7.7: The Secrets of the Q and A’s
Multiple-Choice Questions
True-or-False Questions
Matching Columns
Short Answer Questions
Essay Questions
| Word | What It Means | What the Instructor Is Looking For |
|---|---|---|
| Analyze | Break concept into key parts | Don’t just list the parts; show how they work together and illustrate any patterns. |
| Compare | Show similarities (and sometimes differences) between two or more concepts or ideas | Define the similarities and clearly describe how the items or ideas are similar. Do these similarities lead to similar results or effects? Note that this word is often combined with “contrast.” If so, make sure you do both. |
| Contrast | Show differences between two or more concepts or ideas | Define the differences and clearly describe how the items or ideas are different. How do these differences result in different outcomes? Note that this word is often combined with “compare.” If so, make sure you do both. |
| Critique | Judge and analyze | Explain what is wrong—and right—about a concept. Include your own judgments, supported by evidence and quotes from experts that support your point of view. |
| Define | Describe the meaning of a word, phrase, or concept | Define the concept or idea as your instructor did in class—but use your own words. If your definition differs from what the instructor presented, support your difference with evidence. Keep this essay short. Examples can help illustrate a definition, but remember that examples alone are not a definition. |
| Discuss | Explain or review | Define the key questions around the issue to be discussed and then answer them. Another approach is to define pros and cons on the issue and compare and contrast them. In either case, explore all relevant data and information. |
| Explain | Clarify, give reasons for something | Clarity is key for these questions. Outline your thoughts carefully. Proofread, edit, proofread, and proofread again! Good explanations are often lost in too many words. |
| Illustrate | Offer examples | Use examples from class material or reading assignments. Compare and contrast them to other examples you might come up with from additional reading or real life. |
| Prove | Provide evidence and arguments that something is true | Instructors who include this prompt in an exam question have often proven the hypothesis or other concepts in their class lectures. Think about the kind of evidence the instructor used and apply similar types of processes and data. |
| Summarize | Give a brief, precise description of an idea or concept | Keep it short, but cover all key points. This is one essay prompt where examples should not be included unless the instructions specifically ask for them. (For example, “Summarize the steps of the learning cycle and give examples of the main strategies you should apply in each one.”) |
Checkpoint Exercise
| Across | Down |
|---|---|
| 2. “Always,” “never,” and “every” are words that usually indicate the answer is ___________. | 1. It helps to group words in matching columns by ___________________ ___ _______________. |
| 3. A way to organize your thoughts for an essay | 4. Clarify, give reasons for something |
| 6. Short answer questions require a __________ answer. | 5. Essay questions often have more than one ________ answer. |
| 8. Describe the meaning of a word | 7. Show similarities and differences |
| 9. Give a brief, precise description of an idea or concept | 12. Most common answer in true and false questions |
| 10. Type of question used to evaluate thinking and reasoning | |
| 11. Since instructors need to read many essays, it is important to write _________. |
Nursing Test Question Types
In 2023 the National Council of State Boards of Nursing (NCSBN) made some significant changes to the nursing licensure exam referred to as NCLEX. Designed to evaluate the knowledge of the candidates ability to respond to significant patient and judgement in the clinical setting, several new question formats have been created to assess knowledge. Some of the question formats are:
- Case study: A case study presents a detailed scenario or patient situation. You’ll analyze the information provided, identify problems, and propose nursing interventions. It tests your critical thinking and clinical reasoning skills.
- Matrix (Grid): In a matrix question, you’ll match items from one category to another. For example, you might match nursing diagnoses with appropriate interventions or medications with their side effects.
- Bow-Tie: The bow-tie format involves visualizing a patient’s condition as a “bow-tie.” The center represents the patient, and the two tails represent potential outcomes (positive and negative). You’ll identify risk factors, interventions, and preventive measures.
- Drop-Down (Cloze, Table, Rationale): These questions often appear in computerized exams. You’ll select the correct answer from a dropdown menu. Cloze questions have missing words or phrases that you complete. Tables may present data, and you’ll choose the appropriate action or interpretation. Rationale questions ask you to explain your choice.
- Drag and Drop: These interactive questions require you to move items (e.g., symptoms, medications, nursing actions) to their correct places. They assess your knowledge organization and prioritization skills.
- Extended Multiple Response: These questions are more complex than standard multiple-choice questions. You’ll select multiple correct answers and may need to prioritize or sequence them. They test your depth of understanding.
A more comprehensive explanation of NCLEX item types can be found through many commercial publishers including Elsevier and the NCSBN website .
Activity – Test-Taking Tips
Test-Taking Tips
Write an email with advice to this friend, offering test-taking tips and strategies you think will help him.
RJ believes he is good at organization, and he usually is–for about the first two weeks of classes. He then becomes overwhelmed with all of the handouts and materials and tends to start slipping in the organization department. When it comes to tests, he worries that his notes might not cover all of the right topics and that he will not be able to remember all of the key terms and points–especially for his math class. During tests, he sometimes gets stuck on an item and tends to spend too much time there. He also sometimes changes answers but finds out later that his original selection was correct. He is also easily distracted by other students and noises which makes it hard for him to concentrate sometimes, and, unfortunately, he does admit to occasionally “cramming” the night before.
This page titled 7.8: Test-Taking Strategies(opens in new window) is shared under a CC BY 4.0(opens in new window) license and was authored, remixed, and/or curated by Leslie Jennings, RaeAnna Jeffers, Laura Haygood, and Craig Keaton(opens in new window) via source content(opens in new window) that was edited to the style and standards of the LibreTexts platform.


4: Fractions
Often in life, whole amounts are not exactly what we need. A baker must use a little more than a cup of milk or part of a teaspoon of sugar. Similarly a carpenter might need less than a foot of wood and a painter might use part of a gallon of paint. In this chapter, we will learn about numbers that describe parts of a whole. These numbers, called fractions, are very useful both in algebra and in everyday life. You will discover that you are already familiar with many examples of fractions!
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- 4.1: Visualize Fractions (Part 1)
- A fraction is a way to represent parts of a whole. The denominator b represents the number of equal parts the whole has been divided into, and the numerator a represents how many parts are included. The denominator, b, cannot equal zero because division by zero is undefined. A mixed number consists of a whole number and a fraction. When a fraction has a numerator that is smaller than the denominator, it is called a proper fraction, and its value is less than one.
-
- 4.2: Visualize Fractions (Part 2)
- Equivalent fractions are fractions that have the same value. When working with fractions, it is often necessary to express the same fraction in different forms. To find equivalent forms of a fraction, we can use the Equivalent Fractions Property. We can use the inequality symbols to order fractions. Remember that a > b means that a is to the right of b on the number line. As we move from left to right on a number line, the values increase.
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- 4.3: Multiply and Divide Fractions (Part 1)
- A fraction is considered simplified if there are no common factors, other than 1, in the numerator and denominator. If a fraction does have common factors in the numerator and denominator, we can reduce the fraction to its simplified form by removing the common factors. To multiply fractions, we multiply the numerators and multiply the denominators. Then we write the fraction in simplified form.
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- 4.4: Multiply and Divide Fractions (Part 2)
- The reciprocal of the fraction a/b is b/a, where a ≠ 0 and b ≠ 0. A number and its reciprocal have a product of 1. To find the reciprocal of a fraction, we invert the fraction. This means that we place the numerator in the denominator and the denominator in the numerator. To divide fractions, multiply the first fraction by the reciprocal of the second.
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- 4.5: Multiply and Divide Mixed Numbers and Complex Fractions (Part 1)
- To multiply or divide mixed numbers, convert the mixed numbers to improper fractions. Then follow the rules for fraction multiplication or division and then simplify if possible. A complex fraction is a fraction in which the number and/or denominator contains a fraction. To simplify a complex fraction, rewrite the complex fraction as a division problem. Then follow the rules for dividing fractions and then simplify if possible.
