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Question 1 of 6
2024 Test A English, question 53Passage Excerpt from “It’s Time to Stop Thinking That All Non-Native Species Are Evil”
Excerpt from “It’s Time to Stop Thinking That All Non-Native Species Are Evil”
by Emma Marris
The author of this opinion article attended a symposium, or conference, in Missoula, Montana, at which biologists and other scientists discussed species of plants and animals that are not native to the areas in which they live.
Invasive species are scary. It was ecologist Charles Elton, back in the 1950s, who introduced the militaristic “invasion” metaphor to describe exotic plants and animals—but there’s no question some can be extremely destructive.
The brown tree snake has eaten a dozen kinds of forest birds in Guam to extinction; zebra mussels clog pipes around the Great Lakes; the common house cat turns out to be, in Australia, a mercilessly effective killer of cute, fluffy marsupials like the bilby and the numbat.
As scientists have sounded the alarm about these pests, the public has gotten the message. Citizen groups rip out non-native plants. Native gardens have become increasingly popular, both as ways to celebrate the unique flora of each region and as tiny hot spots of diversity. Native trees provide food for native bugs, which feed native birds. Food chains developed over thousands of years of co-evolution unfold in our backyards. . . .
So we’ve learned, scientists and laypeople alike, that native species are good and non-natives are bad.
Julian Olden, a biologist at the University of Washington, Seattle, who co-organized the symposium, recently polled nearly 2,000 ecologists. Among his findings: a substantial number of them said they would immediately eradicate a hypothetical non-native forest plant, even if it were shown to have no effect on the forest. Olden calls this the “guilty even when proven innocent” approach.
That kind of approach is not very useful on a rapidly changing planet.
Exotics Are Everywhere
Climate change is making it harder even to decide who the invaders are.
How, scientists at the symposium wondered, do you define “native” on a warming planet, when plants and animals are already moving toward the poles or up mountainsides in search of climate conditions they can tolerate? Should we consider them “invasive” in their new homes? Regardless of what we label them, conservationists will be reluctant to remove them from their new environs—to do so would stymie1 their chances of adapting to the warmer future we’re creating.
And then there are the non-natives that we actually like. Most domestic crops are exotic in most of the places they’re grown, but there are even wild exotics that “do good,” forming useful relationships with native species.
Edwin Grosholz of the University of California, Davis, told the recent symposium about one such relationship. On beaches in his state, non-native spartina grass has become important habitat for the endangered California clapper rail, a plump shorebird with a downward curving bill more at home on land than in the air. A project to rip out and poison the spartina—which grows in dense swaths that exclude many other shorebirds—saw clapper rail numbers go tumbling downward.
There are other examples like that. The endangered southwestern willow flycatcher nests in “invasive” tamarisk shrubs. Many native (and beautiful) Hawaiian flowers are now pollinated by the Japanese white-eye bird—because the native pollinators have been driven extinct by other non-native species.
Should we impose further risk on already endangered natives by severing these relationships? Or should we admire the resilience of nature and let such “well-behaved” exotics stay? . . .
Leave them alone, more and more conservationists are arguing, and stop focusing obsessively on categorizing species as native or non-native. Mark Davis, an ecologist at Macalester College in St. Paul, Minnesota, once considered himself an “invasion biologist”—but not anymore. “I am actively trying to get the field to retire the invader narrative,” he said in Missoula.
A Good Thing, Not the Only Thing
After all, nativeness is just one environmental value, and arguably not as important as preventing extinctions and preserving biodiversity. In some cases we can best serve biodiversity by leaving the non-natives alone or even—brace yourself, now—introducing them on purpose.
This is the thinking behind, for example, installing the Aldabra tortoise on the islands of Mauritius. The islands lost their own large tortoises, and the fruiting plants that formerly had their seeds moved around by these fruit-loving reptiles have been on the decline. A tortoise that’s related to the island’s large tortoises—a non-native from the Seychelles in the Indian Ocean that was intentionally introduced in 2004—is now handling some of that work.
Most of the time, for the time being, conserving species still means focusing on supporting them in their historical habitats, planting natives and removing non-natives. We can and should do that in places where it is feasible and important to us.
From “It’s Time to Stop Thinking That All Non-Native Species Are Evil” by Emma Marris from NATIONAL GEOGRAPHIC MAGAZINE, July 24, 2014. Copyright © 2014 by National Geographic Society.

1stymie: hinder or interfere with
Question
The author’s use of cause and effect in paragraphs 10–11 mainly emphasizes the idea that
- Asome non-native species have helped their environments while others have had harmful impacts.
- Battempts to remove non-native species have seldom produced desired results.
- Csome endangered native species have flourished because of the presence of non-native species.
- Dinteractions between endangered native species and non-native species must be carefully monitored.
Show the answer
Correct answer: C
The question asks what the author’s use of cause and effect in paragraphs 10–11 mainly emphasizes.
A. Incorrect. The examples of cause and effect discussed in paragraphs 10–11, such as the spartina grass helping the clapper rail and the Japanese white-eye bird pollinating Hawaiian flowers, are all instances in which non-native species have helped their new environments.
B. Incorrect. While paragraph 10 does mention that efforts to eradicate the non-native spartina grass hurt the native clapper rail shorebird, the main emphasis in both paragraphs 10–11 is on the fact that certain non-native species have helped native species.
C. CORRECT. Paragraphs 10–11 focus on several examples of non-native species that have helped endangered native species flourish: non-native spartina grass providing “important habitat for the endangered California clapper rail” (paragraph 10), non-native tamarisk shrubs providing nesting places for the endangered southwestern willow flycatcher (paragraph 11), and the non-native Japanese white-eye bird pollinating Hawaiian flowers (paragraph 11).
D. Incorrect. While paragraphs 10–11 describe several interactions between non-native and native species, they never discuss monitoring these interactions.
