Curriculum Overview Sample Lessons - Oak Meadowoakmeadow.com/wp-content/uploads/2014/06/8_overview.pdf · Curriculum Overview Sample Lessons ... The Science curriculum focuses on

Curriculum Overview

Sample Lessons

EIGHTH GRADE

Oak MeadowCurriculum & School

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Thank you for your interest in Oak Meadow. Since 1975, we have been supporting homeschooling families and students, both through our creative curriculum and our internationally-accredited distance learning school.

While reading through the complete sample lessons in this curriculum overview, you can begin to imagine what a typical homeschooling week might be like with Oak Meadow. We hope these materials give you a clear sense of the style, content, and scope of our curriculum, and help you decide if Oak Meadow is right for your family.

At Oak Meadow, we offer a unique curriculum that is substantively different from other educational models. The student’s awakening powers of thought are encouraged with a sequence of skills and carefully chosen material which reflects the child’s developmental stages and unfolding sense of self. We seek to foster a healthy balance between the realms of intellectual development, emotional engagement, and solid academic accomplishment. Our goal is to help children become intelligent, capable human beings who are able to respond sensitively and deeply to the world, and able to find meaning and relevance in their contributions to society.

Lessons in the early grades are crafted with a sense of beauty and reverence as the child’s own sense of wonder leads to the foundations of essential literary and mathematical skills. As the student grows into the middle school years, our imaginative, engaging approach develops strong academic abilities, practical problem-solving skills and an ability to consider an issue or problem from many perspectives. Each year’s curriculum is structured in 36 weekly lessons, and the sample lessons in this

overview are representative examples of a full year’s curriculum across all subject areas.

Within the framework of Oak Meadow’s integrated curriculum, you, as the Home Teacher, will be in a position to help your child make personal connections to the curriculum. Finding relevance and inter-relatedness between the material and daily living is one of the true joys of homeschooling. The Oak Meadow curriculum is designed to be used in the home environment and encourages meaningful connections and relationships with the whole family, the local geography, and the wider community.

We encourage you to visit our website (oakmeadow.com) or call our office at 802-251-7250 to learn more about us and about what we can do to support you in your homeschooling journey.

Warmly,

Michelle Simpson-SiegelExecutive Director

OVERVIEW 3

In the middle grades of the Oak Meadow curriculum sequence, questions play a vital role in the learning process. Through engaging stories, experiments, and writing assignments, we prompt students to think about things they may not have previously considered. In grades 5-8, the Oak Meadow curriculum asks questions that challenge the student to think, to explore, and to integrate knowledge gained in other subject areas. We ask questions for which there are no “right” or “wrong” answers, as we lead students to think beyond the facts themselves and to make sense of the world in which they live.

Our syllabi provide each student with in-depth readings on the topics of study, offer assignments and a broad range of activities, and provide ideas for further study or reading. By placing the emphasis upon human values and ideals in grades 5-8, we lay a foundation for a lifelong appreciation of the subjects covered during these middle school years.

Each syllabus is divided into 36 weekly lessons. Within each lesson, you will find everything you need for a complete learning experience. We provide readings, assignments, activities, and suggestions for further study. Most of our lessons contain a range of assignment options so that students can choose projects that best match their learning style.

Grade 5–8 Overview

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english


eighth grade

Math


eighth grade

Physical Science


eighth grade

Civics


eighth grade

teacher Manual


EighthGradeCurriculumOakMeadow’sEighthGradecurriculumintroducesstudentstotheconceptsofcivicsthroughastudyofthechampionsoffreedom,federal,state,andlocalgovernments,andtheeconomicsystem.Students witness their local government in action, explore issues affecting their state, and also become aware of national issues. Our experiential approach to understanding social issues includes practical activities such as community service projects and interviewing local community leaders. Students are encouraged to learn how to make a difference on a local level by learning more about the people and businesses in their area.

In English, students read seven classic novels while studying vocabulary drawn from the reading and concentrating on grammar and composition skills. Weekly assignments in writing, grammar, and usage provide ample practice for the student preparing to enter high school.

The Science curriculum focuses on the principles of physical science, including mass and matter, force, energy, sound, light, color, electricity, magnetism, and mechanics. Emphasis is placed on preparing the student for more advanced science by including assignments that require the student to conduct experiments, perform mathematical calculations, and report on their findings.

Math8The Math 8 curriculum explores the advanced uses of fractions, decimals, and percents and then introduces beginning concepts of algebra in preparation for high school. Lessons include squares and exponents, the order of operations, coefficients, geometry, formulas, scientific notation, and graphing. Students enrolled in the eighth grade may elect to take Pre-Algebra or Algebra with teacher approval.

Projects,Crafts,&Activities• Evaluate a Supreme Court ruling• Participate in a community service project• Interview a member of the fire department• Write a science fiction story• Create your own radio or television

advertisement• Research hybrid vehicles

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CurriculumMaterialsCivics 8; English 8 includes Writing for 100 Days; Physical Science 8; Math 8; The Giver; The Hitchhiker’s Guide to the Galaxy; A Wrinkle in Time; The Hobbit; Lord of the Flies; The Call of the Wild; The Adventures of Tom Sawyer; The Elements of Style

Teacher Manual and Craft Kit are also available for purchase.