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- 4.6: Multiply and Divide Mixed Numbers and Complex Fractions (Part 2)
- Usually, the negative sign is placed in front of the fraction, but you will sometimes see a fraction with a negative numerator or denominator. When the numerator and denominator have different signs, the quotient is negative. If both the numerator and denominator are negative, then the fraction is positive because we are dividing a negative by a negative. Fraction bars act as grouping symbols. The expressions above and below the fraction bar should be treated as if they were in parentheses.
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- 4.8: Add and Subtract Fractions with Different Denominators (Part 1)
- The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators. To find the LCD of two fractions, factor each denominator into its primes. Then list the primes, matching primes in columns when possible, and bring down the columns. Finally, multiply the factors together, the product is the LCM of the denominators which is also the LCD of the fractions.
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- 4.9: Add and Subtract Fractions with Different Denominators (Part 2)
- In fraction multiplication, you multiply the numerators and denominators together, respectively. To divide fractions, you multiply the first fraction by the reciprocal of the second. For fraction addition, add the numerators together and place the sum over the common denominator. If the fractions have different denominators, first convert them to equivalent forms with the LCD. Likewise, for fraction subtraction, subtract the numerators and place the difference over the common denominator.
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- 4.10: Add and Subtract Mixed Numbers (Part 1)
- To add mixed numbers with a common denominator, first rewrite the problem in vertical form. Then, add the whole numbers and the fractions together. Finally, simplify the sum if possible. An alternate method for adding mixed numbers is to convert the mixed numbers to improper fractions and then add the improper fractions. This method is usually written horizontally.
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- 4.11: Add and Subtract Mixed Numbers (Part 2)
- To subtract mixed numbers with common denominators, first rewrite the problem in vertical form and compare the two fractions. If the top fraction is larger than the bottom fraction, subtract the fractions and then the whole numbers. If the top fraction is not larger than the bottom fraction, in the top mixed number, take one whole and add it to the fraction part, making a mixed number with an improper fraction. Then subtract the fractions and then the whole numbers. Lastly, simplify if possible.
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- 4.12: Solve Equations with Fractions (Part 1)
- The steps we take to determine whether a number is a solution to an equation are the same whether the solution is a whole number, an integer, or a fraction. To determine whether a number is a solution to an equation, first substitute the number for the variable in the equation. Then simplify the expressions on both sides of the equation and determine if the resulting equation is true. If it is true, the number is a solution. If it is not true, the number is not a solution.
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- 4.13: Solve Equations with Fractions (Part 2)
- To solve real-world problems, we first need to read the problem to determine what we are looking for. Then we write a word phrase that gives the information to find it. Next we translate the word phrase into math notation and then simplify. Finally, we translate math notation into a sentence to answer the question.
Figure 4.1 - Bakers combine ingredients to make delicious breads and pastries. (credit: Agustín Ruiz, Flickr)
Contributors and Attributions
-
Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (Formerly of Santa Ana College). This content is licensed under Creative Commons Attribution License v4.0 "Download for free at<EMAIL_ADDRESS>."


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albumin
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the most abundant protein circulating in the blood, with many functions within the body; used as a marker for protein status
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body image
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perception a person has about their physical body, including any feelings associated with that perception
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body mass index (BMI)
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a value that is calculated from an individual’s height and weight to provide as measurement relative to the standards for ideal body weight
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calorie
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a unit measure of energy
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carbohydrate
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macronutrient used to fuel the immediate energy needs of the body
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cellular respiration
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the breakdown of energy-rich nutrients (carbohydrates, fats, and proteins) to provide ATP, which fuels cellular functions within the body
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dehydration
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a fluid volume deficit that occurs with inadequate water intake or excessive water loss or both
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Dietary Reference Intake (DRI)
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scientifically developed values for essential nutrients and other food components
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enteral nutrition
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nutrition that is directly administered into the stomach
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esophageal duodenostomy (EGD)
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an invasive procedure performed under anesthesia in which an endoscopic tube is advanced through the pharynx, esophagus, and gastric pouch to check for anomalies such as esophageal strictures and peptic ulcers
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fat
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large, complex molecule made up of fatty acids and glycerol
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food desert
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a geographical area where fresh produce and foodstuffs are either too expensive or unavailable
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food insecurity
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the state of having limited access to adequate food
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ideal body weight (IBW)
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weight at which a person maintains optimal health benefits
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macronutrient
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nutrient consumed in large quantities to meet the body’s energy needs
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malnutrition
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an imbalance between the nutrients consumed and nutrients needed; includes both undernutrition and overnutrition and involves both macronutrients and micronutrients
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metabolism
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the process by which substances are chemically broken down to meet the body’s nutrient and energy needs
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micronutrient
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nutrient found in small quantities within the body but still necessary for physiological functions
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mineral
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essential to physiological processing; some are macronutrients, and some are micronutrients
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modified barium swallow study (MBSS)
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a procedure for viewing the anatomical and swallowing physiology of a bolus of food under video fluoroscopy
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parenteral nutrition (PN)
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nutrition delivered intravenously by a central line
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protein
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macronutrient made up of amino acids
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Recommended Dietary Allowances (RDAs)
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guidelines developed by the U.S. government for consuming the nutrients that make up a healthy diet
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Reference Daily Intake (RDI)
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average daily intake of a population
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vitamin
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essential micronutrient vital to biochemical regulation within the human body


13.1: The Architecture of the Galaxy
Learning Objectives
By the end of this section, you will be able to:
- Explain why William and Caroline Herschel concluded that the Milky Way has a flattened structure centered on the Sun and solar system
- Describe the challenges of determining the Galaxy’s structure from our vantage point within it
- Identify the main components of the Galaxy
The Milky Way Galaxy surrounds us, and you might think it is easy to study because it is so close. However, the very fact that we are embedded within it presents a difficult challenge. Suppose you were given the task of mapping New York City. You could do a much better job from a helicopter flying over the city than you could if you were standing in Times Square. Similarly, it would be easier to map our Galaxy if we could only get a little way outside it, but instead we are trapped inside and way out in its suburbs—far from the galactic equivalent of Times Square.
Herschel Measures the Galaxy
In 1785, William Herschel (Figure \(\PageIndex{1}\)) made the first important discovery about the architecture of the Milky Way Galaxy. Using a large reflecting telescope that he had built, William and his sister Caroline counted stars in different directions of the sky. They found that most of the stars they could see lay in a flattened structure encircling the sky, and that the numbers of stars were about the same in any direction around this structure. Herschel therefore concluded that the stellar system to which the Sun belongs has the shape of a disk or wheel (he might have called it a Frisbee except Frisbees hadn’t been invented yet), and that the Sun must be near the hub of the wheel (Figure \(\PageIndex{2}\)).
To understand why Herschel reached this conclusion, imagine that you are a member of a band standing in formation during halftime at a football game. If you count the band members you see in different directions and get about the same number each time, you can conclude that the band has arranged itself in a circular pattern with you at the center. Since you see no band members above you or underground, you know that the circle made by the band is much flatter than it is wide.
We now know that Herschel was right about the shape of our system, but wrong about where the Sun lies within the disk. As we saw in Between the Stars: Gas and Dust in Space, we live in a dusty Galaxy. Because interstellar dust absorbs the light from stars, Herschel could see only those stars within about 6000 light-years of the Sun. Today we know that this is a very small section of the entire 100,000-light-year-diameter disk of stars that makes up the Galaxy.
HARLOW SHAPLEY: MAPMAKER TO THE STARS
Until the early 1900s, astronomers generally accepted Herschel’s conclusion that the Sun is near the center of the Galaxy. The discovery of the Galaxy’s true size and our actual location came about largely through the efforts of Harlow Shapley. In 1917, he was studying RR Lyrae variable stars in globular clusters. By comparing the known intrinsic luminosity of these stars to how bright they appeared, Shapley could calculate how far away they are. (Recall that it is distance that makes the stars look dimmer than they would be “up close,” and that the brightness fades as the distance squared.) Knowing the distance to any star in a cluster then tells us the distance to the cluster itself.
