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Size And ScaleSize-And-Scale

  • Subject:
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  • Grade(s): 9-12
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  • Duration: One class period

Lesson Plan Sections


Students will understand the following:
1. The relative sizes of bodies in our solar system affect life on Earth.
2. Using mathematical proportions, we can create scale models of parts of our solar system.
3. Making a scale model of the entire solar system is problematic because the distances in space are so great that even a very small scale model would be too large to be practical.


The entire class will require research materials on the solar system, in addition to a computer with Internet access to aid their research. The following materials should be distributed to each group:
Modeling clay


1. Tell your students that during Apollo missions to the moon in the 1960s and '70s, astronauts placed a mirror on the surface of the moon so that precise Earth-to-moon distances could be measured. By reflecting a laser beam from Earth off the mirror, researchers on Earth could observe the beam's round trip time, and the distance to the moon could be calculated to within a centimeter. Now your students will use those measurements to create their own scale models of the Earth-moon system.
2. Divide your class into groups, distributing materials to each group. Either have students obtain the following information through research or provide the information for them: the diameter of the moon is 3,476 kilometers, the diameter of Earth is 12,734 kilometers, and the average distance of Earth from the moon (it changes slightly over time) is 384,000 kilometers.
3. Explain that the marble will represent the moon. Then challenge groups to come up with a method for (a) using the materials they have and the information they have obtained or been given to determine how large to make a model of Earth, using the modeling clay, and (b) using the same materials and information to determine how far to place the model moon from the model Earth to create a scale model of the Earth-moon system.
4. Students should come up with the following methods:
(a) Use the string to measure the circumference of the marble; measure the string; use the equation C =pD to obtain the diameter of the marble; use the actual diameters of the moon and Earth to obtain a scale; apply that scale to the diameter of the marble to arrive at the diameter of the clay model of Earth.
(b) Apply the same scale to the actual average distance of Earth from the moon to obtain the distance to use in the model of the Earth-moon system.
5. Allow time for students to create their scale models of the Earth-moon system.
6. When the groups have completed their models, discuss, as a class, how the distance between the moon and Earth affects life on Earth. (One example is that a slight change in the moon's proximity can greatly affect Earth's tides.)
7. Discuss why it is so difficult to create an entire solar system model that takes into account the sizes of the planets, their distances from the sun, and their distances from each other.

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Younger students will need help figuring out how to determine the size of the clay Earth model and the model Earth-to-moon distance.

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Discussion Questions

1. Hypothesize as to why you think the ostrich, which is a bird, is not able to fly. What other flightless birds, living or extinct, have similar physiology?
2. Debate whether a bumblebee or a hawk would fly the fastest. Under what conditions would each be the better flier?
3. Explain why, when relative proportions are considered, humans are stronger than elephants, and ants are stronger than humans.
4. Discuss the reasons why a smaller, shorter athlete might have to work harder than his or her larger peers to succeed. Now, discuss the reasons why this athlete might not have to work as hard at the same sport as the larger peers.
5. Like the home you live in, a skyscraper is a place where people live and work. Describe all the systems that must be included in a skyscraper to make it a livable workspace. How are these systems different in a skyscraper as compared with a conventional building?
6. What are the advantages and disadvantages to building very tall structures? Do the physical and social costs of skyscrapers outweigh the benefits? State your reasoning.
7. On the scale of the solar system, debate the significance of planet Earth.
8. To see Peoria's solar system model all at once, you'd need to be in an airplane. How much of the real solar system is visible at one time from your location? Describe the factors that influence how much of it you can see at any given time.

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You can evaluate groups on their models using the following three-point rubric:
Three points: groups develop successful plans for determining scale, size, and distance; model accurately constructed to scale
Two points: groups need help developing plans for determining scale, size, and distance; model accurately constructed to scale
One point: group unable to develop plan for determining scale, size, and distance; model inaccurately constructed

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Scale of Flight
Monarch butterflies are known for the great distances of their migration flights. How do these tiny, lightweight fliers succeed? Divide the class into groups of three students. Have each student outline on notebook paper and cut out a shape approximating that of a monarch butterfly with its wings spread. Instruct students to tape an open paper clip in the center to represent the body weight. Each student per group will do one of three experiments (repeating it five times) as the data is captured on a group record sheet. These trials include (1) dropping the butterfly from shoulder height, (2) dropping the butterfly from shoulder height while standing in front of a fan, and (3) dropping a wet (splashed with water) "butterfly" from shoulder height.
The height from which the “b;tterfly" is dropped should be accurately measured and recorded. Data from each group should be averaged and added to a class data set posted on the board. Have students graph the experimental results, and then have a class discussion about what the data tell us about butterfly flight. What factors other than wing beating could affect butterfly flight?