Question analysis
This text-structure question asks what the cause-and-effect examples in two paragraphs of an article about non-native species mainly emphasize. The paragraphs describe a shorebird, a flycatcher and Hawaiian flowers, and students must decide what the examples have in common rather than fixing on any one of them.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Analyzing what a cause-and-effect structure emphasizes is grade 7 work, but these examples involve unfamiliar species and endangered status, and more than one choice is partly supported by the paragraphs, which raises the demand above typical.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly analyze
- What makes it hard
- A very close wrong answer major
- Reading between the lines moderate
- An unfamiliar subject minor
- Evidence
- Answered from several paragraphs or stanzas
- Reading level
- Passage: about grade 11, 815 words; question and choices: about grade 11, 62 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The paragraphs mention harm as well as help, so a balanced statement about both looks accurate and even fair-minded. What the cause-and-effect pairs stress, though, is endangered natives depending on non-natives, and the right answer captures that while overstating it, since a bird whose numbers held up only with spartina's help can hardly be said to have flourished. Students must prefer the statement of the main emphasis to one that is partly supported but off the point.
A very close wrong answer major Choosing the answer
The right choice and the help-and-harm choice both say non-natives have aided their surroundings; they part on harm, which the paragraphs do mention, spartina crowding out shorebirds and other non-natives killing Hawaii's pollinators, but only in passing. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Reading between the lines moderate Working it out
Paragraph 10 states its cause and effect backwards, removing spartina sent clapper rail numbers “tumbling downward”, and the student must turn that around into the grass's presence helping the bird. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
An unfamiliar subject minor Understanding the question
Five unfamiliar species crowd two paragraphs, spartina grass, the California clapper rail, tamarisk shrubs, the southwestern willow flycatcher and the Japanese white-eye, and each one's role must be kept straight. (Recht & Leslie, 1988; Kintsch, 1998)
Strategy: List each cause-and-effect pair in paragraphs 10 and 11, the species involved and what happened to them, then pick the statement that holds for the examples taken together.
Traps
- Too narrow: A single detail offered as the central idea or a summary, or a summary that keeps minor details and leaves out an essential part.
- Too broad or too strong: A choice overstates, generalizes, or uses absolute words the text does not support.
- Outside knowledge: A choice is plausible in the real world but not supported by this text.
The wrong answers, classified
A Too narrow (King et al., 2004)
Accurately notes helpful and harmful non-natives, but the harm is mentioned only in passing, and it leaves out what every example stresses, endangered natives depending on non-natives.
B Too broad or too strong (King et al., 2004)
Generalizes from the single spartina project in paragraph 10 to removal attempts in general, a “seldom” claim that neither paragraph makes.
D Outside knowledge (King et al., 2004; Recht & Leslie, 1988)
Adds a sensible-sounding call for careful monitoring, the kind of advice scientists often give, but neither paragraph says anything about watching over these relationships.
Working it out, step by step
Know what the question asks
In a cause-and-effect pattern, one thing makes another happen. You need the main idea that the causes and effects in paragraphs 10 and 11 stress. Start by listing each pair.
List each cause and effect
- Paragraph 10: non-native spartina grass gives the endangered clapper rail a home, so when people ripped out the grass, clapper rail numbers went “tumbling downward.”
- Paragraph 11: the endangered willow flycatcher nests in non-native tamarisk shrubs.
- Paragraph 11: native Hawaiian flowers are now pollinated by a non-native bird, the Japanese white-eye.
Find the common thread
Endangered means at risk of dying out. Pollinated means a bird or bug carries pollen between flowers so they can make seeds. In every pair, a native species depends on a non-native one. The newcomer gives it a home, a place to nest or a pollinator. Two of the natives, the clapper rail and the flycatcher, are endangered. So the paragraphs stress that some endangered natives do better because non-natives are there.
Check each choice
- C fits: some endangered natives have “flourished,” or done well, because non-natives are present.
- A is wrong because harm comes up only in passing, while every example stresses a native getting help.
- B is wrong because one removal project is not enough to say removal “seldom” works.
- D is wrong because the paragraphs never mention monitoring, or watching over, these relationships.
Watch out: The paragraphs do mention harm. Spartina crowds out some other shorebirds, and other non-natives wiped out Hawaii’s native pollinators. So A sounds balanced, but it misses the main point.
Choose the answer
The causes and effects show struggling natives, two of them endangered, helped by non-natives. So the answer is C.
Why this answer and not the closest wrong one
A comes closest, because the paragraphs mention harm as well as help. But the harm is only a side note. Every cause and effect shows a native relying on a non-native, and two of those natives are endangered birds. C names that main point, even though “flourished” is a strong word for birds that are still endangered.
More questions like this
The original DOE question

The passage “Excerpt from “It’s Time to Stop Thinking That All Non-Native Species Are Evil”” as printed (pages 68–70)



Question 2 of 6
2026 Practice Test C English, question 41Passage Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”
Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”
by Melanie Canales
The author, Melanie Canales, is a first-generation Peruvian American farmer and beekeeper based in Virginia’s Shenandoah Valley, on lands of the indigenous Monacan and Manahoac tribes. Her work focuses on creating healthy relationships between people and their surrounding ecosystems.
Unburdened by the constraints of gravity, red and green peppers jut out at 45-degree angles inside the Advanced Plant Habitat (APH), a sort of space terrarium not much larger than a microwave. Four chile pepper plants stand effortlessly upright, despite the dozens of glossy fruits weighing them down. These plants have lived entirely in space; their leaves have never been chewed on by insects or rustled by a summer breeze, [and] their stems are unfamiliar with bending toward the sun’s arc across the sky. Scissors glint under the tank’s white and blue lights as astronaut Mark Vande Hei and his team snip the stems of those that are ready for harvest. The peppers whirl around their heads until the astronauts catch them and tape them against a board to photograph.
Back on Earth, the Plant Habitat-04 team of engineers and plant scientists are observing and conferring with the astronauts. Of the 26 peppers in this batch, only the 14 finest will stay on the International Space Station [ISS] for consumption. The rest will be wrapped in foil, sealed in a Ziploc bag, then frozen at a brisk −80 degrees, until they can come roaring back to Earth in the next cargo capsule to be studied later. Now, after a 137-day growth cycle, the astronauts remove the plants from the module and trash them. Project Plant Habitat-04 is complete. It’s taco night on the ISS.
