Teaching Materials for Joy Hakim’s
The Story of Science
Aristotle Leads the Way
Chapters 10, 13, and 17
Newton at the Center
Chapters 4, 9, and 13
Excerpted from Teacher’s Quest Guides by The Johns Hopkins University
Published by Smithsonian Books
With Science Notes by Juliana Texley
Supported by the National Science Teachers Association
Table of Contents
3
A Note from Joy Hakim
5
Introduction: Resources for Integration and Implementation
7
Aristotle Leads the Way Teacher and Student Materials
9
Chapter 10, “Getting Atom”
22
25
Chapter 13, “Aristarchus Got It Right—Well, Almost!”
44
48
Science Notes
Chapter 17, “Archimedes’ Claw”
76
80
Science Notes
Science Notes
Newton at the Center Teacher and Student Materials
82
Chapter 4, “Tycho Brahe: Taking Heaven’s Measure”
104
108
Chapter 9, “Moving the Sun and the Earth”
124
127
Science Notes
Science Notesl
Chapter 13, “What’s the Big Attraction?”
136
Science Notes
2
A Note from Joy Hakim
In schools, science is often taught as a body of knowledge—a set of facts and equations. But all
that is just a consequence of scientific activity.
Science itself is something else, something both more profound and less tangible. It is an attitude, a stance towards measuring, evaluating and describing the world that is based on skepticism, investigation and evidence. The hallmark is curiosity; the aim, to see the world as it is…
And it is not something taught so much as acquired during a training in research or by keeping
company with scientists.
—Olivia Judson, New York Times, December 2, 2008
(http://judson.blogs.nytimes.com/2008/12/02/back-to-reality)
“Keeping company with scientists”? How do we do that in a classroom?
We can read stories of the great scientists. We can watch them make mistakes. We can suffer their
frustrations. We can experience the scientific process. We can exult when they triumph.
Writing these books let me keep company with some remarkable minds. Those were years (yes,
it took several years) when I lived with Tycho Brahe and Johannes Kepler and Isaac Newton and a
cluster of fascinating scientists who were laying foundations for the nuclear and electronic revolutions to come.
Galileo, a superstar teacher, filled my room with his dynamism. No wonder the Church felt threatened. I was awed.
Newton was a strange cuss. Thinking of his unhappy childhood almost made me weep. (Some
of your students may relate.) Brahe, arrogant and brilliant, had a sister who may have been equally
talented, but the times didn’t celebrate women. (Her story might best be told in a novel.)
James Clerk Maxwell, a scientist we all should know (but hardly anyone does), gave us four equations that made Einstein and 20th century physics possible. I learned to love the guy.
And then there was William Thomson, Britain’s Lord Kelvin, a mathematician and physicist who
directed the laying of the first successful transatlantic cable (and became rich), was an expert on
thermodynamics (heat), and was one the most respected scientists of his time. People listened when
he spoke, and near the end of the 19th century Thomson made the following statements:
Radio has no future.
X-rays will prove to be a hoax.
3
No balloon and no aeroplane will ever be practically successful.
But his biggest goof came in 1900 when he famously said:
There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.
It’s easy to laugh, but, in 1900, we all would have listened and probably agreed. (Umm, there’s a
lesson there.)
Lord Kelvin lived long enough (until 1907) to understand that x-rays weren’t a hoax and, curious
scientist that he was, he actually had a hand x-rayed. But he didn’t live long enough to learn that the
20th century was the greatest era in physics ever, and that it was filled with new discovery after new
discovery. We now talk of Lord Kelvin’s physics as “classical science.”
I came to understand, writing these books, that when it comes to ideas and hypotheses, scientists
can be as wrong as anyone else. And, of course, the best of them know that. Keep company with
scientists and you’ll understand that today’s certainties may be disproved in the future. Yes, good
science is rooted in skepticism, and curiosity, and also hard work.
I hope you’ll notice the links to the arts and politics of the time. Science does not exist in isolation
from the greater society.
My books attempt to trace the scientific journey—the questions, the answers, the wrong turns,
the productive paths, the exciting breakthroughs—during some of the most creative periods in world
history. I believe they tell a remarkable tale. As to their place in the schoolroom? Well, they represent
a new sort of teaching book, meant to replace the outmoded memorize-the-facts kind of book. My
intent is to train information-age readers and to help make scientific literacy a part of everyone’s
intellectual backpack. I expect my readers to question, to read other sources, to do coordinated experiments and research, and to begin to think like scientists.
4
Introduction:
Resources for Integration and Implementation
The Story of Science is an adventure to be shared. Walking in the footsteps of the giants of natural
philosophy (as it was once called) is an exciting journey at every age and for every age. By repeating
and extending some of the classic inquiries that marked milestones on the path, we can reexperience
the thinking that transformed the lives of humans for all time.
This is a story that has been repeated around the world, in many ways and through many
ages. As we share the history of science with our students, we often tell that story through the
lens of Western civilization. But we know that 800 years ago the astronomers of Peru plotted
the transit of Venus more accurately than any European. The genetic engineers in Mesoamerica
were far more advanced in crossbreeding plants than Gregor Mendel could have dreamed. The
Japanese were doing calculus before Newton, and the best doctors in the world were working
in Moorish Spain. It was merely historical coincidence that spread the insights of European
science across the globe faster and in a more lasting way than in any other time or place. The
printing press, the universities, even simple technologies like paper and soap, all contributed to
a synergy of logic and creativity we call the Renaissance. Where many of the brilliant leaps on
other continents had raised the level of science knowledge in civilizations, only to be forgotten,
the sequence of discoveries that began in Europe about the 14th century became part of a continuous, well-traveled road to progress. The story of Newton and those upon whose shoulders
he stood became the “story of science” for his time and ours. While some civilizations took a
few steps forward, then slowed or stopped, others moved forward and never looked back. Communication technologies made science both lasting and more productive.
That’s why Joy Hakim’s groundbreaking series is so important. The books in this series relate
important leaps for humankind in the context of societal changes and the history of the period. Her
characteristically vibrant prose entices readers to understand not only the scientific content but the
context in which that content was developed and disseminated. The methods of science are interwoven with the words on every page, just waiting for hands-on, minds-on exploration.When we look at
science in a multidimensional way, presenting a variety of activities and ways of knowing, we open
its doors to many more students. We hope that you will lure not only logical-sequential thinkers like
Aristotle and Galileo but creative da Vincis, plodding Brahes, and even antisocial Keplers to science.
Who knows what lights you’ll ignite!
In honor of this International Year of Astronomy, Smithsonian Books, Johns Hopkins University,
and the National Science Teachers Association have collaborated to provide sample supplementary
materials to support The Story of Science. We provide examples of the types of innovative ideas and
5
activities from which professionals might develop a program that meets the needs of all students.
Here you will find three selected chapters from the great material developed by a team at Johns Hopkins University, accompanied by supplementary electronic resources developed especially for the
National Science Teachers Association.
Both the Johns Hopkins activities and the electronic resources from NSTA have been selected
for ease of implementation and involve a minimum of expensive equipment. Wherever possible,
mathematics, geography, language arts, and history notes are included so that the text can easily be
shared and linked with other teachers in the learning community. The three learning units for each
of the first two books in the series provide suggestions for a course that could be implemented for
as long as a school year, using the Hakim text as a foundation, or could be mixed and matched to
integrate this material with your standard textbook or with other subjects in your school’s program.
How education professionals make use of these ideas in their inquiry-based and integrated programs
will be up to them.
6
Teaching Materials for Joy Hakim’s
The Story of Science
Aristotle Leads the Way
Chapters 10, 13, and 17
7
Pages 9–21, 25–43, 48–75 are excerpted from:
Teachers’ Quest Guide to accompany The Story of Science: Aristotle Leads the Way
by Joy Hakim
Curriculum authors: Cora Heiple Teter and Maria Garriott
You Be the Scientist Activities: Juliana Texley
Artwork by Erin Pryor Gill
Cover Design by Brian Greenlee, Johns Hopkins Design & Publications
Interior Design by Jeffrey Miles Hall, ION Graphic Design Works
Johns Hopkins University
Center for Social Organization of Schools
Talent Development Middle Grades Program
Douglas MacIver, Ph.D., Director
This work was supported in part by grants and contracts from the Institute of Education Sciences,
U.S. Department of Education. The opinions expressed herein do not necessarily reflect the views
of the department.
© 2007 The Johns Hopkins University
For more information about the Aristotle Leads the Way Teacher’s and Student’s Quest Guides,
please contact Laura Slook, [email protected], 414-217-2422.
Pages 22–24, 44–47,76–79 are credited as follows:
NATIONAL SCIENCE TEACHERS ASSOCIATION
Francis Q. Eberle, PhD, Executive Director
David Beacom, Publisher
Copyright © 2009 by the National Science Teachers Association.
All rights reserved.
NSTA is committed to publishing material that promotes the best in inquiry-based science education. However, conditions of actual use may vary, and the safety procedures and practices described
in this book are intended to serve only as a guide. Additional precautionary measures may be required. NSTA and the authors do not warrant or represent that the procedures and practices in this
book meet any safety code or standard of federal, state, or local regulations. NSTA and the authors
disclaim any liability for personal injury or damage to property arising out of or relating to the use
of this book, including any of the recommendations, instructions, or materials contained therein.
You may photocopy, print, or email up to five copies of an NSTA book chapter for personal use only;
this does not include display or promotional use. Elementary, middle, and high school teachers only
may reproduce a single NSTA book chapter for classroom- or noncommercial, professional-development use only. Please access www.nsta.org/permissions for further information about NSTA’s rights
and permissions policies.
8
t e ac h e r — C h a p t e r 10
“Getting Atom”
Theme
“Colors, sweetness, bitterness, these exist
by convention; in truth there are atoms and
the void.…”
Democritus
(ca. 460 – ca. 370 B.C.E.)
Goal
Students will understand that ancient Greek
philosophers developed a remarkably advanced
atomic theory. Centuries would pass before scientists would further develop atomic theory.
Who?
Democritus — a fifth-century-B.C.E. Greek
philosopher who believed that atoms were the
smallest particles of matter
Epicurus — a fourth-century-B.C.E. Greek philosopher who believed in atoms and that they
are constantly in motion
”Poor
Democritus!
Imagine
having
“Poor
Democritus! Imagine
having
to waitto wait
2,200 years
toyears
prove
you’re
right!”
eighteen
hundred
to prove
you’re
right!”
Socrates — a fifth-century-B.C.E. Greek philosopher who studied the human soul and told
followers to “know thyself”; taught Plato
Where?
Aristotle — a fourth-century-B.C.E. Greek
scientist/philosopher; did not believe in atoms
Thrace — country west of the Black Sea, birthplace of Democritus
Leucippus — fifth-century-B.C.E. Greek philosopher who conceived idea of atoms as solid,
indestructible, constantly moving particles
When?
460 B.C.E. — birth of Democritus, who developed an early atomic theory
What?
Groundwork
atom — according to Democritus, the basic building block of life; small particles that make up everything in the universe and can’t be cut or destroyed
•Read chapter 10, “Getting Atom” in The Story
of Science: Aristotle Leads the Way.
convention — agreement or custom
•Gather the following materials:
void — an empty space or nothingness; the opposite of matter
For the teacher
transparency masters
9
t e ac h e r — C h a p t e r 10
Scientists Speak: Democritus (page 16)
Professor Quest cartoon #9 (page 17)
ancient scientists—face in trying to prove
a theory of atoms?
For the classroom
photocopy of
Scientists Speak: Democritus (page 16)
2) Students browse through chapter 10 to look
at illustrations and sidebars. Ask students
to pose any additional questions for their
reading based on the theme quotation and
their brief browsing.
For each team
two clear plastic cups
hot and cold water
a few drops of food coloring
3) Write students’ questions on chart paper or
on the chalkboard.
Consider the Quotation
4) Explain that Democritus was born around
460 B.C.E., approximately 100 years after Pythagoras. While Pythagoras believed that everything in the universe could be explained
through mathematics, Democritus sought
to understand the universe by developing
a theory of the smallest universal building
block of life—something he called atoms.
1) Direct students’ attention to the theme quotation by Democritus at the beginning of this
section under “Theme.”
2) Ask students to paraphrase this quotation
from Democritus, assisting them with unfamiliar vocabulary, to be sure they understand its meaning.
5) Direct students’ attention to the map on page
87 in The Story of Science: Aristotle Leads
the Way to locate Thrace. Students pair read
chapter 10 to discover Democritus’s hypothesis of atoms
3) Write student versions on chart paper or the
chalkboard.
4) Tell students that in the chapter they will
read today, “Getting Atom,” they will learn
about an ancient Greek who developed a
remarkably accurate theory of atoms nearly
2,500 years ago.
6) Students revisit the questions posed earlier
in class. Class discussion should include
most of the following points.
Democritus, an ancient Greek philosopher who lived in approximately 400
B.C.E., and his teacher Leucippus believed that everything in the universe
is made of atoms. They believed these
basic building blocks of life were the
smallest substances in the universe,
were hard and solid, were perpetually
in motion, and couldn’t be cut up or
destroyed. After Democritus, however,
the theory of atoms was not advanced
because ancient Greek philosophers
lacked the technology to prove or further
explore this concept. They turned instead to the study of human emotions
and thought. Socrates and his student
Plato turned from physical science to
a study of the human soul. Aristotle,
Plato’s pupil, never believed in atoms.
5) Display the transparency Scientists Speak:
Democritus and tape the photocopy to the
chalkboard. Ask students to prepare during
their reading and discussions to put words
in Democritus’s mouth.
Directed Reading
Read to find out about Democritus’s theory
of atoms
1) Discuss with students the chapter title, “Getting Atom.” Ask students the following questions to stimulate interest.
•What is an atom?
•When did scientists first propose a theory
of atoms?
•What obstacles did scientists—especially
10
t e ac h e r — C h a p t e r 10
You Be the Scientist
8) Display the transparency Scientists Speak:
Democritus on the overhead. What was his
most important idea? What theory did he
state on which future scientists could base
their work? Students review chapter 10 to
determine Democritus’s most important discovery. Write students’ suggestions on the
chalkboard.
1) Direct students to Thinking About the Invisible on page 21 in this supplement. Explain that this activity will help students
understand how molecules act even though
we can’t see them.
2) Distribute materials listed in the unit introduction to each team. As students conduct
the activity, circulate and monitor to answer
any questions and ensure they are on task.
9) Write the statement in the speech balloon on
the transparency.
Cooperative Team Learning
3) In a class discussion, explain that all molecules vibrate and bounce around to some
degree. Heat provides energy to molecules,
making them move more quickly. The physical principle of entropy causes the molecules to become less organized. On a visible
level, we say that the food coloring dissolves
(disperses) throughout the water molecules
faster in warm water than in cold water.
Recognize the difference between hypothesis, theory, and fact
1) Ask students to speculate on the difference
between hypothesis, theory, and fact and
to define each. (These terms were first introduced in The Story of Science: Aristotle
Leads the Way, chapter 2.) It may be helpful
to write the following definitions on chart
paper or on the chalkboard.
Conclusion
hypothesis — a possible and reasonable explanation for a set of observations or facts
1) Display the Professor Quest cartoon #9 on
the overhead projector.
theory — a well-tested explanation of observations or facts; a verified hypothesis
2) Ask students to relate the cartoon to the
theme of the lesson.
fact — information that has been tested and
shown to be accurate by competent observers
of the same event or phenomenon
Homework
2) Tell students that new knowledge and understanding prove many hypotheses and
theories wrong. For example, Pythagoras
believed that the Earth, the Sun, and the
planets all circle a great heavenly fireball.
Of course, we now know that his hypothesis—which he formed after studying the
heavens—is not true.
Students write a letter to Democritus updating
him on developments in atomic theory by Dalton and Thomson.
Curriculum Links
History link — Using library and Internet resources, students research the development of
astronomy in ancient China during the fifth century B.C.E.
3) Students turn to page 19 in this supplement,
Hypothesis, Theory, Or Fact? Working with
a partner, students complete the quest sheet.
Art link — Using library and Internet resources,
students research classical Greek architecture
of this period, such as the Parthenon.
4) Students share their work in a class discussion.
11
t e ac h e r — C h a p t e r 10
History/Language Arts link — Students use
Internet and library resources to research the
historical and political significance of the oracle
at Delphi. Students use this information to design a travel brochure promoting the Oracle.
History link — Confucius, the Chinese philosopher, was born in 480 B.C.E. Using library and
Internet resources, students research the development and beliefs of Confucius.
Science link — Hippocrates, the Greek physician known as the “Father of Medicine,” was
born in 460 B.C.E. Using library and Internet resources, students research the life and legacy of
Hippocrates.
Language Arts link — Using library or Internet
resources, students read excerpts from Lucretius’s On the Nature of the Universe and explore
his belief in Epicureanism and his theory of
atomic structure.
References
Carboni, Giorgio. “The Necklace of Democritus.” Fun Science Gallery.
http://www.funsci.com/fun3_en/democritus/democritus.htm.
Access date April 2009.
Garrett, Jan. “The Atomism of Democritus.” Western Kentucky
University. http://www.wku.edu/~jan.garrett/democ.htm. Access date April 2009.
Hakim, Joy. 2004. The Story of Science: Aristotle Leads the Way.
Washington, DC: Smithsonian Books.
Hawking, Stephen. 1996. The Illustrated A Brief History of Time.
New York: Bantam.
O’Connor, J.J. and Robertson, E.F. “Democritus of Abdera.” School of
Mathematics and Statistics. University of St Andrews, Scotland.
http://www-history.mcs.st-andrews.ac.uk/history/References/
Democritus.html. Access date April 2009.
12
t e ac h e r — C h a p t e r 10
QUEST SHEET Key Student’s Quest Guide (page 19)
Hypothesis, Theory, or Fact?
hypothesis — a possible and reasonable explanation for a set of observations or facts
theory — a well-tested explanation of observations or facts; a verified hypothesis
fact — information that has been tested and shown to be accurate by competent observers of the
same event or phenomenon
Read the following passages from chapter 10 to determine if they are hypothesis, theory, or fact.
Write a brief defense.
1. “The Ionians had come up with those four basic elements: earth, air, fire, and water.”
This hypothesis of the Ionians has been disproved. We now know that there are far more than four
elements in the universe.
2. “He (Democritus) said there had to be a smallest substance in the universe that can’t be cut up
or destroyed and is basic to everything else.”
Democritus’ hypothesis of atoms is partly true. We now know that while atoms are basic to everything else, they can be cut, and are composed of still smaller particles.
3. “Atoms are unable to be cut.”
While the Greek word for “atom” does in fact mean “unable to be cut,” we now know that this hypothesis was not correct. Atoms are composed of still smaller particles and can be split.
13
t e ac h e r — C h a p t e r 10
4. What pattern do you see in your answers? Why do you think this is so?
Democritus and the other ancient Greeks lacked modern technology, so they were unable to prove
or disprove their hypotheses. The technology to prove the existence of atoms did not exist until the
nineteenth century.
5. “Many subatomic particles, such as quarks, leptons, and neutrinos, have been found. Does that
mean Democritus was wrong? Or is there something that unites all those subatomic particles? No
one is sure, but many physicists are betting on Democritus and his hypothesis. They are searching for the smallest unifying particles within all matter. So far, there are clues but no proof.”
As author Joy Hakim points out, there are clues that this hypothesis may be true, but it has not
been proven to be a fact.
Scientists Speak
Democritus (ca. 460 – ca. 370 B.C.E.)
14
t e ac h e r — C h a p t e r 10
Quest Sheet Student’s Quest Guide (page 21)
You Be the Scientist
Thinking about the Invisible
To explain what we see with our eyes, sometimes we have to imagine what we can’t see.
Your Quest: Atoms are the building blocks of matter; the smallest portion of a particular substance.
Atoms combine in an infinite number of ways to form molecules. Can we learn how molecules act if
we can’t see them?
Your Gear: You’ll need two small, plastic cups, some hot and cold water, and a few drops of
food coloring.
Your Routine:
1. Place two flat cups on a firm surface. Fill one with hot water (not too hot!). Fill the other with the
same amount of cold water.
2. Place two drops of food coloring in the cups. Don’t bump the table. Watch the glasses for two
minutes. Draw what you observe.
Reporting Home: What happened?
How could the spread of the food coloring by explained by the motion of atoms? What can we conclude about motion in hot water versus cold water? Why?
Suggest a way that your whole class could model these molecules in a dance. (Suppose one group
of students wore red T-shirts, representing the food coloring, and the rest of the class wore blue Tshirts, representing the water. Write directions for a warm water dance and a cool water dance for
your classmates.)
15
t e ac h e r — C h a p t e r 10
Scientists Speak
Democritus (ca. 460 – ca. 370 B.C.E.)
16
t e ac h e r — C h a p t e r 10
9
“Poor Democritus! Imagine having to wait
”Poor Democritus!
eighteen hundred years to prove you’re right!”
Imagine having to wait 2,200 hundred years to prove you’re right!”
17
s t u d e n t — C h a p t e r 10
“Getting Atom”
Theme
“Colors, sweetness, bitterness, these exist by convention; in truth there are atoms
and the void…”
Democritus
Who?
Democritus — a fifth century B.C.E. Greek
philosopher who believed that atoms were the
smallest particles of matter
Epicurus — a fourth century B.C.E. Greek philosopher who believed in atoms and that they
are constantly in motion
Socrates — a fifth century B.C.E. Greek philosopher who studied the human soul and told
followers to “know thyself”; taught Plato
Aristotle — a fourth century B.C.E. Greek scientist and philosopher; did not believe in atoms
”Poor Democritus!
Imagine
wait twenty“Poor Democritus!
Imaginehaving
having toto
wait
twoeighteen
hundred
years
totoprove
you’re
right!”
hundred
years
prove you’re
right!”
Leucippus — fifth century B.C.E. Greek philosopher who conceived idea of atoms as solid,
indestructible, constantly moving particles
What ?
When?
atom — according to Democritus, the basic
building block of life; small particles that make
up everything in the universe and can’t be cut or
destroyed
460 B.C.E. — birth of Democritus, who developed an early atomic theory
convention — agreement or custom
void — an empty space or nothingness; the opposite of matter
Where?
Thrace — country west of the Black Sea, birthplace of Democritus
18
s t u d e n t — C h a p t e r 10
QUEST SHEET
Hypothesis, Theory, Or Fact ?
hypothesis — a possible and reasonable explanation for a set of observations or facts
theory — a well-tested explanation of observations or facts; a verified hypothesis
fact — information that has been tested and shown to be accurate by competent observers of the
same event or phenomenon
Read the following passages from chapter 10 to determine if they are hypothesis, theory, or fact.