EighthGradeOverview

English

SocialStudies

Science

Math

• Grammar: Prefixes, suffixes, punctuation review, run-on sentences, and sentence fragments

• Vocabulary words and quizzes• Writing: Essays, short stories, writing exercises• Literature: The Giver, The Hitchhiker’s Guide to the Galaxy, Lord of

the Flies, A Wrinkle in Time

• Grammar: Sentence construction, modifiers, and dangling modifiers

• Vocabulary words and quizzes• Writing: Essays, poetry, fiction• Literature: The Call of the Wild, The Adventures of Tom Sawyer,

The Hobbit

CIVICS AND AMERICAN HISTORY• American political heritage• The Constitution and The Bill of Rights• Freedom of Religion• Immigration and citizenship• Community service• Branches of the U.S. government

CIVICS• Criminal justice• Local government• Community leaders• Local politics and zoning laws• Economics and taxes• Communication• Making a difference

PHYSICAL SCIENCE• History of physics• Scientific inquiry• Energy and thermodynamics• Force and gravity• Laws of motion• Machines• Waves: sound and light• Shadows, color, and lenses

PHYSICAL SCIENCE• Electricity• Magnetism• Matter• Heat and pressure• Aerodynamics• Modern machines• Energy use

• Using a calculator• Converting decimals• Squares and exponents• Signed numbers• Order of operations• Equations and variables• Angles and using a compass• Ratio and proportion• Word problems

• Factors• Prime numbers• Equations with exponents• Pythagorean theorem• Pi and geometric solids• Averages• Fractions with exponents• Scientific notation• Coordinates and graphing a line• Base 2

FirstSemester SecondSemester

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Lesson 4: The ConstitutionThe challenge that faced the delegates at the Constitutional Convention was to establish a strong national government without making the states weak. With the new governmen-tal system that emerged, Americans would be citizens of both the national government and the government of their own particular state. Some of the power would be held by the fed-eral government, so it could make some laws to be applied to the whole country. Other pow-ers would be kept by each of the state govern-ments, to make laws that would apply to the people in that state.

There was also a great deal of debate and dis-cussion about the decision making power of the northern states versus the southern states. These two parts of the country had very different geographies, types of crops, and economies. While the North ran small farms, factories, fishing and trapping operations, the South grew cotton, tobacco, and used slaves on large plantations. Each side feared that a federal govern-ment would pass laws regulating shipping and trading that would have negative effects on it. More important was the issue of slavery. There were many slaves in the South, and southern states wanted to include them in the population count so they could have more representation in the new government. At the same time, the southern states didn’t want to count the slaves in the population when it came to determining federal taxes. In opposition, the northern states argued that slaves shouldn’t be counted in determining the number of representatives in the new federal government, because the slaves were treated as property, not as people. At the same time, the North wanted to include slaves in the population count so that more taxes could be collected from the southern states. A strange compromise was reached: it was decided that five slaves would be counted as three people in deciding how many representatives each state could have, and how much tax would be demanded from each state. A slave was not constitutionally considered to be equal to one whole person until 1865!

The basic framework proposed by James Madison was finally adopted in principle. It provided

Independence Hall in Philadelphia, where the Constitutional Convention met

Lesson �: The Constitution 2�

for a strong national government with three branches (similar to the system the individual states were current-ly operating under). These branches are the Legislative, the Executive, and the Judicial Branches. You will be learning more about each of these in turn later.

It was also decided that the Legislative Branch would be a two-house legislature, or Congress. The two houses of Congress would be the House of Representatives and the Senate. In order for a law to pass, both the Senate and the House of Representatives would have to approve it. The House of Representatives would be elected based upon the state’s population, so a larger state would have more Representatives. In the Senate, however, each state would have two Senators regardless of population, so the small states would be represented. This plan, along with the issue of how to count slaves, became known as the Great Compromise. Each side gave up part of what it wanted in order to reach an agreement that would ben-efit both.

In addition to the Legislative Branch, which would make the laws, the Executive Branch was established to enforce the law, and make sure it was carried out properly. In addition, a Judi-cial Branch was established to act as the interpreter of federal law and the Constitution. The convention finally drew to a close with 38 delegates signing the Constitution on September 17, 1787.

Next, the new Constitution had to be ratified or accepted by at least nine states. Immediately, strong opposition arose to this Constitution. Its supporters, which included Alexander Hamil-ton and James Madison and many others, were known as Federalists because they supported a strong federal, or national, government.

Anti-Federalists, such as Patrick Henry, felt that a strong central government would endan-ger the people’s liberties. According to them, a federal government that met so far away from local communities could not truly be called government by consent of the people. The Anti-Federalists believed that representatives of the government should meet in a location close to the people they were protecting and serving. They were concerned that the people themselves would not be properly protected from the federal government. The statement in the Constitu-tion that caused the Anti-Federalists the most difficulty was, “Congress shall have the power to make laws necessary and proper to carry out its stated powers.” They felt that a strong national government might eventually swallow up the state governments.

