass County?
Answer: D
D is right: 47,748 / 158,982 = 0.300, so 30.0%. C is Cass's own share of its residents (a different question). B is the statewide share. A divides by the national total of 3,920,371 instead of the state total.
Question 11 of 20 · Multiple Choice
Use Source 2 and Diagram 1. McIntosh County has the lowest Norwegian share among the 12 counties. What does its German-ancestry share suggest?
Answer: D
D is right: McIntosh is 57.6% German, the highest German share in Source 2, so a different cultural pattern is strong where the Norwegian one is weak. A is contradicted by the data. C is wrong: people may report two ancestries, and many report others. B makes a causal claim that no source supports.
Question 12 of 20 · Multiple Choice
A student wants to know whether Norwegian ancestry varies among neighborhoods within Fargo, in Cass County. Which data would she need?
Answer: B
B is right: neighborhoods are smaller than a county, so she needs a finer unit of analysis, such as census tracts, which the ACS publishes. C is the scale she already has: one number for the whole county cannot show differences inside it. A and D are coarser still.
Question 13 of 20 · Multiple Choice
Which statement about precipitation is supported at both the state scale and the county scale?
Answer: B
B is right: 18.8 inches against 31.3 inches at the state scale, and from Williams (15.4 inches) in the west to Richland (24.2) in the east at the county scale. A reverses both. C contradicts Source 1 and Diagram 2. D gets the first half right but reverses the gradient.
Question 14 of 20 · Multiple Choice
Paragraph 4 of Source 4 calls the six states "a small, hand-picked group." Which change would make Interpretation A's state-scale comparison fairer?
Answer: A
A is right: a full set of states removes the chance that the choice of states created the pattern. B and C make the sample even more hand-picked, since they drop or keep states based on their values. D changes the units, which cannot change a correlation. Even with all 50 states, the result would still be a state-scale pattern, so it would not show why individuals settled where they did.
Question 15 of 20 · Short Answer
Describe the west-to-east variation in precipitation across North Dakota, using at least four values from Source 2. Which scale shows this variation, and why is it invisible in Source 1?
Model answer: Precipitation rises from the west to the east: Williams 15.4 inches and Divide 16.1 in the northwest, Burleigh 18.5 in the middle, Cass 22.8 and Richland 24.2 in the east. Only the county scale shows it; Source 1 gives one statewide average (18.8 inches), which blends the dry west and the wetter east into a single number. Rubric: 1 point for four correct values in order, 1 for naming the county scale, 1 for the reason.
Question 16 of 20 · Short Answer
Compare the spatial pattern on Diagram 1 with the pattern on Diagram 2. Name one region where they seem to match and one where they clearly do not.
Model answer: Diagram 2 is a simple west-to-east gradient. Diagram 1 is patchier: the darkest Norwegian classes are in the north and east (Nelson 43.2%, Griggs 38.6%) but also in the dry northwest (Divide 42.6%), while the lightest classes are in the south-central counties (McIntosh 4.5%) and in Rolette (7.3%). The patterns match in the east-central counties, which are both wet and high in Norwegian share. They do not match in the northwest, which is dry yet high in share, or in McIntosh, which is fairly wet yet low. Rubric: 1 point for each pattern, 1 for a match and 1 for a mismatch, each with a county and value.
Question 17 of 20 · Short Answer
Use Sources 3 and 4 to explain how a conclusion about Norwegian ancestry and precipitation can change with scale.
Model answer: Across six states, r = -0.64: drier states tend to have higher shares, which led Interpretation A to its conclusion. Across North Dakota's 53 counties, r = +0.27, a weak link in the other direction, and paragraph 3 of Source 4 gives counties that break the state-scale pattern. Grouping people into larger units hides the variation inside them, so the relationship one sees depends on the units chosen (the modifiable areal unit problem). Rubric: 1 point for each r with its scale, 1 for the explanation.
Question 18 of 20 · Short Answer
Evaluate Interpretation A (Source 4, paragraphs 1-2). Is its evidence accurate? Is its conclusion supported?
Model answer: A's numbers are accurate: Source 1 shows North Dakota at 20.3% and 18.8 inches and Iowa at 4.2% and 35.5 inches. The conclusion is not supported. It rests on six hand-picked states, it treats a pattern among state averages as a fact about why people settled where they did (the ecological fallacy), and it reads a correlation as a cause. Interpretation B shows that the pattern does not hold inside North Dakota. Rubric: 1 point for checking the evidence, 2 points for two flaws in the reasoning.