Write a brief defense.
1. “The Ionians had come up with those four basic elements: earth, air, fire, and water.”
2. “He (Democritus) said there had to be a smallest substance in the universe that can’t be cut up
or destroyed and is basic to everything else.”
3. “Atoms are unable to be cut.”
19
s t u d e n t — C h a p t e r 10
4. What pattern do you see in your answers? Why do you think this is so?
5. “Many subatomic particles, such as quarks, leptons, and neutrinos, have been found. Does that
mean Democritus was wrong? Or is there something that unites all those subatomic particles? No
one is sure, but many physicists are betting on Democritus and his hypothesis. They are searching for the smallest unifying particles within all matter. So far, there are clues but no proof.”
Scientists Speak
Democritus (ca. 460 - ca. 370 B.C.E.)
20
s t u d e n t — C h a p t e r 10
Quest Sheet
You Be the Scientist
Thinking about the Invisible
To explain what we see with our eyes, sometimes we have to imagine what we can’t see.
Your Quest: Atoms are the building blocks of matter; the smallest portion of a particular substance.
Atoms combine in an infinite number of ways to form molecules. Can we learn how molecules act if
we can’t see them?
Your Gear: You’ll need two small, plastic cups, some hot and cold water, and a few drops of food
coloring.
Your Routine:
1. Place two flat cups on a firm surface. Fill one with hot water (not too hot!). Fill the other with the
same amount of cold water.
2. Place two drops of food coloring in the cups. Don’t bump the table. Watch the glasses for two
minutes. Draw what you observe.
Reporting Home: What happened?
How could the spread of the food coloring be explained by the motion of atoms? What can you conclude about motion in hot water versus cold water? Why?
Suggest a way that your whole class could model these molecules in a dance. (Suppose one group
of students wore red T-shirts, representing the food coloring, and the rest of the class wore blue Tshirts, representing the water. Write directions for a warm water dance and a cool water dance for
your classmates.)
21
SC I ENCE N O TES F O R TEACHERS — CHAPTER 1 0
“Getting Atom”
Science Notes for
Teachers
Ask students to try to solve the mystery of an
imaginary debate between Democritus and his
teacher Leucippus at http://www.funsci.com/fun3_
en/democritus/democritus.htm.
You Be the Scientist:
Making Sense With Our Senses
by Juliana Texley
Democritus looked at a giant sandstone cliff
and imagined each of the sand particles within it.
This became his model for the idea of an atom.
He looked at other forms of matter, and imagined
that they were also composed of atoms—the basic building blocks of the universe.
Teaching Tip for Electronic
Resources
The Johns Hopkins Quest Sheet suggests an
experiment in which students explore the diffusion of one (colored) liquid into another. When
students compare diffusion in warm water with
diffusion in cold water, they can rely on explanations like that of Democritus to help them communicate what’s happening at the particle level.
Thinking of a liquid as a single, homogeneous
substance doesn’t help us understand diffusion,
but thinking of moving particles does. Add more
energy, and the movement increases.
Jean Piaget suggested that it would be very
difficult for students below secondary level to
reason about things they couldn’t touch or otherwise sense. That’s especially true when it comes
to reasoning about the particles of which matter
is composed. But there’s an advantage, as well,
to the challenge of visualizing what we can’t
see. It makes it a bit easier to empathize with
the challenges of early natural philosophers like
Democritus, who imagined and tried to communicate a “particle theory” of matter without any
way to see their ideas—but could only infer that
they were correct by the properties of matter.
Here’s another diffusion experiment that can
provide a model for the particle nature of matter.
Bring a strong (but harmless) odor-producing
substance into the classroom. (Crushed garlic
generally works well. Don’t use something that
might irritate the respiratory system.) Ask students to shut their eyes, and open the container
holding the substance at the far end of the room.
Ask students to shout out a simple signal, such
as “Now!”, when they sense the odor. Have one
student act as the recorder, using a diagram of
the class roster to record at what time each student sensed the odor.
Online Activities:
Imagining the Unseen
Ask students to imagine how small the atomic
particle was that Democritus described. They
can compare it with the size of other things in
our world at the website “Powers of Ten”: http://
microcosm.web.cern.ch/microcosm/P10/english/P-11.
html. Click the numbers on the ruler to see the
amazing size range of matter.
Have students answer the following questions
(answers in bold):
Democritus was challenged to explain his ideas
to others who could not see his “imaginary” particles. Students can follow the logic of Democritus’ theory at this website: http://timelineindex.
com/content/view/1228.
1. How can you explain the pattern in which
students sensed the substance during the
diffusion experiment? The particles of
22
SC I ENCE N O TES F O R TEACHERS — CHAPTER 1 0
the substance are spreading/diffusing
through the particles of air.
2. Think about Democritus’ theory. Can you
predict how the process would change in
warmer air? The particles would move
more quickly, and therefore the process
would occur more quickly.
3. Use one of these Internet simulations to
help explain the process which you have described: http://www.biosci.ohiou.edu/introbioslab/
Bios170/diffusion/Diffusion.html or http://lsvr12.
kanti-frauenfeld.ch/KOJ/Java/Diffusion.html.
Then write a “script” for an explanation that
you might give a group of ancient Greek students for that process.
4. Think of another common process that this
model might explain. Examples are the
spreading of dust from a dust storm or
the spreading of bits of lint in a windy
area.
23
SC I ENCE N O TES F O R S t u d e n t s — CHAPTER 1 0
“Getting Atom”
Science Notes for
Students
Make careful observations as your teacher illustrates how an odor substance spreads through
an area, then answer the following questions.
1. How can you explain the pattern in which
students sensed the substance during the
diffusion experiment?
by Juliana Texley
Online Activities:
Imagining the Unseen
2. Think about Democritus’ theory. Can you
predict how the process would change in
warmer air?
Imagine how small the atomic particle was
that Democritus described! Compare it with the
size of other things in our world at the website
“Powers of Ten” at http://microcosm.web.cern.ch/
microcosm/P10/english/P-11.html. Click the numbers on the ruler to see the amazing size range
of matter.
Democritus was challenged to explain his
ideas to others who could not see his “imaginary” particles. You can follow the logic of Democritus’ theory at http://timelineindex.com/content/
view/1228.
3. Use one of these Internet simulations to
help explain the process which you have described: http://www.biosci.ohiou.edu/introbioslab/
Bios170/diffusion/Diffusion.html or http://lsvr12.
kanti-frauenfeld.ch/KOJ/Java/Diffusion.html.
Then write a “script” for an explanation that
you might give a group of ancient Greek
students for that process.
And you can try to solve the mystery of an
imaginary debate between Democritus and his
teacher Leucippus at http://www.funsci.com/fun3_
en/democritus/democritus.htm.
You Be the Scientist:
Making Sense With Our Senses
Democritus looked at a giant sandstone cliff
and imagined each of the sand particles within it.
This became his model for the idea of an atom.
He looked at other forms of matter, and imagined that they were also composed of atoms—
the basic building blocks of the universe. Now
that you’ve read about Democritus, you should
be able to develop explanations for observations
based on your senses and his particle theory.
Think of another common process that this
model might explain.
`
24
t e ac h e r — C h a p t e r 1 3
“Aristarchus Got
It Right—Well,
Almost!”
Theme
“Aristarchus pointed out, about 260
B.C.E., that the motions of the heavenly
bodies could easily be interpreted if it were
assumed that all the planets, including the
Earth, revolved about the Sun.”
Isaac Asimov
Goal
Students will understand Aristarchus’s contribution to Greek astronomy: that the Earth orbits around the stationary Sun.
Who?
“Keeping up with all these cosmologies
is making my head spin!”
Aristarchus — a third-century-B.C.E. Greek
who believed the Earth rotates on an inclined
axis and revolves around a larger stationary Sun
“Keeping up with all these cosmologies is making my head spin!”
Nicholas Copernicus — a Polish church official who studied Aristarchus’s writings in the
sixteenth century
When?
310 B.C.E. — birth of Aristarchus
What?
270 B.C.E. — when Aristarchus was studying
the heavenly bodies
meticulous — very careful, especially with
small details
Groundwork
canon — a church official
•Read chapter 13, “Aristarchus Got it Right—
Well, Almost!” in The Story of Science: Aristotle Leads the Way.
Where?
•Gather the following materials:
Samos — an island in the Aegean Sea; birthplace of Aristarchus
For the teacher
transparency masters
Scientists Speak: Aristarchus (page 28)
Professor Quest cartoon #13 (page 29)
25
t e ac h e r — C h a p t e r 1 3
For the classroom
photocopy of
Scientists Speak: Aristarchus
Aristarchus believed the Earth revolves
around a stationary Sun, an idea that
his contemporaries found unbelievable. He believed the Sun is larger
than the Earth, and that the Earth rotates on its inclined axis to cause day
and night and seasons. He also got
the size of the Moon almost right and
realized the cause of seasons is the
angle of the Sun’s rays because of the
tilt of the Earth. His contemporaries
ridiculed Aristarchus’s hypotheses,
but 1,700 years later, Copernicus studied Aristarchus’s ideas seriously.
Consider the Quotation
1) Direct students’ attention to the theme quotation by Isaac Asimov on at the beginning of
this section under “Theme.”
2) Ask students to paraphrase this quotation,
assisting them with unfamiliar vocabulary, to
be sure they understand its meaning. Write
student versions on chart paper or the chalkboard. Tell students that the chapter they will
read today, “Aristarchus Got It Right—Well,
Almost!” describes Aristarchus’s idea of a
heliocentric universe.
6) Display the transparency Scientists Speak:
Aristarchus on the overhead. Students review chapter 13 to decide what was Aristarchus’s most important contribution to
science. Write students’ suggestions on the
chalkboard so that the class can formulate
the best statement to put in Aristarchus’s
mouth.
3) Display the transparency Scientists Speak:
Aristarchus and tape the photocopy to the
chalkboard. Ask students to prepare during
their reading and discussions to put words
in Aristarchus’s mouth.
Directed Reading
7) Write the statement in the speech balloon on
the transparency.
Read to find out what Aristarchus got right
Conclusion
1) Discuss with students the chapter title,
“Aristarchus Got It Right—Well, Almost!”
Students speculate: What did he get right?
What did he almost get right?
1) Display the Professor Quest cartoon #13 on
the overhead projector.
2) Write students’ speculations on chart paper
or on the chalkboard.
2) Ask students to relate the cartoon to the
theme of the lesson.
3) Direct students’ attention to Who? What?
Where? When? list on page 30 in this guide.
Homework
4) Students pair read chapter 13 to discover
what Aristarchus got right and what he got
almost right.
In their journals, students write a brief essay
responding to the following.
Aristarchus was not the only scientific thinker whose theories were rejected for years (or
even centuries!) before gaining acceptance. Remember Democritus and the atom? In the early
years of the twentieth century, Alfred Wegener,
a German meteorologist, wrote a book theorizing that all the world’s continents had once existed as a single landmass before splitting apart.
5) Students revisit the questions posed earlier
in class. Class discussion should include
most of the following points.
26
t e ac h e r — C h a p t e r 1 3
This theory—called plate tectonics or continental drift—was rejected for fifty years. Even Albert Einstein, in 1955, wrote an introduction to a
book dismissing plate tectonics (Plate tectonics
is now widely accepted.) Do you think this could
happen in science today? Why or why not? What
can we learn from this?
Curriculum Links
History link — Using library and Internet
sources, students research Cleanthes, the Greek
philosopher who criticized Aristarchus’s Suncentered view of the universe as impious.
History link — A wonder of the ancient world—
the Colossus of Rhodes—was completed during
Aristarchus’ lifetime. Using library and Internet
resources, students research this architectural
marvel.
Language Arts link — Using library and Internet resources, students research the public gladiator contests that began in Rome in 264 B.C.E.
Students write a newspaper article describing
the first such contest.
References
Boorstin, Daniel. 1983. The Discoverers. New York: Random House.
Bryson, Bill. 2003. A Short History of Nearly Everything. New
York: Broadway Books.
Hakim, Joy. 2004. The Story of Science: Aristotle Leads the Way.
Washington, D.C.: Smithsonian Books.
Hawking, Stephen. 1996. The Illustrated A Brief History of Time.
New York: Bantam.
Mitton, Simon and Jacqueline. 1995. The Young Oxford Book of
Astronomy. New York: Oxford University Press.
Sagan, Carl. 1980. Cosmos. New York: Random House.
27
t e ac h e r — C h a p t e r 1 3
Scientists Speak
Aristarchus (ca. 310 – ca. 230 B.C.E.)
28
t e ac h e r — C h a p t e r 1 3
13
“Keeping up with all these cosmologies is making my head spin!”
“Keeping up with all these cosmologies is making my head spin!”
29
student — Chapter 13
“Aristarchus Got
It Right—Well,
Almost!”
Theme
“Aristarchus pointed out, about 260
B.C.E., that the motions of the heavenly
bodies could easily be interpreted if it were
assumed that all the planets, including the
Earth, revolved about the Sun.”
Isaac Asimov
Who?
Aristarchus — a third century B.C.E. Greek
who believed the Earth rotates on an inclined
axis and revolves around a larger stationary
Sun
Nicholas Copernicus — a Polish church official who studied Aristarchus’ writings in the sixteenth century
“Keeping up with all these cosmologies
is making my head spin!”
“Keeping up with all these cosmologies is making my head spin!”
What ?
meticulous — very careful, especially with
small details
canon — a church official
Where?
Samos — an island in the Aegean Sea; birthplace of Aristarchus
When?
310 B.C.E. — birth of Aristarchus
270 B.C.E. — when Aristarchus was studying
the heavenly bodies
30
t e a c h e r — C h a p t e r 1 3 Si d e b a r
“Changing
Seasons”
Theme
“The seasons of the year, as we now
know, are governed by the movements of
the earth around the sun. Each round of the
seasons marks the return of the earth to the
same place in its circuit, a movement from
one equinox (or solstice) to the next.”
Daniel Boorstin,
The Discoverers (1914 – 2004)
Goal
Students will demonstrate how the Earth’s
rotation on an inclined axis affects the length of
days and the amount of sunlight received, and
causes the seasons. Students will record their
findings, draw conclusions, and discuss their
findings with classmates.
“No point in wasting these daylight hours—
I will sleep next winter!”
What?
“No point in wasting these daylight hours -- I will sleep next winter!”
ephemeris — an astronomical almanac
summer solstice — the first day of summer;
the day the Northern Hemisphere receives the
most direct sunlight
tropics — a belt around the Earth’s fattest part,
between the Tropic of Cancer and the Tropic of
Capricorn; because the Sun strikes it directly, its
climate is warm year-round
winter solstice — the first day of winter; the
day the Northern Hemisphere receives the least
direct sunlight
Temperate Zones — areas of the globe that receive indirect sunlight part of the year and thus
have variable temperatures and seasons
Tropic of Cancer — an imaginary line of latitude at 23.5˚ north; marks the northern boundary of the Tropics; the farthest point north at
which the Sun is directly overhead at noon on
the summer solstice
latitude — imaginary lines circling the Earth in
order to measure distance north or south of the
equator
polar regions — areas at the top and bottom
of the Earth that receive indirect sunlight and
remain cold year-round; where because of the
Earth’s tilt, the Sun doesn’t set in summer and
doesn’t rise in winter part of the year
Tropic of Capricorn — an imaginary line of latitude at 23.45˚ south; marks the southern boundary of the Tropics; farthest point south at which
the Sun can be seen directly overhead at noon
on the winter solstice
31
t e a c h e r — C h a p t e r 1 3 Si d e b a r
Groundwork
Without an inclined axis, the Earth
would not experience seasons, and each
day would be of equal length. Because
the surface area on the daytime side of
a planet is angled from the sun by 23.5
degrees, we have seasons. During the
summer in the Northern Hemisphere,
the Earth is tilted toward the Sun. When
the Northern Hemisphere is tilted away
from the Sun, it is winter in that part
of the globe. The variation in the length
of daylight hours is caused by the 23.5
degree inclined angle of the Earth, which
affects where the Sun shines directly
on the Earth on any particular day.
The more direct the rays, the longer
the day and the warmer the season.
•Read “Changing Seasons” on page 116 in The
Story of Science: Aristotle Leads the Way.
•Perform the activities before presenting them
to the class to foresee problems that may
arise.
•Gather the following materials:
For the teacher
transparency master
Professor Quest cartoon #14 (page 38)
a daily newspaper showing sunrise/
sunset times
Consider the Quotation
1) Direct student’s attention to the theme quotation by Daniel Boorstin at the beginning of
this section under “Theme.”
Cooperative Team Learning
2) Ask students to paraphrase this quote from
writer and former Librarian of Congress
Daniel Boorstin. Write student versions on
chart paper or the chalkboard.
Demonstrate how the Earth’s tilt causes
differing lengths of days
1) Tell students that they are to explain why the
Earth has seasons to an alien who is visiting
Earth. Working with teammates, students
write an explanation in their own words.
3) Tell students that in the sidebar, “Changing
Seasons,” they will learn how the tilt of the
Earth causes seasons.
2) After a few minutes, allow representatives
from each team to read their explanations to
the class.
Directed Reading
Read to understand what causes seasons
1) Ask students to pose any questions they
have about what causes the seasons and the
differing lengths of days. Write student questions on chart paper or the chalkboard.
3) Direct students to Sunrise, Sunset, and Solstice on page 40 in this supplement. Explain
that newspapers and almanacs publish the
times of the sunrise and sunset. Ask students
the following questions.
2) Direct students’ attention to the What? list
on page 39 in this supplement.
•For whom might this information be especially important? (fishermen, scientists)
3) Students read “Changing Seasons” on page
116 in The Story of Science: Aristotle Leads
the Way to learn how the tilt of the Earth affects seasons.
•Where does the newspaper get this
information?
5) Show students your sample newspaper with
this information. Explain that newspapers
get this information from sunrise-sunset
charts published in an ephemeris, or an astronomical almanac. Astronomers calculate
4) Students revisit the questions posed earlier
in class. Class discussion should include
most of the following points.
32
t e a c h e r — C h a p t e r 1 3 Si d e b a r
Conclusion
the movements of the planets based on theories that take into account the gravitational
effects of all the bodies involved.
1) Display the Professor Quest cartoon #14 on
the overhead projector.
6) Explain military time to students. Military
time, which is used in most astronomical
almanacs, by law enforcement, and in hospitals, is based on a method of counting first
used by the Sumerians called base 60. In this
notation, 12:01 a.m. is written as 0001 hours;
12:00 noon is 1200 hours; 4:00 p.m. is 1600
hours (or sixteen hours and zero minutes after midnight).
2) Ask students to relate the cartoon to the
theme of the lesson.
Homework
The city of Barrow, Alaska, is located approximately 300 miles north of the Arctic Circle. It
experiences two months of total darkness, but
also has total light from mid-May to early August. Students write a journal entry describing
the advantages and disadvantages to living at
this latitude.
7) As students work, visit each team to make
sure they follow directions and complete the
activities in a timely manner.
8) Periodically stop students to share the results of each activity. Discuss possible reasons for any results that disagree with the
majority (such as not following directions
carefully).
Curriculum Links
You Be the Scientist
Multicultural link — Using library and Internet sources, students gather folk tales and
myths from other cultures explaining the reason
for seasons.
Language Arts link — Using Internet and library sources, students find several quotes
about the seasons.
1) Direct students to the quest sheet, How Does
Your Garden Grow? on pages 42–43 of this
supplement. (Note: The teacher may want to
display a sample photo of each of the four
flowers.)
References
“Aristarchus of Samos.” School of Mathematics and Statistics,
University of St. Andrews, Scotland. http://www-gap.dcs.st-and.
ac.uk/~history/Mathematicians/Aristarchus.html. Access date
May 2004.
2) Working with teammates, students complete
the activity. Students may need to consult a
map of the Western Hemisphere to complete
the activity.
Boorstin, Daniel. 1983. The Discoverers. New York: Random
House.
Answer for Teacher:
Hakim, Joy. 2004. The Story of Science: Aristotle Leads the Way.
Washington, DC.: Smithsonian Books
•The sun will rise from the southeast in
September, and set in the southwest.
“Rise and Set for the Sun for 2003.” U.S. Naval Observatory. http://
aa.usno.navy.mil/cgi-bin/aa_rstablew.pl. Access date April 2003.
•Dusty miller or coxcomb could be planted
at the southwestern edge of the property.
Shugrue, Sylvia. “Astronomy with a Stick.” National Science
Teachers Association. http://www.nsta.org/awsday. Access
date April 2003.
•Coleus could be planted anywhere on the
property; shade is found on the northern
edge.
“The Seasons and Axis Tilt.” Enchanted Learning Online. http://
www.enchantedlearning.com/subjects/astronomy/planets/
earth/Seasons.shtml. Access date April 2003.
VanCleave, Janice. 2000. Solar System: Spectacular Science Projects. New York: John Wiley & Sons, Inc.
“What Causes the Seasons?” The National Weather Service Forecast Office. http://www.crh.noaa.gov/fsd/astro/season.htm. Access date May 2004.
33
t e a c h e r — C h a p t e r 1 3 Si d e b a r
QUEST SHEET Key Student’s Quest Guide page 40
Sunrise, Sunset, and Solstice
Predict:
How does the tilt of the Earth’s axis affect the length of days and the amount of daylight received?
Observe:
Use data from the sunrise/sunset table below to figure the length of the daylight hours for the following days. Note that all times are given in military form.
First, translate the military time into standard time (the first ones have been done for you). Then
subtract the sunrise from the sunset to determine the length of each day.
Sunrise-Sunset Table for Washington, D.C.
December
Date
1
15
21
30
Time of
Sunrise
Time of
Sunrise
707
1647
(7:07 a.m.)
(4:47 p.m.)
719
1647
(7:19 a.m.)
(4:47 p.m.)
723
1649
(7:23 a.m.)
(4:49 p.m.)
726
1655
(7:26 a.m.)
(4:55 p.m.)
June
# hours/
minutes
sunlight
Time of
Sunrise
Time of
Sunset
# hours/
minutes
sunlight
9 hrs.
40 min.
445
1927
14 hrs.
82 min.
(4:45 a.m.)
(7:27 p.m.)
(15 hrs.
22 min.)
9 hrs.
28 min.
442
1935
14 hrs.
93 min.
(4:42 a.m.)
(7:35 p.m.)
(15 hrs.
33 min.)
9 hrs.
26 min.
443
1937
14 hrs.
94 min.
(4:43 a.m.)
(7:37 p.m.)
(15 hrs.
34 min.)
9 hrs.
29 min.
446
1937
14 hrs.
91 min.