Patrick Henry addresses the Constitutional Congress

SAMPLE LESSON—GRADE 8 7

2� Oak Meadow Civics Syllabus

Thomas Jefferson, who was in Europe during the Consti-tutional Convention and therefore didn’t attend, agreed with many concerned people, particularly the Anti-Fed-eralists, that a Bill of Rights, which would detail spe-cific rights or liberties for the American people, should be added to the Constitution. Many argued that the Con-stitution should not be ratified without it, but eventually it was agreed that the Bill of Rights could be added later. The Constitution was finally ratified in mid-1788, and the Bill of Rights was added in 1791.

Choose one of these assignments:

Learn about one or two Federalists and one or two Anti-Federalists. Write at least two pages, discuss-ing these men’s particular viewpoints and concerns. What role did each of them play in helping America gain independence? What role did they each play in the establishing of the new government? What were their arguments and concerns about a strong central government versus strong state governments?

Compose a discussion between at least one Federalist and one Anti-Federalist. Using correct punctuation for dialogue, engage these men in a conversation which makes their opinions and ideas clear to each other and to your reader. Write at least one full page, single spaced.

If you had lived during the time when the Constitution was being written, would you have been a Federalist or an Anti-Federalist? Explain your answer and include specific examples to back up your opinion.

The Preamble (introduction) to the Constitution states the goals of our government:

To form a more perfect union. (To unite the thirteen separate states under one central government.)To establish justice through the legal system. (To have a system of laws that would be used to settle conflicts in a court of law.)To ensure domestic tranquillity. (To establish a peaceful society in which people in all the states are protected.) To provide for the common defense. (To be able to protect individuals and the society from enemies, and to establish an army.)To promote the general welfare. (To work for the health, prosperity, and happiness of the citizens; done through many institutions such as the Post Office, Social Security

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Thomas Jefferson

Lesson �: The Constitution 2�

Administration, Food and Drug Admin-istration, etc.)To secure the blessings of liberty to our-selves and our posterity. (The freedom to choose both for ourselves and our descen-dants; current and future citizens are free and are protected by the Constitution.)

Choose one of these assignments:

Copy, by hand, the Preamble to the Con-stitution. The Preamble may be found in an encyclopedia or from an Internet resource. (Note: The Constitution is a primary source of information. It is the original document, not a discussion about an original document.)

Memorize the Preamble to the Constitution and present it orally (on tape) for your teacher to hear. (If you like, you can play dramatic or patriotic music in the background during the taping of your speech.)

Choose one of these assignments to complete:

Choose the goal described in the Preamble to the Constitution that you think is the most important one. Discuss your opinion, offering details and examples. Write at least one page, single spaced.

Are there additional goals that you think should be added to the Preamble? What are they? Why are they important enough to be added? Write a page about your ideas.

Following the Preamble is the plan for our government. This plan is organized into seven parts called Articles. A series of Amendments (additions) follow the seven Articles. The first ten Amendments are called the Bill of Rights and were added in response to the concerns of the Anti-Federalists. Since the Bill of Rights was included, only sixteen other Amendments have been added.

Extra reading ideas:

Ssh! We’re Writing the Constitution, by Jean Fritz

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ratifying the Constitution

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Lesson 14:A Wrinkle in Time, Chapters 1-3

Foreshadowing

This week you will begin reading Madeleine L’Engle’s A Wrinkle in Time. The first three chapters of this novel demonstrate an excellent use of foreshadowing. Foreshadowing is a literary technique by which an author drops hints, or leaves clues, about what is to come later on in the story. Though these clues do not usually “spoil the ending,” they set up future events by building character and setting. A good example is Arthur Dent’s house in The Hitchhiker’s Guide to the Galaxy: Arthur’s home is destroyed, and very soon afterward his home planet is destroyed. The first destruction foreshadows the second.

Foreshadowing can also allow you to use plot twists that might otherwise confuse your readers or strain their credibility. For example, in The Giver Jonas steals out of town, taking Gabriel with him. This astonishing act is easier to believe since we have seen how much Jonas cares for Gabriel all throughout the book. His attention to Gabriel foreshadows his action at the end of the book, and lays the groundwork for it.

This week you are reading the first three chapters of A Wrinkle in Time, which are full of fore-shadowing and clues about what is to come. Meg, for example, is doing poorly in school even though her parents are brilliant scientists. Reading this, we feel that Meg’s true potential has not yet been discovered, and we look forward to watching her character develop. Similarly, Mrs. Whatsit’s mention of a tesseract, before we even know what one is, suggests that it is going to become very important, and also that it’s somewhat mysterious to the other characters in the scene as well.

The first three chapters of this novel are full of hints like this, that can give you some sense of what is to come in the story. Future events are not explicitly laid out in detail, but you can infer in broad strokes how characters or events may develop. In this week’s assignment, you’ll get to make some guesses about the foreshadowing in A Wrinkle in Time and what it portends.