Globular clusters can be found in regions that are free of interstellar dust and so can be seen at very large distances. When Shapley used the distances and directions of 93 globular clusters to map out their positions in space, he found that the clusters are distributed in a spherical volume, which has its center not at the Sun but at a distant point along the Milky Way in the direction of Sagittarius. Shapley then made the bold assumption, verified by many other observations since then, that the point on which the system of globular clusters is centered is also the center of the entire Galaxy (Figure \(\PageIndex{3}\)).
Shapley’s work showed once and for all that our star has no special place in the Galaxy. We are in a nondescript region of the Milky Way, only one of 200 to 400 billion stars that circle the distant center of our Galaxy.
Born in 1885 on a farm in Missouri, Harlow Shapley at first dropped out of school with the equivalent of only a fifth-grade education. He studied at home and at age 16 got a job as a newspaper reporter covering crime stories. Frustrated by the lack of opportunities for someone who had not finished high school, Shapley went back and completed a six-year high-school program in only two years, graduating as class valedictorian.
In 1907, at age 22, he went to the University of Missouri, intent on studying journalism, but found that the school of journalism would not open for a year. Leafing through the college catalog (or so he told the story later), he chanced to see “Astronomy” among the subjects beginning with “A.” Recalling his boyhood interest in the stars, he decided to study astronomy for the next year (and the rest, as the saying goes, is history).
Upon graduation Shapley received a fellowship for graduate study at Princeton and began to work with the brilliant Henry Norris Russell (see the Henry Norris Russell feature box in Section 18.4). For his PhD thesis, Shapley made major contributions to the methods of analyzing the behavior of eclipsing binary stars. He was also able to show that cepheid variable stars are not binary systems, as some people thought at the time, but individual stars that pulsate with striking regularity.
Impressed with Shapley’s work, George Ellery Hale offered him a position at the Mount Wilson Observatory, where the young man took advantage of the clear mountain air and the 60-inch reflector to do his pioneering study of variable stars in globular clusters.
Shapley subsequently accepted the directorship of the Harvard College Observatory, and over the next 30 years, he and his collaborators made contributions to many fields of astronomy, including the study of neighboring galaxies, the discovery of dwarf galaxies, a survey of the distribution of galaxies in the universe, and much more. He wrote a series of nontechnical books and articles and became known as one of the most effective popularizers of astronomy. Shapley enjoyed giving lectures around the country, including at many smaller colleges where students and faculty rarely got to interact with scientists of his caliber.
During World War II, Shapley helped rescue many scientists and their families from Eastern Europe; later, he helped found UNESCO, the United Nations Educational, Scientific, and Cultural Organization. He wrote a pamphlet called Science from Shipboard for men and women in the armed services who had to spend many weeks on board transport ships to Europe. And during the difficult period of the 1950s, when congressional committees began their “witch hunts” for communist sympathizers (including such liberal leaders as Shapley), he spoke out forcefully and fearlessly in defense of the freedom of thought and expression. A man of many interests, he was fascinated by the behavior of ants, and wrote scientific papers about them as well as about galaxies.
By the time he died in 1972, Shapley was acknowledged as one of the pivotal figures of modern astronomy, a “twentieth-century Copernicus” who mapped the Milky Way and showed us our place in the Galaxy.
To find more information about Shapley’s life and work , see the entry for him on the Bruce Medalists website. (This site features the winners of the Bruce Medal of the Astronomical Society of the Pacific, one of the highest honors in astronomy; the list is a who’s who of some of the greatest astronomers of the last twelve decades.)
Disks and Haloes
With modern instruments, astronomers can now penetrate the “smog” of the Milky Way by studying radio and infrared emissions from distant parts of the Galaxy. Measurements at these wavelengths (as well as observations of other galaxies like ours) have given us a good idea of what the Milky Way would look like if we could observe it from a distance.
Figure \(\PageIndex{4}\) sketches what we would see if we could view the Galaxy face-on and edge-on. The brightest part of the Galaxy consists of a thin, circular, rotating disk of stars distributed across a region about 100,000 light-years in diameter and about 1000 light-years thick. (Given how thin the disk is, perhaps a CD is a more appropriate analogy than a wheel.) In addition to stars, the dust and gas from which stars form are also found mostly in the thin disk of the Galaxy. The mass of the interstellar matter is about 15% of the mass of the stars in this disk.
As the diagram in Figure \(\PageIndex{4}\) shows, the stars, gas, and dust are not spread evenly throughout the disk but are concentrated into a central bar and a series of spiral arms. Recent infrared observations have confirmed that the central bar is composed mostly of old yellow-red stars. The two main spiral arms appear to connect with the ends of the bar. They are highlighted by the blue light from young hot stars. We know many other spiral galaxies that also have bar-shaped concentrations of stars in their central regions; for that reason they are called barred spirals. Figure \(\PageIndex{5}\) shows two other galaxies—one without a bar and one with a strong bar—to give you a basis for comparison to our own. We will describe our spiral structure in more detail shortly. The Sun is located about halfway between the center of the Galaxy and the edge of the disk and only about 70 light-years above its central plane.
Our thin disk of young stars, gas, and dust is embedded in a thicker but more diffuse disk of older stars; this thicker disk extends about 1000 light-years above and 1000 light-years below the midplane of the thin disk and contains only about 5% as much mass as the thin disk. The stars thin out with distance from the galactic plane and don’t have a sharp edge. Approximately 2/3 of the stars in the thick disk are within 1000 light-years of midplane.
Close in to the galactic center (within about 10,000 light-years), the stars are no longer confined to the disk but form a central bulge (or nuclear bulge). When we observe with visible light, we can glimpse the stars in the bulge only in those rare directions where there happens to be relatively little interstellar dust. The first picture that actually succeeded in showing the bulge as a whole was taken at infrared wavelengths (Figure \(\PageIndex{6}\)).
The fact that much of the bulge is obscured by dust makes its shape difficult to determine. For a long time, astronomers assumed it was spherical. However, infrared images and other data indicate that the bulge is about two times longer than it is wide, and shaped rather like a peanut. The relationship between this elongated inner bulge and the larger bar of stars remains uncertain. At the very center of the nuclear bulge is a tremendous concentration of matter, which we will discuss later in this chapter.
In our Galaxy, the thin and thick disks and the nuclear bulge are embedded in a spherical halo of very old, faint stars that extends to a distance of at least 150,000 light-years from the galactic center. Most of the globular clusters are also found in this halo.
The mass in the Milky Way extends even farther out, well beyond the boundary of the luminous stars to a distance of at least 200,000 light-years from the center of the Galaxy. This invisible mass has been give the name dark matter because it emits no light and cannot be seen with any telescope. Its composition is unknown, and it can be detected only because of its gravitational effects on the motions of luminous matter that we can see. We know that this extensive dark matter halo exists because of its effects on the orbits of distant star clusters and other dwarf galaxies that are associated with the Galaxy. This mysterious halo will be a subject of the section on The Mass of the Galaxy, and the properties of dark matter will be discussed more in the chapter on The Big Bang.
Some vital statistics of the thin and thick disks and the stellar halo are given in Table \(\PageIndex{1}\), with an illustration in Figure \(\PageIndex{7}\). Note particularly how the ages of stars correlate with where they are found. As we shall see, this information holds important clues to how the Milky Way Galaxy formed.
| Table \(\PageIndex{1}\): Characteristics of the Milky Way Galaxy | |||
|---|---|---|---|
| Property | Thin Disk | Thick Disk | Stellar Halo (Excludes Dark Matter) |
| Stellar mass | 4 × 10 10 \(M_{\text{Sun}}\) | A few percent of the thin disk mass | 10 10 \(M_{\text{Sun}}\) |
| Luminosity | 3 × 10 10 \(L_{\text{Sun}}\) | A few percent of the thin disk luminosity | 8 × 10 8 \(L_{\text{Sun}}\) |
| Typical age of stars | 1 million to 10 billion years | 11 billion years | 13 billion years |
| Heavier-element abundance | High | Intermediate | Very low |
| Rotation | High | Intermediate | Very low |
Establishing this overall picture of the Galaxy from our dust-shrouded viewpoint inside the thin disk has been one of the great achievements of modern astronomy (and one that took decades of effort by astronomers working with a wide range of telescopes). One thing that helped enormously was the discovery that our Glaxy is not unique in its characteristics. There are many other flat, spiral-shaped islands of stars, gas, and dust in the universe. For example, the Milky Way somewhat resembles the Andromeda galaxy, which, at a distance of about 2.3 million light-years, is our nearest neighboring giant spiral galaxy. Just as you can get a much better picture of yourself if someone else takes the photo from a distance away, pictures and other diagnostic observations of nearby galaxies that resemble ours have been vital to our understanding of the properties of the Milky Way.