(4:46 a.m.)
(7:37 p.m.)
(15 hrs.
31 min.)
34
t e a c h e r — C h a p t e r 1 3 Si d e b a r
Answer the following questions. (Student’s Quest Guide page 41)
What is the shortest day of the year? December 21
What happens after this day? The days begin to lengthen.
What is the longest day of the year? June 21
What happens after this day? The days begin to shorten.
From what you know of seasons, how do you explain this phenomenon?
Because the equator is tilted 23.5°, the amount of direct light the Northern and Southern Hemispheres receive varies during the year. On June 21, the summer solstice, the Northern Hemisphere
receives the most concentrated light. On December 21, the winter solstice, the Northern Hemisphere receives the least concentrated light.
How would this be different if the Earth’s tilt was 0°?
If the Earth’s axis were not tilted, there would be no variation in the amount of concentrated light
the hemispheres receive. Seasons as we know them would not exist.
35
t e a c h e r — C h a p t e r 1 3 Si d e b a r
Quest Sheet Key Student’s Quest Guide page 42
You Be the Scientist
How Does Your Garden Grow?
Gardeners throughout the ages have used their knowledge of the Sun to plan their gardens.
Your Quest: One of the most important applications of science throughout history has been for agriculture. Understanding the movement of the Sun through the seasons helped people plant and raise
healthy crops. Can you use that same understanding to plan a modern garden?
Your Gear: You may need to consult a map showing where Michigan is located in relation to
the equator.
Your Routine: Imagine you have been asked to help a friend plant a garden in Alpena, Michigan.
Your friend wants the garden to be at its peak in September for the annual charity tour. Here’s a map
of your friend’s property. Select some appropriate plants and decide where they should be planted.
To help your planning, think about where the shadows of the sun will fall at noon in the middle of
September. Then think about where the shadows of the trees will fall on the property. Use at least
three plants.
Plant
When it blooms
Light needed
Impatient
Spring
Partial sun
(Dies if there is too much heat)
Coxcomb
Summer
Direct sunlight
Coleus
Late summer
Shade
Dusty Miller
Summer
Direct sunlight
36
t e a c h e r — C h a p t e r 1 3 Si d e b a r
How Does Your Garden Grow Map
37
t e a c h e r — C h a p t e r 1 3 Si d e b a r
14
“No point in wasting these daylight hours -- I will sleep next winter!”
“No point in wasting these daylight hours—I will sleep next winter!”
38
S t u d e n t — C h a p t e r 1 3 Si d e b a r
“Changing
Seasons”
Theme
“The seasons of the year, as we now
know, are governed by the movements of
the earth around the sun. Each round of the
seasons marks the return of the earth to the
same place in its circuit, a movement from
one equinox (or solstice) to the next.”
Daniel Boorstin,
The Discoverers (1914-2004)
What?
ephemeris — an astronomical almanac
summer solstice — the first day of summer; the
day the northern hemisphere receives the most
direct sunlight
winter solstice — the first day of winter; the
day the northern hemisphere receives the least
direct sunlight
“No point in wasting these daylight hours—
I will sleep next winter!”
“No point in wasting these daylight hours -- I will sleep next winter!”
Tropic of Cancer — an imaginary line of latitude at 23.5˚ north; marks the northern boundary of the tropics; the farthest point north at
which the Sun is directly overhead at noon on
the summer solstice
latitude — imaginary lines circling the Earth in
order to measure distance north or south of the
equator
Tropic of Capricorn — an imaginary line of latitude at 23.45˚ south; marks the southern boundary of the tropics; farthest point south at which
the Sun can be seen directly overhead at noon
on the winter solstice
polar regions — areas at the top and bottom of
the Earth that receive indirect sunlight and remain cold all year round; where because of the
Earth’s tilt, the Sun doesn’t set in summer and
doesn’t rise in winter part of the year
tropics — a belt around the Earth’s fattest part,
between the Tropic of Cancer and the Tropic of
Capricorn; because the Sun strikes it directly, its
climate is warm all year round
Temperate Zones — areas of the globe that receive indirect sunlight part of the year and thus
have variable temperatures and seasons
39
S t u d e n t — C h a p t e r 1 3 Si d e b a r
QUEST SHEET
Sunrise, Sunset, and Solstice
Predict
How does the tilt of the Earth’s axis affect the length of days and the amount of daylight received?
Observe
Use data from the sunrise/sunset table below to figure the length of the daylight hours for the following days. Note that all times are given in military form.
First, translate the military time into standard time (the first ones have been done for you). Then
subtract the sunrise from the sunset to determine the length of each day.
Sunrise Sunset Table for Washington, D.C.
December
Date
1
15
21
30
Time of
Sunrise
Time of
Sunrise
June
# hrs/
minutes
sunlight
Time of
Sunrise
Time of
Sunset
707
1647
445
1927
(7:07 a.m.)
(4:47 p.m.)
(4:45 a.m.)
(7:27 p.m.)
719
1647
442
1935
(____ a.m.)
(_____p.m.)
(____ a.m.)
(____ p.m.)
723
1649
443
1937
(____ a.m.)
(____ p.m.)
(____ a.m.)
(____ p.m.)
726
1655
446
1937
(____ a.m.)
(____ p.m.)
(____ a.m.)
(____ p.m.)
40
# hrs/
minutes
sunlight
S t u d e n t — C h a p t e r 1 3 Si d e b a r
Answer the following questions.
What is the shortest day of the year? What happens after this day? What is the longest day of the year? What happens after this day? From what you know of seasons, how do you explain this phenomenon?
How would this be different if the Earth’s tilt was 0 degrees?
41
S t u d e n t — C h a p t e r 1 3 Si d e b a r
Quest Sheet
You Be the Scientist
How Does Your Garden Grow?
Gardeners throughout the ages have used their knowledge of the Sun to plan their gardens.
Your Quest: One of the most important applications of science throughout history has been for agriculture. Understanding the movement of the Sun through the seasons helped people plant and raise
healthy crops. Can you use that same understanding to plan a modern garden?
Your Gear: You may need to consult a map showing where Michigan is located in relation to the
equator.
Your Routine: Imagine you have been asked to help a friend plant a garden in Alpena, Michigan.
Your friend wants the garden to be at its peak in September for the annual charity tour. Here’s a map
of your friend’s property. Select some appropriate plants and decide where they should be planted.
To help your planning, think about where the shadows of the Sun will fall at noon in the middle of
September. Then think about where the shadows of the trees will fall on the property. Use at least
three plants.
Plant
When they bloom
Light needed
Impatient
Spring
Partial sun
(Dies if there is too much heat)
Coxcomb
Summer
Direct sunlight
Coleus
Late summer
Shade
Dusty Miller
Summer
Direct sunlight
42
S t u d e n t — C h a p t e r 1 3 Si d e b a r
How Does Your Garden Grow Map
43
SC I ENCE N O TES F O R TEACHERS — CHAPTER 1 3
“Aristarchus Got
It Right—Well,
Almost!”
Science Notes for
Teachers
Earth, Earth rotated on its axis, and that axis tilted! This model helped him explain the seasons.
The Internet includes many simulations that
compare the models of the early astronomers.
These simulations can help modern students of
astronomy imagine in the ways that the early
astronomers did. Have students start with the
simulation of Ptolemy’s model at http://astro.
unl.edu/naap/ssm/animations/ptolemaic.html; a
video of the model is at http://www.youtube.com/
watch?v=GvX78dpQ7GM. Ask students to explain
why the zodiac symbols surround the model (answer in bold). In ancient Greece, astronomy
and astrology were the same science. People
believed that the stars’ positions could influence their lives, and so they studied the
movement of the stars (and planets) to get
clues to the future.
by Juliana Texley
Teaching Tip for Electronic
Resources
Have students compare the simulation of Ptolemy’s model with a simulation of a Sun-centered
(heliocentric) model at http://astro.unl.edu/naap/
ssm/heliocentric.html, or in video format at http://
www.youtube.com/watch?v=VyQ8Tb85HrU&NR=1.
They can also look at a modern simulation of all
planetary orbits from NASA at http://neo.jpl.nasa.
gov/orbits/2003el61.html.
In this International Year of Astronomy, it’s
tempting to bring many of the amazing discoveries about the solar system and the movement of
the Earth into elementary classrooms. Check out
the National Science Education Standards for
suggestions on the developmentally appropriate
places to begin this content area with elementary students; in general, the Standards suggest
beginning with phenomena that can be directly
observed, such as light and shadows, Moon phases, and the wandering of observable planets like
Venus. The logical reasoning of the early Greek
astronomers (who had only naked-eye observations from which to reason) provides a great
context for these observations.
In order to explain day and night and the seasons in a Sun-centered solar system, Aristarchus
had to imagine that Earth spun on its axis. Ask
students to explain why the Earth would have to
spin to explain night and day if the Earth went
around the Sun (answer in bold). If the Sun
stood still, then the observer must move.
Related Class Activity
Online Activities: Almost Only
Counts in Horseshoes—
and Sometimes in Science
You can reproduce these simulations outside
on the school asphalt or other hard surface, tracing the orbits with sidewalk chalk and asking
individual students to represent the Earth, the
Sun, and Mars. For each model, ask the student
representing the Earth what he or she sees at any
specific point.
Aristarchus looked at the same sky that Aristotle did—about a century later. But he interpreted what he saw in a very different way. In
Aristarchus’ model, the Sun was larger than the
44
SC I ENCE N O TES F O R TEACHERS — CHAPTER 1 3
Crossfire Across a Century
Imagine that Aristotle could have had a realtime conversation with Aristarchus. Their conversation might have begun with the following
questions from Aristotle. Compose answers that
Aristarchus might have made to these questions,
based on his observations and theories (answers
in bold).
1. If the Sun stands still and the Earth goes
around it, the Earth would have to spin on
an axis in order to explain night and day. But
if the Earth really turned on its axis, why
wouldn’t objects fly off the planet like a hat
might fly off a rider on a merry-go-round?
Aristotle and Ptolemy had no idea about
gravitation.
2. If the Earth really moved around the Sun,
why wouldn’t things in the sky (like clouds
and birds) always fly off in the same direction (like your hair streaming behind you on
that merry-go-round)? Gravitation causes
the atmosphere to be attracted to the
Earth; the atmosphere and objects in
it have the same inertia due to Earth’s
revolution.
3. When an object is farther away, its distance can be inferred from parallax. So if
the Earth was really going around the Sun,
why wouldn’t the same parallax effect be
observed? Aristotle did not have a good
idea of how great the distance was from
the Earth to the Sun.
Get more information from NSTA in their
Science Object “Universe: The Sun as a Star” at
http://learningcenter.nsta.org/search.aspx?action=
browse&subject=38&product=object.
45
SC I ENCE N O TES F O R S t u d e n t s — CHAPTER 1 3
“Aristarchus Got
It Right—Well,
Almost!”
Science Notes for
Students
Compare the simulation of Ptolemy’s
model with a simulation of a Sun-centered
(heliocentric) model at http://astro.unl.
edu/naap/ssm/heliocentric.html, or in
video format at http://www.youtube.com/
watch?v=VyQ8Tb85HrU&NR=1. You can also
look at a modern simulation of all planetary
orbits from NASA at http://neo.jpl.nasa.gov/
orbits/2003el61.html.
In order to explain day and night and the seasons in a Sun-centered solar system, Aristarchus
had to imagine that Earth spun on its axis. Explain why the Earth would have to spin to explain
night and day if the Earth went around the Sun.
by Juliana Texley
Online Activities: Almost Only
Counts in Horseshoes—
and Sometimes in Science
Aristarchus looked at the same sky that Aristotle did—about a century later. But he interpreted what he saw in a very different way. In
Aristarchus’ model, the Sun was larger than the
Earth, Earth rotated on its axis, and that axis tilted! This model helped him explain the seasons.
Related Class Activity
You can reproduce these simulations outside
on the school asphalt or other hard surface, tracing the orbits with sidewalk chalk and having individual students represent the Earth, the Sun,
and Mars. For each model, the person representing Earth should say what he or she sees at any
specific point.
The Internet includes many simulations that
compare the models of the early astronomers.
These simulations can help modern students
of astronomy imagine in the ways that the
early astronomers did. Start with the simulation of Ptolemy’s model at http://astro.unl.edu/
naap/ssm/animations/ptolemaic.html
(you
can “pause” the animation repeatedly, to take
time to understand what Ptolemy imagined); a
video of the model is at http://www.youtube.com/
watch?v=GvX78dpQ7GM.
Crossfire Across a Century
Imagine that Aristotle could have had a realtime conversation with Aristarchus. Their conversation might have begun with the following
questions from Aristotle. Compose answers that
Aristarchus might have made to these questions,
based on his observations and theories.
Explain why the zodiac symbols surround
the model.
1. If the Sun stands still and the Earth goes
around it, the Earth would have to spin on
an axis in order to explain night and day. But
if the Earth really turned on its axis, why
wouldn’t objects fly off the planet like a hat
might fly off a rider on a merry-go-round?
46
SC I ENCE N O TES F O R S t u d e n t s — CHAPTER 1 3
2. If the Earth really moved around the
Sun, why wouldn’t things in the sky (like
clouds and birds) always fly off in the
same direction (like your hair streaming behind you on that merry-go-round)?
3. When an object is farther away, its distance
can be inferred from parallax. So if the Earth
was really going around the Sun, why wouldn’t
the same parallax effect be observed?
Get more information from NSTA in their
Science Object “Universe: The Sun as a Star” at
http://learningcenter.nsta.org/search.aspx?action
=browse&subject=38&product=object.
47
t e ac h e r — C h a p t e r 1 7
“Archimedes’
Claw”
pages 146-150, paragraph 3; page 153, paragraph
2, through page 157 in The Story of Science: Aristotle Leads the Way.
Theme
“Give me somewhere to stand and I will
move the Earth.”
Archimedes
(282 – 121 B.C.E.)
Goals
Students will learn about Archimedes’ practical applications of mathematics.
Students will learn about the law of the lever.
Who?
“Oh dear,
it’sit’s
a weight
lossdiet
diet
“Oh dear,
a weight-loss
for for
me!”me!”
Archimedes — a third-century-B.C.E. mathematician who used geometry and mathematics
to solve practical problems
When?
What?
212 B.C.E. — siege of Syracuse by the Romans
fulcrum — the fixed support under a lever
Groundwork
law of the lever — to achieve balance with a
lever, the product of weight times distance on
both sides of the fulcrum must be equal
Where?
•Read chapter 17, “Archimedes’ Claw,” pages
146-150, paragraph 3; page 153, paragraph
2, through page 157 in The Story of Science:
Aristotle Leads the Way
Syracuse — a city-state on the island of Sicily
•Gather the following materials:
Carthage — a city-state in Tunisia on the north
coast of Africa
For the teacher
transparency masters
Three Classes of Levers (page 52)
Scientists Speak: Archimedes (page 53)
Professor Quest cartoon #19 (page 54)
Corinth — a city-state in Greece
Rome — a city-state in Italy
48
t e ac h e r — C h a p t e r 1 7
For the classroom
their reading and discussion to put words in
Archimedes’ mouth.
photocopy of
Scientists Speak: Archimedes
4) Direct students’ attention to the map on page
150 in The Story of Science: Aristotle Leads
the Way to locate Syracuse in Sicily, where
Archimedes lived, Carthage in Africa, and
Rome, Italy. Look at the map on page 122 to
find Alexandria, Egypt. Although Alexandria
is not marked on the map on page 150, ask
students to point to where it is (about half
inch to the left of the right border on the
north coast of Africa).
Consider the Quotation
1) Direct students’ attention to the theme quotation by Archimedes at the beginning of this
section under “Theme.”
2) Ask students their opinion of this statement.
Is Archimedes’ claim possible?
3) Tell students that in this lesson they will
learn how Archimedes lived up to this claim
and how he put scientific knowledge to work
in practical applications.
5) Call students’ attention to the Who? What?
Where? When? terms on page 55 in this supplement to assist in their reading
6) Students pair read chapter 17, “Archimedes’
Claw,” starting at the beginning of the chapter through the third paragraph on page 150,
skipping pages 151 and 152, and beginning
again with the second paragraph on page
153 (“What about moving the Earth?) to the
end of the chapter to find the answers to
their questions.
Directed Reading
Read to discover how Archimedes put
scientific knowledge to work in practical
applications
1) Direct students’ attention to the title of chapter 17, “Archimedes’ Claw,” and ask them to
speculate about its meaning.
7) When they have finished their reading, students share the answers to their questions in
a class discussion. They should understand
the following points.
2) Students browse through chapter 17, looking at the illustrations, headings, and sidebars to form questions about Archimedes.
Write students’ questions on chart paper or
the chalkboard.
Archimedes was a brilliant mathematician who, though he thought that ideas
were more important than inventions,
3) Display the transparency Scientists Speak:
Archimedes. Ask students to prepare during
Scientists Speak
Archimedes (287–121 B.C.E.)
49
t e ac h e r — C h a p t e r 1 7
2) Discuss with students the law of the lever
on page 153, paragraph 3, and the diagram at
the top of the page. Tell students that this is
the simple machine that Archimedes would
use to lift the world. Scientists do not know
the weight of Earth (one estimate is 6.5 billion trillion tons).
applied his mathematical genius to
many practical purposes. He had a
special interest in geometry. In his book,
The Sand Reckoner, he used math to
estimate the number of grains of sand
that would fill the universe. He lived in
Syracuse, a city that both the Carthaginians and the Romans wanted to control.
Although Archimedes had no interest in
politics, he gave in to the king’s requests
for war machines. He also met the king’s
challenge to launch a heavy ship. This he
accomplished using the law of the lever.
Archimedes invented war machines that
foiled the Romans’ attacks on Syracuse.
The historian Plutarch described these
machines: huge mirrors that reflected
the Sun’s rays to blind the sailors and
set their ships’ sails on fire; a catapult
that fired rocks at the Roman ships, and
a giant claw that lifted the ships high out
of the water, shook the soldiers into the
sea, and dropped the ship in after them.
3) Display the transparency Three Classes
of Levers (page 52). In a class discussion,
complete the transparency. As students discuss each class of levers, ask them to think
of other examples (first-class — crowbar,
scissors, car jack, pliers; second-class
— nutcracker, bottle opener, door; thirdclass—rake, shovel, tennis racket, hockey
stick, weight lifter’s arm).
Conclusion
1) On the overhead projector, display Professor Quest cartoon #19 (page 54).
2) Ask students to relate the cartoon to the
theme of the lesson.
8) Again display the Scientists Speak: Archimedes (page 53) on the overhead projector
and ask students to put an appropriate statement in the scientist’s mouth. What was his
most important idea?
Homework
Students read “Is It a Claw or a Flaw?” and write
a brief entry in their journals answering the
question asked in the title of this supplement.
Did Archimedes’ claw really work as Plutarch
described on page 157? Or would the flaws be
too great to allow the claw to work? Students
support their answers.
9) Write students’ suggestions on the chalkboard so that the class can formulate the best
statement to put in Archimedes’ mouth.
10)Write the statement in the speech balloon on
the transparency.
Curriculum Links
Art link — Although Archimedes expressed
contempt for practical applications of science,
he used his knowledge for interesting and effective inventions. Using library and Internet
resources, students read descriptions of Archimedes’ war machines and draw imaginative illustrations of them in use.
Classwide Activity
Learn about levers
1) Direct students’ attention again to the theme
quotation. Ask students to reconsider whether Archimedes was serious in his comment
or was boasting. What would Archimedes
use to lift the world?
History link — Using library and Internet resources, students research the life and inventions
50
t e ac h e r — C h a p t e r 1 7
of Archimedes and write a brief biography in their
journals.
Language Arts link — Plutarch, a Roman historian (44-125 C.E.) wrote biographies about
famous Greeks and Romans, including Archimedes. Students find and read passages from
Plutarch’s writing.
Science link — Students choose a branch of
science to research in the library or on the Internet to list as many applications of mathematics
as they can that are important to that science
(For example, in astronomy, measuring and calculating time, distance, temperature, and size
are important.)
References
Hakim, Joy. 2004. The Story of Science: Aristotle Leads the Way.
Washington, DC: Smithsonian Books.
Johnson, Gordon P. et al. 1988. Physical Science. Menlo Park, California: Addison-Wesley.
Nave,C. R. “Hyperphysics — Archimedes’ Principle.” Georgia
State University. http://hyperphysics.phy-astr.gsu.edu/hbase/
pbuoy.html. Access date April 2009.
O’Connor, John and Edmund R. Robinson. “Archimedes of
Syracuse.” School of Mathematics and Statistics, University of St. Andrews, Scotland. http://www-gap.dcs.st-and.
ac.uk/~history/Mathematicians/Archimedes.html. Access date
April 2009.
51
t e ac h e r — C h a p t e r 1 7
Three Classes of Levers
What?
lever — a machine that accomplishes work by moving around a fulcrum
fulcrum — the point on the lever that does not move
effort force — the force applied to move the lever
resistance force — the weight of the object being lifted
Label the parts of the lever in the illustrations below.
A seesaw is a first-class lever
(the fulcrum is between the two forces).
resistance force
fulcrum
effort force
A wheelbarrow is a second-class lever
(the fulcrum is at one end, the effort
force is at the other end, the resistance
force is between them).
effort force
resistance force
fulcrum
A broom is a third-class lever (the fulcrum is at
the top end, the resistance force is at the other
end, and the effort force is between them).
fulcrum
effort force
resistance force
52
t e ac h e r — C h a p t e r 1 7
Scientists Speak
Archimedes (287 – 121 B.C.E.)
53
t e ac h e r — C h a p t e r 1 7
19
“Oh dear, it’s a weight-loss diet for me!”
“Oh dear, it’s a weight loss diet for me!”
54
student — Chapter 17
“Archimedes’
Claw”
pages 146-150, paragraph 3; page 153, paragraph
2 through page 157
Theme
“Give me somewhere to stand and I will
move the Earth.”
Archimedes
Who?
Archimedes — a third century B.C.E. mathematician who used geometry and mathematics
to solve practical problems
What ?
fulcrum — the fixed support under a lever
law of the lever — to achieve balance with a
lever, the product of weight times distance on
both sides of the fulcrum must be equal
“Oh dear,
it’sit’s
a weight
lossdiet
diet
“Oh dear,
a weight-loss
for for
me!”me!”
Where?
Rome — a city state in Italy
Syracuse — a city state on the island of Sicily
When?
Carthage — a city state in Tunisia on the north
coast of Africa
212 B.C.E. — siege of Syracuse by the Romans
Corinth — a city state in Greece
Scientists Speak
Archimedes (287-121 B.C.E.)