Madeleine L’Engle (born 1918)

Born in New York City to a pianist and a writer, Madeleine L’Engle Camp wrote her first story at five years old and kept a journal nearly all her life. Even so, she found school difficult and

�� Oak Meadow 8th Grade English Syllabus

was even called “stupid” by some of her teachers. She retreated into her own world of writing, persevered, and graduated from Smith College in 1941. Her fi rst novel, Th e Small Rain, was published in 1945.

During a cross-country camping trip in 1959, L’Engle fi rst began thinking of the ideas that would become A Wrinkle in Time. Th ough several dozen publishers rejected the novel, it fi nally saw print in 1962.

L’Engle continued writing throughout the following thirty years, living in New York City as the writer-in-residence at the Cathedral of St. John the Divine.

A Wrinkle in Time won the Newbery Medal in 1964. It is the fi rst book in a series, the Time Quintet. Th e story of Meg Murry, Charles-Wallace, and Calvin O’Keefe continues in the second book, A Wind in the Door.

In addition to the stories of the Murry family (often referred to as the “Kairos” novels), L’Engle wrote another series, about the Austin family, called the “Chronos” novels. Th ese books, begin-ning with Meet the Austins (1960), are not entirely separate from the Kairos series, and they share many characters and events between them.

Th e theme that pervades A Wrinkle in Time, that of science, magic, and religion intertwined, continues throughout many of her works. She believes that these elements are only diff erent facets of a larger reality.

Reading

Read pages 30-32 in 100 Days.

In Strunk & White, read Rule 11 (pages 13-14), and page 52.

Begin reading A Wrinkle in Time, starting this week with Chapters 1-3. You will be writ-ing on this book in Lesson 18.

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Vocabulary

constable gambol literally scud

dilapidated inadvertent morass stole [noun]

disillusion inaugurate peremptory supine

exclusive intone prodigious tractable

Assignments

Complete either Exercise A or B on page 31 of 100 Days.

Following the suggestions on page 32 of 100 Days, compose a one-half to one-page story on a subject of your choice. Use plenty of misplaced and dangling modifiers. Then re-write your story, eliminating the misplaced and dangling modifiers. Send both versions of the story to your teacher.

Foreshadowing exercise: Do this before you move on to Chapter 4. Find three examples of foreshadowing from the first three chapters of A Wrinkle in Time. For each one, write a paragraph explaining why it is foreshadowing, and make a guess as to its meaning: What do you think will happen later in the book? Your guesses need not be concrete or specific. Just explain what the foreshadowing suggests to you.

Literally, Literally!Page 52 of Strunk & White includes a brief, almost nonchalant, admonition not to use the word literally “in support of exaggeration.” We’re going to go a bit farther here, as the word has been so mangled and tortured that its meaning has nearly been lost.

Literal means “taking words in their most basic sense without metaphor or allegory.” Thus, the adverb literally is a way to assure your readers that you are employing no figures of speech, no hyperbole, and that what you say is what you mean, word for word:

The first draft of that story was so bad I literally had to throw it out and start all over.

I drove that car until it literally fell apart.

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In the first example, the writer in question really threw the story out; and we mean physically: He picked up the paper on which the story was written, and put it in the trash can. In the second example, the car actually came to pieces. The word is useful here because you are using phrases that might otherwise be taken for figures of speech: “throw it out;” “fell apart.” You are assuring your reader that those things actually happened, that you are not being figurative. Figuratively, of course, is the antonym of literally.

What’s happening now in our language, however, is that literally is being used as an intensi-fier, and thus is being used for exactly the opposite of its original purpose. As you’ll notice in the examples above, the word does serve somewhat to intensify the sentence, since it assures us, for example, that the car completely fell apart rather than simply suffering some minor break-down. In a minor breakdown, I might have said, figuratively, that my car “fell apart,” but in the sentence above, I really mean it. This intensification has expanded, tragically, to include a wide range of absurd misuses of the word:

It’s literally raining cats in the Puget Sound area, as local shelters are overrun with felines, and they’re asking for the public’s help to save them.

There may be a lot of cats around Puget Sound, but this sentence assures us that they are actu-ally falling from the sky.

“Arizona is in play like never before,” said David Waid, chairman of the state’s Demo-cratic Party. “And the Republicans are literally handing it to us.”

“Confound it, Hawkins, when I said I meant that literally, that was just a figure of speech.”

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How many Republicans does it take to lift an entire state?

“As a city, we literally turned our backs to the river for a long time,” says Doni Green-berg, a columnist for the Redding Record Searchlight. “But now we’re recognizing it for the recreational gem it is.”

It must have gotten tiring for all those townspeople, standing with their backs to the river all that time!

Here is an example from Chapter 2 of Mark Twain’s The Adventures of Tom Sawyer, which you will be reading next semester:

And when the middle of the afternoon came, from being a poor poverty-stricken boy in the morning, Tom was literally rolling in wealth.