The Milky Way Galaxy in myth and legend
To most of us living in the twenty-first century, the Milky Way Galaxy is an elusive sight. We must make an effort to leave our well-lit homes and streets and venture beyond our cities and suburbs into less populated environments. Once the light pollution subsides to negligible levels, the Milky Way can be readily spotted arching over the sky on clear, moonless nights. The Milky Way is especially bright in late summer and early fall in the Northern Hemisphere. Some of the best places to view the Milky Way are in our national and state parks, where residential and industrial developments have been kept to a minimum. Some of these parks host special sky-gazing events that are definitely worth checking out—especially during the two weeks surrounding the new moon, when the faint stars and Milky Way don’t have to compete with the Moon’s brilliance.
Go back a few centuries, and these starlit sights would have been the norm rather than the exception. Before the advent of electric or even gas lighting, people relied on short-lived fires to illuminate their homes and byways. Consequently, their night skies were typically much darker. Confronted by myriad stellar patterns and the Milky Way’s gauzy band of diffuse light, people of all cultures developed myths to make sense of it all.
Some of the oldest myths relating to the Milky Way are maintained by the aboriginal Australians through their rock painting and storytelling. These legacies are thought to go back tens of thousands of years, to when the aboriginal people were being “dreamed” along with the rest of the cosmos. The Milky Way played a central role as an arbiter of the Creation. Taking the form of a great serpent, it joined with the Earth serpent to dream and thus create all the creatures on Earth.
The ancient Greeks viewed the Milky Way as a spray of milk that spilled from the breast of the goddess Hera. In this legend, Zeus had secretly placed his infant son Heracles at Hera’s breast while she was asleep in order to give his half-human son immortal powers. When Hera awoke and found Heracles suckling, she pushed him away, causing her milk to spray forth into the cosmos (Figure \(\PageIndex{8}\)).
The dynastic Chinese regarded the Milky Way as a “silver river” that was made to separate two star-crossed lovers. To the east of the Milky Way, Zhi Nu, the weaving maiden, was identified with the bright star Vega in the constellation of Lyra the Harp. To the west of the Milky Way, her lover Niu Lang, the cowherd, was associated with the star Altair in the constellation of Aquila the Eagle. They had been exiled on opposite sides of the Milky Way by Zhi Nu’s mother, the Queen of Heaven, after she heard of their secret marriage and the birth of their two children. However, once a year, they are permitted to reunite. On the seventh day of the seventh lunar month (which typically occurs in our month of August), they would meet on a bridge over the Milky Way that thousands of magpies had made (Figure \(\PageIndex{8}\)). This romantic time continues to be celebrated today as Qi Xi, meaning “Double Seventh,” with couples reenacting the cosmic reunion of Zhi Nu and Niu Lang.
To the Quechua Indians of Andean Peru, the Milky Way was seen as the celestial abode for all sorts of cosmic creatures. Arrayed along the Milky Way are myriad dark patches that they identified with partridges, llamas, a toad, a snake, a fox, and other animals. The Quechua’s orientation toward the dark regions rather than the glowing band of starlight appears to be unique among all the myth makers. Likely, their access to the richly structured southern Milky Way had something to do with it.
Among Finns, Estonians, and related northern European cultures, the Milky Way is regarded as the “pathway of birds” across the night sky. Having noted that birds seasonally migrate along a north-south route, they identified this byway with the Milky Way. Recent scientific studies have shown that this myth is rooted in fact: the birds of this region use the Milky Way as a guide for their annual migrations.
 Although our perspective on the Milky Way is based on scientific investigations, we share with our forebears an affinity for telling stories of origin and transformation. In these regards, the Milky Way continues to fascinate and inspire us.
Key Concepts and Summary
The Milky Way Galaxy consists of a thin disk containing dust, gas, and young and old stars; a spherical halo containing populations of very old stars, including RR Lyrae variable stars and globular star clusters; a thick, more diffuse disk with stars that have properties intermediate between those in the thin disk and the halo; a peanut-shaped nuclear bulge of mostly old stars around the center; and a supermassive black hole at the very center. The Sun is located roughly halfway out of the Milky Way, about 26,000 light-years from the center.
Glossary
- dark matter halo
- the mass in the Milky Way that extends well beyond the boundary of the luminous stars to a distance of at least 200,000 light-years from the center of the Galaxy; although we deduce its existence from its gravity, the composition of this matter remains a mystery
- halo
- the outermost extent of our Galaxy (or another galaxy), containing a sparse distribution of stars and globular clusters in a more or less spherical distribution
- Milky Way Galaxy
- the band of light encircling the sky, which is due to the many stars and diffuse nebulae lying near the plane of the Milky Way Galaxy
- central bulge
- (or nuclear bulge) the central (round) part of the Milky Way or a similar galaxy
Contributors and Attributions
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Andrew Fraknoi (Foothill College), David Morrison (NASA Ames Research Center), Sidney C. Wolff (National Optical Astronomy Observatory) with many contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at https://openstax.org/details/books/astronomy ).


39.2: Common Multiples
Lesson
Let's use multiples to solve problems.
Exercise \(\PageIndex{1}\): Notice and Wonder: Multiples
Circle all the multiples of 4 in this list.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Circle all the multiples of 6 in this list.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
What do you notice? What do you wonder?
Exercise \(\PageIndex{2}\): The Florist's Order
A florist can order roses in bunches of 12 and lilies in bunches of 8. Last month she ordered the same number of roses and lilies.
- If she ordered no more than 100 of each kind of flower, how many bunches of each could she have ordered? Find all the possible combinations.
- What is the smallest number of bunches of roses that she could have ordered? What about the smallest number of bunches of lilies? Explain your reasoning.
Exercise \(\PageIndex{3}\): Least Common Multiple
The least common multiple of 6 and 8 is 24.
- What do you think the term “least common multiple” means?
- Find all of the multiples of 10 and 8 that are less than 100. Find the least common multiple of 10 and 8.
- Find all of the multiples of 7 and 9 that are less than 100. Find the least common multiple of 7 and 9.
Are you ready for more?
- What is the least common multiple of 10 and 20?
- What is the least common multiple of 4 and 24?
- In the previous two questions, one number is a multiple of the other. What do you notice about their least common multiple? Do you think this will always happen when one number is a multiple of the other? Explain your reasoning.
Exercise \(\PageIndex{4}\): Prizes on Grand Opening Day
Lin’s uncle is opening a bakery. On the bakery’s grand opening day, he plans to give away prizes to the first 50 customers that enter the shop. Every fifth customer will get a free bagel. Every ninth customer will get a free blueberry muffin. Every 12th customer will get a free slice of carrot cake.
- Diego is waiting in line and is the 23rd customer. He thinks that he should get farther back in line in order to get a prize. Is he right? If so, how far back should he go to get at least one prize? Explain your reasoning.
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Jada is the 36th customer.
- Will she get a prize? If so, what prize will she get?
- Is it possible for her to get more than one prize? How do you know? Explain your reasoning.
- How many prizes total will Lin’s uncle give away? Explain your reasoning.
Summary
A multiple of a whole number is a product of that number with another whole number. For example, 20 is a multiple of 4 because \(20=5\cdot 4\).
A common multiple for two whole numbers is a number that is a multiple of both numbers. For example, 20 is a multiple of 2 and a multiple of 5, so 20 is a common multiple of 2 and 5.
The least common multiple (sometimes written as LCM) of two whole numbers is the smallest multiple they have in common. For example, 30 is the least common multiple of 6 and 10.
One way to find the least common multiple of two numbers is to list multiples of each in order until we find the smallest multiple they have in common. Let's find the least common multiple for 4 and 10. First, we list some multiples of each number.