55
t e ac h e r — C h a p t e r 1 7 s i d e ba r
“Archimedes’
Claw”
Eureka!
page 150, paragraph 4, through page 153,
paragraph 2
Theme
“Any object when immersed in a liquid
will displace a volume of liquid equal to the
object’s own volume.”
Archimedes
Goal
Students will learn about Archimedes’ Principle and demonstrate that it is true.
What?
mass — the amount of matter an object contains
volume — the amount of space an object occupies
“That
goldsmith is in big trouble now!”
“That goldsmith is in big trouble now!”
weight — the amount of gravity that holds an
object on Earth
density — a physical property of matter: mass
divided by volume
For the teacher
buoyancy — an upward force working on an
object in water (The force equals the weight of
the fluid that the object displaces.)
transparency masters
Archimedes’ Bathtub (pages 64–68)
Density and Buoyancy Graphs (page 69)
Professor Quest cartoon #20 (page 70)
Groundwork
•Read chapter 17, page 150, paragraph 4,
through second paragraph, page 153, stopping with the sentence, “The king had been
cheated.”
variety of pennies from before 1983
and after 1983
identical pieces of heavy,
waterproof modeling clay
sawdust
•Perform the activities before presenting them
to the class to foresee problems that may arise.
clear container into which
clay crown will fit
•Gather the following materials and set them
up in two types of stations for cooperative
learning teams to visit:
For each team
56
flat dish
graduated cylinder
t e ac h e r — C h a p t e r 1 7 s i d e ba r
balance scale
water
paper towels
had been cheated”) to narrate the cartoon;
also see page 63 in this supplement.
2) Students refer to the What? on page 71 in
this supplement to assist with vocabulary
terms in the cartoon.
Station 1
beaker with graduated markings
water
steel nail or bolt
cork
aluminum foil
marble
balsa wood
paper towels
balance
Cooperative Team Learning—
Science Session
Perform activities to demonstrate density
and buoyancy
1) Read and discuss the directions for each
station on the quest sheet Density and
Buoyancy (page 69).
Station 2
30-centimeter squares of heavy-duty
aluminum foil (two for each team)
beaker with graduated markings
water
paper towels
2) Teams visit stations and perform the activities. As students work, circulate among stations, ask and answer questions, and ensure
that everyone remains on task and follows
directions.
Consider the Quotation
3) Ask students to share and explain the results of their activities in a class discussion.
Record the results of activity 1 on the transparency Density and Buoyancy Graphs as
students complete their individual graphs.
1) Direct students’ attention to the theme quotation by Archimedes at the beginning of this
section under “Theme.”
2) Direct students to the What? terms on page
71 in this supplement to help them paraphrase the statement.
Classwide Activity
Re-create Archimedes’ test of the king’s
crown
3) Tell students that in this lesson they will
learn how Archimedes arrived at this idea,
which is called Archimedes’ Principle. They
will also demonstrate the properties of mass,
volume, and density in several substances.
1) Show students two pieces of clay and place
them in cups on opposite ends of the balance
to confirm that they are identical in weight
and mass.
Directed Reading
2) Tell students that these pieces of clay represent gold that belonged to the king of Syracuse. Retell the story of Archimedes and
the crown and re-create it in the following
steps.
Read the story of how Archimedes arrived
at his principle
1) Display the transparency Archimedes’ Bathtub on the overhead projector to tell the
story in cartoon form of how Archimedes arrived at his principle. Use the passages from
the text (chapter 17, page 150, paragraph 4
through paragraph 2 on page 153, “The king
3) The king gave the goldsmith a piece of gold
to make a crown (Remove one piece of clay
from the balance and show it to the students.)
57
t e ac h e r — C h a p t e r 1 7 s i d e ba r
4) The goldsmith was not honest and took
some of the gold for himself. (Pinch off a
small piece of the clay and put the larger
piece back on the balance.)
10)Ask the students to
Predict: Will the sawdust/clay crown displace
more or less water?
5) But, he had to replace the gold he stole with
a less expensive metal so that the crown
would be the same mass as the gold that the
king had given to him. (Add sawdust to the
cup with clay so that it balances with the untouched piece of clay.)
Observe: Refill the clear container to the absolute brim with water. Immerse the sawdust/
clay crown in the clear beaker. Carefully remove the clear container from the basin and
pour the overflow water into the beaker with
graduated markings. Record how much water
overflowed.
6) Then he made the crown. (Knead the sawdust
into the clay so that it is well blended. Model
a crown from the sawdust/clay blend.)
Explain: Ask students to summarize the results of the demonstration.
7) When the goldsmith delivered the crown, the
king was suspicious. But how could he tell
whether the crown was all gold? The king
knew how much gold he had given the goldsmith, and the crown had the same mass.
(Again, show students on the balance that
the pure piece of clay and the sawdust/clay
crown have the same mass.)
You Be the Scientist
8) The king asked Archimedes for help. Archimedes knew the answer when he observed
that the water in his bathtub overflowed
when he immersed his body. He realized
that the volume of his body was equal to the
volume of the water it displaced. A dense
object would displace less water than a less
dense object. Gold is very dense. Silver and
other metals the goldsmith might have substituted would likely be less dense. (In this
demonstration, clay is more dense than sawdust. If students are skeptical, balance the
untouched piece of clay with an equal mass
of sawdust.
3) After each team performs the experiment,
record each team’s findings on a transparency or on the chalkboard.
1) Distribute materials for each team. Give
each team an equal number of pennies from
before 1983 and after 1983.
2) Direct students to A Penny for Your Thoughts
on page 75 in this supplement.
Conclusion
1) In a class discussion, students relate their
findings in the activities to Archimedes’
Principle.
2) On the overhead projector, display Professor Quest cartoon #20. Ask students
•Who is Professor Quest chasing?
•Explain what that person is shouting.
9) He immersed the same amount of gold that
the king had given the goldsmith in water
and measured the amount of water it displaced (Show students the clear container
within the container. Fill the clear container
to the absolute brim with water. Immerse
the pure clay in the water. Carefully remove
the clear container from the basin and pour
the overflow water into the beaker with
graduated markings. Record how much water overflowed.)
•Explain Professor Quest’s comment.
3) Ask students to relate the cartoon to the
theme of the lesson.
References
Hakim, Joy. 2004. The Story of Science: Aristotle Leads the Way.
Washington, DC: Smithsonian Books.
Jones, Larry. “Density Notes.” Pickens County School District.
http://www.sciencebyjones.com/density_notes.htm. Access
date May 2003.
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t e ac h e r — C h a p t e r 1 7 s i d e ba r
QUEST SHEET Key Student’s Quest Guide page 72
Density and Buoyancy
Activity 1
Density is expressed in grams per cubic centimeter (g/cm3).
The density of water is 1 g/cm3. In other words, if you had one cubic centimeter of water, it would
have a mass of 1 gram. If you had 2 cubic centimeters of water, its mass would be 2 grams, but its
density would not change.
mass
density = _________
volume
Use the information in this table and the equation for density to calculate the density of each substance.
Substance
Mass
Volume
Density (Mass/Volume)
glass
24 g
10 cm3
2.4 g/cm3
balsa wood
1.2 g
10 cm3
0.12 g/cm3
aluminum
27 g
10 cm3
2.7 g/cm3
steel
79 g
10 cm3
7.9 g/cm3
water
10 g
10 cm3
1.0 g/cm3
cork
2.2 g
10 cm3
0.22 g/cm3
Predict:
Which objects will float when you put them in the water? Which will sink?
Which will displace the most water?
Observe:
Fill the beaker with water to about an inch from the top. One at a time, drop each object into the
water in the beaker. Note whether the object floats. Remove the object before repeating the procedure with the next object.
Substance
Floats? (prediction)
Floats? (test)
glass
balsa wood
aluminum
steel
water
cork
59
t e ac h e r — C h a p t e r 1 7 s i d e ba r
Explain: Student’s Quest Guide page 73
Were your predictions correct? How does the graph relate to your results?
Use the information in both tables and the What? terms to explain your results.
The objects with greater density than water, the aluminum, steel bolt, and glass marble, sink . The
objects with lower density than water, the balsa wood and the cork, float.
Activity 2
Shape one piece of aluminum foil into a boat with a wide, flat bottom. Fill the beaker with water.
Predict:
Will the aluminum foil boat float? How will it affect the water level?
Observe:
Place the aluminum boat in the beaker of water. Does it float? Record any change in the water level.
Predict:
What will happen if you fold an identical piece of foil into an airtight wad and put it in the beaker of
water?
60
t e ac h e r — C h a p t e r 1 7 s i d e ba r
Observe: Student’s Quest Guide page 74
Fold the second piece of foil repeatedly, smoothing any air out between each fold until it forms a
wad. Put the wad into the beaker of water. What happens? Record any change in the water level.
Explain:
Which has the greater mass, the foil boat or the wad of foil?
They both have the same mass because they are made from pieces of foil of identical size.
Which has the greater volume, the foil boat or the wad of foil?
The boat has greater volume than the wad because it occupies more space.
Which object has greater density? Use the What? terms to explain your results.
The wad of aluminum has greater density than the aluminum boat because it has the same
mass but less volume; the same amount of aluminum occupies less space in the wad.
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t e ac h e r — C h a p t e r 1 7 s i d e ba r
QUEST SHEET Student’s Quest Guide page 75
You Be the Scientist
A Penny for Your Thoughts
Archimedes figured out that the king’s crown was a bad deal! His methods are still useful today.
Many people think that pennies are made of copper. Once they were—at least 95 percent copper and
5 percent zinc. But in 1983, the percentage of copper and zinc in pennies changed. Today’s pennies
are 98 percent zinc, with a thin copper coating.
Your Quest:
Does a change in the percentage of metals lead to a change in density?
Your Gear:
About fifty pennies from the last twenty-five to thirty years, a balance, a graduated cylinder (with a
diameter larger than a penny’s), a flat dish or plate, a paper towel, and water.
Your Routine:
1. Put all the pennies from before 1983 together, then divide the mass by the number of pennies to
get the average mass of one pre-1983 penny.
2. Put a graduated cylinder on top of a flat dish and fill it to the very top. Gently slip all the pennies from before 1983 into the water. Catch the water that spills out. Empty the entire graduated
cylinder, shake out all the extra water drops, and carefully measure the spilled water. This is the
volume of the pre-1983 pennies.
3. Divide that water volume by the number of pennies to get the average volume of a penny. Then
divide the mass of a pre-1983 penny by the volume of the penny to get the density.
4. Repeat procedure for pennies made after 1983.
Mass of All
Pennies
Average
Mass Of
One Penny
(divide)
Volume
(Spilled
Water) Of
All Pennies
Pre-1983
Pennies
Post-1983
Pennies
62
Average
Volume Of
One Penny
(divide)
Mass/
Volume =
Density
(divide)
t e ac h e r — C h a p t e r 1 7 s i d e ba r
Archimedes’ Bathtub (pages 64–69)
Professor Quest tells the story of Archimedes’
bathtub. (transparency cartoon)
Frame 1 Goldsmith’s cart exiting on edge
of frame, sign on back of cart says “Bamboozeledes, Goldsmith to the King.” The
king, looking worried, is handing crown to
Archimedes.
Page 150, paragraph 4 “Then the king came …
to page 151 “And that included Archimedes.”
Frame 2 Archimedes in overflowing bathtub with speech balloon with question
marks, cleaning lady holding mop looking
annoyed in background
Page 151, paragraph 1 “He started to think…” to
paragraph 4, “…when the answer came to him.”
Frame 3 Back view of Archimedes running
naked down the street, speech balloon
says “Eureka!” Citizens looking shocked,
covering eyes, fainting, little boy snickering and pointing
Page 152 “He was so excited…” to page 152,
paragraph 2 “...to the object’s own volume.”
Frame 4 Archimedes holding balance with
crown on one side and a bag of gold on the
other
Page 152, paragraph 2 “Now all Archimedes
had to do…” to end of paragraph “…given the
jeweler.”
Frame 5 Archimedes lowering crown in
clear bowl of water, water spilling over
the rim of the bowl. In another bowl the
gold is deeper in the water. Watching king
clenching fists and looking very angry
Page 153, paragraph 1 “Did the king’s crown…”
to the end of the paragraph “The king had been
cheated.”
63
t e ac h e r — C h a p t e r 1 7 s i d e ba r
Archimedes’ Bathtub / 1
64
t e ac h e r — C h a p t e r 1 7 s i d e ba r
Archimedes’ Bathtub / 2
???
65
t e ac h e r — C h a p t e r 1 7 s i d e ba r
Archimedes’ Bathtub / 3
Eureka!
66
t e ac h e r — C h a p t e r 1 7 s i d e ba r
Archimedes’ Bathtub / 4
67
t e ac h e r — C h a p t e r 1 7 s i d e ba r
Archimedes’ Bathtub / 5
68
t e ac h e r — C h a p t e r 1 7 s i d e ba r
Unit III – Lesson 6 – Chapter 17
Density and Buoyancy Graphs
Substance
Mass
Volume
glass
24 g
10 cm3
balsa wood
1.2 g
10 cm3
aluminum
27 g
10 cm3
steel
79 g
10 cm3
water
10 g
10 cm3
cork
2.2 g
10 cm3
Substance
Floats? (prediction)
Density (Mass/Volume)
Floats? (test)
glass
balsa wood
aluminum
steel
water
cork
69
t e ac h e r — C h a p t e r 1 7 s i d e ba r
20
Eureka!
“That goldsmith
now!”
“That
goldsmithisisininbig
bigtrouble
trouble
now!”
70
student — Chapter 17 sidebar
“Archimedes’
Claw”
Eureka!
page 150, paragraph 4, through page 153, paragraph 2
Theme
“Any object when immersed in a liquid
will displace a volume of liquid equal to the
object’s own volume.”
Archimedes
What?
mass — the amount of matter an object contains
volume — the amount of space an object occupies
weight — the amount of gravity that holds an
object on Earth
density — a physical property of matter: mass
divided by volume
“That
goldsmith is in big trouble now!”
“That goldsmith is in big trouble now!”
buoyancy — an upward force working on an
object in water (The force equals the weight of
the fluid that the object displaces.)
71
student — Chapter 17 sidebar
QUEST SHEET
Density and Buoyancy
Activity 1
Density is expressed in grams per cubic centimeter. (g/cm3)
The density of water is1 g/ cm3. In other words, if you had one cubic centimeter of water, it would
have a mass of 1 gram. If you had two cubic centimeters of water, its mass would be 2 grams, but its
density would not change.
mass
density = _________
volume
Use the information in this table and the equation for density to calculate the density of each substance.
Substance
Mass
Volume
glass
24 g
10 cm
balsa wood
1.2 g
10 cm3
aluminum
27 g
10 cm3
steel
79 g
10 cm3
water
10 g
10 cm3
cork
2.2 g
10 cm3
Density (Mass/Volume)
3
Predict
Which objects will float when you put them in the water? Which will sink?
Which will displace the most water?
Observe
Fill the beaker with water to about an inch from the top. One at a time, drop each object into the
water in the beaker. Note whether the object floats. Remove the object before repeating the procedure with the next object.
Substance
Floats? (prediction)
Floats? (test)
glass
balsa wood
aluminum
steel
water
cork
72
student — Chapter 17 sidebar
Explain
Were your predictions correct? How does the graph relate to your results?
Use the information in both tables and the What? terms to explain your results.
Activity 2
Shape one piece of aluminum foil into a boat with a wide, flat bottom. Fill the beaker with water.
Predict
Will the aluminum foil boat float? How will it affect the water level?
Observe
Place the aluminum boat in the beaker of water. Does it float? Record any change in the water
level.
Predict
What will happen if you fold an identical piece of foil into an airtight wad and put it in the beaker of
water?
73
student — Chapter 17 sidebar
Observe
Fold the second piece of foil repeatedly, smoothing any air out between each fold until it forms a
wad. Put the wad into the beaker of water. What happens? Record any change in the water level.
Explain
Which has the greater mass, the foil boat or the wad of foil?
Which has the greater volume, the foil boat or the wad of foil?
Which object has greater density? Use the What? terms to explain your results.
74
student — Chapter 17 sidebar
Quest Sheet
You Be the Scientist
A Penny for Your Thoughts
Archimedes figured out that the King’s crown was a bad deal! His methods are still useful today.
Many people think that pennies are made of copper. Once they were—at least 95% copper and 5%
zinc. But in 1983, the percentage of copper and zinc in pennies changed. Today’s pennies are 98 %
zinc, with a thin copper coating.
Your Quest:
Does a change in the percentage of metals lead to a change in density?
Your Gear:
About fifty pennies from the last twenty-five to thirty years, a balance, a graduated cylinder (with a
diameter larger than a penny’s), a flat dish or plate, paper towel and water.
Your Routine:
1. Put all the pennies from before 1983 together, then divide the mass by the number of pennies to
get the average mass of one pre-1983 penny.
2. Put a graduated cylinder on top of a flat dish and fill it to the very top. Gently slip all the pennies from before 1983 into the water. Catch the water that spills out. Empty the entire graduated
cylinder, shake out all the extra water drops, and carefully measure the spilled water. This is the
volume of the pre-1983 pennies.
3. Divide that water volume by the number of pennies to get the average volume of a penny. Then
divide the mass of a pre-1983 penny by the volume of the penny to get the density.
4. Repeat procedure for pennies made after 1983.
Mass of All
Pennies
Average
Mass Of
One Penny
(divide)
Volume
(Spilled
Water) Of
All Pennies
Pre-1983
Pennies
Post-1983
Pennies
75
Average
Volume Of
One Penny
(divide)
Mass/
Volume =
Density
(divide)
SC I ENCE N O TES F O R TEACHERS — CHAPTER 1 7
“Archimedes’
Claw”
Science Notes for
Teachers
• Before his time the Greeks could not express
numbers above 10,000. He invented a decimal notation that could enumerate to 1064.
• He was the first geometer to study the area
under curves.
• He invented the science of statics.
• He developed a way to determine the center
of gravity of oddly shaped objects.
by Juliana Texley
Today, researchers interested in the history
of science have used the science of model building to check out what would actually have been
possible for Archimedes, and much of their work
is available on the web. Have students look at
an engineer’s version of the Claw at https://www.
math.nyu.edu/%7Ecrorres/Archimedes/Claw/claw_
animation.gif or the QuickTime movie at http://
www.math.nyu.edu/%7Ecrorres/Archimedes/Claw/
harris/anim-b.mov. They can see more illustrations and animations of Archimedes’ Claw at
http://194.27.7.1/bdfe/2006/030557005/archimedes_
claw.htm and read more about the invention at
http://www.math.nyu.edu/%7Ecrorres/Archimedes/
Claw/harris/rorres_harris.doc.
Teaching Tip for Electronic
Resources
Students may have heard many “tall” stories
about Archimedes and so may have some difficulty appreciating the reality of his accomplishments. As students investigate Archimedes’ Claw
and his use of other simple machines, allot some
time for them to talk about why myths and legends develop from true stories. (It’s likely that
the stories are easier to understand than the actual mathematics and science that Archimedes
developed.) In addition to the story of the Claw
told in Hakim’s text, students can identify and try
to evaluate other legends about Archimedes at
http://194.27.7.1/bdfe/2006/030557005/home.htm.
By the Numbers:
Using Mathematical Models
It is probably true that Archimedes used some
form of lever to tip over Roman ships that were
heavily laden with soldiers and armor, thus contributing to a great military victory. Using the
Internet and the engineering reports of modern
builders who have attempted to recreate Archimedes’ feat, students can evaluate the truth of
the stories using mathematical models.
Online Activities:
Science Myth and Magic
Most people are familiar with Archimedes and
the many stories about his accomplishments;
they may have heard that he defeated an armada
by burning the ships with reflected sunlight, that
he defeated an entire army by himself, and that
he lifted Roman ships with a single rope. None of
these stories are probably precisely true, but the
very real accomplishments of this great philosopher dwarf the rumors:
1. Look at the 5% scale model at http://www.
math.nyu.edu/%7Ecrorres/Archimedes/Claw/
ianno/claw_ianno_1.jpg and estimate the
size of the real invention (answer in bold).
(The Roman troop-carrying ship, called a
quinquereme, was about 35 meters long
and 5 meters wide. Its mass was about
76
SC I ENCE N O TES F O R TEACHERS — CHAPTER 1 7
75 tons, and if you add its crew of over
400, it could have weighed an additional
25 metric tons for a total of 100 tons. So
if Archimedes actually constructed a lever that lifted this ship and used a lever
15 meters long with the fulcrum at 5 meters, he would have had to exert a force
of 50 tons. Students may realize that a
wooden lever would not hold that sort of
torque without breaking.)
5. Archimedes boasted, “Give me somewhere
to stand and I will move the earth!” Do you
think this boast was the truth or an exaggeration, and why?
2. Envision the size and mass of the ship that
Archimedes wanted to lift by tracing it with
sidewalk chalk on the school asphalt. Imagine
400 crew members on that ship! (The heavy
load of passengers and their armor probably
made the ships relatively easy to tip over.)
3. Build a 1% scale model of a quinquereme
that’s 35 centimeters long and 5 centimeters
wide, and give it a mass of 0.75 kilograms by
adding clay or sand. Then experimentally determine how long a lever would have to be
and how much counter-mass would have to
be applied to lift it. Think about the strength
of the material you’d use for your lever, too;
the Greeks had only wood, so a very long,
thin lever would break. For example, if they
used tree trunks that were 50 centimeters
in diameter, your proportional lever would
have to be no more than 0.5 centimeter in
diameter—about the thickness of a wooden
chopstick or kabob stick.
4. Use mathematics to determine the advantage that a “claw” (a simple machine called
a lever) might have given Archimedes and
his crew using one of these websites: http://
www.edinformatics.com/math_science/simple_
machines/lever.htm or http://www.mca.k12.nf.ca/
sm/lever/lever.htm. For example, if the 50-centimeter tree trunk was 15 meters long, and
it had to lift 100 tons, and the fulcrum was
placed at 10 meters, you would still need 50
tons of counter-mass and the 10-meter length
of tree trunk might break! But for the legend
to be true, it’s not necessary that the ship be
totally lifted, only tipped.
77
SC I ENCE N O TES F O R S t u d e n t s — CHAPTER 1 7
edu/%7Ecrorres/Archimedes/Claw/claw_animation.
gif or the QuickTime movie at http://www.math.
nyu.edu/%7Ecrorres/Archimedes/Claw/harris/anim-b.
mov. You can see more illustrations and animations of Archimedes’ Claw at http://194.27.7.1/
bdfe/2006/030557005/archimedes_claw.htm
and
read more about the invention at http://www.
math.nyu.edu/%7Ecrorres/Archimedes/Claw/harris/
rorres_harris.doc.