Question 19 of 20 · Short Answer
Interpretation B wants to know "where immigrants from Norway first settled and when." Describe one data set that could answer this, the scale you would use, and what result would support or weaken A's idea.
Model answer: Historical census counts of people born in Norway, by county, from around 1900-1920, mapped at the county scale. If Norway-born settlers had clustered in the driest counties no matter when land was available, that would support A; if they settled wherever land opened first, wet or dry, that would weaken A and point to history rather than precipitation. Rubric: 1 point for a fitting data set, 1 for the scale, 1 for a clear supporting and weakening result.
Question 20 of 20 · Short Answer
Rolette County contains the Turtle Mountain Reservation, home of the Turtle Mountain Band of Chippewa Indians (U.S. Census Bureau, 2023 AIANNH Gazetteer), and its Norwegian share is 7.3%. What does this suggest about mapping only one ancestry, and what second data layer would you add?
Model answer: A low Norwegian share does not mean a county lacks a strong cultural identity; it may mean that most residents have other heritages, as is likely in a county that includes a reservation. A map of one ancestry shows only one strand of a place's culture. I would add a layer from the ACS race and ethnicity tables, such as the share of residents who report American Indian and Alaska Native identity, or an ancestry layer for another group. Rubric: 1 point for the limit, 1 for a fitting second layer.
0 of 20 answered · 0 correct
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Frequently Asked Questions
10 Questions
What does D2.Geo.3.9-12 mean?
D2.Geo.3.9-12 asks high school students to use real geographic data to analyze how spatial patterns vary at more than one scale. Students look at a cultural characteristic and an environmental characteristic at, for example, the national, state and county levels, and explain what changes when they zoom in or out.
What does "at multiple scales" mean in D2.Geo.3.9-12?
It means comparing the same pattern using different sizes of area. Geographic scale is about the units being compared (countries, states, counties, neighborhoods), not the ratio printed on a map. A pattern can look different, or even reverse, from one scale to another.
How is D2.Geo.3.9-12 different from the grades 6-8 version?
D2.Geo.3.6-8 focuses on making and reading maps and graphs, on paper and on a computer. The 9-12 indicator assumes those skills and adds analysis of variation across scales, using geographic data such as census estimates and climate records.
Why use ancestry data from the American Community Survey?
The ACS is the Census Bureau's yearly survey, and it publishes the same tables for the nation, states, counties and smaller areas, which makes it ideal for comparing scales. Ancestry is self-reported heritage, so it is a cultural characteristic rather than a birthplace. Five-year estimates are used for counties because they pool more responses.
Where can students get the data themselves?
ACS tables such as B04006 (ancestry) and B01003 (total population) are free on data.census.gov. County, state and national precipitation series are free from NOAA's Climate at a Glance at ncei.noaa.gov. Both download as spreadsheets.
What is the ecological fallacy, and why does it matter here?
It is the mistake of reading a pattern among areas as a fact about individuals. A correlation between state averages cannot tell you why any one family settled where it did, so geographers test ideas at other scales and with other evidence.
Do students need to calculate correlation coefficients by hand?
No. A spreadsheet function such as CORREL gives r in seconds. The skill this indicator needs is interpretation: knowing that r runs from -1 to +1, that values near 0 are weak, and that r measures association, not cause.
How should teachers handle margins of error?
Treat them as part of the data. ACS estimates for counties with few people have wide margins, so small differences between small counties may not be real. Ask students to check whether two ranges overlap before they rank places.
Is this lesson about immigration history?
Only as a question to investigate. The lesson uses present-day ancestry data and does not claim why people settled where they did; students propose historical data, such as old census counts of people born abroad, that could test explanations.
What comes after D2.Geo.3.9-12?
Related 9-12 indicators ask students to explain human-environment interactions (D2.Geo.4.9-12) and to evaluate how political and economic decisions shaped places (D2.Geo.5.9-12). The scale reasoning practiced here carries into any course that uses census or climate data.
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Related Standards
5 standards
These standards connect to D2.Geo.3.9-12: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
D2.Geo.3.6-8Prerequisite
Use paper and electronic maps and graphs to show and analyze spatial patterns
Evaluate how long-term climate variability affects migration, settlement and land use
Lesson coming soon
Standard text: National Council for the Social Studies (NCSS), The College, Career, and Civic Life (C3) Framework for Social Studies State Standards: Guidance for Enhancing the Rigor of K-12 Civics, Economics, Geography, and History (Silver Spring, MD: NCSS, 2013). NCSS was not involved in the production of this lesson and does not endorse it.