- Multiples of 4: 4, 8, 12, 16, 20 , 24, 28, 32, 36, 40 , 44 . . .
- Multiples of 10: 10, 20 , 30, 40 , 50, . . .
20 and 40 are both common multiples of 4 and 10 (as are 60, 80, . . . ), but 20 is the smallest number that is on both lists, so 20 is the least common multiple.
Glossary Entries
Definition: Common Factor
A common factor of two numbers is a number that divides evenly into both numbers. For example, 5 is a common factor of 15 and 20, because \(15\div 5=3\) and \(20\div 5=4\). Both of the quotients, 3 and 4, are whole numbers.
- The factors of 15 are 1, 3, 5 , and 15.
- The factors of 20 are 1, 2, 4, 5 , 10, and 20.
Definition: Common Multiple
A common multiple of two numbers is a product you can get by multiplying each of the two numbers by some whole number. For example, 30 is a common multiple of 3 and 5, because \(3\cdot 10=30\) and \(5\cdot 6=30\). Both of the factors, 10 and 6, are whole numbers.
- The multiples of 3 are 3, 6, 9, 12, 15 , 18, 21, 24, 27, 30 , 33 . . .
- The multiples of 5 are 5, 10, 15 , 20, 25, 30 , 35, 40 . . .
The common multiples of 3 and 5 are 15, 30, 45, 60 . . .
Definition: Greatest Common Factor
The greatest common factor of two numbers is the largest number that divides evenly into both numbers. Sometimes we call this the GCF. For example, 15 is the greatest common factor of 45 and 60.
- The factors of 45 are 1, 3, 5, 9, 15 , and 45.
- The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15 , 20, 30, and 60.
Definition: Least Common Multiple
The least common multiple of two numbers is the smallest product you can get by multiplying each of the two numbers by some whole number. Sometimes we call this the LCM. For example, 30 is the least common multiple of 6 and 10.
- The multiples of 6 are 6, 12, 18, 24, 30 , 36, 42, 48, 54, 60 . . .
- The multiples of 10 are 10, 20, 30 , 40, 50, 60, 70, 80 . . .
Practice
Exercise \(\PageIndex{5}\)
- A green light blinks every 4 seconds and a yellow light blinks every 5 seconds. When will both lights blink at the same time?
- A red light blinks every 12 seconds and a blue light blinks every 9 seconds. When will both lights blink at the same time?
- Explain how to determine when 2 lights blink together.
Exercise \(\PageIndex{6}\)
- List all multiples of 10 up to 100.
- List all multiples of 15 up to 100.
- What is the least common multiple of 10 and 15?
Exercise \(\PageIndex{7}\)
Cups are sold in packages of 8. Napkins are sold in packages of 12.
- What is the fewest number of packages of cups and the fewest number of packages of napkins that can be purchased so there will be the same number of cups as napkins?
- How many sets of cups and napkins will there be?
Exercise \(\PageIndex{8}\)
- Plot and connect these points to form a polygon.
\((-5,3),\qquad (3,3),\qquad (1,-2),\qquad (-3,-2)\)
- Find the lengths of the two horizontal sides of the polygon.
(From Unit 7.3.5)
Exercise \(\PageIndex{9}\)
Rectangle ABCD is drawn on a coordinate plane. \(A = (-6,9)\) and \(B = (5,9)\). What could be the locations of points C and D?
(From Unit 7.3.4)
Exercise \(\PageIndex{10}\)
A school wants to raise $2,500 to support its music program.
- If it has met 20% of its goal so far, how much money has it raised?
- If it raises 175% of its goal, how much money will the music program receive? Show your reasoning.
(From Unit 3.4.5)


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active euthanasia
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administration of an outside agent, such as a lethal amount of a drug, to cause death
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advance directive
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legal document that specifies what a person’s wishes are in the event they are unable to express them at some point in the future
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assisted suicide
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(also, medical aid in dying [MAID]) procedure in which a doctor knowingly prescribes a dose of medication knowing the patient intends to use it to end their life
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bereavement
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experience of the death of a loved one
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biological death
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permanent state of death in which vital organs have stopped working and cannot be resuscitated
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blunting
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coping style associated with avoiding information, particularly bad news
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brain death
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death that occurs when the brain has permanently stopped working
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cardiopulmonary death
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death that occurs when heartbeat and breathing have stopped and cannot be restarted through cardiopulmonary resuscitation (CPR) or other means
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clinical death
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potentially temporary state of death in which a person’s vital organs have stopped working but could be resuscitated
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complicated grief
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form of grief that lasts longer than is typical and is also associated with long-term adjustment problems; described as “prolonged grief disorder” in the
DSM-V-TR
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death anxiety
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person’s concern about what awaits them after death
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do not hospitalize (DNH)
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legal document stating that a person does not want to be hospitalized (and therefore receive unwanted medical treatment) in the event of serious illness
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do not intubate (DNI)
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legal document stating that a person does not want breathing tubes inserted into their nose or mouth in the event they stop breathing
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do not resuscitate (DNR)
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legal document stating that if a person’s heart stops beating or breathing stops, they do not want CPR or other measures taken to revive them
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dual-process model
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model of grieving consisting of two stages: loss orientation and restoration orientation; developed by Stroebe and Schut
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durable power of attorney for health care
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legal document authorizing a specific person to make health-care decisions for someone else
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dying trajectory
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pathway to death that varies on dimensions such as the nature and rate of decline
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euthanasia
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act of ending life in a painless manner to relieve pain and suffering
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excess mortality
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number of deaths above what would typically occur in a given time period
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executor
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person in charge of filing relevant paperwork and fulfilling the conditions in someone’s will
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grief
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internal, emotional reaction to loss
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health-care proxy
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person legally authorized to make health-care decisions for someone, or a legal document that gives a person that authority
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home care
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medical services provided in the patient’s residence
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hospice care
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type of care provided if a person’s condition is uncurable or treatment would be too stressful; includes managing physical symptoms, including pain, as well as addressing the spiritual and emotional needs of the patient and their loved ones
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intestate
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circumstance of dying without a will
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Kübler-Ross’s themes of grief
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cognitive, emotional, and behavioral reactions to our own impending death, encompassing denial, anger, bargaining, depression, and acceptance
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legacy activities
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activities in which a person creates an artifact that represents their life and for which they want to be remembered, such as a photo album, scrapbook, cookbook, or letters written to loved ones
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life review
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thoughtful examination of our own life, often focused on integrating both positive and negative memories into a coherent whole
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life satisfaction
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contentment with our current circumstances
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living will
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legal document specifying a person’s wishes regarding life-sustaining medical treatment in the event they are unable to express these wishes when treatment is needed
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loss orientation
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reaction to loss in which the bereaved person addresses the emotional aspects of the loss by accepting the situation and sharing grief with others
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middle knowledge
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intermediate step of grieving in which a person knows a loss is coming or has occurred but has not fully accepted the reality of it
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monitoring
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coping style characterized by the seeking out of information
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mourning
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outward, behavioral manifestation of grief
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outgroup bias
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negative feelings about people we feel are different than us
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palliative care
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type of medical care that manages symptoms and relieves pain but does not try to cure the underlying medical condition
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passive euthanasia
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withdrawal or withholding of potentially life-sustaining treatment
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probate court
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type of legal court that handles matters related to wills and guardianships
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quality of life
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person’s perception of how good their life is in the context of their values, goals, and cultural norms
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rationing of care
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practice of limiting the use of health-care resources for patients who have little or no chance of recovery
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reminiscence
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recollection and sharing of memories and stories, typically pleasant ones
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restoration orientation
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reaction to loss in which the bereaved person copes with the changes brought about by a loved one’s death, including changes to or the addition of relationships and roles
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social death
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exclusion from social interactions and considerations; when a person is viewed as not being part of society
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terror management theory
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theory that when our sense of self is threatened, we try to preserve it by becoming more committed to cultural values and showing more outgroup bias
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thanatologist
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researcher who studies the biological, psychological, and/or social aspects of death
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will
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legal document containing instructions for what to do with a person’s assets, property, and dependents after death


6.3: Working with Sources- Part I
They Say/I Say Approach To Sources
Recall from prior chapters that writing academic papers is about joining a conversation. You’re contributing your own original thinking to some complex problem, be it interpretive, theoretical, or practical. Citing sources helps situate your ideas within that ongoing conversation. Sometimes you’re citing a research finding that provides strong evidence for your point; at other times you’re summarizing someone else’s ideas in order to explain how your own opinion differs or to note how someone else’s concept applies to a new situation. Graff and Birkenstein 1 encourage you to think about writing with sources is a “They Say/I Say” process. You first report what “they” say (“they” being published authors, prevalent ideas in society at large, or maybe participants in some kind of political or social debate). Then you respond by explaining what you think: Do you agree? Disagree? A little of both?