“Archimedes’
Claw”
Science Notes for
Students
by Juliana Texley
By the Numbers:
Using Mathematical Models
Online Activities:
Science Myth and Magic
Most people are familiar with Archimedes and
the many stories about his accomplishments;
they may have heard that he defeated an armada
by burning the ships with reflected sunlight, that
he defeated an entire army by himself, and that
he lifted Roman ships with a single rope. (Some
of the legends about Archimedes can be found at
http://194.27.7.1/bdfe/2006/030557005/home.htm.)
None of these stories are probably precisely
true, but the very real accomplishments of this
great philosopher dwarf the rumors:
• Before his time the Greeks could not express
numbers above 10,000. He invented a decimal notation that could enumerate to 1064.
• He was the first geometer to study the area
under curves.
• He invented the science of statics.
• He developed a way to determine the center
of gravity of oddly shaped objects.
Today, researchers interested in the history
of science have used the science of model building to check out what would actually have been
possible for Archimedes, and much of their work
is available on the web. Look at an engineer’s
version of the Claw at https://www.math.nyu.
78
It is probably true that Archimedes used some
form of lever to tip over Roman ships that were
heavily laden with soldiers and armor, thus contributing to a great military victory. Using the
Internet and the engineering reports of modern
builders who have attempted to recreate Archimedes’ feat, you can evaluate the truth of the stories using mathematical models.
1. Look at the 5% scale model at http://www.
math.nyu.edu/%7Ecrorres/Archimedes/Claw/
ianno/claw_ianno_1.jpg and estimate the size
of the real invention.
2. Envision the size and mass of the ship that
Archimedes wanted to lift by tracing it with
sidewalk chalk on the school asphalt. Imagine
400 crew members on that ship! (The heavy
load of passengers and their armor probably
made the ships relatively easy to tip over.)
3. Build a 1% scale model of a quinquereme
that’s 35 centimeters long and 5 centimeters
wide, and give it a mass of 0.75 kilograms by
adding clay or sand. Then experimentally determine how long a lever would have to be
and how much counter-mass would have to
SC I ENCE N O TES F O R S t u d e n t s — CHAPTER 1 7
be applied to lift it. Think about the strength
of the material you’d use for your lever, too;
the Greeks had only wood, so a very long,
thin lever would break. For example, if they
used tree trunks that were 50 centimeters
in diameter, your proportional lever would
have to be no more than 0.5 centimeter in
diameter—about the thickness of a wooden
chopstick or kabob stick.
4. Use mathematics to determine the advantage that a “claw” (a simple machine called
a lever) might have given Archimedes and
his crew using one of these websites: http://
www.edinformatics.com/math_science/simple_
machines/lever.htm or http://www.mca.k12.nf.ca/
sm/lever/lever.htm. For example, if the 50-centimeter tree trunk was 15 meters long, and
it had to lift 100 tons, and the fulcrum was
placed at 10 meters, you would still need 50
tons of counter-mass and the 10-meter length
of tree trunk might break! But for the legend
to be true, it’s not necessary that the ship be
totally lifted, only tipped.
5. Archimedes boasted, “Give me somewhere
to stand and I will move the earth!” Do you
think this boast was the truth or an exaggeration, and why?
79
Teaching Materials for Joy Hakim’s
The Story of Science
Newton at the Center
Chapters 4, 9, and 13
Pages 82–103, 108–123, 127–135 are excerpted from:
Teacher’s Quest Guide to accompany The Story of Science: Newton at the Center by Joy Hakim
Curriculum authors: Cora Heiple Teter, Maria Garriott, and Kristin Brodowski, Ph.D.
You Be the Scientist Activities were developed with Juliana Texley
Artwork by Erin Pryor Gill
Cover Design by Erin Pryor Gill
Interior Design by Jeffrey Miles Hall, ION Graphic Design Works
Johns Hopkins University
Center for Social Organization of Schools
Talent Development Middle Grades Program
Douglas MacIver, Ph.D., Director
This work was supported in part by grants and contracts from the Institute of Education Sciences,
U.S. Department of Education. The opinions expressed herein do not necessarily reflect the views
of the department.
© 2008 The Johns Hopkins University
ISBN: 978-1-58834-252-2
ISBN 10: 1-58834-252-2
For more information about the Newton at the Center Teacher’s and Student’s Quest Guides, please
contact Laura Slook, [email protected], 414-217-2422.
Pages 104–107, 124–126, 136–139 are credited as follows:
NATIONAL SCIENCE TEACHERS ASSOCIATION
Francis Q. Eberle, PhD, Executive Director
David Beacom, Publisher
Copyright © 2009 by the National Science Teachers Association.
All rights reserved.
NSTA is committed to publishing material that promotes the best in inquiry-based science education. However, conditions of actual use may vary, and the safety procedures and practices
described in this book are intended to serve only as a guide. Additional precautionary measures
may be required. NSTA and the authors do not warrant or represent that the procedures and practices in this book meet any safety code or standard of federal, state, or local regulations. NSTA
and the authors disclaim any liability for personal injury or damage to property arising out of or
relating to the use of this book, including any of the recommendations, instructions, or materials
contained therein.
You may photocopy, print, or email up to five copies of an NSTA book chapter for personal use only;
this does not include display or promotional use. Elementary, middle, and high school teachers only
may reproduce a single NSTA book chapter for classroom- or noncommercial, professional-development use only. Please access www.nsta.org/permissions for further information about NSTA’s rights
and permissions policies.
81
T E A C H E R — C ha p ter 4
“Tycho Brahe:
Taking Heaven’s
Measure”
Theme
“[This was] a tremendous idea—that to
find something out, it is better to perform
some careful experiments than to carry on
deep philosophical arguments.”
Richard Feynman
American physicist (1918 – 1988)
Goals
Students will understand the contributions
Tycho Brahe made to modern astronomy.
Students will learn how, beginning with Tycho Brahe, scientists began to base their conclusions on empirical rather than on rational
thinking.
will
that perfect,
“This will “This
shake up
thatshake
perfect,up
unchanging
universe theory!”
unchanging universe theory!”
Who?
Tycho Brahe — Danish astronomer and mathematician whose observation of a supernova
proved that changes take place in the universe
and whose observation of a comet proved that
crystal spheres do not exist
comet — a heavenly body that orbits the Sun
(tiny in comparison with the planets) with a
nucleus of rock and ice and a tail of dust and
gases
What?
Where?
rational — relying on reason and logic
Denmark — northern European country on the
Baltic Sea; in the sixteenth century it also encompassed modern Sweden.
empirical — relying on experiences and
observation
Hven — the island given to Brahe where he built
his castle/observatory Uraniborg
nova — from the Latin, nova stella or new star;
an apparent “new” star, that is, a star that suddenly increases in light intensity and then gradually grows fainter
Baltic Sea — body of water between Denmark
and modern Sweden
Prague — city in Bohemia (present-day Czech
Republic) where Brahe built another observatory
supernova — a dying star that runs out of fuel
and explodes with a great intensity of light
82
T E A C H E R — C ha p ter 4
When?
3) Ask students the following questions.
1572 — Tycho Brahe sees a supernova.
•On which kind of thinking did scientists
rely up until the sixteenth century?
1577 — Tycho Brahe observes a comet and records its path.
•On which kind of thinking did scientists
begin to rely in the sixteenth century?
•What is needed for empirical thinking?
Groundwork
•What would account for the change in the
way scientists thought?
•In The Story of Science: Newton at the Center,
read chapter 4, “Tycho Brahe: Taking Heaven’s Measure.”
4) Students’ discussion should include the following points.
•Gather the following materials:
For each student
Before the sixteenth century, scientists
relied on rational thinking, what the
Greeks called pure thought. They had
deep discussions about their observations of the universe, but philosophy,
religion, and reverence of the ancient
Greeks’ beliefs influenced how they
interpreted their observations and
reached their conclusions. In a way,
they applied what they saw to prove
the truths that they already believed.
transparency sheets and markers (optional)
For the teacher
transparency masters
Aristotle’s Universe (page 89)
Copernicus’s Universe (page 90)
Modern Solar System (page 91)
Tycho Brahe’s Universe (page 88)
Scientists Speak: Tycho Brahe (page 87)
Professor Quest cartoon #5 (page 92)
For the classroom
In the sixteenth century, scientists,
such as Tycho Brahe, used empirical thinking, drawing their conclusions from what they observed and
experienced. Sometimes their findings contradicted beliefs that had been
held as absolute truth for centuries.
photocopy of
Scientists Speak: Tycho Brahe
Consider the Quotation
1) Direct students’ attention to the theme quotation by Richard Feynman at the beginning
of this section. Ask students to paraphrase
this quotation. Write student versions on
chart paper or the chalkboard.
5) Tell students that scientists moved from rational thinking to empirical thinking in part
because of the atmosphere of inquiry in European universities. In addition, improved
technology gave the opportunity to make
more accurate observations and to explore
the truth of long-held beliefs. Without his
improved astronomical instruments, the
astronomer Tycho Brahe, about whom they
will read in this lesson, could not have recorded the accurate measurements that
disproved the theory of the unchangeable
nature of the universe.
2) Call students’ attention to two vocabulary
words and their meanings in the What? list
on page 93 in this guide.
•rational — relying on reason and logic
•empirical — relying on experiences and
observation
Tell students that this quotation refers to a
change in the way scientists thought before Copernicus and Tycho Brahe, and how these men
changed the way scientists reached conclusions.
83
T E A C H E R — C ha p ter 4
Directed Reading
ies beyond the Moon in place, how could
comets pass through the crystal spheres?
Brahe could only conclude that Aristotle
was mistaken on this point as well.
Read to understand Tycho Brahe’s contributions to modern astronomy
Tycho Brahe was one of the first astronomers to rely on observation and experience—empirical knowledge—rather than
on rational knowledge. His improved
astronomical instruments and careful, constant observations allowed him
to record more accurate information
about the heavens than his predecessors. Future astronomers would base
their work on his accurate information.
1) Tell students that there were two widely held
Aristotelian beliefs. (The universe beyond the
Moon is perfect and unchanging; the planets
and stars are held in place by rotating crystal
spheres.)
2) Tell students that Tycho Brahe made major
contributions to astronomy by disproving
these ancient scientific “facts.” In doing so,
he used empirical thinking.
3) Direct students to skim quickly through
chapter 4, “Tycho Brahe: Taking Heaven’s
Measure” in The Story of Science: Newton
at the Center, to form questions about Brahe
and his discoveries. Write students’ questions on chart paper or the chalkboard.
Classwide Activity
Scientists Speak
1) Display the transparency of Tycho Brahe
(page 87) on the overhead. Tell students
that they will put the words in the scientist’s
mouth (page 94). What was his most important idea? What statement did he make
on which future scientists could base their
work?
4) Students pair read chapter 4 in The Story
Science: Newton at the Center to find the
answers to their questions. As students read,
they use the Who? What? Where? terms on
page 93 of this supplement and the map on
page 45 in The Story Science: Newton at the
Center to assist them with new terms and
places.
2) Students review chapter 4 in The Story of
Science: Newton at the Center to find what
important statement Brahe made. Write students’ suggestions on the chalkboard so that
the class can formulate the best statement.
Write the statement in the speech balloon on
the transparency.
5) At the close of the reading, students share their
findings in a class discussion. The discussion
should include the following information.
When Tycho Brahe observed a supernova
in the constellation of Cassiopeia in
1572, he knew that it was not a comet,
and he knew that it was beyond the
Moon. Therefore, Aristotle’s assertion
that the universe beyond the Moon is
unchanging could not be true. When in
1577 Brahe tracked a comet, he knew
from his nightly observations with his
improved astronomical instruments that
the comet was also beyond the Moon.
How could this be true? If rotating
crystal spheres held the heavenly bod-
Cooperative Team Learning
Construct Brahe’s model of the universe
and compare it with Copernicus’s model
1) Students work in their cooperative learning
teams to complete the activity on page 95 in
this supplement. Remind students to support team members and share information
in their discussions before they complete
their quest sheets individually. Students may
draw their universe models on transparen84
T E A C H E R — C ha p ter 4
History link — Students use library and Internet resources to research the astronomical
instruments that Tycho Brahe invented or improved. Some possibilities include the brass
azimuthal quadrant, the armillary sphere, the
revolving quadrant, the triangular sextant, and
the great equatorial armillary. In their journals,
students illustrate the instrument and describe
how it worked.
cies and share them with the class on the
overhead projector.
2) When students have completed their illustrations, ask volunteers to show and describe
their Brahe models. Discuss how Brahe
agreed or disagreed with Copernicus. Show
the transparencies Brahe’s Universe, Aristotle’s Universe, Copernicus’ Universe, and
the Modern Universe.
Art link — Students think of creative ways to
depict historic events.
3) Ask students to comment on the correctness
of each model.
Science link — Students use library and Internet resources to research comets and make
a poster to teach fellow students about these
heavenly bodies.
•Which scientist came closer to the truth?
•Why would Brahe disagree so much with
Copernicus?
4) Help students to understand that even with
his superior instruments and careful observations, Brahe came to some wrong conclusions. Like many people of his time, he could
not believe that the Earth could move or that
it could not be at the center of the universe.
References
Charbonneau, Paul. “Tycho Brahe (1546-1601).” High Altitude Observatory, National Center for Atmospheric Research. http://
www.hao.ucar.edu/Public/education/bios/tycho.html. Access
date April 2009.
Crump, Thomas. 2001. A Brief History of Science as Seen through
the Development of Scientific Instruments. London: Constable.
Conclusion
Field, J. V. “Tycho Brahe.” School of Mathematics and Statistics,
University of St. Andrews, Scotland. http://www-history.mcs.
st-andrews.ac.uk/history/Mathematicians/Brahe.html. Access
date April 2009.
1) On the overhead projector, display Professor Quest cartoon #5 (page 92). To whom
is Professor Quest speaking? What are they
observing? Explain Professor Quest’s comment.
Gribbin, John. 2002. Science: A History 1543-2001. New York:
Penguin Books.
Hakim, Joy. 2005. The Story of Science: Newton at the Center.
Washington, DC: Smithsonian Books.
2) Ask students to relate the cartoon to the
theme of the lesson.
“The Observations of Tycho Brahe.” Department of Physics and
Astronomy, University of Tennessee. http://csep10.phys.utk.
edu/astr161/lect/history/brahe.html. Access date April 2009.
Homework
“Tycho Brahe.” The Electronic Universe, University of Oregon.
http://abyss.uoregon.edu/~js/glossary/brahe.html. Access date
April 2009.
Students imagine that they work as an assistant to Tycho Brahe. Write a journal entry
describing their boss and a day’s (night’s) work
with him.
Van Helden, Albert. “Comets.” Galileo Project, Rice University.
http://es.rice.edu/ES/humsoc/Galileo/Things/comet.html. Access date April 2009.
Van Helden, Albert. “Tycho Brahe (1546-1601).” Galileo Project,
Rice University. http://es.rice.edu/ES/humsoc/Galileo/People/
tycho_brahe.html. Access date April 2009.
Curriculum Links
Research link — Students go on a mystery
hunt in the library to find out what happened to
Tycho Brahe’s astronomical instruments after
he died. It is a sad story.
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T E A C H E R — C ha p ter 4
Quest Sheet Answers
What Brahe Said about the Universe (page
94)
Copernicus said that the universe is perfect;
Brahe proved by his observation of a supernova
and a comet that it is not perfect.
Copernicus said that the Sun is the center of the
universe; Brahe said the Earth is at the center.
Copernicus said that the Earth moves in three
ways; Brahe said that the Earth is motionless.
Copernicus said that the stars do not move;
Brahe said that the sphere of fixed stars rotates
daily around the Earth.
Unit i — Lesson 5 — ChaPter 4
Unit i — Lesson 5 — ChaPter 4
QUEST SHEET
Paying careful attention to Tycho Brahe’s description of the universe, draw a detailed diagram.
What Brahe Said about the Universe
Tycho Brahe’s Universe
Directions:
Read with your teammates the following statements that Tycho Brahe made about the universe.
•TheEarthisthecenteroftheuniverse.
•TheEarthismotionless.
•TheMoonrevolvesaroundtheEarth.
•TheSunrevolvesaroundtheEarth.
•Thesphereofthefixedstarsiscenteredonthe
Earth.
•Thesphereofthefixedstarsrotatesdaily
around the Earth.
•TheplanetsrevolvearoundtheSuninthefollowing order.
• Mercury
• Venus
• Mars
• Jupiter
• Saturn
•CometsarebeyondtheMoon.
•Theuniverseischangeable.
•Crystalspheresdonotexist.
Scientists Speak
Tycho Brahe (1546 – 1601)
Look back at page 18 in this guide to compare Copernicus’s description of the universe with Tycho
Brahe’s description. List at least three points on which Brahe and Copernicus disagree in their models of the universe.
21
22
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T E A C H E R — C ha p ter 4
Scientists Speak
Tycho Brahe (1546 – 1601)
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T E A C H E R — C ha p ter 4
Saturn
Jupiter
Mars
Comet of 1577
Sun
Mercury
Venus
Moon
Earth
Fixed Stars
Tycho Brahe’s Universe
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T E A C H E R — C ha p ter 4
Sphe
re o f th e P r i me M ov e r
Fixed Stars
Saturn
Jupiter
Mars
Sun
Venus
Mercury
Moon
Earth
Aristotle’s Universe
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T E A C H E R — C ha p ter 4
Fixed Stars
Saturn
Jupiter
Mars
Moon
Earth
Venus
Mercury
Sun
Copernicus’s Universe
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T E A C H E R — C ha p ter 4
Neptune
Uranus
Saturn
Jupiter
Moon
Earth
Venus
Mercury
Mars
Pluto
Modern Solar System*
* In 2006, the International Astronomical Union, an organization that establishes the official
names of all celestial bodies, voted to demote Pluto from “classical” planetary status to that of a
“dwarf planet.”
The orbits of the classical planets are ellipses with the Sun at one focus. However, with the exception of Mercury’s orbit, they are all very nearly circular as depicted in this figure.
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T E A C H E R — C ha p ter 4
#5
“This will shake up that perfect, unchanging universe theory!”
“This will shake up that perfect, unchanging universe theory!”
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S T U D E N T — C ha p ter 4
“Tycho Brahe:
Taking Heaven’s
Measure”
Theme
“[This was] a tremendous idea—that to
find something out, it is better to perform
some careful experiments than to carry on
deep philosophical arguments.”
Richard Feynman
American physicist (1918 – 1988)
Who?
Tycho Brahe — Danish astronomer and mathematician whose observation of a supernova
proved that changes take place in the universe
and whose observation of a comet proved that
crystal spheres do not exist
will
that perfect,
“This will “This
shake up
thatshake
perfect,up
unchanging
universe theory!”
What?
unchanging universe theory!”
rational — relying on reason and logic
empirical — relying on experiences and
observation
Hven — the island given to Brahe where he built
his castle/observatory Uraniborg
nova — from the Latin, nova stella or new
star; an apparent “new” star, that is, a star that
suddenly increases in light intensity and then
gradually grows fainter
Baltic Sea — body of water between Denmark
and modern Sweden
Prague — city in Bohemia (present-day Czech
Republic) where Brahe built another observatory
supernova — a dying star that runs out of fuel
and explodes with a great intensity of light
When?
comet — a heavenly body that orbits the Sun (tiny
in comparison with the planets) with a nucleus of
rock and ice and a tail of dust and gases
1572 — Tycho Brahe sees a supernova.
1577 — Tycho Brahe observes a comet and records its path.
Where?
Denmark — northern European country on the
Baltic Sea; in the sixteenth century it also encompassed modern Sweden.
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S T U D E N T — C ha p ter 4
Quest Sheet
What Brahe Said about the Universe
Directions:
Read with your teammates the following statements that Tycho Brahe made about the universe.
•The Earth is the center of the universe.
•The Earth is motionless.
•The Moon revolves around the Earth.
•The Sun revolves around the Earth.
•The sphere of the fixed stars is centered on the
Earth.
•The sphere of the fixed stars rotates daily
around the Earth.
•The planets revolve around the Sun in the following order.
•Mercury
•Venus
•Mars
•Jupiter
•Saturn
•Comets are beyond the Moon.
•The universe is changeable.
•Crystal spheres do not exist.
Scientists Speak
Tycho Brahe (1546 – 1601)
Look back at page 18 in this guide to compare Copernicus’s description of the universe with Tycho
Brahe’s description. List at least three points on which Brahe and Copernicus disagree in their models of the universe.
94
S T U D E N T — C ha p ter 4
Paying careful attention to Tycho Brahe’s description of the universe, draw a detailed diagram.
Tycho Brahe’s Universe
95
T E A C H E R — C ha p ter 4 F eature
Directed Reading
“Holding a Ruler
to the Sky”
Read to learn about Tycho Brahe’s use of
parallax to understand the supernova and
the comet
Goals
1) Call students’ attention to the meaning of parallax on page 100 in this supplement.
Students will demonstrate parallax of near
objects.
2) Direct students to turn to “Holding a Ruler
to the Sky” on page 58 in Newton at the Center and study the illustration of parallax shift
on the bottom left side of the page. Help
students to re-create what this illustration
shows by following these directions.
Students will demonstrate how distance
affects parallax, recording how it decreases as
the distance between an object and the observer
increases.
•Hold up a thumb and center it on one spot
on the classroom wall with one eye closed.
Students will understand how Tycho Brahe
came to a wrong conclusion about the position
of the Earth in the solar system because he could
not measure the parallax of the distant stars.
•Open the closed eye and close the open eye.
3) Ask students to explain what their thumbs
appear to do. (They appear to move in relation to the spot on the classroom wall.) Tell
students that the baseline in this demonstration is the distance between their eyes. This
apparent change of position of the thumb in
relation to a fixed object on the classroom
wall is parallax.
What?
parallax — the apparent movement of an object in relation to other objects when viewed
from different positions along a baseline
Groundwork
4) Tell students to listen as you read “Holding a
Ruler to the Sky” aloud to learn more about
parallax.
•Read “Holding a Ruler to the Sky” page 58,
The Story of Science: Newton at the Center
•Gather these materials for each team of two
students:
Classwide Activity
small marshmallow or gumdrop
toothpick
pen
meterstick
masking-tape strip at least 60 cm long
flat table or desk surface at least 1 x 1 m
Demonstrate parallax
1) To further understand parallax, students
perform the following demonstration.
•Volunteer A (the object) stands in the
middle of the classroom.