Since 2014, NASA1 has experimented with growing lettuces, brassicas,2 and zinnias3 in space, an endeavor that relies on highly specialized technology over 50 years in the making. [Fall 2021’s] two successful pepper harvests . . . will provide data on the nutritional and psychological benefits of growing vegetables on-craft, as well as a crop’s ability to reliably produce long-term in microgravity. While controlled environmental agriculture is not new, the APH experiment represents an evolution in specialized growth habitats. It doesn’t aim to re-create Earth’s conditions, but to perfect each isolated variable of plant growth in the clinical environment of a spaceship.
“The Advanced Plant Habitat is the most complex plant growth system on orbit today,” says Lashelle Spencer, a plant scientist at NASA’s Kennedy Space Center. Its more than 180 sensors control and monitor temperature, humidity, and carbon dioxide. The astronauts can adjust the color and intensity of the light, and how much moisture the plants’ roots are getting. It waters itself.
It’s the day after Thanksgiving, and Spencer has been at Kennedy since 5 a.m. to facilitate the peppers’ final harvest. As part of the project team, she played a crucial role in preparing the seeds that were sent hurtling into space in June and guiding the astronauts through maintaining the plants in orbit. . . . Though astronauts can spend upwards of 100 days in space, their on-mission meals come dehydrated and pre-packaged; their vitamins and minerals are isolated in supplements, which lose nutritional value the longer they’re stored. Spencer’s goal is to create the conditions necessary for cultivating healthy plants in space, so those plants can sustain healthy astronauts on long-term missions. Astronaut food is great, she says—“especially the shrimp cocktail. But you’re missing that crunch. You’re missing that fresh pop of flavor, the green flavor that’s not there in that packaged food.”
The sensory experience of growing productive crops can also help mitigate4 the psychological effects of long-term space travel. . . . Spencer says the team cracked open the door of the APH every day to observe their vegetable companions with all the tenderness of home gardeners. When harvest day came, they batted their bounty around the ISS, taking selfies and delighting in watching the fruits pirouetting around the spacecraft. . . .
“We were thinking no heat, so that [the peppers] wouldn’t be dangerous, but maybe the astronauts need a little spice in their life,” says Paul Bosland, who along with his colleagues at the Chile Pepper Institute genetically engineered5 the NuMex Española Improved chile pepper seeds grown in Plant Habitat-04. . . .
Working with NASA, Bosland cultivated a variety that could accommodate both the nutritional needs of astronauts as well as the logistics of growing a plant in space. . . .
. . . The experiment is helping gather the data necessary to determine the nutritional content of crops grown in space, and therefore how many people they can feed, and for how long. Though much is still unknown, Spencer is certain of one thing that future astronauts will need to do: “I think in an optimal world, a scientist like me would say that they would be growing plants from day one. From the day they left to the day they came back, they would be growing them.”
From “Growing Peppers on the ISS Is Just the Start of Space Farming” by Melanie Canales from WIRED, December 21, 2021. Copyright © 2021 Condé Nast. All rights reserved.
1NASA: National Aeronautics and Space Administration
2brassicas: a large genus of herbs, such as broccoli and cabbage
3zinnias: a genus of herbs and low shrubs that have flowers at their heads
4mitigate: to make something less severe or harmful
5genetically engineered: combined parts of DNA from different plants to produce a new plant
Question
How is the quotation from Lashelle Spencer at the end of paragraph 9 relevant to the discussion of the peppers referred to in paragraph 2?
- AThe quotation indicates that larger batches of peppers need to be grown during future missions and suggests a slight criticism of the astronauts discussed in paragraph 2 for not dedicating more of their time to growing peppers during their mission.
- BThe quotation explains why the 137-day growth cycle mentioned in paragraph 2 is necessary and provides a suggestion on how to grow more peppers during the same growth cycle in future missions.
- CThe quotation helps explain why some of the peppers discussed in paragraph 2 needed to be sent back to Earth and that increasing the overall number of peppers grown in space will be important in future missions.
- DThe quotation provides context for understanding why the peppers discussed in paragraph 2 must be sealed and frozen prior to their return to Earth and suggests how this method might be improved in upcoming missions.
Show the answer
Correct answer: C
The question asks how the quotation from Lashelle Spencer at the end of paragraph 9 is relevant to the discussion of the peppers referred to in paragraph 2.
A. Incorrect. The quotation from Spencer in paragraph 9 suggests that astronauts should spend more time on growing larger and more continuous batches of peppers during long missions, but it does not criticize astronauts for discarding plants and ending the experiment after the 137-day growth cycle.
B. Incorrect. While the quotation from Spencer in paragraph 9 stresses the value of spending more time growing plants in space, it does not provide specific details about the 137-day growth cycle or offer specific methods for producing more peppers within the same time frame.
C. CORRECT. The quotation from Spencer in paragraph 9 is relevant to the discussion of the peppers on the ISS in paragraph 2 because it emphasizes the importance of expanding plant-growing efforts on future space missions. Spencer suggests that rather than ending the experiment after the 137-day growth cycle, astronauts could continually replant and replenish their food supply from the beginning to the end of a long mission.
D. Incorrect. Although the quotation from Spencer in paragraph 9 conveys the importance of dedicating more time to growing plants in space, it does not explain why the peppers were sealed and frozen, nor does it suggest how this method for preserving them might be improved.
Question analysis
This question asks how Lashelle Spencer’s quotation at the end of the space-farming excerpt, her view of what future astronauts will need to do, relates to the account in paragraph 2 of how the pepper harvest was handled. Students must connect the article’s ending to its opening, and every choice is a long two-part statement whose halves have to be checked separately.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 readers explain how parts of a text relate, usually neighboring ones. This item links the last paragraph to the second, and its four choices run about forty words each in two parts, so it asks more than typical grade 7 work.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly analyze
- What makes it hard
- Reading between the lines moderate
- A very close wrong answer moderate
- A lot to read moderate
- Evidence in several places minor
- Evidence
- Answered from several paragraphs or stanzas
- Reading level
- Passage: about grade 10, 890 words; question and choices: about grade 16, 163 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Each choice has one half that sounds connected to the quotation, so students must test both halves of all four. The criticism choice is the hardest to reject, since it correctly hears a call for more growing and only then misreads Spencer’s tone. The key itself is not airtight: its first half leans on the sentence before the quotation, about gathering nutrition data, so the answer is best confirmed by ruling out the others.