This “They Say/I Say” approach can help you find balance in your use of sources. On one extreme, some students think that they aren’t allowed to make any claims without citing one or more expert authors saying the same thing. When their instructors encourage them to bring more original thinking into their writing, they’re confused about how to do it. On the other extreme, some students tend to describe, more or less accurately, what sources say about a topic but then go on to state opinions that seem unrelated to the claims they just summarized. For example, a student writer may draw on expert sources to explain how the prevention and early detection of cancer has saved lives 2 but then argue for more funding for curing advanced cancer without making any explicit link to the points about prevention and screening. On one extreme, the sources are allowed to crowd out original thinking; on the other, they have seemingly no impact on the author’s conclusions.
How can you know when you’re avoiding both of these extremes? In other words, what kinds of thesis (“I Say”) can count as an original claim and still be grounded in the sources (“They Say”)? Here are five common strategies:
- Combine research findings from multiple sources to make a larger summary argument . You might find that none of the sources you’re working with specifically claim that early 20th century British literature was preoccupied with changing gender roles but that, together, their findings all point to that broader conclusion.
- Combine research findings from multiple sources to make a claim about their implications . You might review papers that explore various factors shaping voting behavior to argue that a particular voting-reform proposal will likely have positive impacts.
- Identify underlying areas of agreement . You may argue that the literature on cancer and the literature on violence both describe the unrecognized importance of prevention and early intervention in order to claim that insights about one set of problems may be useful for the other.
- Identify underlying areas of disagreement . You may find that the controversies surrounding educational reform—and its debates about accountability, curricula, school funding—ultimately stem from different assumptions about the role of schools in society.
- Identify unanswered questions . Perhaps you review studies of the genetic and behavioral contributors to diabetes in order to highlight unknown factors and argue for more in-depth research on the role of the environment.
There are certainly other ways authors use sources to build theses, but these examples illustrate how original thinking in academic writing involves making connections with and between a strategically chosen set of sources.
Incorporating Sources
Here’s a passage of academic writing (an excerpt, not a complete paper) that illustrates several ways that sources can figure into a “They Say/I Say” approach 3 :
Willingham (2011 ) draws on cognitive science to explain that students must be able to regulate their emotions in order to learn. Emotional self-regulation enables students to ignore distractions and channel their attention and behaviors in appropriate ways. Other research findings confirm that anxiety interferes with learning and academic performance because it makes distractions harder to resist ( Perkins and Graham-Bermann, 2012 ; Putwain and Best, 2011 ). Other cognitive scientists point out that deep learning is itself stressful because it requires people to think hard about complex, unfamiliar material instead of relying on cognitive short-cuts.
Kahneman (2011) describes this difference in terms of two systems for thinking: one fast and one slow. Fast thinking is based on assumptions and habits and doesn’t require a lot of effort. For example, driving a familiar route or a routine grocery-shopping trip are not usually intellectually taxing activities. Slow thinking, on the other hand, is what we do when we encounter novel problems and situations. It’s effortful, and it usually feels tedious and confusing. It is emotionally challenging as well because we are, by definition, incompetent while we’re doing it, which provokes some anxiety. Solving a tough problem is rewarding, but the path itself is often unpleasant.
These insights from cognitive science enable us to critically assess the claims made on both sides of the education reform debate. On one hand, they cast doubt on the claims of education reformers that measuring teachers’ performance by student test scores is the best way to improve education. For example, the
Center for Education Reform
promotes “the implementation of strong, data-driven, performance-based accountability systems that ensure teachers are rewarded, retained and advanced based on how they perform in adding value to the students who they teach, measured predominantly by student achievement” (
http://www.edreform.com/issues/teacher-quality/#what-we-believe
). The research that Willingham (2011) and Kahneman (2011) describe suggests that frequent high-stakes testing may actually work against learning by introducing greater anxiety into the school environment.
At the same time, opponents of education reform should acknowledge that these research findings should prompt us to take a fresh look at how we educate our children. While Stan Karp of
Rethinking Schools
is correct when he argues that “data-driven formulas [based on standardized testing] lack both statistical credibility and a basic understanding of the human motivations and relationships that make good schooling possible” (
www.rethinkingschools.org/archive/26_03/26_03_karp.shtm
), it doesn’t necessarily follow that all education reform proposals lack merit. Challenging standards, together with specific training in emotional self-regulation, will likely enable more students to succeed.
4
In that example, the ideas of Willingham and Kahneman are summarized approvingly, bolstered with additional research findings, and then applied to a new realm: the current debate surrounding education reform. Voices in that debate were portrayed as accurately as possible, sometimes with representative quotes. Most importantly, all references were tied directly to the author’s own interpretative point, which relies on the quoted claims.
Student Quotation:
I think the most important lesson for me to learn about sources was that the best way to use them is to create a new point. What I mean by this is instead of using them only to back up your points, create your own conclusion from what your sources say. As a psychology major, I look at a lot of data from researchers who have created a conclusion from a meta-analysis (a combination of many studies about the same thing). So that’s how I like to think of using sources, I will look at many articles about the same subject and then come up with my own opinion. After using your sources, it is very important to cite them correctly. Personally, I want to be a respected and trustworthy scholar. However, if any of my papers were to be found without proper citations, all of my hard work would be for nothing and people would be wary about the rest of my work.
Aly Button
As you can see, there are times when you should quote or paraphrase sources that you don’t agree with or do not find particularly compelling. They may convey ideas and opinions that help explain and justify your own argument. Similarly, when you cite sources that you agree with, you should choose quotes or paraphrases that serve as building blocks within your own argument. Regardless of the role each source plays in your writing, you certainly don’t need to find whole sentences or passages that express your thinking. Rather, focus on what each of those sources is claiming, why, and how exactly their claims relate to your own points.
The remainder of this chapter explains some key principles for incorporating sources, principles which follow from the general point that academic writing is about entering an ongoing conversation.
Principle 1: Listen to your Sources
Have you ever had the maddening experience of arguing with someone who twisted your words to make it seem like you were saying something you weren’t? Novice writers sometimes inadvertently misrepresent their sources when they quote very minor points from an article or even positions that the authors of an article disagree with. It often happens when students approach their sources with the goal of finding snippets that align with their own opinion. For example, the passage above contains the phrase “measuring teachers’ performance by student test scores is the best way to improve education.” An inexperienced writer might include that quote in a paper without making it clear that the author(s) of the source actually dispute that very claim. Doing so is not intentionally fraudulent, but it reveals that the paper-writer isn’t really thinking about and responding to claims and arguments made by others. In that way, it harms his or her credibility.
Academic journal articles are especially likely to be misrepresented by student writers because their literature review sections often summarize a number of contrasting viewpoints. For example, sociologists Jennifer C. Lee and Jeremy Staff wrote a paper in which they note that high-schoolers who spend more hours at a job are more likely to drop out of school. 5 However, Lee and Staff’s analysis finds that working more hours doesn’t actually make a student more likely to drop out. Instead, the students who express less interest in school are both more likely to work a lot of hours and more likely to drop out. In short, Lee and Staff argue that disaffection with school causes students to drop-out, not working at a job. In reviewing prior research about the impact of work on dropping out, Lee and Staff write “Paid work, especially when it is considered intensive, reduces grade point averages, time spent on homework, educational aspirations, and the likelihood of completing high school” 6 . If you included that quote without explaining how it fits into Lee and Staff’s actual argument, you would be misrepresenting that source.