•For the cooperative team learning activity,
place strips of masking tape down the center
of enough tables to accommodate the number
of two-student teams in the class. If the tables
are long enough, two teams can work on opposite ends of one table.
•The baseline is the classroom wall facing
Volunteer A.
•Volunteer B stands in the corner of the
classroom at one end of the baseline wall
and describes the Volunteer A’s location in
relation to objects on the opposite classroom wall (the wall behind Volunteer A).
•Practice the activity beforehand to foresee
any problems students may encounter.
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T E A C H E R — C ha p ter 4 F eature
•Volunteer B moves to the other corner (end
of the baseline wall facing Volunteer A) and
describes Volunteer A’s location in relation
to objects on the opposite classroom wall.
•The parallax in centimeters (vertical axis)
is the amount of the apparent change in
the location of the “star” when viewed by
the observer from two positions (left and
right eyes).
2) Ask students the following questions.
5) Ask students to make a statement about how
distance from the viewer affects the parallax
of an object. (The closer an object is to the
viewer, the more evident the parallax. The
farther away the object is from the viewer,
the less evident the parallax.)
•Does Volunteer A’s position appear
changed in relation to the objects on the
classroom wall opposite the baseline? (yes)
•Has Volunteer A’s position actually
changed? (no)
•What has changed? (Volunteer B’s position on the baseline and his/her angle of
viewing Volunteer A)
Conclusion
This apparent movement of the object (Volunteer A) in relation to the classroom wall is the
object’s parallax.
1) Tell students that astronomers use parallax
to measure the distance of heavenly objects,
but the objects must be close enough for
parallax to be apparent.
Cooperative Team Learning
2) Study the illustrations on pages 60 and 61 of
The Story of Science: Newton at the Center
to understand how parallax is evident when
observing the moon.
Measure and record parallax
1) Students turn to A Parallax Performance on
page 101 in this supplement. Tell students
that in this activity they will discover how
the distance of the object from the viewer
affects its parallax.
3) Tell students to imagine that in their demonstration, their heads represented the Earth.
They kept their heads still while observing
their “star.” Tycho Brahe could not perceive
parallax for the very distant stars as he could
for the closer Moon and Sun. What might he,
therefore, conclude about the Earth? Is this
an accurate conclusion?
2) Read the directions on the student sheet with
students and answer questions. As students
work, visit each team to make sure they are
following directions in marking the tape and
making and recording their observations.
Homework
3) When students have completed their work,
ask for volunteers to share their results and
record an average on the Parallax Table
transparency (page 95). If results vary widely, ask students how they would account
for the differences (different baselines i.e.,
distance between individual’s eyes, moving
head while observing, inaccurate reading
and recording of measurements).
In their journals, students explain parallax
in their own words and draw a diagram to illustrate this concept.
References
Hakim, Joy. 2005. The Story of Science: Newton at the Center.
Washington, DC: Smithsonian Books.
Hatch, Robert A. “ Stellar Parallax Heliocentric System.” University of Florida History of Science Study Guide. http://web.
clas.ufl.edu/users/rhatch/pages/03-Sci-Rev/SCI-REV-Teaching?
his-SCI_Stud. Access date April 2009.
4) Explain to students the following.
•The distance in centimeters (horizontal
axis) is the distance of the “star” from the
observer.
StarDate Online. “Astroglossary.” http://stardate.org/resources/
astroglossary/glossary_P.html. Access date April 2009.
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T E A C H E R — C ha p ter 4 F eature
Weinrich, Dave. 1994. “The Parallax of a Star.” A Teacher Resource
to Enhance Astronomy Education: Project Spica. Edited by
Nadine Butcher Ball, Harold P. Coyle, and Irwin I. Shapiro.
Dubuque, Iowa: Kendall/Hunt.
U n i t i — L e s s o n 6 — C h a P t e r 4 F e at U r e
QUEST SHEET
A Parallax Performance
Parallax is the apparent movement of an object in relation to other objects when viewed from
different positions along a baseline. In this experiment, you will be sighting a “star” at various
locations in the “universe” and determining its parallax.
Materials:
Quest Sheet Answers
Small marshmallow or gumdrop, toothpick, pen, meterstick, masking-tape strip at least 60 cm long,
flat table or desk surface at least 1 x 1m
A Parallax Performance
Student’s Quest Guide, page 103
Directions:
1) Note that your teacher has placed the 60-cm tape along the center of a table to its edge.
2) Working with a partner, use the meterstick to mark a line down the center of the tape. Then along the
length of the tape, measure and mark 10-cm intervals to 60 cm. Begin with 0 cm at the table edge.
1) The baseline is the distance between the left
and right eyes.
3) Place the meterstick perpendicular to the tape on its thin edge at the 60-cm position along the length
toothpick
meterstick on the tape.
of the tape. Be sure
to line up the 50-cm mark on the meterstick with the centerline
25
50
75
60
50
toothpick
marshmallow
2) The parallax decreases with the distance
from the viewer.
meterstick
tabletop
40
tape
30
20
50
25
60
10
75
50
40
marshmallow
tape
30
20
tabletop
10
3) Astronomers can measure the parallax angle between the Earth and other heavenly
objects and then use trigonometry—the
mathematics of triangles—to calculate the
distance to the object.
4) Push the toothpick into the marshmallow so that it sticks straight up. This is your “star.”
meterstick
“star”
meterstick
“star”
4) When the object is too far away to detect
any parallax
24
U n i t i — L e s s o n 6 — C h a P t e r 4 F e at U r e
U n i t i — L e s s o n 6 — C h a P t e r 4 F e at U r e
Now you are ready to begin your observations.
1) What is the baseline in this experiment?
5) Partner A places the “star” at the markings on the tape, beginning at the 10-cm mark. Be sure the
“star” is exactly on the tape centerline.
6) Partner B takes a position eye level with the table [nose touching the table at the center of the
tape, 0-cm mark] and observes the “star” first with the right eye and then with the left eye, calling out the apparent location of the toothpick as measured against the meterstick in the background.
7) Partner A records on Partner B’s chart his or her observation but does not fill in the Parallax column.
8) After observing the “star” at all distances, the partners trade tasks and repeat the activity.
2) What trend in parallax versus distance do you see in the data?
9) Partners A and B calculate the parallax in their measurements by subtracting the left eye measurement at a given distance from the right eye measurement at that same distance and taking
the result’s absolute value (that is, making the difference a positive number if the subtraction
yields a negative number).
Distance
Right Eye
Left Eye
Parallax (the absolute value of the
difference between
right and left eye
measurements)
3) How could parallax be used to compute the distance to heavenly objects? Consult page 60 in
Newton at the Center for a hint.
right eye – left eye
10 cm
20 cm
4) Under what conditions would parallax not be useful in measuring astronomical distances?
30 cm
40 cm
50 cm
25
26
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T E A C H E R — C ha p ter 4 F eature
Parallax Data Table
Distance
Right Eye
Left Eye
Parallax
(the absolute
value of the
difference between right and
left eye
measurements)
|right eye – left
eye|
10 cm
20 cm
30 cm
40 cm
50 cm
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S T U D E N T — C ha p ter 4 F eature
What?
“Holding a Ruler
to the Sky”
parallax — the apparent movement of an object in relation to other objects when viewed
from different positions along a baseline
Neptune
Uranus
Saturn
Jupiter
Moon
Earth
Venus
Mercury
Mars
Pluto
Modern Solar System*
* In 2006, the International Astronomical Union, an organization that establishes the official
names of all celestial bodies, voted to demote Pluto from “classical” planetary status to that of a
“dwarf planet.”
The orbits of the classical planets are ellipses with the Sun at one focus. However, with the exception of Mercury’s orbit, they are all very nearly circular as depicted in this figure.
100
S T U D E N T — C ha p ter 4 F eature
Quest Sheet
A Parallax Performance
Parallax is the apparent movement of an object in relation to other objects when viewed from
different positions along a baseline. In this experiment, you will be sighting a “star” at various
locations in the “universe” and determining its parallax.
Materials:
Small marshmallow or gumdrop, toothpick, pen, meterstick, masking-tape strip at least 60 cm long,
flat table or desk surface at least 1 x 1m
Directions:
1) Note that your teacher has placed the 60-cm tape along the center of a table to its edge.
2) Working with a partner, use the meterstick to mark a line down the center of the tape. Then along the
length of the tape, measure and mark 10-cm intervals to 60 cm. Begin with 0 cm at the table edge.
3) Place the meterstick perpendicular to the tape on its thin edge at the 60-cm position along the length
toothpick
meterstick on the tape.
of the tape. Be sure to line up the 50-cm mark on the meterstick with the centerline
25
50
75
60
50
toothpick
marshmallow
meterstick
tabletop
40
tape
30
20
50
25
60
10
75
50
40
marshmallow
tape
30
20
tabletop
10
4) Push the toothpick into the marshmallow so that it sticks straight up. This is your “star.”
meterstick
“star”
meterstick
“star”
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S T U D E N T — C ha p ter 4 F eature
Now you are ready to begin your observations.
5) Partner A places the “star” at the markings on the tape, beginning at the 10-cm mark. Be sure the
“star” is exactly on the tape centerline.
6) Partner B takes a position eye level with the table [nose touching the table at the center of the
tape, 0-cm mark] and observes the “star” first with the right eye and then with the left eye, calling out the apparent location of the toothpick as measured against the meterstick in the background.
7) Partner A records on Partner B’s chart his or her observation but does not fill in the Parallax column.
8) After observing the “star” at all distances, the partners trade tasks and repeat the activity.
9) Partners A and B calculate the parallax in their measurements by subtracting the left eye measurement at a given distance from the right eye measurement at that same distance and taking
the result’s absolute value (that is, making the difference a positive number if the subtraction
yields a negative number).
Distance
Right Eye
Left Eye
Parallax (the absolute value of the
difference between
right and left eye
measurements)
right eye – left eye
10 cm
20 cm
30 cm
40 cm
50 cm
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S T U D E N T — C ha p ter 4 F eature
1) What is the baseline in this experiment?
2) What trend in parallax versus distance do you see in the data?
3) How could parallax be used to compute the distance to heavenly objects? Consult page 60 in
Newton at the Center for a hint.
4) Under what conditions would parallax not be useful in measuring astronomical distances?
103
S C I E N C E N O T E S F O R T E A C H E R S — C ha p ter 4 F eature
Tycho Brahe:
Taking Heaven’s
Measure
Science Notes for
Teachers
by Juliana Texley
Teaching Tip for Electronic
Resources
When humans make observations, they often
filter them through their own experience, making
different interpretations of what they see. Show
some complex image or animation to your students quickly, and ask them to write down what
they saw. Then discuss how their observations
might differ from those of other students who
saw the same image or animation—and why. Observations are often interpreted differently depending on context. For example, a person who
expects to see a monster might see a floating
log and interpret it as an animal. A person who
thinks that people in sports cars drive faster than
others might make a judgment of a quick glimpse
of a traffic accident based on that assumption.
Looking at Supernovas
Here are three observations of supernovas
from different parts of the world. Ask students
to discuss how observers might differ and put
their own background into what they see. The
first two observations describe the supernova of
1054.
From Europe:
And at the very hour of [Pope Leo’s] passing there appeared in the heavens, not only in
Rome where his body lay, but indeed to men
throughout the whole world, an orb of extraordinary brilliance for the space of about half an
hour.—Tractatus de Ecclesia S. Petri Aldenburgensi (chronicle of the Church of St. Peter in Oudembourg, in present-day Belgium; see http://hal.
archives-ouvertes.fr/docs/00/04/25/93/PDF/pm.pdf)
From Kaifeng, China:
On the 1st year of the Chih-ho reign period,
7th month, 22nd day [August 27, 1054]...Yang
Wei-te said “I humbly observe that a guest star
has appeared. Above the star in question there
is a faint glow, yellow in colour. If one carefully
examines the prognostications concerning the
emperor, the interpretation is as follows: The
fact that the guest star does not trespass against
Pi and its brightness is full means that there is
a person of great worth. I beg that this be handed
over to the Bureau of Historiography.”—Sung
dynasty chronicles; see http://super.colorado.
edu/~astr1020/sung.html
The third observation is from Shakespeare,
apparently describing a supernova he saw at
age 8 through Barnardo’s lines in Hamlet, Act 1,
Scene 1 (http://hubblesite.org/newscenter/archive/
releases/2004/34):
What we have two nights seen…
Last night of all,
When yond same star that’s westward from the pole
Had made his course to illume that part of
heaven
Where now it burns…
Online Activities:
As Clear as the Nose on Your Face
Students can use the Internet to explore ancient and modern observatories and see how different observers might interpret the same skies.
For example, Tycho Brahe built a castle and observatory on Hven (see the illustration on page
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S C I E N C E N O T E S F O R T E A C H E R S — C ha p ter 4 F eature
52 of Newton at the Center), and students can
observe the Moon and share their data at “Tycho Brahe’s Observatory,” an online cooperative
project of the Center for Improved Engineering
and Science Education (CIESE): http://ciese2.org/
curriculum/tycho/information(invitationtocollaborat
e).html
Long before the Hven observatory was built,
the Chinese astronomer Guo Shoujing built a
“sky measuring tower” in Henan Province (latitude 35o north). The tower, built in about 1276
AD, looked like a pyramid sundial but also had
a long bar that cast a shadow. It was especially
valuable on the winter and summer solstices,
but records show that many other observations
were made there and at some 26 other Chinese
observatories of the time. Students can learn
more about the Henan tower, now known as the
Dengfeng Astro Observatory, at the Henan Museum website: http://www.hawh.cn/Template/home/
chnmuse/Exhibition/exhibition_show_astro_dengfeng.
jsp?mid=20060822232370
Ask students to compare the design of the
Henan observatory
June 21
with Tycho Brahe’s
observatory on Hven
(sample answer in
bold). The Henan December 21
observatory
had
special
mechanisms to ensure
geologic stability, because it was in a seismic zone.
Ask students to describe the geologic and atmospheric conditions that would be best if they
were choosing a site for an observatory today
(answer in bold). Observatories require clear
air, low light pollution, and a stable geology.
Have students pick one of the observatories
at the “American Observatory Webcams” website
(http://observatories.hodar.com/webcams.html) and
describe how the site is good for observations.
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S C I E N C E N O T E S F O R S T U D E N T S — C ha p ter 4 F eature
Taking Heaven’s
Measure
Science Notes for
Students
by Juliana Texley
Looking at Supernovas
Here are three observations of supernovas
from different parts of the world. Think about
and discuss how observers might differ and put
their own background into what they see. The
first two observations describe the supernova of
1054.
From Europe:
And at the very hour of [Pope Leo’s] passing there appeared in the heavens, not only in
Rome where his body lay, but indeed to men
throughout the whole world, an orb of extraordinary brilliance for the space of about half an
hour.—Tractatus de Ecclesia S. Petri Aldenburgensi (chronicle of the Church of St. Peter in Oudembourg, in present-day Belgium; see http://hal.
archives-ouvertes.fr/docs/00/04/25/93/PDF/pm.pdf)
From Kaifeng, China:
On the 1st year of the Chih-ho reign period,
7th month, 22nd day [August 27, 1054]...Yang
Wei-te said “I humbly observe that a guest star
has appeared. Above the star in question there
is a faint glow, yellow in colour. If one carefully
examines the prognostications concerning the
emperor, the interpretation is as follows: The
fact that the guest star does not trespass against
Pi and its brightness is full means that there is
a person of great worth. I beg that this be handed
over to the Bureau of Historiography.”—Sung
dynasty chronicles; see http://super.colorado.
edu/~astr1020/sung.html.
The third observation is from Shakespeare,
apparently describing a supernova he saw at
age 8 through Barnardo’s lines in Hamlet, Act 1,
Scene 1 (http://hubblesite.org/newscenter/archive/
releases/2004/34):
What we have two nights seen…
Last night of all,
When yond same star that’s westward from the pole
Had made his course to illume that part of
heaven
Where now it burns…
Online Activities:
As Clear as the Nose on Your Face
You can use the Internet to explore ancient
and modern observatories and see how different
observers might interpret the same skies. For
example, Tycho Brahe built a castle and observatory on Hven (see the illustration on page 52
of Newton at the Center), and you can observe
the Moon and share your data at “Tycho Brahe’s
Observatory,” an online cooperative project at
http://ciese2.org/curriculum/tycho/information(invit
ationtocollaborate).html.
Long before the Hven observatory was built,
the Chinese astronomer Guo Shoujing built a
“sky measuring tower” in Henan Province (latitude 35o north). The tower, built in about 1276
AD, looked like a pyramid sundial but also had
a long bar that cast a shadow. It was especially
valuable on the winter and summer solstices, but
records show that many other observations were
made there and at some 26 other Chinese observatories of the time. Learn more about the Henan
tower, now known as the Dengfeng Astro Observatory, at http://www.hawh.cn/Template/home/chnmuse/Exhibition/exhibition_show_astro_dengfeng.
jsp?mid=20060822232370.
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S C I E N C E N O T E S F O R S T U D E N T S — C ha p ter 4 F eature
June 21
December 21
Compare the design of the Henan observatory
with Tycho Brahe’s observatory on Hven. Describe the geologic and atmospheric conditions that would be best if you were choosing
a site for an observatory today:
Pick one of the observatories at the “American Observatory Webcams” website (http://
observatories.hodar.com/webcams.html) and describe how the site is good for observations.
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T E A C H E R — C ha p ter 9
“Moving the Sun
and the Earth”
Theme
“I do not feel obliged to believe that the
same God who has endowed us with sense,
reason and intellect has intended us to forgo
their use.”
Galileo
Italian scientist (1564 – 1642)
Goal
Students will understand how Galileo improved the telescope and used this instrument
to impress the Venetians and, by further proving
Aristotle wrong, upset church authorities.
Who?
Galileo — Italian scientist who improved the
telescope as a useful instrument to observe distant things on land and in the heavens
“If“Ifonly
Aristotle
could
be here.”
only Aristotle
could
be here.”
What?
Where?
magnify — to make something appear larger
and closer
Venice — the Italian city-state where Galileo
demonstrated his telescope
telescope — an instrument for magnifying and
viewing distant objects
University of Padua — university where Galileo received a lifetime appointment
colloquial — familiar, informal
undaunted — bold, courageous
Tuscany — Italian city-state where Galileo accepted a court appointment.
convex lens — a lens whose surface curves
outward on one or both sides, used to bend and
focus light rays
Groundwork
concave lens — a lens whose surface curves
inward on one or both sides, used to bend and
spread light rays apart
•Read chapter 9, “Moving the Sun and the
Earth” in The Story of Science: Newton at the
Center.
plano-concave or convex lens — a concave or
convex lens with one flat side
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T E A C H E R — C ha p ter 9
•Gather the following materials:
3) When students have finished reading and
recording, students from each cooperative
team who read the same passage form a
new group to discuss the passage, the information they recorded, and the main ideas
that their teammates need to know. Each
group appoints a discussion leader to call on
group members who raise hands and to be
sure that everyone contributes. As students
work, visit each group to answer questions
and to ensure that the discussion leader is
keeping the group on task and involving all
group members.
For each team of two students
small marshmallow or gumdrop
toothpick
pen
meterstick
masking-tape strip at least 60 cm long
flat table or desk surface at least 1 x 1 m
For the teacher
transparency masters
Professor Quest cartoon #12 (page 114)
Consider the Quotation
4) Students return to their original cooperative
teams to share the information from their
passages. Each student is responsible for listening and recording information about passages read by teammates. As students work,
visit each team to answer questions and to
ensure that students are sharing information
and taking notes to complete their individual
quest sheets.
1) Direct students’ attention to the quotation
by Galileo at the beginning of this section
under “Theme.” Ask students to paraphrase
this quotation. Write students’ versions on
chart paper or the chalkboard.
2) Ask students to relate this statement by Galileo to past discussions about rational and
empirical science. To prompt their thinking,
review the definitions of these terms.
You Be the Scientist
3) Tell students that in this lesson they will
learn how Galileo’s commitment to empirical science led to his significant contributions to scientific understanding.
1) Students turn to the quest sheet, Mad About
the Moon on page 120 in this supplement.
Students complete the quest sheet.
2) Explain to students that the crater Archimedes was formed after the lava flow that
formed the mare. It probably melted and rehardened the lava (basalt) rock. Crater Tycho
has clear lines of ejecta (splashes) that can
be traced. Where Tycho’s ejecta line crosses
over a crater, the crater is older than Tycho;
if the line is interrupted by the crater, the crater is younger. By this same logic, Tycho is
younger than Copernicus. A telescope could
see dynamic (active, changing) events so it
would be more accurate for observations.
Directed Reading/
Cooperative Team Learning
Read, record, and share information about
Galileo’s later life
1) Students turn to the quest sheet Read–Record–
Share, pages 116–119 in this supplement.
Each team member takes responsibility for
one of the four passages in chapter 9.
2) Students use the Who? What? Where? on
page 115 in this supplement to assist in their
reading. Students read their passages and
record information using the questions on
the corresponding quest sheet to guide their
reading and note taking.
Conclusion
1) Ask for volunteers to share the main ideas of
each of the passages in the chapter.
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T E A C H E R — C ha p ter 9
2) On the overhead projector, display Professor Quest cartoon #12. Ask students to relate the cartoon and the main ideas of each
passage to the theme of the lesson.
“Historical Developments in Chinese Calendar.” LunarCal. http://
www.lunarcal.org/History.html. Access date April 2009.
Mandel, Steve. Galaxy Images. http://www.galaxyimages.com/
astrophotographybystevemandel.html. Access date April 2009.
Quest Sheet Answers
Homework
Do You See What I See? (page 116)
Students imagine they were among the Venetian senators who climbed the church tower in
Venice to look through Galileo’s first telescope.
Students write a journal entry describing this experience and speculating what changes the telescope might bring about in the life of the city.
1) Galileo copied the Dutch viewing tube (telescope) and improved it by using one concave
lens and one convex lens so the image seen
appears upright.
2) They are amazed.
Curriculum Links
3) Venice depended on sea trade, and the telescope enabled people to see ships 55 kilometers (about 35 miles) away. They could
see if a ship was an enemy or friend.
Science link — Students use library and Internet
resources to research sunspots. In their journals
they answer these questions: What do the
sunspots prove? What do they disprove?
4) It could be used to judge the intentions of
sea traffic, to study sunspots, and to track
the movement of the planets and moons.
Science link — Students read “Jupiter’s SpaceTraveling Companions” on pages 102-103 in
The Story of Science: Newton at the Center and
use library and Internet resources to further research Jupiter’s moons. Some of Galileo’s contemporaries thought these were new planets.
In a journal entry, students answer these questions: Are they? How do you know?
5) Answers will vary.
