D1.3.6-8: Explaining Where Experts Agree on a Supporting Question

Overview

Lesson Procedure

60-70 minutes of class time across 5 phases.

1. Warm-Up5-10 minutes
2. Direct Instruction20 minutes
3. Guided Practice15 minutes
4. Independent Practice15 minutes
5. Closure5-10 minutes

1. Warm-Up5-10 minutes

   Warm-Up Prompt

   "Your family asks three different people how long it takes to bake bread: a baker, a cookbook writer and your neighbor. All three say 'about an hour.' Then they give different tips. Which answer would you trust most, and why?"

   Take four or five answers. Many students will say they trust the hour because all three said it. Name the idea: when people who know a subject well say the same thing, that shared answer is a point of agreement, and it is usually a strong place to start. The tips are different, so they are not points of agreement, even if each tip is good.

   Show a world map drawn on the Mercator projection (one method of drawing the round Earth on flat paper, explained in Direct Instruction) next to a globe, if you have them. Ask: "Greenland and South America: which looks bigger on the map? Which is bigger on the globe?" Leave the question open; the sources will answer it.

2. Direct Instruction20 minutes

   Part 1: The words of this standard. Write these on the board and keep them up all lesson.

   • A compelling question is a big question worth arguing about, such as "Do world maps tell the truth?"
   • A supporting question is a smaller question that helps answer the big one. It can usually be answered with sources, such as "What does a Mercator map show well, and what does it show badly?"
   • An expert is a person who has studied a subject closely, often as their job: a mapmaker, an economist, a historian, a judge.
   • A disciplinary concept is a big idea that one field of social studies uses. Map projection is a geography concept; supply is an economics concept; a rule or law is a civics concept.
   • An interpretation is an explanation of what an idea means or what it shows. "The map makes Greenland look too big" is an interpretation.
   • An application is a statement about how to use the idea, or what to do because of it. "Use this map to steer a ship" is an application.
   • A point of agreement is something that every expert you are reading says, even if they use different words.

   D1.3.6-8 asks students to explain points of agreement, so a list is not enough. A full explanation names the point, shows the words each expert uses, and says whether the point is about interpretation or application.

   Part 2: The geography words in Sources 1 and 2. The topic is a vehicle for the skill; students do not need to master map math. Explain these words before reading:

   • Map projection: a method for drawing the round Earth on a flat sheet. Every projection stretches or squeezes something. The Mercator projection is one method, named for Gerard Mercator, who published it on a world map in 1569 (the book quoted in Source 1 gives this history on page 101). Diagram 2 shows how much the Mercator map enlarges areas at different latitudes.
   • Equator: the imaginary line around the middle of the Earth. Latitude tells how far north or south of the Equator a place is, in degrees (°), from 0° at the Equator to 90° at the poles. Parallels are the east-west lines of latitude; meridians are the north-south lines.
   • Area: how much surface a place covers. To exaggerate is to make something look bigger than it is.
   • Navigation: finding the way, especially for ships. A compass course, or bearing, is one direction kept the whole way, such as "northwest." A marine chart is a map for sailors.
   • Equal-area map: a map that shows every place at its true size compared with every other place.

   1The parallel of 60° latitude is just one-half of the length of the Equator. A square-degree quadrangle at 60° of latitude has the same length north and south as has such a quadrangle at the Equator, but the extent east and west is just one-half as great. Its area, then, is approximately one-half the area of the one at the Equator. Now, on the Mercator projection the longitude at 60° is stretched to double its length, and hence the scale along the meridian has to be increased an equal amount. The area is therefore increased fourfold. At 80° of latitude the area is increased to 36 times its real size, and at 89° an area would be more than 3000 times as large as an equal-sized area at the Equator. This excessive exaggeration of area is a most serious matter if the map be used for general purposes, and this fact ought to be emphasized because it is undoubtedly true that in the majority of cases peoples' general ideas of geography are based on Mercator maps. On the map Greenland shows larger than South America, but in reality South America is nine times as large as Greenland. As will be shown later, this projection has many good qualities for special purposes, and for some general purposes it may be used for areas not very distant from the Equator. No suggestion is therefore made that it should be abolished, or even reduced from its position among the first-class projections, but it is most strongly urged that no one should use it without recognizing its defects, and thereby guarding against being misled by false appearances.