Being the Right Size
Divide students into groups of four and give each student a different-sized and different-colored lump of modeling clay. Each student is to create a freestanding, four-legged animal from the clay only. Students are challenged to have their animals display realistic body proportions and to make them as tall as possible without falling over. At the completion of animal construction, each group should summarize for the class its conclusions about designing the "right-sized" animal.

Using the Internet, CD-ROMs, and traditional library resources, have students research the design and construction of a famous high-rise structure. A list of skyscraper projects, completed and under construction, can be found atInformation Please. Have students present their findings to the class by relaying information on the height, time to complete, amounts of materials, and overall cost of the skyscraper project. Presentations can include visual models, drawings, PowerPoint presentations, Web pages, or trifold (cardboard) representations of students' findings. Students can form cooperative groups to conduct research and present information.

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Suggested Readings

Bugs of the World
George C. McGavin. Facts on File, 1993.
Did you know that bugs form a distinct order among insects and represent over 80,000 species found throughout the world? Reading this book will help you learn how to collect and classify bugs and also gives you information about their structure, diseases, enemies, defenses, food, mating, and interaction with people, which can be harmful, helpful, or benign.

The Science Times Book of Birds
Nicholas Wade, ed. Lyons Press, 1997.
Read the fascinating columns that have appeared in The New York Times' Science Times section written by award-winning journalists about birds around the world. Did you know that some birds measure the health of their mate by the symmetry of their tails and that not all birds mate for life?

Diatoms to Dinosaurs: The Size and Scale of Living Things
Chris McGowan. Island Press/Shearwater Books, 1994.
This is a wonderful book about evolution and mechanisms of organisms. Of course, you already know what a dinosaur is, but do you know what a diatom is? Read this book and find out! (Dictionary definition: numerous microscopic, single-celled marine or freshwater algae).

Cats' Paws and Catapults: Mechanical Worlds of Nature and People
Steven Vogel. W.W. Norton & Co., 1998.
Explore and compare the fascinating world of biomechanics: nature's mechanical aspects in animals and in people. Read how living things work, walk, run, jump, fly, and grow and how size affects mechanics.

Skyscrapers: Form & Function
David Bennett. Simon & Schuster, 1995.
The beautiful photography in this book complements the text, which provides the history of skyscrapers around the world, tells of the creativity and engineering that helped erect them, and offers a look at "a day in the life" of a skyscraper.

Neil Stevenson. DK Publishing, 1997.
This beautifully illustrated book looks at the history of buildings around the world and how they reflect the societies that created them. The author believes that buildings reflect human nature, ingenuity, and the collaborative efforts used to build them.

The Whole Shebang: A State-of-the-Universe(s) Report
Timothy Ferris. Simon & Schuster, 1997.
This book summarizes what we currently know about the universe but it also speculates about what we might know about the future. This is the field of cosmology, the study of the structure and history of the universe.

Astronomy: A Beginner's Guide to the Universe
Eric Chaisson and Steve McMillan. Prentice Hall, 1995.
This book provides descriptions about all aspects of astronomy. Want easy access to any topic on the universe? This is a great book to help you explore. Try answering the questions in the back of the book.

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Petronas Twin Towers
Information and facts on the soon-to-be world's largest building, to be located in Malaysia.

Journey of a Lifetime: Magnificent Skyscrapers
An overview of the tallest buildings in the world with an Architectural Hall of Fame and interesting details about skyscrapers.

New York Sky Scrapers
Facts and figures dedicated to the New York's most famous skyscrapers are the essence of this site.

An Overview of the Solar System
A good overview of the Solar System that relates to the scale and magnitude of the system.

Size and Scale Activity
An activity for students that explains the scale of the solar system.

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Click on any of the vocabulary words below to hear them pronounced and used in a sentence.

speaker    lift
Definition: An upward force that opposes the pull of gravity.
Context: Rockets could not go up without the energy and upward force of lift.

speaker    pectoralis muscles
Definition: Moving tissues that connect the ventral walls of the chest with the bones of the upper arm and shoulder.
Context: He wore an armor breastplate to protect his pectoralis muscles during battle.

speaker    physiology
Definition: A branch of biology that deals with the functions and activities of life or of living matter (as organs, tissues, or cells) and of the physical and chemical phenomena involved.
Context: Physiology is anatomy at work.

speaker    vortices
Definition: Whirlpools or eddies in a fluid such as wind.
Context: The thistle down spun in a circle in midair as it was caught by the wind's vortices.