Reading between the lines moderate Working it out
Spencer’s quotation never mentions paragraph 2; the link is that plants grown “from day one” to “the day they came back” contrast with one 137-day batch harvested and thrown away. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
A very close wrong answer moderate Choosing the answer
The criticism choice shares the key’s call for more growing on future missions and differs in its other half, a slight criticism of the crew that Spencer’s hopeful “in an optimal world” never makes. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
A lot to read moderate Understanding the question
The four choices run 32 to 40 words, and each joins two claims with “and,” so eight separate statements must be checked against the quotation and paragraph 2. (Kintsch, 1998; Gorin & Embretson, 2006; Freedle & Kostin, 1993)
Evidence in several places minor Working it out
The two parts to connect are the excerpt’s second paragraph and its last sentence, with six paragraphs on the habitat, Spencer and Bosland in between. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
Strategy: Put Spencer’s closing quotation into your own words and recall how the pepper project ended in paragraph 2, then weigh both halves of every choice and keep the one the quotation and its paragraph best support.
Traps
- Half right: One half of a two-part choice is right and the other is not.
- Twists what the text says: Uses the text's topic and ideas but changes what it says: who did it, how much, when, or why.
The wrong answers, classified
A Half right (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Rightly hears a call for larger, continuous harvests in “from day one,” then adds a criticism of the crew, though Spencer describes an ideal and blames no one.
B Twists what the text says (King et al., 2004)
Connects the quotation to the 137-day cycle because both concern time, but Spencer neither explains why the cycle lasted that long nor suggests packing more peppers into it.
D Twists what the text says (King et al., 2004)
Ties the quotation to the foil, sealing and freezing in paragraph 2 and to improving that method, though Spencer’s improvement is growing plants all mission long, not storing peppers.
Working it out, step by step
Figure out what the question asks
This question links the end of the article to its beginning. Spencer speaks at the end of paragraph 9. Paragraph 2 tells what happened to the peppers. You need the choice that best explains how her words connect to those peppers. Each choice has two parts, and both must be true.
Recall the peppers in paragraph 2
Paragraph 2 says only “the 14 finest” peppers stay on the ISS to eat. The rest are frozen and sent “back to Earth in the next cargo capsule to be studied later.” Then, “after a 137-day growth cycle, the astronauts remove the plants from the module and trash them.” So the crew grew one batch, ate some, sent some home and threw the plants away.
Read the end of paragraph 9
Just before Spencer speaks, paragraph 9 says: “The experiment is helping gather the data necessary to determine the nutritional content of crops grown in space, and therefore how many people they can feed, and for how long.” Then Spencer says that in “an optimal world,” meaning the best possible world, astronauts “would be growing plants from day one.” She adds: “From the day they left to the day they came back, they would be growing them.”
Connect the two parts
The peppers sent home are studied. That gives the data paragraph 9 describes: how healthy space crops are and how many people they can feed. Spencer’s plan needs that data. You must know what a crop can feed before you plan meals for a whole trip. Her words also point to the future. Instead of one batch that ends in the trash, crews would grow plants all trip long. That means many more peppers.
Check each choice
- A is wrong. Spencer wants more growing, but she doesn’t criticize the crew. “In an optimal world” describes a hope, not a complaint.
- B is wrong. She never says why the cycle took 137 days. She doesn’t suggest squeezing more peppers into it, either.
- C is right. The returned peppers give the data, and growing “from day one” means more peppers in the future.
- D is wrong. She says nothing about freezing the peppers or a better way to store them.
Watch out: A gets the first half right. The criticism in its second half is what makes it wrong.
Choose the answer
Her words explain why some peppers went home to be studied and why more growing matters next time. So the answer is C, “The quotation helps explain why some of the peppers discussed in paragraph 2 needed to be sent back to Earth and that increasing the overall number of peppers grown in space will be important in future missions.”
Why this answer and not the closest wrong one
A is the closest wrong answer. Like C, it hears Spencer calling for more plants on future trips. But A also says she criticizes the astronauts. She doesn’t. She calmly describes a perfect world. C keeps the right half and adds a link the paragraph supports: the peppers sent home give the data.
More questions like this
The original DOE question

The passage “Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”” as printed (pages 50–51)


Question 3 of 6
2024 Test B English, question 20Passage Excerpt from “How Exercise Could Help You Learn a New Language”
Excerpt from “How Exercise Could Help You Learn a New Language”
by Gretchen Reynolds
Many scientists suspect that exercise alters the biology of the brain in ways that make it more malleable and receptive to new information, a process that scientists refer to as plasticity.
But many questions have remained unanswered about movement and learning, including whether exercise is most beneficial before, during or after instruction and how much and what types of exercise might be best.
So for a new study, which was published recently in PLOS One, researchers in China and Italy decided to home in on language learning and the adult brain.
Language learning is interesting. As young children, almost all of us picked up our first language easily. We didn’t have to be formally taught; we simply absorbed words and concepts.
But by early adulthood, the brain generally begins to lose some of its innate language capability. It displays less plasticity in areas of the brain related to language. As a result, for most of us, it becomes harder to learn a second language after childhood.
To see what effects exercise might have on this process, the researchers first recruited 40 college-age Chinese men and women who were trying to learn English. The students had some facility with this second language but were far from proficient.
The researchers then divided the students into two groups. Those in one group would continue to learn English as they had before, primarily while seated in rote vocabulary-memorization sessions.
The others would supplement these sessions with exercise.
Specifically, the students would ride exercise bikes at a gentle pace (about 60 percent of their maximum aerobic capacity) beginning 20 minutes before the start of the lessons and continuing throughout the 15 minutes or so of instruction.
Both groups learned their new vocabulary by watching words projected onto large screens, together with comparable pictures, such as “apple” and a Red Delicious. They were shown 40 words per session, with the sequence repeated several times.