   [...]

   2In view of the frequent misunderstanding of the properties of this projection, a few words as to its true merits may be appropriate. It is by no means an equal-area representation, and the mental adjustment to meet this idea in a map of the world has caused unnecessary abuse in ascribing to it properties that are peculiarly absent. But there is this distinction between it and others which give greater accuracy in the relative size or outline of countries—that, while the latter are often merely intended to be looked at, the Mercator projection is meant seriously to be worked upon, and it alone has the invaluable property that any bearing from any point desired can be laid off with accuracy and ease. It is, therefore, the only one that meets the requirements of navigation and has a world-wide use, due to the fact that the ship's track on the surface of the sea under a constant bearing is a straight line on the projection.

   1The distance between successive parallels increases rapidly with the latitude, and the poles are at infinity. Hence it is obvious that the projection is entirely unsuited for representing high latitudes.

   2The values of y are tabulated, and the projection is very easy to draw. It is usual to find in Atlases a map of the World on Mercator's projection, and these maps are responsible for very much misconception as to the size of northern countries such as Siberia, Greenland, or the northern portions of the Dominion of Canada. [...]

   3Use in navigation. The great distortion in the north and south makes Mercator's projection altogether unsuitable for a land map. Its celebrity is due to the fact that it is invaluable for marine charts, and the reason is easily seen: the compass course between any two points on a Mercator chart is the straight line joining them. [...] Hence a ship's course from point to point can be taken at once from the chart. [...] The fact that a long voyage is not generally made on a uniform compass bearing does not alter the fact that the use of the Mercator chart in navigation is almost universal.

   Part 3: Who are these experts? Source 1 was written in 1921 by two map experts at the U.S. Coast and Geodetic Survey, a federal mapping agency; the book's title page lists Charles Deetz as its cartographer. Source 2 was written in 1912 by Arthur Hinks, who taught mapmaking at the University of Cambridge in England. They worked nine years apart, in different countries. When experts like that say the same thing, the point is hard to dismiss.

   Part 4: Model the move. Think aloud through the examples below. For each one, say four things: the supporting question, the point both experts make, each expert's own words, and whether the point is an interpretation or an application. Then show students one trap (Example 3): an expert who says something stronger than the other is not in full agreement with them.

   • Interpretation, geography (Sources 1 and 2)

     Supporting question: Does a Mercator world map show the true sizes of countries far from the Equator?

     Result: Point of agreement: no; both experts say the map makes lands far from the Equator look much larger than they are. Source 1, paragraph 1: "This excessive exaggeration of area is a most serious matter." Source 2, paragraph 1: the projection is "entirely unsuited for representing high latitudes." Type: interpretation, because it explains what the map shows.

   • Application, geography (Sources 1 and 2)

     Supporting question: What job is a Mercator map best for?

     Result: Point of agreement: steering ships. Source 1, paragraph 2: it is "the only one that meets the requirements of navigation." Source 2, paragraph 3: it is "invaluable for marine charts." Both give the same reason: a ship holding one compass course follows a straight line on this map. Type: application, because it says how to use the map.

   • A trap: one expert goes further (Sources 1 and 2)

     Supporting question: Should people ever use a Mercator map for land?

     Result: Not a full point of agreement. Source 2, paragraph 3, calls the map "altogether unsuitable for a land map." Source 1, paragraph 1, says it "may be used for areas not very distant from the Equator." The safe shared point is narrower: neither expert trusts it for comparing the sizes of lands far from the Equator.

   Ask the warm-up question again: Greenland or South America? Source 1, paragraph 1, gives the answer and the reason. Students who said "the map shows Greenland bigger" were reading the map correctly; the map itself is what misleads.

3. Guided Practice15 minutes

   Now the same skill in a different field. Pairs read Source 3, three invented economists answering one supporting question about strawberry prices. Words to know: supply is the amount of something for sale; demand is how much of it people want to buy; a fruit is in season when local farms are harvesting it. Pairs fill in a chart with three columns: Point, Who says it (with their words), and Interpretation or application? They mark a point "agreement" only if all three experts say it.