Principle 2: Provide Context
Another error beginners often make is to drop in a quote without any context. If you simply quote, “Students begin preschool with a set of self-regulation skills that are a product of their genetic inheritance and their family environment” (Willingham 24), your reader is left wondering who Willingham is, why he or she is included here, and where this statement fits into his or her larger work. The whole point of incorporating sources is to situate your own insights in the conversation. As part of that, you should provide some kind of context the first time you use that source. Some examples:
Willingham, a cognitive scientist, claims that …
Research in cognitive science has found that … (Willingham, 2011).
Willingham argues that “Students begin preschool with a set of self-regulation skills that are a product of their genetic inheritance and their family environment” (Willingham 24). Drawing on findings in cognitive science, he explains “…”
As the second example above shows, providing a context doesn’t mean writing a brief biography of every author in your bibliography—it just means including some signal about why that source is included in your text.
Even more baffling to your reader is when quoted material does not fit into the flow of the text. For example, a novice student might write,
Schools and parents shouldn’t set limits on how much teenagers are allowed to work at jobs. “We conclude that intensive work does not affect the likelihood of high school dropout among youths who have a high propensity to spend long hours on the job” (Lee and Staff 171). Teens should be trusted to learn how to manage their time.
The reader is thinking, who is this sudden, ghostly “we”? Why should this source be believed? If you find that passages with quotes in your draft are awkward to read out loud, that’s a sign that you need to contextualize the quote more effectively. Here’s a version that puts the quote in context:
Schools and parents shouldn’t set limits on how much teenagers are allowed to work at jobs. Lee and Staff’s carefully designed study found that “intensive work does not affect the likelihood of high school dropout among youths who have a high propensity to spend long hours on the job” (171). Teens should be trusted to learn how to manage their time.
In this latter example, it’s now clear that Lee and Staff are scholars and that their empirical study is being used as evidence for this argumentative point. Using a source in this way invites the reader to check out Lee and Staff’s work for themselves if they doubt this claim.
Many writing instructors encourage their students to contextualize their use of sources by making a “ quotation sandwich ”; that is, introduce the quote in some way and then follow it up with your own words. If you’ve made a bad habit of dropping in unintroduced quotes, the quotation sandwich idea may help you improve your skills, but in general you don’t need to approach every quote or paraphrase as a three-part structure to have well integrated sources. You should, however, avoid ending a paragraph with a quotation. If you’re struggling to figure out what to write after a quote or close paraphrase, it may be that you haven’t yet figured out what role the quote is playing in your own analysis. If that happens to you a lot, try writing the whole first draft in your own words and then incorporate material from sources as you revise with “They Say/I Say” in mind.
Principle 3: Use Sources Efficiently
Some student writers are in a rut of only quoting whole sentences. Some others get overly enamored of extended block quotes and the scholarly look they give to the page. 7 (A block quote is an indented paragraph of quoted text.) These aren’t the worst sins of academic writing, but they get in the way of one of the key principles of writing with sources: shaping quotes and paraphrases efficiently. Efficiency follows from the second principle, because when you fully incorporate sources into your own explicit argument, you zero in on the phrases, passages, and ideas that are relevant to your points. It’s a very good sign for your paper when most quotes are short (key terms, phrases, or parts of sentences) and the longer quotes (whole sentences and passages) are clearly justified by the discussion in which they’re embedded. Every bit of every quote should feel indispensable to the paper. An overabundance of long quotes usually means that your own argument is undeveloped. The most glowing quotes will not hide that fact from your professor.
Also, some student writers forget that quoting is not the only way to incorporate sources. Paraphasing and summarizing are sophisticated skills that are often more appropriate to use than direct quoting. In fact, in science writing especially, quotes are rarely used. The first two paragraphs of the example passage above do not include any quotations, even though they are both clearly focused on presenting the work of others. Student writers may avoid paraphrasing out of fear of plagiarizing, and it’s true that a poorly executed paraphrase will make it seem like the student writer is fraudulently claiming the wordsmithing work of others as his or her own. Sticking to direct quotes seems safer. However, it is worth your time to master paraphasing because it often helps you be more clear and concise, drawing out only those elements that are relevant to the thread of your analysis.
For example, here’s a passage from a hypothetical paper with a block quote that is fully relevant to the argument but, nevertheless, inefficient:
Drawing on a lifetime of research, Kahneman concludes our brains are prone to error: 8
System 1 registers the cognitive ease with which it processes information, but it does not generate a warning signal when it becomes unreliable. Intuitive answers come to mind quickly and confidently, whether they originate from skills or from heuristics. There is no simple way for System 2 to distinguish between a skilled and a heuristic response. Its only recourse is to slow down and attempt to construct an answer on its own, which it is reluctant to do because it is indolent. Many suggestions of System 1 are casually endorsed with minimal checking, as in the bat-and-ball problem.
While people can get better at recognizing and avoiding these errors, Kahneman suggests, the more robust solutions involve developing procedures within organizations to promote careful, effortful thinking in making important decisions and judgments.
Even a passage that is important to reference and is well contextualized in the flow of the paper will be inefficient if it introduces terms and ideas that aren’t central to the analysis within the paper. Imagine, for example, that other parts of this hypothetical paper use Kahneman’s other terms for System 1 (fast thinking) and System 2 (slow thinking); the sudden encounter of “System 1” and “System 2” would be confusing and tedious for your reader. Similarly, the terms “heuristics” and “bat-and-ball problem” might be unfamiliar to your reader. Their presence in the block quote just muddies the waters. In this case, a paraphrase is a much better choice. Here’s an example passage that uses a paraphrase to establish the same points more clearly and efficiently:
Drawing on a lifetime of research, Kahneman summarizes that our brains are prone to error because they necessarily rely on cognitive shortcuts that may or may not yield valid judgments. 9 We have the capacity to stop and examine our assumptions, Kahneman points out, but we often want to avoid that hard work. As a result, we tend to accept our quick, intuitive responses. While people can get better at recognizing and avoiding these errors, Kahneman suggests that the more robust solutions involve developing procedures within organizations to promote careful, effortful thinking in making important decisions and judgments.
Not only is the paraphrased version shorter (97 words versus 151), it is clearer and more efficient because it highlights the key ideas, avoiding specific terms and examples that aren’t used in the rest of the paper. If other parts of your paper did refer to Kahneman’s System 1 and System 2, then you might choose to include some quoted phrases to make use of some of Kahneman’s great language. Perhaps something like this:
Drawing on a lifetime of research, Kahneman summarizes that our brains are prone to error because they necessarily rely on cognitive shortcuts that may or may not yield valid judgments. 10 System 1, Kahneman explains, “does not generate a warning signal when it becomes unreliable.” 11 System 2 can stop and examine these assumptions, but it usually wants to avoid that hard work. As a result, our quick, intuitive responses are “casually endorsed with minimal checking.” 12 While people can get better at recognizing and avoiding these errors, Kahneman suggests, the more robust solutions involve developing procedures within organizations to promote careful, effortful thinking in making important decisions and judgments.
Whether you choose a long quote, short quote, paraphrase or summary depends on the role that the source in playing in your analysis. The trick is to make deliberate, thoughtful decisions about how to incorporate ideas and words from others.
Paraphrasing, summarizing, and the mechanical conventions of quoting take a lot of practice to master. Numerous other resources explain these practices clearly and succinctly. Bookmark some good sources and refer to them as needed. If you suspect that you’re in a quoting rut, try out some new ways of incorporating sources.