Mooning over the Heavens (page 117)
1) He discovered the Moon has mountains and
valleys and is not a smooth disk.
Science link — Students read “Today’s Telescopes” on page 109 in The Story of Science:
Newton at the Center and scan newspapers, magazines, and the Internet news for reports about
NASA’s current explorations of outer space and
bring clippings to share with the class.
2) He realized that four moons orbit Jupiter.
3) He saw spots on the Sun moving across its
surface and believed the Sun rotates. The
Sun did not appear perfect as Aristotle
believed.
Multicultural link — From the fourth century B.C.E. to the beginning of the Common Era,
Chinese astronomers charted the heavens, accurately recorded the movements of the planets, and viewed sunspots. Students use library
and Internet resources to research the advanced
progress of Chinese astronomy and write reports in their journals.
4) He realized the Milky Way is made up of innumerable stars.
5) Answers will vary.
The Unmovable Galileo (page 118)
1) The position in Tuscany paid well, was prestigious, and enabled Galileo to write, study,
and experiment. But Tuscany was not as
open-minded about his ideas.
References
Hakim, Joy. 2005. The Story of Science: Newton at the Center.
Washington, DC: Smithsonian Books.
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T E A C H E R — C ha p ter 9
Reporting Home (page 123): A telescope could
see dynamic (active, changing) events so it
would be more accurate for observations.
2) If Aristotle or his followers looked through
Galileo’s telescope, they would realize the
Earth does revolve around the Sun.
3) He was a stubborn, self-confident (even arrogant) man; he knew he was right, and he
refused to back down.
4) Answers will vary.
Give Credit Where Credit Is Due (page 119)
1) Leonard Digges, the likely inventor of the telescope, took part in a plot to overthrow Queen
Mary and his property was confiscated.
2) Hans Lippershey’s apprentice showed his
boss that using two lenses, one in front of
the other, magnified faraway objects.
3) The Dutch ruling body decided it was so
easy to duplicate the instrument that there
was no point in awarding it a patent.
4) Galileo’s telescope was a tube of lead with
glass lenses at each end, one plano-convex and
the other plano-concave (near the eyepiece).
5) Answers will vary.
Mad about the Moon (page 120)
1) The craters were formed after the lava flow
that formed the mare, so they are younger.
They probably melted and re-hardened the
lava (basalt) rock.
2) The craters are indentations in the mare.
3) Crater Tycho has clear lines of ejecta (splashes) that can be traced. These show how a
meteorite impacted the Moon’s surface.
4) Where Tycho’s ejecta line crosses over a
crater, the crater is older than Tycho; if the
line is interrupted by the crater, the crater is
younger.
5) If an ejecta line crosses over a crater, that
crater is older than the crater that created
the ejecta lines. Tycho is younger than
Copernicus.
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T E A C H E R — C ha p ter 9
Unit ii — Lesson 6 — Chapter 9
Unit ii — Lesson 6 — Chapter 9
QUEST SHEET
QUEST SHEET
Read – Record – Share: Do You See What I See?
Read – Record – Share: The Unmovable Galileo
(Passage 1, chapter 9, “Moving the Sun and the Earth,” pages 98-100 to the end of the first full
paragraph on page 100 “… and he always seems to be broke.”)
(Passage 3, chapter 9, “Moving the Sun and the Earth,” page 104 from the first full paragraph,
“Galileo loves the acclaim…,” to the end of the chapter on page 105)
1) What Dutch invention did Galileo copy? How did he make it better?
1) Why did Galileo move to Florence in Tuscany? Explain why it was or was not a good move.
2) What did the Venetian senators think when Galileo showed them his invention?
2) Why did Galileo wish Aristotle, or at least his followers, could look through the telescope?
3) Why would Galileo’s invention prove especially valuable to Venice?
3) When Galileo realized that his discoveries made church leaders uncomfortable, how did he
respond?
4) Name three uses that Galileo found for his invention.
5) Use Who? What? and Where? terms to write one or two meaningful sentences that state the main
idea of this passage.
4) Use Who? What? and Where? terms to write one or two meaningful sentences that state the main
idea of this passage.
62
64
Unit ii — Lesson 6 — Chapter 9
Unit ii — Lesson 6 — Chapter 9
QUEST SHEET
You Be the Scientist
Read – Record – Share: Mooning over the Heavens
Mad about the Moon
(Passage 2, chapter 9, “Moving the Sun and the Earth,” page 100 from the second full paragraph,
“As a young man…,” to the top of page 104, skip the green pages on pages 102-103.)
You can learn a lot about the Moon by just looking—ask Galileo!
Your Quest:
Like Galileo, can you tell the story of a section of the Moon by carefully observing?
1) Describe what Galileo discovered about the Moon.
Your Gear:
While you could do these observations with a telescope, we’ll make it easy by giving you photographs of the lunar surface.
Your Routine:
Galileo thought the large circles on the surface of the Moon were seas. We know that the large,
smooth areas are hardened lava rock, but we still call them “mare” (Latin for “sea”). Here are several
other important landforms found on the Moon:
2) What did Galileo realize when he observed Jupiter through his telescope?
Impact crater — circular indentation created when something strikes the surface
Crater ejecta — material thrown out (ejected) from and deposited around an impact crater
Ray — bright streak or line of material ejected out of an impact crater
Lava flow — when underground magma breaks through to the surface
By examining the landforms of the moon, you can find clues about its geologic history. Remember
Archimedes, the Greek physicist and mathematician (287-212 B.C.E.)? He has a great crater
named after him. Marked “A” below, it’s at lunar latitude 29.7°, longitude -4°, and is about 82 km in
diameter.
3) What did Galileo discover about the Sun using his telescope that further disproved Aristotle’s
statements about the universe?
A = the crater Archimedes
B = the crater Aristillus
C = the mare
D = the crater Autolycus
1) Are these craters (A, B, and D) younger or older than the rock in the “sea (C)?” ______________
2) Why do you think so?
4) Describe a fourth discovery that Galileo made with his telescope.
Three Craters in a Lunar “Sea” (NASA photo)
5) Use Who? and What? terms to write one or two meaningful sentences that state the main idea of
this passage.
C
A
B
D
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66
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T E A C H E R — C ha p ter 9
Unit ii — Lesson 6 — Chapter 9
Unit ii — Lesson 6 — Chapter 9
QUEST SHEET
Crater Copernicus and Crater Tycho
Picture credit: Steve Mandel, who built an observatory in his backyard (Hidden Valley Observatory) took this photo.
Read – Record – Share: Give Credit Where Credit Is Due
(Passage 4, “Who Did Invent the Telescope?” pages 106-108)
1) Why does the likely true inventor of the telescope not receive credit for it? Who was he?
2) Who else contributed to the invention of the telescope and did not receive credit?
3) Why did the Dutch States-General refuse to grant a patent for the telescope?
4) Describe Galileo’s telescope.
5) The crater Copernicus, which is about 93 km in diameter, is at upper left. The crater Tycho is at
the lower right. Can you guess which is younger? Give reasons for your answer.
5) Use Who? What? terms to write one or two meaningful sentences that state the main idea of
this passage.
65
68
Unit ii — Lesson 6 — Chapter 9
Unit ii — Lesson 6 — Chapter 9
Reporting Home:
Here’s the crater Tycho (named after Tycho Brahe). Tycho is located in the lunar southern highlands at 43° south latitude and 11° west longitude. This crater is 85 km in diameter.
Crater Tycho (NASA photo)
Galileo wrote Johannes Kepler that those who refused to use a telescope were “…. afflicted with the
stubbornness of a mule.…” Why would a telescope be more scientifically useful than photographs
for these studies?
3) What features of this photo give you a clue as to how the crater was formed?
As you have seen, many Moon features are named after famous scientists. Others have more poetic
names, such as the Ocean of Storms. Research the names of various Moon features, see how many
names you recognize, and list them below. If you were to discover new features on the Moon, what
would you name them?
4) It’s certainly rough on the surface of the Moon. While there are fewer meteors hitting it now than
when the solar system was young, it’s battered and bumped. Find several other craters in the
photograph of Crater Tycho. Then use clues in the photo to predict if they are younger or older
than Tycho.
67
69
113
T E A C H E R — C ha p ter 9
#12
“If only Aristotle could be here.”
“If only Aristotle could be here.”
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S T U D E N T — C ha p ter 9
“Moving the Sun
and the Earth”
Theme
“I do not feel obliged to believe that the
same God who has endowed us with sense,
reason and intellect has intended us to forgo
their use.”
Galileo
Italian scientist (1564 – 1642)
Who?
Galileo — Italian scientist who improved the
telescope as a useful instrument to observe
distant things on land and in the heavens
What?
magnify — to make something appear larger
and closer
“If“Ifonly
Aristotle
could
be here.”
only Aristotle
could
be here.”
telescope — an instrument for magnifying and
viewing distant objects
colloquial — familiar, informal
University of Padua — university where Galileo received a lifetime appointment
undaunted — bold, courageous
convex lens — a lens whose surface curves
outward on one or both sides, used to bend and
focus light rays
Tuscany — Italian city-state where Galileo accepted a court appointment.
concave lens — a lens whose surface curves
inward on one or both sides, used to bend and
spread light rays apart
plano-concave or convex lens — a concave or
convex lens with one flat side
Where?
Venice — the Italian city-state where Galileo
demonstrated his telescope
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S T U D E N T — C ha p ter 9
QUEST SHEET
Read – Record – Share: Do You See What I See?
(Passage 1 in The Story of Science: Newton at the Center, chapter 9, “Moving the Sun and the
Earth,” pages 98-100 to the end of the first full paragraph on page 100 “… and he always seems to be
broke.”)
1) What Dutch invention did Galileo copy? How did he make it better?
2) What did the Venetian senators think when Galileo showed them his invention?
3) Why would Galileo’s invention prove especially valuable to Venice?
4) Name three uses that Galileo found for his invention.
5) Use Who? What? and Where? terms to write one or two meaningful sentences that state the main
idea of this passage.
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S T U D E N T — C ha p ter 9
QUEST SHEET
Read – Record – Share: Mooning over the Heavens
(Passage 2 in The Story of Science: Newton at the Center, chapter 9, “Moving the Sun and the
Earth,” page 100 from the second full paragraph, “As a young man…,” to the top of page 104, skip the
green pages on pages 102-103.)
1) Describe what Galileo discovered about the Moon.
2) What did Galileo realize when he observed Jupiter through his telescope?
3) What did Galileo discover about the Sun using his telescope that further disproved Aristotle’s
statements about the universe?
4) Describe a fourth discovery that Galileo made with his telescope.
5) Use Who? and What? terms to write one or two meaningful sentences that state the main idea of
this passage.
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S T U D E N T — C ha p ter 9
QUEST SHEET
Read – Record – Share: The Unmovable Galileo
(Passage 3 in The Story of Science: Newton at the Center, chapter 9, “Moving the Sun and the
Earth,” page 104 from the first full paragraph, “Galileo loves the acclaim…,” to the end of the chapter
on page 105)
1) Why did Galileo move to Florence in Tuscany? Explain why it was or was not a good move.
2) Why did Galileo wish Aristotle, or at least his followers, could look through the telescope?
3) When Galileo realized that his discoveries made church leaders uncomfortable, how did he
respond?
4) Use Who? What? and Where? terms to write one or two meaningful sentences that state the main
idea of this passage.
118
S T U D E N T — C ha p ter 9
QUEST SHEET
Read – Record – Share: Give Credit Where Credit Is Due
(Passage 4 in The Story of Science: Newton at the Center, “Who Did Invent the Telescope?” pages
106-108)
1) Why does the likely true inventor of the telescope not receive credit for it? Who was he?
2) Who else contributed to the invention of the telescope and did not receive credit?
3) Why did the Dutch States-General refuse to grant a patent for the telescope?
4) Describe Galileo’s telescope.
5) Use Who? What? terms to write one or two meaningful sentences that state the main idea of
this passage.
119
S T U D E N T — C ha p ter 9
You Be the Scientist
Mad about the Moon
You can learn a lot about the Moon by just looking—ask Galileo!
Your Quest:
Like Galileo, can you tell the story of a section of the Moon by carefully observing?
Your Gear:
While you could do these observations with a telescope, we’ll make it easy by giving you photographs of the lunar surface.
Your Routine:
Galileo thought the large circles on the surface of the Moon were seas. We know that the large,
smooth areas are hardened lava rock, but we still call them “mare” (Latin for “sea”). Here are several
other important landforms found on the Moon:
Impact crater — circular indentation created when something strikes the surface
Crater ejecta — material thrown out (ejected) from and deposited around an impact crater
Ray — bright streak or line of material ejected out of an impact crater
Lava flow — when underground magma breaks through to the surface
By examining the landforms of the Moon, you can find clues about its geologic history. Remember
Archimedes, the Greek physicist and mathematician (287-212 B.C.E.)? He has a great crater
named after him. Marked “A” below, it’s at lunar latitude 29.7°, longitude -4°, and is about 82 km in
diameter.
A = the crater Archimedes
B = the crater Aristillus
C = the mare
D = the crater Autolycus
1) Are these craters (A, B, and D) younger or older than the rock in the “sea (C)?” ______________
2) Why do you think so? Three Craters in a Lunar “Sea” (NASA photo)
C
B
A
D
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S T U D E N T — C ha p ter 9
Here’s the crater Tycho (named after Tycho Brahe). Tycho is located in the lunar southern highlands at 43° south latitude and 11° west longitude. This crater is 85 km in diameter.
Crater Tycho (NASA photo)
3) What features of this photo give you a clue as to how the crater was formed?
4) It’s certainly rough on the surface of the Moon. While there are fewer meteors hitting it now than
when the solar system was young, it’s battered and bumped. Find several other craters in the
photograph of Crater Tycho. Then use clues in the photo to predict if they are younger or older
than Tycho.
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S T U D E N T — C ha p ter 9
Crater Copernicus and Crater Tycho
Picture credit: Steve Mandel, who built an observatory in his backyard (Hidden Valley Observatory), took this photo.
5) The crater Copernicus, which is about 93 km in diameter, is at upper left. The crater Tycho is at
the lower right. Can you guess which is younger? Give reasons for your answer.
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S T U D E N T — C ha p ter 9
Reporting Home:
Galileo wrote Johannes Kepler that those who refused to use a telescope were “…. afflicted with the
stubbornness of a mule.…” Why would a telescope be more scientifically useful than photographs
for these studies?
As you have seen, many Moon features are named after famous scientists. Others have more poetic
names, such as the Ocean of Storms. Research the names of various Moon features, see how many
names you recognize, and list them below. If you were to discover new features on the Moon, what
would you name them?
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S C I E N C E N O T E S F O R T E A C H E R S — C ha p ter 9
“Moving the Sun
and the Earth”
Science Notes for
Teachers
by Juliana Texley
Teaching Tip for Electronic
Resources
Astronomy is a very important topic at the
middle elementary level, but you need to begin
with astronomical objects that students can see
and with skills that they can hone in a developmentally appropriate way. Today students can
access modern telescopes through the Internet,
but many of these instruments are computer enhanced so they don’t challenge students’ observational skills the way optical telescopes might.
The best place to start building those skills is by
studying Earth’s Moon.
Online Activities:
Getting Your Name in Lights
Galileo’s map of the Moon in 1609 wasn’t
the first. That honor goes to English mapmaker
Thomas Harriot. But Harriot’s work was never
published, so it did not become famous. Emphasize Galileo’s great
observational skills
by having students
visit Rice University’s
Galileo Project website, http://galileo.rice.
edu/sci/observations/
moon.html, as well
as the Linda Hall Li-
brary web page on Galileo at http://www.lindahall.
org/events_exhib/exhibit/exhibits/moon/p1.htm.
Ask students to identify and label lunar landmarks on Galileo’s map. They should be able to
see the outlines of the Sea of Rains and Sea of
Serenity clearly.
Ask students to compare Galileo’s map with
the NASA map shown here (or view it online
at
http://rst.gsfc.nasa.gov/Sect19/moonscan3.
jpg) and determine
which
landforms
are not accurately
scaled (sample answer in bold). (A
map that can be
enlarged for class
viewing is found at
http://nssdc.gsfc.nasa.
gov/planetary/lunar/
moon_landing_map.
jpg.) The crater
Ptolemaeus (Ptolemy) is a bit larger in Galileo’s sketch.
Next, have them look at the names on the
NASA map. Which names would Galileo know?
Which names honor people who lived after Galileo? (Sample answers in bold.) Eratosthenes,
Plato, and Archimedes were ancient philosophers. Galileo would also know who Copernicus and Kepler were. Burg and Franklin
lived after Galileo.
Stars or Moons?
Ask students to
look at Galileo’s diagram from 1610 of the
four largest moons of
Jupiter and label Ganymede, Callisto, Io, and
Europa.
Galileo realized they
were actually moons
only a few months before his famous book
was published. Ask stu-
124
Source: http://www2.jpl.
nasa.gov/galileo/ganymede/
manuscript1.jpg.
S C I E N C E N O T E S F O R T E A C H E R S — C ha p ter 9
dents to make a list of the reasons that Galileo
believed these were moons and not stars, including at least one that is not mentioned on page
102 of Newton at the Center (sample answer in
bold). Their movement is erratic, and they
sometimes move behind the planet.
Have students do research to answer the
following question: How many moons have we
identified around Jupiter today? Note that this
number changes periodically; at the time of writing the number was 63.
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S C I E N C E N O T E S F O R S T U D E N T S — C ha p ter 9
“Moving the Sun
and the Earth”
Science Notes for
Students
by Juliana Texley
Online Activities:
Getting Your Name in Lights
__________________________________________
__________________________________________
__________________________________________
__________________________________________
Now look at the names on the NASA map.
Which names would Galileo know? Which names
honor people who lived after Galileo?
__________________________________________
__________________________________________
__________________________________________
__________________________________________
__________________________________________
__________________________________________
Stars or Moons?
Galileo’s map of the Moon in 1609 wasn’t the
first. That honor goes
to English mapmaker
Thomas Harriot. But
Harriot’s work was
never published, so
it did not become famous. You can learn
more about Harriot’s
and Galileo’s observations at the Galileo Project website,
http://galileo.rice.edu/sci/observations/moon.html
and at http://www.lindahall.org/events_exhib/exhibit/
exhibits/moon/p1.htm. After visiting these websites,
identify and label the lunar landmarks you can
see on Galileo’s map.
Compare Galileo’s
map with the NASA
map shown here or at
http://nssdc.gsfc.nasa.
gov/planetary/lunar/
moon_landing_map.
jpg and determine
which landforms are
not accurately scaled.
__________________________________________
__________________________________________
Look at Galileo’s diagram from 1610 of the
four largest moons of
Jupiter and label Ganymede, Callisto, Io, and
Europa.
Galileo realized they
were actually moons
only a few months
before his famous book
was published. Make
a list of the reasons
Source: http://www2.jpl.
that Galileo believed
nasa.gov/galileo/ganymede/
these were moons and
manuscript1.jpg.
not stars, including at
least one that is not
mentioned on page 102 of The Story of Science:
Newton at the Center. __________________________________________
__________________________________________
__________________________________________
__________________________________________
__________________________________________
__________________________________________
How many moons have we identified around
Jupiter today? _____________________________
126
T E A C H E R — C ha p ter 1 3
“What’s the Big
Attraction?”
Theme
“I began to think of gravity extending to
the orb of the Moon . … [Then I] compared
the force requisite [necessary] to keep the
Moon in her Orb with the force of gravity at
the surface of the earth and found them answer pretty nearly.”
Isaac Newton
English scientist (1642 – 1727)
Goal
Students will appreciate the contributions of
Isaac Newton to astronomy, physics, and mathematics. Students will be introduced to the Law
of Universal Gravitation and in turn will better
understand the difference between mass and
weight.
“Lookout
out below!
below!” ”
“Look
Who?
Isaac Newton — English scientist who discovered the physics and mathematics of universal
gravity
gravitational force becomes ¼ as strong. When
distance quadruples, the force is 1/16 as strong.
weight — the force exerted on an object with
mass by gravity; can be computed by Newton’s
Law of Universal Gravitation
What?
mass — the quantity of matter in an object
Groundwork
universal gravity — the force of attraction between masses no matter what or where they are
in the universe; the force that keeps the Moon,
stars, and planets in their orbits and keeps our
feet on the ground
•Read chapter 13, “What’s the Big Attraction?”
in The Story of Science: Newton at the Center.
•Gather the transparency master for Professor
Quest cartoon #15 (page 131).
Law of Universal Gravitation — a mathematical law of physics discovered by Newton:
The greater the mass of an object, the greater
its attraction to another object. This attraction
(gravity) weakens over distance, by the square
of that distance. When distance doubles, the
Consider the Quotation
1) Direct students’ attention to the quotation
by Isaac Newton at the beginning of this
127
T E A C H E R — C ha p ter 1 3
Classwide Activity
section under “Theme.” Ask students for
their definitions of gravity. Ask students to
paraphrase this quotation to be sure they
understand its meaning. Write student
versions on chart paper or the chalkboard.
Illustrate the difference between mass
and weight using the Law of Universal
Gravitation
2) Tell students that Isaac Newton developed a
theory of gravity that revolutionized astronomy. He concluded that the fall of an apple
to the Earth and the orbit of the Moon about
the Earth are controlled by the same force.
1) Direct students to Mass? Weight? What’s the
Difference? on page 121 in this supplement.
As a class, work through the examples of the
difference between mass and weight using
Newton’s equation of the Law of Universal
Gravitation. Read the narrative out loud or
consider employing various student readers.
Directed Reading
Read to gain information about Newton’s
background, early life, and discovery of
universal gravity
Conclusion
1) On the overhead projector, display Professor Quest cartoon #15.
1) Students preview chapter 13 in The Story of
Science: Newton at the Center by looking
at illustrations, maps and sidebars. Help
students set goals for reading. Ask, “Have
you ever faced an obstacle or problem that
you thought was too hard?” Explain that the
scientist they will read about faced many
serious setbacks and yet is now considered,
arguably, the most influential scientist of all
time.
2) Ask students to relate the cartoon to the
theme of the lesson.
Homework
2) Students pair read chapter 13 in The Story of
Science: Newton at the Center. As students
read, they briefly list the obstacles Newton
faced in his early life.
In their journals, students respond to what
they have learned about Isaac Newton’s productive life in light of the obstacles he faced. What
do they think of this? Is it still possible for young
people today to overcome such obstacles to become successful adults? Can they think of contemporary examples?
3) Students share their lists of obstacles. Their
lists should include the following points.