   1An invented seventh-grade class was studying the compelling question "Is it fair that some foods cost more at certain times of year?" The class wrote a supporting question, "Why do strawberries cost more at the Millbrook market in January than in June?", and asked three invented economists to answer it.

   2Dr. Ruiz: In June, dozens of local farms pick strawberries at the same time. The supply, the amount for sale, is large, and sellers lower their prices so the berries sell before they spoil. In January no local farm has any. The berries come by truck from far away, and fewer of them reach the market. When the supply falls and people still want berries, the price rises.

   3Ms. Okafor: The price depends on supply and demand. Demand is how much people want to buy. In January the supply of strawberries in Millbrook is small, so the price goes up. A family that wants to save money can buy frozen berries in winter, or buy apples, which are in season then.

   4Mr. Lind: The long truck trip adds a cost in January, and that cost is part of the price. But the bigger reason is the small supply: shoppers who still want strawberries compete for fewer of them. My advice to the market is to post a chart showing which fruits are in season each month, so families can plan what to buy.

   Teacher key.

   • Point of agreement (interpretation): the price rises in January because the supply of strawberries is small. Dr. Ruiz, paragraph 2: "When the supply falls and people still want berries, the price rises." Ms. Okafor, paragraph 3: "the supply of strawberries in Millbrook is small, so the price goes up." Mr. Lind, paragraph 4: "the bigger reason is the small supply."
   • Not a point of agreement: the truck trip. Dr. Ruiz mentions the berries coming by truck, and Mr. Lind says the trip "adds a cost," but Ms. Okafor never mentions it.
   • Partial agreement about application: Ms. Okafor and Mr. Lind both say families can plan their buying around the seasons (frozen berries or apples; a chart of in-season fruit). Dr. Ruiz gives no advice, so this is agreement between two experts, not all three. Say so in those words.

   Discuss: "Is the truck trip wrong just because not everyone mentions it?" No. A point can be true and still not be a point of agreement. The skill is about what the experts share.

4. Independent Practice15 minutes

   Each student writes a short explanation, four to six sentences, answering the supporting question "What do the two map experts agree a Mercator map is good for and bad for?" The explanation must include one point of agreement about interpretation and one about application, with words from each source and a paragraph number for each quote. Post this frame for students who need it:

   Both experts agree that ___. Source 1 says "___" (paragraph __), and Source 2 says "___" (paragraph __). This is an interpretation/application because ___.

   Students who finish early find one thing that only one of the two experts says, and explain why it is not a point of agreement. Collect the explanations and check them with the rubric under the homework.

5. Closure5-10 minutes

   Exit ticket: On an index card, answer: "Why is it not enough to say 'the experts agree'? What else must you show?" Strong answers say you must name the point and show each expert's own words.

   Teacher note on the sources: Sources 1 and 2 are quoted exactly from their 1921 and 1912 printings, with left-out text marked [...]; a few obvious scanning errors in the digital copy of Source 1 were corrected to match the printed words. Source 1 says that at 80° of latitude an area is shown "36 times its real size." On a globe-shaped Earth the Mercator stretch at 80° works out to about 33 times, so the book's figure is a little high; its other figures (four times at 60°, more than 3,000 times at 89°) match the formula. Source 1's "nine times" for South America and Greenland is also a little high: with modern figures (South America about 17.8 million square kilometers, Greenland about 2.17 million) South America is about eight times as large. The point the two experts share does not depend on the exact numbers. Sources 3, 4 and 5 are invented scenarios written for this page; the people in them are not real.

   Quiz passage. Questions 11-18 of the quiz use Source 4, an invented student council question.

   1The student council at the invented Lakeview Middle School has a constitution, a set of written rules for how the council works. One rule says: "Council money may be spent only on things that serve the whole student body." The chess club asked the council to buy club uniforms. The council asked three invented experts the supporting question "What does the club fund rule mean, and does it allow the council to buy uniforms for the chess club?"

   2Ms. Haddad, a civics teacher: The rule means the money belongs to all students, so it should pay for things that all students can use. The uniforms would be worn by the 15 members of the chess club and no one else, so the rule does not allow them. The council could buy chess sets for the library instead, since any student can borrow those.