Does Twain mean this “literally?” You decide.

Even though this is a Rant, we are not going to argue that you should always mean exactly what you say — that would get tiresome. Figurative language is beautiful, artistic, exciting, and hilarious. It is the essence of great writing. How sad it would be, however, to lose the one word in the English language that is supposed to guarantee “no figurative language here.” As writers, we have literally hundreds (!) of ways to intensify our writing or give it flair. Literally means that, for this sentence at least, you mean what you say. That is too valuable a tool to be misused.

Another word that suffers similar abuse, though not quite so pervasive, is unique:

Chicago is no less unique an American city than New York or San Francisco.

You know what the word unique means. It means “the only one of its kind.” There is only one Chicago, therefore it is unique. It can’t be “less” so than any other city. Beware of modifiers with this word: It’s impossible to be somewhat unique, or more unique, or the most unique.

Physical Science Lesson 4 - 1

Physical Science~~~~~~~~~~~~~~~~Lesson 4

ENERGY

Go outside and look around you. You can see and hear activity all around you.The wind rustles the leaves on the trees. You feel the heat of the sun. You see cars andbicycles move by. People are moving, talking, working and playing. All of thesethings require energy for them to happen. We use energy to keep ourselves alive. Weuse it to work and to make our work easier. Energy runs all living things; energy runsus and our machines. We live in a sea of energy; energy is all around us.

Energy is the capacity for movement and change. It produces changes in matter.You get energy from the sun and from the food you eat that stores the sun’s energy.In fact, most of the energy on earth comes from this one source - the sun. Your bodyuses energy every time it does anything. Energy is needed to make anything move,even the smallest cell. And whenever anything moves, energy is used.

Most of this course is about energy and the different forms that it takes. Thislesson is an overview of the types of energy that we will be studying in more detailthroughout the course.

Energy

• Runs all living things• Is everywhere


Lesson 4 - 2 Physical Science

TYPES OF ENERGY

There are many different types of energy. All of them concern some type ofmotion. Everything has at least one type of energy and many things have severaldifferent types of energy. We will discuss some of the most common ones in turn.

Thermal or heat energy is the energy inmoving molecules. All things contain some heatenergy. Rub your hand on your arm and it willbecome warm. Adding heat energy to anythingmakes its molecules move faster. When you boilwater, the water molecules move faster; they moveso fast that some molecules begin to leave thecontainer as the water boils away and evaporates.Heat can turn a solid into a liquid and a liquidinto a gas. With each of these transitions, the molecules are able to move about moreand more freely.

Light energy comes from the sun to Earth in the form of light waves. Wecannot see these waves, but they are very much like ocean waves. (We will learn moreabout light waves in Lessons 16 and 17.) Light waves travel in a straight directionwhich is described as a ray of light. Anything that gives off light has light energy.Plants grow by using light energy. Photography is an excellent example of the abilityof light to cause change. Light can form an image on photographic film by changingthe state of the silver coating on the film.

Electrons are one of the types of atomic particles we looked at in Lesson 3.Electrical energy is the energy that is in moving electrons. Light bulbs, radios, andappliances use this type of energy. Electrical energy can turn a motor, and it cantransfer your ideas onto a magnetized tape in a tape recorder or onto a magnetizeddisc in a computer. It can send your voice thousands of miles through a telephonesystem. You will learn more about electrical energy in future lessons.

Chemical energy is energy that is stored in chemicals. It is released in chemicalreactions or whenever two or more chemicals interact. Chemical energy heats yourhome when you burn coal, wood, gas or oil. It is in batteries and changes to electricalenergy when the battery is used. Chemical energy is what your body runs on whenyou digest food.


Mechanical energy (kinetic energy) is the energy that is in moving things, andthings that can move. Wind, falling rocks and moving water all have mechanicalenergy. So do all machines that move and so do you, when you are running across afield or swimming in a pool. An object that possesses mechanical energy is able to dowork. You will learn more about mechanical energy - and the related ideas of work,power and force - in Lessons 6 through 10.

Gravitational energy is the energy that pulls things towards each other. Allobjects have gravitational energy; the greater the mass, the greater the gravitationalattraction. Since the earth is so large, we experience it as the energy that pulls thingstowards the earth. The sun has gravity which holds all the planets in orbit. It is actuallya type of mechanical energy. You will learn more about gravity and gravitational energyin Lesson 7.

Sound energy is energy caused by vibrating objects. The object vibrating causesthe air to vibrate, and the sound wave travels through the air to our ears. Have youever felt the house shake from a really loud thunder crack? That is sound wavescausing the house to vibrate. This is sound energy. So is the music you hear fromyour CD, and the sound of a kettle of hot water whistling on the stove. We willdiscuss more about sound energy and sound waves in Lessons 14 and 15.