Curriculum Links
•Premature birth
Language Arts link — Newton wrote letters
to John Locke, an important philosopher of his
day, and Samuel Pepys, who is famous for keeping a diary filled with gossip about his contemporaries. Read more about these men and samples
of their writings.
•Loss of father
•Most relatives illiterate
•Stepfather sent Isaac away
•Isaac’s anger at parents
Science link — Using library and Internet resources, students investigate further the differences in gravitational force among the planets
in our solar system and the influence of such
forces on weight. See especially Your Weight on
Other Worlds at http://www.exploratorium.edu/
ronh/weight/.
•Poor school performance
•Failed at managing farm
•Criminal conviction
•Didn’t have many friends
•College studies interrupted by plague
128
T E A C H E R — C ha p ter 1 3
Science link — Isaac Newton boarded with an
apothecary. Using library and Internet resources,
students research the history of apothecary.
Students create a poster illustrating what they
learn.
3)
Increase
Change to an Airplane
or
That Would Affect Its Weight Decrease
in Weight?
Art link — The paintings of Dutch artist Jan
Vermeer (1632–1675), a contemporary of Isaac
Newton, demonstrate his mastery of light and
color. Using Internet and library sources, students research Vermeer’s life and work.
Add payload (luggage, passen- Increase
gers, fuel). This would increase
the mass of the airplane, the numerator in the equation.
Subtract payload (luggage, pas- Decrease
sengers) or burn fuel. This would
decrease the mass of the airplane,
the numerator in the equation.
References
Davis, Kenneth C. 2001. Don’t Know Much about the Universe.
New York: HarperCollins.
Fly the airplane at the same mass Decrease
but at an altitude above the Earth.
This would increase the distance
from the center of the Earth, the
denominator in the equation.
Filson, Brent. 1986. “Isaac Newton (Light).” Famous Experiments
and How to Repeat Them. New York: Julian Messner.
Fowler, Michael. “ Isaac Newton.” University of Virginia Physics Department. http://galileoandeinstein.physics.virginia.edu/
lectures/newton.html. Access date April 2009.
Francis Thompson Quotes. Thinkexist.com. http://thinkexist.com/
quotation/all_things_by_immortal_power-near_and_far/187731.
html. Access date April 2009.
4) You are farther (and closer) from the center
of the Earth—“r” is changing in the denominator of the equation.
Gardner, Robert. 1990. “Isaac Newton.” Famous Experiments You
Can Do. New York: Franklin Watts.
Hakim, Joy. 2005. The Story of Science: Newton at the Center.
Washington, DC: Smithsonian Books.
5) The vehicle will weigh less on the Moon. In
fact, it will weigh about 1/6 of what it weighs
on Earth for the same mass. The Moon is a
smaller mass and its distance from center
to surface is smaller, too. One has to do the
math to determine the combined effects of
these two variables. It turns out the fraction: mass of Moon/(distance from surface
to center of Moon)2 is about one-sixth of the
same fraction on Earth. So, a 30,000 pound
lunar lander would weigh 5,000 pounds on
the Moon. Engineers must take this fact into
account in their design of the landing control system.
The Weight Equation. NASA Glenn Research Center. http://www.
grc.nasa.gov/WWW/K-12/airplane/wteq.html. Access date April
2009.
Weisstein, Eric. Wolfram’s World of Research. http://scienceworld.
wolfram.com/biography/Newton.html. Access date April 2009.
Your Weight on Other Worlds. Exploratorium, the Museum of Science, Art and Human Perception. http://www.exploratorium.
edu/ronh/weight/. Access date April 2009.
Quest Sheet Answers
Mass? Weight? What’s the Difference?
(page 134)
1) increase
6) If Jupiter were the same size as the Earth (r
the same), the spacecraft would weigh 318
times what it weighs on Earth. But Jupiter
has a radius eleven times that of the Earth,
so this size reduces the pull of its gravity by
112. Indeed, the spacecraft will weigh more
on Jupiter, but only about 2½ times the
amount.
2) decrease
129
T E A C H E R — C ha p ter 1 3
Unit iii — Lesson 2 — Chapter 13
Unit iii — Lesson 2 — Chapter 13
QueST SheeT
1) What happens when the numerator of a fraction increases? Does the value of the fraction increase
or decrease?
Mass? Weight? What’s the Difference?
Newton says there’s a big difference, and don’t you forget it! Again, it all has to do with gravity …
Mass and weight … some folks use these words interchangeably. But Newton would turn over in
his grave to hear it! They are related terms but different in an important way. Read on to find out.
2) What happens when the denominator of a fraction increases? Does the value of the fraction
increase or decrease?
Mass is the quantity of matter in an object, the amount of “stuff” it contains. Newton invented
the term so he could make a distinction between “stuff” (mass) and “stuff under the influence of a
gravitational force” (weight).
Weight is the force exerted on an object by gravity. We understand that the Earth pulls on us with
its gravity, keeping our feet on the floor and making balls fall down, not up. This pull, the force of
gravity, on our bodies is called our weight. So mass is independent of gravity, and weight depends on
mass and the gravitational force.
Now that we remember how fractions work, let’s consider what it means to be in Earth’s gravitational field in determining the weight of objects. Keep in mind Newton’s equation and how it can be
changed to affect weight.
Newton was able to be even more precise with the relationship between weight and mass.
Remember Newton’s big discovery (or one of them), the Law of Universal Gravitation?
F
=
The pull of
gravity between
two objects
G
a gravitational
constant
3) Consider an airplane, say a Boeing 767, weighing 10,000 pounds on the ground at Washington
Dulles Airport. Looking at Newton’s equation, list three different ways that the weight of this
airplane could be changed. Then for each way, indicate whether the weight would increase or
decrease with this change. In your thinking, consider both the numerator and the denominator
of the fraction in Newton’s Law of Universal Gravitation.
mass of object 1 x mass of object 2
x
r2
(the distance between the two objects) 2
Change to an Airplane
That Would Affect Its Weight
OR
Weight
of object
=
a gravitational
constant
x
mass of the Earth x mass of object
Increase or Decrease in Weight?
(distance of object to center of Earth) 2
This mathematical law actually defines the relationship between your (or any object’s) mass and
weight. It says that the force on a mass due to Earth’s gravity, the weight, is equal to a special constant multiplied by the mass of the Earth times the mass of the object divided by the distance from
the center of the Earth to the object squared.
Hmmm … notice that certain quantities in this equation are changeable and certain ones are
not. G, the gravitational constant, doesn’t change anywhere in the universe and the mass of the
Earth is very stable. But what about the other quantities—the mass of the object and distance of the
object from the center of the Earth—do these quantities change? And if they do, what effect do they
have on the weight of the object? Consider the fraction in Newton’s equation when answering these
questions.
The distance to the center of the Earth from its surface is about 4,000 miles. If an airplane is flying at
an altitude of 35,000 feet (about 7 miles above the Earth), its distance from Earth’s center is now 4,007
miles, a quantity made squared in the denominator of the fraction in Newton’s equation. The change in
altitude alone will then decrease the weight of the airplane, apart from any change in its mass (such as
burning fuel). This 10,000-pound airplane on the ground at Dulles would weight only 9,965 pounds at
35,000 feet; it has lost 35 pounds just by being farther from the center of the Earth.
4) Do you know that you weigh a tiny bit less at the top of a mountain and a tiny bit more in a valley?
Why would this be?
75
76
Unit iii — Lesson 2 — Chapter 13
We learned that Newton’s Law of Universal Gravitation is universal. That is, it applies everywhere
to any two objects: the airplane and the Earth; the Earth and the Moon; the Sun and the Earth. Let’s
consider NASA’s newest lunar lander, now in design as a part of the Constellation Project and due to
return to the Moon around 2020. If this spacecraft weighs 30,000 pounds on the launchpad at NASA
Kennedy Space Center, how much will it weigh when it lands on the Moon (we’ll ignore mass changes in the vehicle)? Note that when it is close to the Moon, the dominant force will be the Moon’s (not
the Earth’s) gravity, so Newton’s equation will contain the Moon’s mass and the distance from the
Moon’s center.
5) You make your prediction — will the lunar lander weigh more or less on the Moon? Why?
6) What if the same spacecraft were built to land on the largest of the planets in the solar system:
Jupiter. Jupiter has 318 times more mass than Earth. Would that mean that the spacecraft weighs
318 times more than it weighs on Earth when in Jupiter’s gravitational field? Why or why not?
What else does weight depend upon?
By Newton’s Law of Universal Gravitation, it is clear that every object in the universe influences
every other object, even if that influence is so small as to be imperceptible. For example, even poor
demoted-planet Pluto exerts an infinitesimally small gravitational force on you! And you can calculate
the amount of that force from Newton’s equation. Of course, the force of Pluto’s gravity is not enough
to change your life in any way, but it is never zero no matter how far away you are. Perhaps Francis
Thompson (English poet and writer, 1859-1907) was pondering this fact when he wrote his poem:
All things by immortal power,
Near and far
Hiddenly
To each other linked are,
That thou canst not stir a flower
Without troubling of a star.
Mass (“stuff”) and weight (force due to gravity) … weight and mass … you’ll never confuse them
again. Newton would be proud.
77
130
T E A C H E R — C ha p ter 1 3
#15
“Look out below!”
“Look out below!”
131
S T U D E N T — C ha p ter 1 3
“What’s the Big
Attraction?”
Theme
“I began to think of gravity extending to
the orb of the Moon . … [Then I] compared
the force requisite [necessary] to keep the
Moon in her Orb with the force of gravity at
the surface of the earth and found them answer pretty nearly.”
Isaac Newton
English scientist (1642 – 1727)
Who?
Isaac Newton — English scientist who discovered the physics and mathematics of universal
gravity
What?
mass — the quantity of matter in an object
“Lookout
out below!”
“Look
below!”
universal gravity — the force of attraction between masses no matter what or where they are
in the universe; the force that keeps the Moon,
stars, and planets in their orbits and keeps our
feet on the ground
Law of Universal Gravitation — a mathematical law of physics discovered by Newton:
The greater the mass of an object, the greater
its attraction to another object. This attraction
(gravity) weakens over distance, by the square
of that distance. When distance doubles, the
gravitational force becomes ¼ as strong. When
distance quadruples, the force is 1/16 as strong.
weight — the force exerted on an object with
mass by gravity; can be computed by Newton’s
Law of Universal Gravitation
132
S T U D E N T — C ha p ter 1 3
Quest Sheet
Mass? Weight? What’s the Difference?
Newton says there’s a big difference, and don’t you forget it! Again, it all has to do with gravity …
Mass and weight … some folks use these words interchangeably. But Newton would turn over in
his grave to hear it! They are related terms but different in an important way. Read on to find out.
Mass is the quantity of matter in an object, the amount of “stuff” it contains. Newton invented
the term so he could make a distinction between “stuff” (mass) and “stuff under the influence of a
gravitational force” (weight).
Weight is the force exerted on an object by gravity. We understand that the Earth pulls on us with
its gravity, keeping our feet on the floor and making balls fall down, not up. This pull, the force of
gravity, on our bodies is called our weight. So mass is independent of gravity, and weight depends on
mass and the gravitational force.
Newton was able to be even more precise with the relationship between weight and mass.
Remember Newton’s big discovery (or one of them), the Law of Universal Gravitation?
F
=
The pull of
gravity between
two objects
G
a gravitational
constant
mass of object 1 x mass of object 2
x
r2
(the distance between the two objects) 2
OR
Weight
of object
=
a gravitational
constant
x
mass of the Earth x mass of object
(distance of object to center of Earth) 2
This mathematical law actually defines the relationship between your (or any object’s) mass and
weight. It says that the force on a mass due to Earth’s gravity, the weight, is equal to a special constant multiplied by the mass of the Earth times the mass of the object divided by the distance from
the center of the Earth to the object squared.
Hmmm … notice that certain quantities in this equation are changeable and certain ones are
not. G, the gravitational constant, doesn’t change anywhere in the universe and the mass of the
Earth is very stable. But what about the other quantities—the mass of the object and distance of the
object from the center of the Earth—do these quantities change? And if they do, what effect do they
have on the weight of the object? Consider the fraction in Newton’s equation when answering these
questions.
133
S T U D E N T — C ha p ter 1 3
1) What happens when the numerator of a fraction increases? Does the value of the fraction increase
or decrease?
2) What happens when the denominator of a fraction increases? Does the value of the fraction
increase or decrease?
Now that we remember how fractions work, let’s consider what it means to be in Earth’s gravitational field in determining the weight of objects. Keep in mind Newton’s equation and how it can be
changed to affect weight.
3) Consider an airplane, say a Boeing 767, weighing 10,000 pounds on the ground at Washington
Dulles Airport. Looking at Newton’s equation, list three different ways that the weight of this
airplane could be changed. Then for each way, indicate whether the weight would increase or
decrease with this change. In your thinking, consider both the numerator and the denominator
of the fraction in Newton’s Law of Universal Gravitation.
Change to an Airplane
That Would Affect Its Weight
Increase or Decrease in Weight?
The distance to the center of the Earth from its surface is about 4,000 miles. If an airplane is flying at
an altitude of 35,000 feet (about 7 miles above the Earth), its distance from Earth’s center is now 4,007
miles, a quantity made squared in the denominator of the fraction in Newton’s equation. The change in
altitude alone will then decrease the weight of the airplane, apart from any change in its mass (such as
burning fuel). This 10,000-pound airplane on the ground at Dulles would weight only 9,965 pounds at
35,000 feet; it has lost 35 pounds just by being farther from the center of the Earth.
4) Do you know that you weigh a tiny bit less at the top of a mountain and a tiny bit more in a valley?
Why would this be?
134
S T U D E N T — C ha p ter 1 3
We learned that Newton’s Law of Universal Gravitation is universal. That is, it applies everywhere
to any two objects: the airplane and the Earth; the Earth and the Moon; the Sun and the Earth. Let’s
consider NASA’s newest lunar lander, now in design as a part of the Constellation Project and due to
return to the Moon around 2020. If this spacecraft weighs 30,000 pounds on the launchpad at NASA
Kennedy Space Center, how much will it weigh when it lands on the Moon (we’ll ignore mass changes in the vehicle)? Note that when it is close to the Moon, the dominant force will be the Moon’s (not
the Earth’s) gravity, so Newton’s equation will contain the Moon’s mass and the distance from the
Moon’s center.
5) You make your prediction — will the lunar lander weigh more or less on the Moon? Why?
6) What if the same spacecraft were built to land on the largest of the planets in the solar system:
Jupiter. Jupiter has 318 times more mass than Earth. Would that mean that the spacecraft weighs
318 times more than it weighs on Earth when in Jupiter’s gravitational field? Why or why not?
What else does weight depend upon?
By Newton’s Law of Universal Gravitation, it is clear that every object in the universe influences
every other object, even if that influence is so small as to be imperceptible. For example, even poor
demoted-planet Pluto exerts an infinitesimally small gravitational force on you! And you can calculate
the amount of that force from Newton’s equation. Of course, the force of Pluto’s gravity is not enough
to change your life in any way, but it is never zero no matter how far away you are. Perhaps Francis
Thompson (English poet and writer, 1859-1907) was pondering this fact when he wrote his poem:
All things by immortal power,
Near and far
Hiddenly
To each other linked are,
That thou canst not stir a flower
Without troubling of a star.
Mass (“stuff”) and weight (force due to gravity) … weight and mass … you’ll never confuse them
again. Newton would be proud.
135
S C I E N C E N O T E S F O R T E A C H E R S — C ha p ter 1 3
“What’s the Big
Attraction?”
Science Notes for
Teachers
Closer and Closer
Show students a small egg and ask them to
estimate the volume. Most will realize that it’s a
complex problem.
Next, ask students to imagine how they could
estimate the volume of the egg by calculating the
sum of simpler objects; the egg could be approximated by five cylinders.
Volume = ∑ volumes of each cylinder (area
of base × height)
by Juliana Texley
(V = ∏2h where r = radius of cylinder and h
is the height or length of cylinder)
Teaching Tip for Electronics
Resources
The word calculus is often associated with
very complex and unreachable mathematics. This
is an ideal time for students to build confidence
in their ability to master new math skills and understand their usefulness. In the course of many
discussions of real-world problems, teachers can
reinforce this idea by asking students what math
tool they might use to solve the problems. The resources for this chapter include a demonstration
to illustrate the most basic principle of calculus
(the idea of a limit) and an opportunity to access
a number of NSTA’s Science Objects directly to
simulate the phenomena that Newton described
with this tool.
Using Math Tools:
Ask students to imagine what would happen if they calculated 10 cylinders, or 15. They
should realize that each time they increase the
number of cylinders, the approximation will get
closer to the real volume of the egg. The greater
the number of slices (N), the smaller the difference between the real volume of the egg and the
approximation.
Poultry scientists use the formula ∏lh2/6,
where l = long axis and h = short axis, to calculate the volume of an egg. Another way might be
to empty the egg and fill it with water.
The “thought exercise” of estimating the volume of an egg illustrates one of the first concepts
that calculus students explore, that of limits.
Students can build confidence in their ability to
understand this important mathematical tool by
analyzing these problems:
1. Imagine you had a thin sheet of gold leaf, and
cut it in half, then half again, then half again,
then half again... (You have very special tools
so you can continue to cut the sheet again and
again.) Describe the smallest size the sheet
could get (answer in bold). If students continue to imagine tinier and tinier tools,
they will realize that the piece would approach zero but never really get there.
2. A long-distance walker has a practice of
taking one step forward, and then one step
backward exactly half as long as the forward
step. He sets a target of going exactly 100 ki-
136
S C I E N C E N O T E S F O R T E A C H E R S — C ha p ter 1 3
lometers. Will he ever get there? (Answer in
bold). If the backward step is always the
last step, no.
Online Activities:
Function Machines
A function is a mathematical operation—
something you do to any number. It’s often compared to a “number machine” and expressed
as an equation. Explore functions more fully at
these function machine websites:
• Force and Motion: Newton’s Third Law:
http://learningcenter.nsta.org/product_detail.aspx?id=10.2505/7/SCB-FM.4.1
Newton’s most important idea became the
basis for our understanding of universal gravitation. The story that Newton developed this law
after an apple fell on his head is probably a myth;
it actually took many sorts of observations to
come to that conclusion. But once students understand how masses attract one another, they
can do amazing things—like put a satellite into
orbit using this simulation: http://www.lon-capa.
org/~mmp/kap7/orbiter/orbit.htm.
• http://teams.lacoe.edu/documentation/
classrooms/amy/algebra/3-4/activities/
functionmachine/functionmachine3_4.
html (TEAMS Educational Resources)
• h t t p : / / n l v m . u s u . e d u / e n / n a v / f r a m e s _
asid_191_g_4_t_2.html (Utah State University)
It’s the Law!
Scientists use the term law to describe a
principle that they’ve established from many
experiments and that can be used to make new
predictions. Laws are often expressed in mathematical terms. An idea cannot become a law unless it has been verified in many ways.
In each of the following online modules students can explore Newton’s laws in simulations,
get ideas for experiments, and make their own
predictions. The modules are free from NSTA.
• Force and Motion: Newton’s First Law: http://
learningcenter.nsta.org/product_detail.
aspx?id=10.2505/7/SCB-FM.2.1
• Newton’s Force and Motion: Position and
Motion: http://learningcenter.nsta.org/product_
detail.aspx?id=10.2505/7/SCB-FM.1.1
137
S C I E N C E N O T E S F O R S T U D E N T S — C ha p ter 1 3
“What’s the Big
Attraction?”
Science Notes for
Students
by Juliana Texley
But, of course, that’s not exactly it. The spaces
near the corners of each cylinder are missing.
Next, imagine what would happen if you
calculated 10 cylinders, or 15. Each time you
increased the number of cylinders, the approximation would get closer to the real volume of
the egg. The greater the number of slices (N), the
smaller the difference between the real volume
of the egg and the approximation. We say that
the limit of this process of dividing again and
again is the real volume of the egg!
The limit is one mathematical idea that Isaac
Newton used in the development of the mathematical process we call calculus. Here are two
more problems to help you understand the concept of limits:
Using Math Tools:
Closer and Closer
1. Imagine you had a thin sheet of gold leaf,
and cut it in half, then half again, then half
again, then half again... (You have very
special tools so you can continue to cut the
sheet again and again.) Describe the smallest size the sheet could get.
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
Calculating the volume of an egg is quite difficult. Here’s a way that you can approximate the
volume of an egg using simple math tools:
Instead of drawing an egg, draw five disks
with total height equaling the height of the egg.
The middle disk should be the width of the egg.
Now you can approximate the volume of the
egg by calculating the volume of five disks, or
cylinders:
Volume = ∑ volumes of each cylinder (area
of base × height)
(V = ∏r2h where r = radius of cylinder and h
is the height or length of cylinder)
2. A long distance walker has a practice of
taking one step forward, and then one step
backward exactly half as long as the forward step. He sets a target of going exactly
100 kilometers. Will he ever get there?
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
Each of these situations involves a mathematical process (dividing, or moving forward, then
back). A mathematical process with specific
rules is called a function; the process does the
138
S C I E N C E N O T E S F O R S T U D E N T S — C ha p ter 1 3
same thing to any number (an X) that you enter
into the function.
Online Activities:
Function Machines
law after an apple fell on his head is probably
a myth; it actually took many sorts of observations to come to that conclusion. But once you
understand how masses attract one another, you
can do amazing things—like put a satellite into
orbit using this simulation: http://www.lon-capa.
org/~mmp/kap7/orbiter/orbit.htm. Try it!
Explore functions more fully at these function machine websites:
• http://teams.lacoe.edu/documentation/
classrooms/amy/algebra/3-4/activities/
functionmachine/functionmachine3_4.
html
• h t t p : / / n l v m . u s u . e d u / e n / n a v / f r a m e s _
asid_191_g_4_t_2.html
It’s the Law!
Scientists use the term law to describe a
principle that they’ve established from many
experiments and that can be used to make new
predictions. Laws are often expressed in mathematical terms. An idea cannot become a law unless it has been verified in many ways.
In each of the following online modules you
can explore Newton’s laws in simulations, get
ideas for experiments, and make your own predictions.
• Force and Motion: Newton’s First Law: http://
learningcenter.nsta.org/product_detail.
aspx?id=10.2505/7/SCB-FM.2.1
• Newton’s Force and Motion: Position and
Motion:
http://learningcenter.nsta.org/
product_detail.aspx?id=10.2505/7/SCBFM.1.1
• Force and Motion: Newton’s Third Law:
http://learningcenter.nsta.org/product_
detail.aspx?id=10.2505/7/SCB-FM.4.1
Newton’s most important idea became the
basis for our understanding of universal gravitation. The story that Newton developed this
139