   3Mr. Brandt, a city council clerk: "Serve the whole student body" means the benefit must be open to every student, even if not every student chooses to use it. Uniforms belong only to club members, so they do not fit the rule. A school-wide chess tournament with free entry would fit.

   4Dr. Osei, a law professor: Rules like this one exist so that a small group cannot spend everyone's money on itself. The uniforms fail that test. I would add that the council should write down its reason every time it spends money, so students can check its choices.

   Homework passage. The homework uses Source 5, an invented town's question about why its old sawmill closed.

   1The invented town of Pine Hollow had a large sawmill from 1880 to 1912. Today the town owns a young forest and must write a plan for cutting it. The town committee asked three invented historians the supporting question "Why did the Pine Hollow sawmill close in 1912?"

   2Dr. Ames: The mill closed because the forest near it was gone. By 1910 the mill's own records show it was hauling logs from 30 miles away, compared with 2 miles in 1885. Hauling logs that far cost more than the lumber was worth. If the town wants its forest to last, it should cut trees slowly enough that the forest can grow back.

   3Ms. Ito: Photographs in the town museum show bare hills around Pine Hollow by 1905. The company cut the nearby trees much faster than new ones could grow. When the close trees were gone, the mill could no longer make money. A forest plan should count how much wood the forest grows each year and cut less than that.

   4Mr. Delgado: Newspapers in 1912 blamed a fire at the mill. But the fire was small, and the owners chose not to rebuild. I think they did not rebuild because the timber nearby was used up. I would also like to find out whether lumber prices fell in 1911 and 1912.

Differentiation Strategies

Assessment Guidance

1. Question 1 of 20 · Multiple Choice

   Source 1, paragraph 1, and Source 2, paragraph 2, share a point of agreement about how Mercator world maps have affected people. What is it?

   AMercator maps were the first maps ever drawn of the whole world BShips that used Mercator maps were often lost at sea in the north CMercator maps have given many people wrong ideas about sizes DMercator maps cost too much to print for most school atlases

2. Question 2 of 20 · Multiple Choice

   Source 2, paragraph 1, says the Mercator projection is "entirely unsuited for representing high latitudes." Which words from Source 1 make the same point with a number?

   A"At 80° of latitude the area is increased to 36 times its real size" B"The parallel of 60° latitude is just one-half of the length of the Equator" C"It is by no means an equal-area representation" D"the ship's track on the surface of the sea under a constant bearing is a straight line"

3. Question 3 of 20 · Multiple Choice

   Which sentence from Source 1 is an application rather than an interpretation?

   A"It is by no means an equal-area representation" B"No suggestion is therefore made that it should be abolished" C"This excessive exaggeration of area is a most serious matter" D"The area is therefore increased fourfold"

4. Question 4 of 20 · Multiple Choice

   Two invented historians write about the invented town of Elm Falls. Historian 1: "The town grew after the bridge opened in 1890, because farmers could now reach its market." Historian 2: "Once the 1890 bridge let farm wagons cross the river, the Elm Falls market doubled." What is their point of agreement?

   AThe town market doubled in size during 1890 BFarmers were the most important people in Elm Falls CThe bridge was built mainly to help the farmers of the town DThe bridge helped the town by linking farms to its market

5. Question 5 of 20 · Multiple Choice

   Two invented economists answer the question "Why did bread prices rise in the invented town of Redfield last year?" Which of their statements is an application?

   A"A poor wheat harvest meant less flour for the bakeries" B"The town should store extra flour in good harvest years" C"When flour is scarce, bakeries pay more for each sack" D"Bread rose more than other foods because it uses so much flour"

6. Question 6 of 20 · Multiple Choice

   Which statement best describes a point of agreement?

   ASomething every expert you read says, in any words BSomething the most famous expert says about a question CSomething that is true, whether or not experts say it DSomething you agree with after reading all the experts

7. Question 7 of 20 · Multiple Choice

   A student writes a claim that needs checking: "Both map experts agree that Mercator maps are bad." What is the best response?