SOME TYPES OF ENERGY

Heat or Thermal Mechanical or Motion

Light Gravitational

Electrical Sound

Chemical Atomic

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Atomic or nuclear energy is the energy that isstored in the nucleus (nucleus is another word for centeror core) of an atom. The sun produces light and heatfrom atomic energy. The destructive power of atomicenergy is easy to see in pictures of Hiroshima andNagasaki after the explosion of the atomic bombs inWorld War II. We will learn more about atomic energyin Lessons 34 and 35.

1. Sit quietly alone in a room for a while. Listen and watch carefully. Aftera time, you will start to hear and see signs of energy around you - perhapsa family member walks by in the hall, or a bicyclist goes by on the street.Perhaps you can feel air coming through a vent, or see a curtain movingin the breeze. Write down the signs of energy you find, and describe whichtype of energy it is.

2. For each of the eight types of energy just discussed, write down anexample of how or where this energy type occurs. Describe how yourexample shows that type of energy.

3. For the following story, list the types of energy present. Your answersshould include at least one of each of the eight energy types you havelearned about:

Pat and her friend Kevin rode to the park on their bicycles (____a___).The sun was shining brightly (__b__) and by the time they got there,they were hot and tired (____c____). They were also hungry, sothey pulled out two sandwiches and ate them (_____d______); soonthey felt much better. They sat on the swings for a while, swingingback and forth (__e____) and talking (____f___). After awhile, theydecided to listen to some music on their portable radio (___g____)but soon realized that their batteries were low (___h___), so theyrode home and listened to the stereo (____i_____) at Pat’s house.


POTENTIAL ENERGY AND KINETIC ENERGY

All types of energy can be divided into two states: kinetic energy and potentialenergy. The word kinetic means moving. Kinetic energy is energy in motion or in use.When you are bouncing a ball, it has kinetic energy because the energy is moving.When we refer to kinetic energy, we are usually referring to energies where visiblemovement occurs: mechanical or gravitational energy. But sound and electrical energyalso involve movement, so could technically fall under this category.

What about when you aren’t bouncing the ball and it just sits on a shelf in yourroom? Then the ball has potential energy - stored up energy that is waiting to bereleased. If the ball got a chance, it would roll off the shelf and fall to the floor. We cansay that the ball has gravitational potential energy. Potential energy is stored energy.Energy does not have to show itself in order to exist. Energy still exists even whenyou can’t see it.

Potential energy usually exists as a result of the position of an object. Gravitationalpotential energy is everywhere. Birds have it when they are in the air or in trees. Treeshave it; if disturbed they fall down. You have it as you hold yourself up. When you aretired, what do you do? You lie down to lower your potential energy!

Potential energy is energy that is just waiting to happen!

Though gravitational potential energy is quite common, you can see potentialenergy in other places. There is electrical potential energy; we call it voltage. It isstored electrical energy. When it is released it’s not an object that moves, but anelectrical charge (electrons). Electrical potential energy is also found in batteries. Thisenergy is released when you turn on the portable CD player orthe flashlight. There is also chemical potential energy stored inmolecules. This can be released by a chemical reaction.

When you open a jack-in-the-box, the potential energy ofthe coiled spring inside is released. If you stretch a rubber band,it has potential energy until it is released and snaps back to itsnormal position. This is called elastic potential energy, and it is aform of mechanical potential energy.



Another example of potential energy is a piledriver. (A “pile” is another word for a big post, suchas the piles which hold up a pier.) A pile driver is amachine with a huge weight on the end of a heavymetal cord. The huge weight is raised up high andthen dropped. As it falls, it goes faster and faster andby the time it hits its target, it has enough energy todrive a huge post into the ground. It acquired thatenergy because as it was raised against gravity, theamount of gravitational potential energy increased. Thepotential energy was then changed into kinetic energy(energy of motion) when it was released.

Any system wants to get to the lowest potential energy possible. That’s whythings fall down! If you leave the lights of your car on, the electrical energy will flowfrom the battery, eventually getting to the point where the battery has no electricalpotential energy! In other words, you have a dead battery. If you wind up a springloaded toy, it will release and unwind at the first possible chance. When you thinkabout whether something has potential energy, think about whether that thing willmove on its own if whatever is holding it in place is removed. A kitchen appliance thatplugs into a wall doesn’t have potential energy of its own, as it needs to have energyadded to it to run. (OK, it does have some gravitational potential energy because it’ssitting on the shelf!). A ball sitting on the ground doesn’t have potential energy unlessit’s at the top of a hill.

4. Think of and write down two different examples of potential energy(energy waiting to happen). The examples should be different from theones listed in this lesson describing potential energy. Then describe whatcan happen to create kinetic energy in each of your examples.

5. Take a rubber band, and stretch it between the thumb and index finger ofone hand. Hold it there for as long as you can. At what state is the energyin the rubber band? As your hand gets tired, what state of energy is itfighting against? Release the rubber band from your finger. At what stateis the energy in the rubber band as it is released?