Afterward, the students all rested briefly and then completed a vocabulary quiz, using computer keys to note as quickly as possible whether a word was with its correct picture. They also responded to sentences using the new words, marking whether the sentences were accurate or, in the case of “The apple is a dentist,” nonsensical. Most linguists1 feel that understanding sentences shows greater mastery of a new language than does simple vocabulary improvement.
The students completed eight vocabulary sessions over the course of two months.
And at the end of each lesson, the students who had ridden bikes performed better on the subsequent vocabulary tests than did the students who sat still.
They also became more proficient at recognizing proper sentences than the sedentary students, although that difference did not emerge until after several weeks of instruction.
Perhaps most interesting, the gains in vocabulary and comprehension lingered longest for the cyclists. When the researchers asked the students to return to the lab for a final round of testing a month after the lessons—without practicing in the meantime—the cyclists remembered words and understood them in sentences more accurately than did the students who had not moved.
“The results suggest that physical activity during learning improves that learning,” says Simone Sulpizio, a professor of psychology and linguistics at the University Vita-Salute San Raffaele in Milan, Italy, and a study co-author.
These improvements extend beyond simply aiding in memorization, she added. The exercise also deepened language learners’ grasp of how to use their newly acquired words.
This study involved college students performing relatively light exercise, though, and cannot tell us whether other people completing other types of exercise would achieve the same results.
It also offers no clues about what is occurring inside the brain that might be contributing to the benefits of the exercise. But many past studies have shown that exercise prompts the release of multiple neurochemicals in the brain that increase the number of new brain cells and the connections between neurons, Dr. Sulpizio says. These effects improve the brain’s plasticity and augment the ability to learn.
From a real-world standpoint, the study’s implications might seem at first to be impractical. Few classrooms are equipped with stationary bicycles. But specialized equipment is probably unnecessary, Dr. Sulpizio says.
“We are not suggesting that schools or teachers buy lots of bicycles,” she says. “A simpler take-home message may be that instruction should be flanked by physical activity.”
From “How Exercise Could Help You Learn a New Language” by Gretchen Reynolds from THE NEW YORK TIMES, August 16, 2017. Copyright © 2017 The New York Times Company.
1linguists: scientists who study language
Question
Read these sentences from paragraph 17.
These improvements extend beyond simply aiding in memorization, she added. The exercise also deepened language learners’ grasp of how to use their newly acquired words.
Which sentence from the excerpt best explains why Sulpizio feels confident in the conclusion stated in these sentences?
- A“They were shown 40 words per session, with the sequence repeated several times.” (paragraph 10)
- B“They also responded to sentences using the new words, marking whether the sentences were accurate or, in the case of ‘The apple is a dentist,’ nonsensical.” (paragraph 11)
- C“And at the end of each lesson, the students who had ridden bikes performed better on the subsequent vocabulary tests than did the students who sat still.” (paragraph 13)
- D“They also became more proficient at recognizing proper sentences than the sedentary students, although that difference did not emerge until after several weeks of instruction.” (paragraph 14)
Show the answer
Correct answer: D
The question asks which sentence from the excerpt best supports Sulpizio’s assertion in paragraph 17 that exercise went beyond helping with memorization to deepen the language learners’ ability to use new vocabulary.
A. Incorrect. This sentence merely describes what the language-learning sessions were like, without making any claims about how the exercise affected the subjects’ understanding of how to use new words.
B. Incorrect. While this sentence does address the fact that learners were required to think about how the new words should be used rather than just memorizing the words, it does not discuss results such as how the exercise affected their ability to do this.
C. Incorrect. This sentence establishes only that exercise helped with the memorization of new words, not that exercise deepened learners’ grasp of how to use the new words.
D. CORRECT. The fact that learners who exercised were better at identifying when the new words were used correctly in sentences directly supports Sulpizio’s assertion that the exercise deepened their grasp of how to use the new words.
Question analysis
This textual evidence question quotes Simone Sulpizio’s conclusion that exercise did more than help learners memorize new English words. Students choose the sentence from the article that best explains why she can be confident of it. All four choices come from the article’s account of the study, so students must match evidence to the exact claim rather than to its general topic.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 evidence questions usually match a quotation to a stated claim. This claim has two parts, gains beyond memorizing and a better grasp of usage, and two quotations touch it closely, a sharper test than typical grade 7 work.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly evaluate
- What makes it hard
- A very close wrong answer major
- Reading between the lines moderate
- Evidence in several places minor
- Evidence
- Answered from several paragraphs or stanzas
- Reading level
- Passage: about grade 11, 764 words; question and choices: about grade 11, 142 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Sulpizio’s claim has two parts, gains beyond memorizing and a better grasp of using words, and two of the quotations each touch one part. The vocabulary result is real evidence that exercise helped, but of the very memorizing she says the gains went beyond, and the sentence-task description mentions using words but reports no result. Only a result about sentences proves the claim, so the question rewards asking of each line what it shows, not what it is about.
A very close wrong answer major Choosing the answer
The vocabulary-test result in paragraph 13 and the sentence result in paragraph 14 are worded alike, cyclists outperforming students who sat still; only the skill measured, memorizing words or using them, separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Reading between the lines moderate Working it out
Students must map the claim’s two halves onto the study’s two measures: vocabulary tests show memorization, and recognizing proper sentences shows the “grasp of how to use” new words. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Evidence in several places minor Working it out
The four quotations come from paragraphs 10, 11, 13 and 14, and each must be weighed against a claim made later, in paragraph 17. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
Strategy: Pin down what the quoted claim says the exercise achieved, then test each sentence by asking whether it reports a result that proves that specific achievement.
Traps
- Supports only part of the claim: In a question about evidence: a line that backs one half of the claim but not the other, or a related point rather than the claim itself.
- True but not the answer: A choice says something accurate about the text that does not answer this question.
The wrong answers, classified
A True but not the answer (King et al., 2004; Embretson & Wetzel, 1987)
Picks a sentence about how the lessons were run, 40 words repeated several times, accurate but silent on what the exercise did for the learners.
B Supports only part of the claim (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Matches the claim’s focus on using words to the sentence-judging task, but this line only describes the task and reports no result showing that exercise helped.