Principle 4: Choose Precise Verbs of Attribution
It’s time to get beyond the all-purpose “says.”  Here’s a list of 15 useful alternatives: 13
- Claims
- Asserts
- Relates
- Recounts
- Complains
- Reasons
- Proposes
- Suggests (if the author is speculating or hypothesizing)
- Contests (disagrees)
- Concludes
- Shows
- Argues
- Explains
- Indicates
- Points out
- Offers
More precise choices like these carry a lot more information than “says”, enabling you to relate more with fewer words. For one thing, they can quickly convey what kind of idea you’re citing: a speculative one (“postulates”)? A conclusive one (“determines”)? A controversial one (“counters”)? You can further show how you’re incorporating these sources into your own narrative. For example, if you write that an author “claims” something, you’re presenting yourself as fairly neutral about that claim. If you instead write that the author “shows” something, then you signal to your reader that you find that evidence more convincing. “Suggests” on the other hand is a much weaker endorsement. Saying more with less makes your writing much more engaging.
Student Quotation
Sources are your best friend. They either help you reaffirm your thesis or offer a differing opinion that you can challenge in your paper. The biggest thing to worry about, when it comes to sources, is citing. However, there are a multitude of resources to help you cite properly. My personal favorite is called Knightcite.com. You just pick the type of resource, fill in the information on it and voila, you have a perfectly cited resource!
Kaethe Leonard
Conclusion
Like so many things in adult life, writing in college is often both more liberating and burdensome than writing in high school and before. On the one hand, students have expressed that their high-school experiences made it seem that their own opinions didn’t matter in academic writing, and that they can’t make any claims that aren’t exactly paralleled by a pedigreed quotation. Writing papers based on their own insights and opinions can seem freeing in contrast. At the same time, a college student attending full time may be expected to have original and well considered ideas about pre-Columbian Latin American history, congressional redistricting, sports in society, post-colonial literatures, and nano-technology, all in about two weeks. Under these conditions, it’s easy to see why some would long for the days when simple, competent reporting did the job. You probably won’t have an authentic intellectual engagement with every college writing assignment, but approaching your written work as an opportunity to dialog with the material can help you find the momentum you need to succeed with this work.
Contributors and Attributions
- Adapted from Listening to Sources, Talking to Sources. Authored by: Amy Guptil. License: CC-BY-SA
This page most recently updated on June 4, 2020.


29.3B: Modern Amphibians
- Differentiate among the orders of amphibians
Modern Amphibians
Amphibia comprises an estimated 6,770 extant species that inhabit tropical and temperate regions around the world. Amphibians can be divided into three clades: Urodela (“tailed-ones”), the salamanders; Anura (“tail-less ones”), the frogs; and Apoda (“legless ones”), the caecilians.
Urodela: Salamanders
Salamanders are amphibians that belong to the order Urodela. Living salamanders include approximately 620 species, some of which are aquatic, other terrestrial, and some that live on land only as adults. Adult salamanders usually have a generalized tetrapod body plan with four limbs and a tail. They move by bending their bodies from side to side, called lateral undulation, in a fish-like manner while “walking” their arms and legs back and forth. It is thought that their gait is similar to that used by early tetrapods. Respiration differs among the species. The majority of salamanders are lungless, with respiration occurring through the skin or through external gills. Some terrestrial salamanders have primitive lungs; a few species have both gills and lungs.
Unlike frogs, virtually all salamanders rely on internal fertilization of the eggs. The only male amphibians that possess copulatory structures are the caecilians, so fertilization among salamanders typically involves an elaborate and often prolonged courtship. Such a courtship allows the successful transfer of sperm from male to female via a spermatophore. Development in many of the most highly-evolved salamanders, which are fully terrestrial, occurs during a prolonged egg stage, with the eggs guarded by the mother. During this time, the gilled larval stage is found only within the egg capsule, with the gills being resorbed, and metamorphosis being completed, before hatching. Hatchlings resemble tiny adults.
Anura: Frogs
Frogs are amphibians that belong to the order Anura. Anurans are among the most diverse groups of vertebrates, with approximately 5,965 species occurring on all of the continents except Antarctica. Anurans have a body plan that is more specialized for movement. Adult frogs use their hind limbs to jump on land. Frogs have a number of modifications that allow them to avoid predators, including skin that acts as camouflage. Many species of frogs and salamanders also release defensive chemicals that are poisonous to predators from glands in the skin.
Frog eggs are fertilized externally. As with other amphibians, frogs generally lay their eggs in moist environments. This is required as eggs lack a shell and will dehydrate quickly in dry environments. Frogs demonstrate a great diversity of parental behaviors: some species lay many eggs and exhibit little parental care; other species carry eggs and tadpoles on their hind legs or backs. The life cycle of frogs, as with other amphibians, consists of two distinct stages: 1) the larval stage followed by 2) metamorphosis to an adult stage. The larval stage of a frog, the tadpole, is often a filter-feeding herbivore. Tadpoles usually have gills, a lateral line system, long-finned tails, and lack limbs. At the end of the tadpole stage, frogs undergo metamorphosis into the adult form. During this stage, the gills, tail, and lateral line system disappear, and four limbs develop. The jaws become larger and are suited for carnivorous feeding, while the digestive system transforms into the typical short gut of a predator. An eardrum and air-breathing lungs also develop. These changes during metamorphosis allow the larvae to move onto land in the adult stage.
Apoda: Caecilians
An estimated 185 species comprise caecilians, a group of amphibians that belong to the order Apoda. Although they are vertebrates, a complete lack of limbs leads to their resemblance to earthworms in appearance. They are adapted for a soil-burrowing or aquatic lifestyle; they are nearly blind. These animals are found in the tropics of South America, Africa, and Southern Asia. They have vestigial limbs which is evidence that they evolved from a legged ancestor.
Contributions and Attributions
- OpenStax College, Biology. October 17, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44688/latest/?collection=col11448/latest . License : CC BY: Attribution
- OpenStax College, Biology. October 23, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44688/latest/?collection=col11448/latest . License : CC BY: Attribution
- Boundless. Provided by : Boundless Learning. Located at : www.boundless.com//biology/definition/cutaneous-respiration . License : CC BY-SA: Attribution-ShareAlike
- Boundless. Provided by : Boundless Learning. Located at : www.boundless.com//biology/definition/pedicellate-teeth . License : CC BY-SA: Attribution-ShareAlike
- Boundless. Provided by : Boundless Learning. Located at : www.boundless.com//biology/definition/auricular-operculum . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Amphibians. October 17, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44688/latest...e_29_03_01.jpg . License : CC BY: Attribution
- Boundless. Provided by : Boundless Learning. Located at : www.boundless.com//biology/definition/lateral-undulation . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Biology. October 17, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44688/latest/?collection=col11448/latest . License : CC BY: Attribution
- spermatophore. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/spermatophore . License : CC BY-SA: Attribution-ShareAlike
- metamorphosis. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/metamorphosis . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Amphibians. October 17, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44688/latest/Figure_29_03_01.jpg . License : CC BY: Attribution
- OpenStax College, Amphibians. October 17, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44688/latest...e_29_03_04.jpg . License : CC BY: Attribution
- OpenStax College, Amphibians. October 17, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44688/latest...e_29_03_02.jpg . License : CC BY: Attribution
- OpenStax College, Amphibians. October 17, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44688/latest...e_29_03_03.jpg . License : CC BY: Attribution
Key Points
- Adult salamanders usually have four limbs and a tail, moving by lateral undulation in a fish-like manner while “walking” their arms and legs forward and back.
- The majority of salamanders are lungless; respiration occurs through the skin or through external gills; some terrestrial salamanders have primitive lungs; a few species have both lungs and gills.
- Salamanders utilize internal fertilization after males transfer sperm to the eggs via the spermatophore; there is a prolonged egg phase; metamorphosis occurs before hatching.
- Caecilians are blind, limbless vertebrates that resemble earthworms and are adapted for a soil-burrowing or an aquatic lifestyle.
- Adult frogs use their hind legs to jump; they fertilize externally, laying their shell-less eggs in moist environments.
- Tadpoles (the larval stage of a frog) have gills, a lateral line system, long-finned tails, and lack limbs; when tadpoles become adults, gills, tails, and the lateral line disappear, while an eardrum and lungs develop.
Key Terms
- lateral undulation : movement by bending the body from side to side
- spermatophore : a capsule or mass created by males, containing sperm and transferred in entirety to the female during fertilization
- metamorphosis : a change in the form and often habits of an animal after the embryonic stage during normal development