6. Choose one of the following:

a. Think of a person standing still at the end of a springboard, gettingready to make a dive into a pool. When the diver is ready, he willmake several jumps on the springboard, and then dive into thewater. Describe each step of his dive, identifying the points wherethe amount of potential and kinetic energy change.

b. Think of a rollercoaster standing still as passengers board. Then itstarts up, climbing to a high point before beginning its first descent.As it goes along the track it goes up and down, around turns, andperhaps around loops several times. Describe an imaginary rollercoaster ride, identifying the points where the amount of potentialand kinetic energy change.

ENERGY CAN CHANGE FORM

Think about what happens when you strike a match. You are holding a match inone hand and the match box with a striker on it in the other. You, the match, the boxand all their components have potential energy. You strike the match on the box,changing your potential energy into mechanical energy as you move. The chemical inthe match head sparks (chemical energy) and the match head explodes into flame(heat energy) and makes a “whooshing” sound (sound energy). The chemical energyin the burning match continually changes into heat and light. You blow the match out(mechanical energy again) and the match gives off smoke (chemical energy) as itcools.

This is just one example of how a simple action can produce many energychanges. There are many examples of changing forms of energy all around us all ofthe time. Our muscles are continually changing the chemical energy that we derivefrom the food we eat into mechanical energy as we move. A CD player turns electricalenergy into mechanical energy (motor that plays the CD) and sound energy (themusic that you hear) and heat energy (heat is released from the back of the CDplayer).

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Take some time to consider how energy can change form. For example, thinkabout chemical energy. The chemical energy in food changes form in your body togive you the energy to move (mechanical energy). What energy was changed in orderto give energy to the food? The sun’s atomic and light energy was transformed forfood to grow. The food stored the sun’s energy and released it into your body in theform of chemical energy.

USED ENERGY AND HEAT ENERGY

When energy is used, there is one thing that always happens: heat energy isproduced. No matter which type of energy is used, heat is produced. To put itanother way, whenever energy changes form, heat is produced. To understand this,let’s look at some examples.

Here is an example of used mechanical energy making heat. Have you ever benta thin piece of metal back and forth to break it in half? What happens to the metal asyou bend it back and forth? The mechanical energy that you are supplying is transferredto the stress point, which becomes warm until it snaps. (The snap is sound energy.)You can feel the heat from the broken metal. The heat is slowly released into the airuntil the metal cools.

When electrical energy is used, it also releases heat. Electrical energy is used tooperate a CD player, stereo, television, or video tape player. If you ever looked at theback of any of these appliances you would see a grill covering a vent through whichheat is released. When you buy a new appliance and set it up, the instructions will tellyou to place the appliance away from the wall with enough room for the heat in theback to escape. Heat is produced whenever you use electrical energy to operate oneof these appliances.

Using chemical energy also releases heat. If you are running, your muscles usea lot of chemical energy through the food you eat to keep you moving. The activity ofrunning warms your body. You actually radiate much of this heat out and away fromyou, warming the air around you (even though you may not notice that you’re doingthis). As your body uses chemical energy, heat is released. Have you ever been in aroom with a lot of people dancing or playing an active game? The room warms upwith all of the heat being given off from the moving bodies as they use chemicalenergy.


Whenever energy changes form, some of it is always changed into heat energyand released. Scientists and engineers try very hard to minimize this loss of heatbecause it is considered “wasted” energy. Imagine that you like to eat ice cream, butyou only like it when it is frozen. You can’t stand to eat melted ice cream, but everytime you eat a bowl of frozen ice cream some of it melts. Some of the ice cream iswasted because it changes into a form that you won’t eat. Has the wasted ice creamdisappeared? No, it has just changed into a form that is not useful to you.

Even when a machine is supposed to produce heat - like a toaster oven - someof the electrical energy that could be put into making the inside of the toaster oven hotescapes to the air around it. In every use or change of energy, some is “lost” as heat.

When energy is used, heat energy is always produced.

This problem of escaping heat energy is termed by engineers as a problem ofefficiency. If all of the electrical energy were used by a CD player in order to producemusic, the CD player would be considered 100% efficient. This is not possiblehowever, as some energy is always converted to heat energy and wasted. Somemachines are more efficient than others in using the energy put into them. A highlyefficient machine is one that uses most of the energy that is put into it and releasesvery little as heat energy. Efficiency is an important factor to consider when you aredeciding which model of an appliance to buy. When an appliance is labeled as “energyefficient,” what it is referring to is how efficient the appliance is at converting theelectrical energy or fuel it runs on into the work the appliance is designed to do, whilereleasing a minimal amount of heat.

Why can’t we have 100% efficient machines? Why is heat energy always releasedwhen energy is used? Does energy disappear? Is energy created? In the next Lesson,we will learn about the Laws of Thermodynamics and get the answers to these questions.

7. Examine some appliances around your house. Find where the heat isreleased. Write down what appliances you looked at and what you found.


Math 8 Lesson 1 - 1

Math 8 ~~~~~~~~~~~~~~~~~~~~ Lesson 1

USING A CALCULATOR

In grades K-7, we don't encourage students to use calculators, because we believe it's important to develop a solid understanding of the basic operations of math before you begin relying upon an external tool to perform those operations.