C Supports only part of the claim (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Picks a real finding in favor of the cyclists, but better vocabulary-test scores show only the memorizing that Sulpizio says the gains went beyond.
Working it out, step by step
Figure out what the question asks
Sulpizio says the exercise did more than help students memorize words. It “deepened language learners’ grasp of how to use their newly acquired words.” A grasp is an understanding. You need the sentence that best proves this claim. Proof should be a result, not just a description.
Break the claim into two parts
- Part 1: the gains went “beyond simply aiding in memorization.” Memorization is learning words by heart.
- Part 2: the cyclists got better at using the words.
So the proof must show the bike riders did better with words in sentences. A test that only checks memory won’t prove it.
Check each choice
- A (paragraph 10) tells how many words were shown. It gives no result.
- B (paragraph 11) describes the sentence task. But it doesn’t say who did better.
- C (paragraph 13) is a result. But it is about “vocabulary tests,” which check memory. That is the part she says the gains went beyond.
- D (paragraph 14) says the cyclists “became more proficient at recognizing proper sentences than the sedentary students.” Proficient means skilled. Sedentary means sitting still. That is a result about using words.
Pick the answer
Watch out: C is very tempting. It shows that exercise helped. But it proves the wrong kind of help. Only one choice shows the cyclists did better at using words in sentences. So the answer is D.
Why this answer and not the closest wrong one
C is the closest wrong answer. Both C and D say the bike riders beat the students who sat still. The difference is the skill that was tested. C’s vocabulary tests show memory. D’s sentence test shows the learners knew how to use the words, which is exactly Sulpizio’s claim.
More questions like this
The original DOE question

The passage “Excerpt from “How Exercise Could Help You Learn a New Language”” as printed (pages 171–172)


Question 4 of 6
2026 Practice Test C Math, question 15Question
A grocery store sells 1-gallon containers of milk for $3.99. The store also sells orange juice in a 6-pack of 5.5-fluid-ounce bottles for $1.79. Suppose the store wants to sell its orange juice in gallon containers instead. To the nearest dollar, how much more would a gallon of orange juice cost than a gallon of milk?
Enter your answer in the space.
Fill-in question: work out the answer and type it as a number.
Show the answer
Correct answer: 3
To determine the cost of a gallon of orange juice, begin by finding the total number of ounces in the 6-pack of bottles:
So, 33 oz of orange juice costs $1.79.
There are 128 oz in 1 gallon. Set up a proportion using the $1.79 cost per 33 oz of orange juice and the unknown cost (x) per 1 gallon of orange juice:
Cross multiply to solve for x in the proportion:
So, the orange juice costs $6.94 per gallon, and the milk costs $3.99 per gallon.
Subtract the cost per gallon of milk from the cost per gallon of orange juice.
Round the difference to the nearest dollar.
$2.95 rounds to $3.
Question analysis
A store sells milk by the gallon for $3.99 and orange juice in six-packs of 5.5-fluid-ounce bottles for $1.79. Students work out what a gallon of the juice would cost at the same price per ounce and how much more that is than the milk, to the nearest dollar. The ounces in a gallon must be known, and several steps involve decimals.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Unit prices are grade 6 and 7 work, but this chains five steps with decimals and needs a fact the question does not give, the number of fluid ounces in a gallon. Typing a rounded difference, with no choices, adds risk.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Something you must already know moderate
- Many steps moderate
- Error-prone arithmetic minor
- An answer in an unexpected form minor
- Solution
- 5 steps
- Reading level
- Question and choices: about grade 5, 60 words.
- Corrected from the DOE handbook
- A rounded value in the explanation is now marked as approximate (≈ instead of =).
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The calculation is long, and its key fact is missing from the page. Students who know the 128 fluid ounces still face a division by 33 that does not come out evenly, which tempts them to round the price per ounce to 5 cents and lose about 50 cents a gallon. Keeping the exact quotient to the end, or scaling 33 ounces up by about 3.9, keeps the difference near $2.95, which rounds to 3.
Something you must already know moderate Working it out
The question never says that a gallon holds 128 fluid ounces, yet the whole comparison depends on it; the 6-pack holds only 6 × 5.5 = 33 ounces. (Anderson & Krathwohl, 2001)
Many steps moderate Working it out
Five moves follow one another: the ounces in a pack, the scale-up to 128 ounces, the division by 33, the subtraction of $3.99 and the rounding to a whole dollar. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
Error-prone arithmetic minor Working it out
1.79 × 128 = 229.12 and 229.12 ÷ 33 are long decimal calculations without a calculator, and a slip in either moves the price of a gallon. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
An answer in an unexpected form minor Choosing the answer
The rounded difference is typed with no choices, so an unrounded $2.95, or a figure rounded too soon, looks just as finished as the whole-dollar answer. (Enright, Morley & Sheehan, 2002)
Strategy: Find the ounces in one six-pack, scale its price up to the 128 fluid ounces in a gallon, subtract the milk's price, and round only at the end.
Traps
- Stops one step early: A choice is a number from partway through the solution.
- Rounds too early: Rounds a value partway through, or rounds the wrong way, so the final answer drifts from the exact one.
- Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".
The wrong answers, classified
7 Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds the juice's cost per gallon, about $6.94, rounds it to $7, and enters that without subtracting the $3.99 price of the milk.
2 Rounds too early (King et al., 2004)
Rounds the price per ounce, 1.79 ÷ 33 ≈ 0.054, to $0.05, so a gallon costs $6.40 and the difference, $2.41, rounds to 2.
2.95 Misreads the question (Hegarty, Mayer & Monk, 1995)
Works out the difference of $2.95 correctly but enters it as it stands, though the question asks for it to the nearest dollar.
What was corrected from the DOE handbook, and why
- Explanation: The DOE’s explanation goes from 33x = $229.12 to “x = $6.94”. But 229.12 ÷ 33 = 6.9430…, so $6.94 is the cost per gallon rounded to the cent. The site writes x ≈ $6.94. Nothing else changes: $6.94 − $3.99 = $2.95, which rounds to $3, and the unrounded cost gives the same answer.