   AIt is correct, because both experts list the map's defects BIt is too broad, because both experts also praise the map at sea CIt is wrong, because neither expert finds any defect in the map DIt is correct, because Source 2 says the map is unsuitable for land

8. Question 8 of 20 · Multiple Choice

   Sources 1 and 2 were written nine years apart by experts in two different countries. Why does that matter when they agree?

   AIt means the two experts copied each other's books BIt means one of the two experts must be wrong CIt makes a shared point harder to dismiss DIt shows that maps did not change at all between 1912 and 1921

9. Question 9 of 20 · Multiple Choice

   Two invented geographers answer the question "Why does the Clear River flood the town of Oakdale?" Geographer 1: "Heavy spring rain falls on the hills above town, and the water rushes down into the narrow valley." Geographer 2: "The river floods in spring, when the snow on the hills melts and runs into the valley." What is their point of agreement?

   AHeavy rain is the main cause of the floods BMelting snow is the main cause of the floods CHill water fills the valley each spring DOakdale should move to higher ground soon

10. Question 10 of 20 · Short Answer

    Explain the difference between an interpretation and an application. Give one example of each about any idea from social studies (it does not have to come from this page).

    Show model answer

11. Question 11 of 20 · Multiple Choice

    In Source 4, what do all three experts agree the club fund rule means?

    ASpending must benefit something open to all students BThe council must write down a reason for every purchase COnly clubs with more than 15 members may receive money DThe council should never spend money on any club at all

12. Question 12 of 20 · Multiple Choice

    What point of agreement about application do all three experts in Source 4 share?

    AThe council should buy chess sets for the library BThe council should hold a free chess tournament CThe council should ask the students to vote on it DThe council should not buy the uniforms

13. Question 13 of 20 · Multiple Choice

    Which statement in Source 4 is NOT a point of agreement?

    AThe chess club uniforms are not allowed under the rule BSpending must serve all students, not just one club CThe council should write down its reasons for spending DA benefit for only 15 club members does not fit the rule

14. Question 14 of 20 · Multiple Choice

    Ms. Haddad suggests chess sets for the library and Mr. Brandt suggests a free chess tournament. How should a student treat these two ideas?

    AAs a disagreement, so the rule has no clear meaning BAs two examples that fit the rule's shared meaning CAs two points of agreement, since both are about chess DAs proof that the uniforms are allowed after all

15. Question 15 of 20 · Multiple Choice

    Which paragraph of Source 4 explains why rules like the club fund rule exist?

    AParagraph 1 BParagraph 2 CParagraph 3 DParagraph 4

16. Question 16 of 20 · Multiple Choice

    Mr. Brandt is a city council clerk, not a school expert. What does his agreement with the other two experts add?

    ANothing, since only school experts count on a school rule BIt shows the rule is a law of the city as well as the school CIt shows the same reading from another kind of work DIt proves that the chess club will never get any money

17. Question 17 of 20 · Short Answer

    The Lakeview council is now asked to pay for a bus to take the 30 members of the school band to a music contest. Use the points of agreement in Source 4 to explain what the three experts would most likely say. Quote at least two experts.

    Show model answer

18. Question 18 of 20 · Short Answer

    A weak sample answer to fix. A student wrote: "The experts in Source 4 agree because they all talk about the chess club." Explain what is wrong with this sample, then rewrite it as a correct point of agreement.

    Show model answer

19. Question 19 of 20 · Short Answer

    Question 1 named one point of agreement between Sources 1 and 2. Write a supporting question that this point answers, and explain in two sentences how the point helps answer the compelling question "Do world maps tell the truth?"

    Show model answer

20. Question 20 of 20 · Short Answer

    Two invented civics experts answer the question "What does the town rule 'no loud music after 10 p.m.' mean?" Expert 1: "The rule protects neighbors' sleep, so it covers any music a neighbor can hear inside their home." Expert 2: "The rule is about neighbors' rest; music heard through a neighbor's wall breaks it. Many towns also give special permits for festivals." Name their point of agreement, name one statement that is not a point of agreement, and explain why.

    Show model answer

These standards connect to D1.3.6-8: prerequisites to review first, parallel standards at the same level, and next steps that build on it.

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.