speaker    gravity
Definition: A fundamental physical force that is responsible for interactions that occur because of mass between objects.
Context: The force of gravity made it hard to lift the heavy box and easy to drop it.

speaker    proportion
Definition: A ratio—the relation of one part to another or to a whole.
Context: A high proportion of his wages was used to pay rent while a small proportion was used to buy food.

speaker    volume
Definition: The amount of space occupied by a three-dimensional object as measured in cubic units.
Context: The volume of the crowd was too great to fit any more people inside the room.

speaker    conduits
Definition: Pipes, tubes, or tiles that are part of a building's design used for protecting electric wires or cables, plumbing, or other aspects of building construction.
Context: The systems engineer designs all the conduits take make the building a place where people can live and work, such as plumbing, water, and air conditioning.

speaker    ingenuity
Definition: Having great skill at solving problems or inventing things.
Context: Skyscrapers have come to symbolize the ingenuity and excesses of our modern technological culture.

speaker    astronomical unit (AU)
Definition: The average distance of separation between the sun and Earth.
Context: One astronomical unit is equal to 93 million miles. It takes light a little over eight minutes to travel this distance.

speaker    Light year (ly)
Definition: The distance light travels in one year; equivalent to approximately 5.87 trillion miles.
Context: Light travels at 186,000 miles per second. Multiply this speed by the number of seconds in a minute, times the number of minutes in an hour, times the number of hours in a day, times the number of days in a year. The result is roughly 6 trillion miles. That distance is what astronomers call a light year.

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This lesson plan may be used to address the academic standards listed below. These standards are drawn from Content Knowledge: A Compendium of Standards and Benchmarks for K-12 Education: 2nd Edition and have been provided courtesy of theMid-continent Research for Education and Learningin Aurora, Colorado.
Grade level: 6-8, 9-12
Subject area: science
Understands motion and the principles that explain it.
(6-8)Understands effects of balanced and unbalanced forces on an object's motion (e.g., if more than one force acts on an object along a straight line, then the forces will reinforce or cancel one another, depending on their direction and magnitude; unbalanced forces such as friction will cause changes in the speed or direction of an object's motion).

(9-12)Knows that laws of motion can be used to determine the effects of forces on the motion of objects (e.g., objects change their motion only when a net force is applied; whenever one object exerts force on another, a force equal in magnitude and opposite in direction is exerted on the first object; the magnitude of the change in motion can be calculated using the relationship F=ma, which is independent of the nature of the force).

Grade level: 6-8, 9-12
Subject area: science
Understands the scientific enterprise.
(6-8)Knows that the work of science requires a variety of human abilities, qualities, and habits of mind (e.g., reasoning, insight, energy, skill, creativity, intellectual honesty, tolerance of ambiguity, skepticism, openness to new ideas).

(9-12)Understands that science involves different types of work in many different disciplines (e.g., scientists in different disciplines ask different questions, use different methods of investigation, and accept different types of evidence to support their explanations; many scientific investigations require the contributions of individuals from different disciplines; new disciplines of science, such as geophysics and biochemistry, often emerge at the interface of older disciplines).

Grade level: 6-8, 9-12
Subject area: science
Understands the nature of scientific knowledge.
(6-8)Knows that all scientific ideas are tentative and subject to change and improvement in principle, but for most core ideas in science, there is much experimental and observational confirmation.

(9-12)Understands how scientific knowledge changes and accumulates over time (e.g., all scientific knowledge is subject to change as new evidence becomes available; some scientific ideas are incomplete and opportunity exists in these areas for new advances; theories are continually tested, revised, and occasionally discarded).

Grade level: 6-8, 9-12
Subject area: technology
Understands the nature of technological design.
(6-8)Identifies appropriate problems for technological design (e.g., identifies a specific need, considers its various aspects, considers criteria for a suitable product).

(9-12)Designs a solution or product, taking into account needs and constraints (e.g., cost, time, trade-offs, properties of materials, safety, aesthetics).

Grade level: 6-8
Subject area: space science
Understands essential ideas about the composition and structure of the universe and the Earth's place in it.
Knows characteristics and movement patterns of the nine planets in our solar system (e.g., planets differ in size, composition, and surface features; planets move around the sun in elliptical orbits; some planets have moons, rings of particles, and other satellites orbiting them).

Grade level: 6-8
Subject area: math
Understands and applies basic and advanced properties of the concepts of measurement.
Solves problems involving units of measurement and converts answers to a larger or smaller unit within the same system (i.e., standard or metric).

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