Worked solution, step by step
Formulas used
- Fluid ounces in a gallon
- A gallon holds 128 fluid ounces. This is a fact you must know, because the question does not give it. A fluid ounce measures an amount of liquid. Multiply gallons by 128 to change them into fluid ounces.
- Cross-multiplying a proportion
- A proportion says two ratios are equal. Here each ratio is ounces over dollars. a and c are the tops, and b and d are the bottoms. Multiply each top by the other bottom, and the two products are equal. That turns the proportion into an equation.
Sort out the question
Milk costs $3.99 for 1 gallon. Orange juice comes in a 6-pack of 5.5-fluid-ounce bottles for $1.79. You need how much more a gallon of juice would cost than a gallon of milk. Round to the nearest dollar.
The question doesn’t say how big a gallon is. You must know this fact: 1 gallon is 128 fluid ounces.
Find the ounces in a 6-pack
Each of the 6 bottles holds 5.5 fluid ounces:
So $1.79 buys 33 fluid ounces of juice.
Set up a proportion
Let x be the cost in dollars of a gallon, 128 fluid ounces, of juice. The price per ounce stays the same. So ounces over dollars is the same for the pack and the gallon:
Cross-multiply:
Find the cost of a gallon
Divide both sides by 33:
The sign ≈ means about equal. The exact value is 6.943…, so a gallon of juice costs about $6.94.
Watch out: don’t round too early. One ounce costs about $0.054. Rounding that to $0.05 makes a gallon $6.40, and your answer becomes 2.
Subtract the milk’s price
Find how much more the juice costs:
A gallon of juice costs $2.95 more than a gallon of milk.
Watch out: entering 7, the juice’s price, forgets to subtract the milk.
Round and enter it
The question asks for the nearest dollar. $2.95 is between $2 and $3. Its cents, 95, are 50 or more, so it rounds up to $3. Do not enter 2.95.
Type only the number in the box. So you would enter 3.
Check your answer
Estimate. 128 ounces is almost 4 packs, since . Four packs cost dollars, so a gallon costs a bit less than that. Milk costs about $4. About $7 minus $4 is $3, which matches.
More questions like this
The original DOE question

Question 5 of 6
2026 Practice Test D Math, question 36Question
Leah has set a goal to read a total of 500 pages of a textbook. The table shows the book page numbers for the reading she did during three days.
DAILY READING LOG
| Day | Pages Read |
|---|---|
| 1 | pages 45–90, inclusive |
| 2 | pages 100–135, inclusive |
| 3 | pages 145–190, inclusive |
What percentage of her 500-page goal did Leah read on these three days? Round your answer to the nearest tenth.
Enter your answer in the space.
Fill-in question: work out the answer and type it as a number.
Show the answer
Correct answer: 25.6%
First, determine the number of pages read each day. Since the pages per assignment are inclusive, subtract the first page from the last page assigned and then add 1 to determine the pages read for each day.
Day 1: pages
Day 2: pages
Day 3: pages
Leah read a total of 128 pages, since .
To determine the percent, express 128 pages out of 500 pages as a fraction.
Question analysis
Leah's daily reading log lists three ranges of textbook pages, each marked inclusive, and her goal is 500 pages. This percent question asks what percentage of the goal she read over the three days, rounded to the nearest tenth and typed in. Counting the pages in each inclusive range correctly is the tricky step before the percent.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Finding what percent one number is of another is grade 6 and 7 work. This adds three inclusive page ranges to count, which takes more care than subtracting, then a rounding step, all typed with no choices to check against.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Something you must already know moderate
- Many steps moderate
- An answer in an unexpected form minor
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 3, 66 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Counting pages in a range is the whole difficulty; the percent at the end is routine once the total is right. Subtracting first from last feels natural, and here it even rewards the student with a round 25%, so nothing looks wrong. Checking the rule on a tiny range, pages 1 to 3, which is 3 pages and not 2, fixes the count, and the instruction to round to the nearest tenth hints that the answer is not a whole number.
Something you must already know moderate Working it out
Every row says inclusive, but nothing says that pages 45 to 90 hold 90 − 45 + 1 = 46 pages; subtracting alone loses one page on each of the three days. (Anderson & Krathwohl, 2001)
Many steps moderate Working it out
Three page counts, a sum, a division by 500 and a change to a percent come in sequence, and a one-page error in each count carries through to the end. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
An answer in an unexpected form minor Choosing the answer
The answer is typed with no choices, and the miscounted total, 125 pages, gives a tidy 25% that looks more finished than the right value with its tenth. (Enright, Morley & Sheehan, 2002)
Strategy: Count each day's pages carefully, testing your method on a short range such as pages 1–3, add the three days, divide by 500, and write the result as a percent to the nearest tenth.
Traps
- Counting the ends: Inclusive or exclusive ends, fence posts, consecutive numbers: an answer that is one too many or too few, or an endpoint drawn open where it belongs closed (or the reverse).
- Stops one step early: A choice is a number from partway through the solution.
- Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".
The wrong answers, classified
25 Counting the ends (Brown & Burton, 1978)
Subtracts the first page from the last for each day, 45 + 35 + 45 = 125 pages, forgetting that an inclusive range counts both end pages, so 125 ÷ 500 = 25%.
0.256 Stops one step early (King et al., 2004; Gierl et al., 2017)
Counts the 128 pages and divides by 500 correctly, then enters the decimal 0.256, one step short of multiplying by 100 to make a percent.
26 Misreads the question (Hegarty, Mayer & Monk, 1995)
Finds 25.6% correctly but rounds it to the nearest whole percent, overlooking the instruction to round to the nearest tenth.
Worked solution, step by step
Formulas used
- Counting pages in an inclusive range
- Inclusive means the first and last pages are both read. Subtracting counts the steps from the first page to the last. That misses one page, so add 1. Test it: pages 1 to 3 are 3 pages, and 3 − 1 + 1 = 3.
- Percent of a total
- The part is the amount you have, here the pages read. The whole is the amount you compare with, here the 500-page goal. Dividing gives a decimal. Multiplying by 100 turns it into a percent, a number out of 100.