In eighth grade, however, we begin to explore some concepts that require extensive calculation, and if you have to do all of these calculations by hand you would lose sight of the broader concepts and patterns that are involved. In addition, calculators of various kinds are commonly used in our society, so it's important that you learn how to use them effectively. For these reasons, we require that you purchase a pocket calculator to use with the exercises in this course. Unless we mention otherwise, calculators may be used for all operations throughout this course, including skill practices, tests, reviews, and exams.

When you're using a calculator, it's very important to remember this: a calculator can do amazing things, but it's not intelligent. If you give a calculator correct information, it will give you correct answers, but it doesn't have any way of knowing if the information you've given it is correct. So if you enter the wrong information, it will give you the wrong answers. In the computer industry, there is a term for this: GIGO. That stands for "Garbage In, Garbage Out." To avoid giving out garbage as answers, follow this basic rule: review every answer you get and consider if it makes sense. For example, if you're adding 48.9 and 8.4, you can see that the answer should certainly be less than 100. So if you forget to input the decimal in 48.9 and come up with an answer of 497.4, you know that the answer is wrong. When that happens, enter the information again more carefully. If you follow this rule, your calculator will be a valuable tool for you in math.

There are a wide variety of calculators available, and some are quite advanced. For the purposes of this course, however, you only need a calculator that can perform the four basic processes of arithmetic (addition, subtraction, multiplication and division), calculate square roots, and perform percentage calculations. Since there are variations in the way that

Math 8 Lesson 1 - 2

calculators operate, we will only provide general guidelines for using a calculator to perform various operations. You should study the instructions included with your calculator to learn the specific principles of operation for your calculator.

If you don't already have a calculator, purchase one now and read the instructions that are included with your calculator to learn how to use it effectively. When you are familiar with the operation of your calculator, continue with the next section of this lesson.

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Math 8 Lesson 9 - 1

Math 8 ~~~~~~~~~~~~~~~~~~~~ Lesson 9

DIVISION RULE FOR EQUATIONS

We have learned that we can add and subtract numbers on both sides of an equation without changing the value of the equation. These addition and subtraction rules are useful for solving equations like these:

x 8 12− =

c 7 9+ =

But there are other kinds of equations for which the addition and subtraction rules don't help us to solve the equations. For example:

2x 8=

In an equation like this, it wouldn't help to add something to both sides of the equation, so we need another operation to help us solve the equation. Remember, to solve an equation, we always want to get the unknown by itself. In the previous example, the unknown is not by itself; it is being multiplied by 2. So we don't know the value of x; we only know the value of 2x. To remove the 2 from the x, we need to use the division rule for equations:

If both sides of an equation are divided by the same number (except zero), the value of the equation remains the same.

Using this rule, we can solve the example as follows:

Example 1: 2x 8=

We divide both sides of the equation by 2, because 2 is the number that we want to remove so we can get the unknown (x) by itself.

2x 882x

2 2

=

=

Math 8 Lesson 9 - 2

This enables us to cancel out the 2 that is beside the x, as we would if we were canceling numerators and denominators in a fraction. The result is as follows:

1

1

2x 8

1x 4

2x 822

=

=

=

Since 1x is the same as x, we can drop the 1, for a final answer of:

x 4=

Example 2: 13 4c=

Once again, we want to get the unknown (c) by itself, so we have to get rid of the 4. To do this, we divide both sides by 4.

1

11414

13 4c

3 1c3 c

4c134 4

=

=

==

By using the division rule for equations, we're able to get the unknown by itself and find its value.

Note: Equations that have the unknown on the right side of the equation, as in the previous example, can be solved by leaving the unknown where it is, as we did above. Many students prefer to reverse the equation so that the unknown is on the left. This is acceptable and will not affect the value of the equation, as long as all of the terms remain the same. If you wish to reverse the equation in this way, do it at the very beginning then solve the equation as usual. For example,

9 3x3x 9

x 3

3x 93 3

==

=

=


Math 8 Lesson 23 - 1

Math 8 ~~~~~~~~~~~~~~~~~~~ Lesson 23

EVALUATING VARIABLES WITH EXPONENTS

We have learned how to evaluate an algebraic expression by substituting numerical values for the variables, as in the following example:

Example 1: Evaluate 3x if x = 2

We substitute the given value into the expression and simplify:

( )3x 3 2 6= =

If one of the variables is the base of an exponential expression, we can evaluate it the same way, by substituting the given value for the variable.

Example 2: Evaluate if x = 3 2x


92 2x 3 3 3= = ⋅ =

This same process applies if the variable is the exponent itself, rather than the base, as in the following example.

Example 3: Evaluate if x = 2


5

x5

x 25 5 5 5 2= = ⋅ =

This same process also applies when we are evaluating roots. Look at the following examples:

Example 4: Evaluate 4 n if n = 81

Math 8 Lesson 23 - 2


4 4n 81 3= =

We can also substitute for the power of the root, as follows:

Example 5: Evaluate n 125 if n = 3


3n 125 125 5= =

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