Sort out the question
Leah’s goal is 500 pages. The log shows three days:
- Day 1: pages 45 to 90
- Day 2: pages 100 to 135
- Day 3: pages 145 to 190
Each range is inclusive. You need the percent of 500 pages she read, rounded to the nearest tenth.
Count the pages each day
Use the rule for an inclusive range: last page minus first page, plus 1.
Watch out: subtracting alone gives 45, 35 and 45 pages. That is 125 pages, which is exactly 25%. A round answer like that can hide the mistake.
Add the three days
Add the pages from all three days to get her total:
Leah read 128 pages in all. This is the part you compare with the goal.
Change to a percent
Divide the pages read by the goal, then multiply by 100:
Leah read 25.6% of her goal. That already ends in tenths, so no rounding is needed.
Watch out: 0.256 is a decimal, not a percent. And 26 rounds to a whole number, not to the nearest tenth.
Enter the answer
The box has no % sign, but the question asks for a percentage, so the number in the box is the percent. Type it with its decimal point. Typing 25.6% also counts on this site. So you would enter 25.6.
Check your answer
Estimate. 10% of 500 pages is 50 pages. 128 pages is a bit more than 2 × 50 = 100, so the answer is between 20% and 30%. Then check exactly: pages. It matches.
More questions like this
The original DOE question

Question 6 of 6
2026 Practice Test D Math, question 48Question
The perimeter of square W is twice the perimeter of equilateral triangle X. What is the ratio of the length of one side of square W to the length of one side of equilateral triangle X?
- A3:8
- B2:3
- C3:2
- D2:1
Show the answer
Correct answer: C
First, set up the ratio of the perimeter of the square to the triangle as 2:1 because the question states that the perimeter of the square is twice the perimeter of the triangle.
Recognizing that the square has 4 equal sides and that an equilateral triangle has 3 sides, use division to find the ratio of the sides.
Perimeter:
Sides:
Question analysis
The perimeter of square W is twice the perimeter of equilateral triangle X, and students find the ratio of a side of the square to a side of the triangle. This ratio question uses perimeters of regular shapes with no lengths given. Turning a comparison of perimeters into one of sides, and keeping the ratio in the order asked, are the tricky parts.
- NYS standards
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 ratio problems usually supply numbers to work with. This one gives only a relationship between two perimeters, so students must bring in the number of sides of each shape themselves and keep the ratio in the order asked.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Turning words into math moderate
- Variables instead of numbers moderate
- A very close wrong answer minor
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 9, 36 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The question turns a statement about perimeters into a ratio of sides, and the natural guess, that the sides keep the perimeters’ 2 to 1, ignores that the square shares its perimeter among 4 sides and the triangle among 3. Choosing a triangle perimeter such as 12 makes the comparison concrete. The order of the ratio still has to be checked at the end, because its reverse is listed too.
Turning words into math moderate Understanding the question
“The perimeter of square W is twice the perimeter of equilateral triangle X” must become 4s = 2 × 3t, with the 2 on the triangle’s side; written backward, it gives the triangle the larger perimeter. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Variables instead of numbers moderate Understanding the question
No side length is given, so students must either work with letters for the two sides or choose a convenient perimeter themselves, such as 12 for the triangle. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)
A very close wrong answer minor Choosing the answer
The ratios 3:2 and 2:3 use the same two numbers, so only keeping the square’s side first, as the question orders it, separates the answer from its reverse. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Strategy: Pick an easy side length for the triangle, find its perimeter, double that for the square, divide by the square's number of sides, and write square to triangle.
Traps
- Misunderstands the concept: A wrong belief about a concept: that percents can be added, that area grows like length, that averages can be averaged, that a bigger denominator means a bigger fraction.
- Wrong operation: Adds instead of multiplying, divides the wrong way round, turns a ratio or rate upside down, or undoes a step in the wrong direction (subtracts what should be added back).
- Equation written backwards: Writes a comparison the wrong way round, word for word: "six times as many students as professors" as 6S = P. The bigger quantity gets the bigger number.
The wrong answers, classified
A Equation written backwards (Clement, Lochhead & Monk, 1981)
Writes the comparison backward, 2 × 4s = 3t, giving the triangle the larger perimeter, so the ratio of the sides comes out 3:8.
B Wrong operation (Hegarty, Mayer & Monk, 1995; King et al., 2004)
Finds the right relationship but turns the ratio upside down, giving the triangle’s side to the square’s instead of the square’s side first.
D Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Assumes the sides are in the same ratio as the perimeters, 2:1, ignoring that the square has 4 sides and the triangle only 3.
Worked solution, step by step
Formulas used
- Perimeter of a square
- P is the perimeter, the distance around the shape. s is the length of one side. A square has 4 equal sides, so its perimeter is 4 times one side.
- Perimeter of an equilateral triangle
- An equilateral triangle has 3 equal sides. t is the length of one side. So its perimeter is 3 times one side.
- Ratio
- A ratio compares two amounts in order. a : b means a compared with b. The order matters, so write the amounts in the order the question names them.
Sort out the question
Square W has a perimeter twice as long as the perimeter of triangle X. Equilateral means all 3 sides of X are equal.
You need the ratio of one side of the square to one side of the triangle, in that order. No lengths are given, so you can pick a size to try.
Pick a size for the triangle
Choose an easy side length for the triangle, such as 2 units. All 3 sides are 2, so its perimeter is:
Find the square’s side
The square’s perimeter is twice the triangle’s:
The square has 4 equal sides, so divide by 4:
Each side of the square is 3 units.
Write the ratio in order
The square comes first, then the triangle. Their sides are 3 and 2, so the ratio is 3 : 2.
Watch out: 2 : 1, choice D, compares the perimeters, not the sides. The square splits its perimeter into 4 sides, the triangle into only 3. Choice B, 2 : 3, puts the triangle first. Choice A, 3 : 8, comes from giving the triangle the bigger perimeter.
So the answer is C, 3:2.
Check your answer
Try a different size. Give the triangle sides of 4. Its perimeter is 12, so the square’s is 24. Each side of the square is . The ratio 6 : 4 simplifies to 3 : 2. The size does not change the ratio.
More questions like this
The original DOE question
