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Providing excellence in home school education since 1988


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Providing excellence in home school education since 1988


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General Information and Instructions

Providing excellence in home school education since 1988


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We at the English Language School, Adult Education Division are glad to be a part of your educational journey. This program is a comprehensive way for you to complete the necessary requirements you need to receive a diploma. With over 20 years of experience and know-how, we are dedicated to helping you reach your goals and achieve your dreams… We’ll walk with you each step of the way until you have total success. Our High School Diploma Program is a division of the English Language School and was specifically designed and created for people with a busy schedule and lifestyle. It utilizes the opportunities of Home Schooling as a great alternative for earning your high school diploma. The major differences between home schooling and traditional high school are:     

You can work at your own pace No time limits and no mandatory classes to attend, You can do all of the work from your home. You may re-take the test as often as you need at no additional charge You can earn your diploma in at least 30 days

This program prepares adult students to:  Earn a high school diploma under the 1State of Texas Home School rule  Review and prepare for college entrance  Improve reading, writing and math skills for job promotion opportunities  Prepare for the GED (General Education Development Diploma) tests This program uses a self-paced, independent study model and is structured to meet your personal learning style and time requirements. Our focus is on helping you succeed. You will use this workbook in conjunction with the following:    

Video and Print Lesson Library Live Tutoring sessions from computer, iPad or i-Phone Tutorials and Practice Tests Text Book and Resource Library for enhanced learning

Email, or Call student support for questions, assistance or tutoring support To be eligible you must be 18 years or older and no longer in a traditional high school program. To take the GED tests, you must be 19 years old or meet conditions for an age waiver.

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To home school legally in Texas, you must follow three state law requirements: 1) The instruction must be bona fide |The curriculum must be in visual form (e.g., books, workbooks, video monitor). | 3) The curriculum must include the five basic subjects of reading, spelling, grammar, mathematics, and good citizenship

Providing excellence in home school education since 1988


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The Course Your Pathway to Success 1. Enrollment  Complete the Application on the web site  Upload or mail a copy of the required personal identification documents  Register for the course with (Active Network) portal 2. Student Information and Operations Guides  Course Syllabus (Outline and Description  Your Workbook and Study Guide  Your student ID number via email  Welcome letter and New Student Kit  Links to study tools and downloadable print lessons  Tutoring registration instructions 3. Personal Study Program System  Complete this course workbook and all exercises  View video lessons from Video Library  Read Print Library Lessons and Book recommendations  Attend Tutoring Sessions with instructors (Optional )  Read recommended Supplementary Study Materials 4. Complete the Examination and Essays  Take all the practice tests  Register to take the test  Complete and send in all required essays  Complete the examination with a passing score of 70% or more  Re-take the test at any time as often as needed (at no charge) 5. Receive Your Diploma  Send in your request for diploma and transcripts  Receive your diploma and sealed notarized transcripts within 10 days 6. Post Graduate Assistance  Attend tutoring sessions to prepare for job and school tests  Job search and Promotion in the Workplace seminars  Personal documentation assistance

Providing excellence in home school education since 1988


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You may contact our offices or customer service by phone Monday – Saturday between 9:00 AM and 8PM CST.

Phone Home Office

210.579.4905

Washington D.C.

202.900.0937

Email Student Assistance

info@esl180.com

Tutoring Class Information

tutorHSD@esl180.com

Technical Assistance

tech@esl180.com

Monday 10:00 AM Language Arts 12:30 PM Math 7:00 PM Language Arts  

Tuesday Science English Science

Wednesday Social Studies Essay Writing Social Studies

Thursday Friday Math English Language Arts Science Math English

Saturday Essay Writing Social Studies Essay Writing

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Tutoring will be held 3 times a day for one hour. The classes will rotate by subject determined by requests and popularity (will change & be posted monthly ) All students have access to Study tools, Videos and Live On Line classes every day. Teachers are available each day at the classroom times above. Classes will have no more than 10 students per teacher

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Click on the class name for the specific subject Log in to the live class session and join other students and your teachers May email in advance to be certain the issue or subject most needed will be covered Walk-in’s will be on standby and must give way to s cheduled students Computer room can accommodate 4 students at a time.

Download the printed lessons from the web site Watch the related lesson videos (click links)

Providing excellence in home school education since 1988


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Providing excellence in home school education since 1988


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to personal reasons. We offer a second chance for students to complete their studies and earn a diploma. We meet the Texas U.S.A. education code requirements and the materials in the test correspond to what you would have learned if you had continued your high school education. It covers subjects that you already have an idea about. However, this should not make you lax about preparing for the test. During your preparation you should follow the curriculum thoroughly and revise well so that you can pass the test in the first chance. To help you prepare for the test the various features are discussed in the following section.

After you have read and studied the materials in the workbook, the video library and printed lessons you may apply to take the test. This examination will test your high school knowledge or subjects you would have covered if you had continued your studies in a government or private school.

Language Arts Reading: You read short stories, passages and poetries listed in your workbook. You will also learn to analyze and understand the passages provided. This section of the test will reflect your knowledge of literature of high school level. The test will include comprehension as well as application questions..

The test is divided into 5 parts (the Language Arts is divided into 2 subsections) and the subject matter of each section is as follows:

Social Studies: In this section your high school knowledge of World History, Civics, Geography and Economics will be tested. You will be tested on World History and US history to the present date.

Language Arts (Writing Part 1): This is where your grammatical skills will be tested. You will have to check sentences given for mistakes. You will also check the organization of the sentences or the paragraphs given. You will also have to check them for meaning and coherence. This will test your understanding of English grammar. Language Arts (Writing Part 2): You will write timed essays on specific topics (45 minutes). This tests your proficiency and ability to organize your thoughts and conveying them in a logical manner. In this section you will develop your arguments in a logical manner so that the reader can clearly understand your ideas. All essays will also consider vocabulary, grammar and punctuation.

Science: The questions will be on subjects that you already have some knowledge about. However, you will need to update your knowledge of Science. The 3 main subjects that the questions for this section are taken from are as follows: 1. Life Science or Biology 2. Physical Science (Physics and Chemistry) 3. Earth and Space Science Mathematics: This section covers basic mathematics including interpretation of graphs, charts and tables. Your analytical skills and problem solving skills will be tested here. It will also present questions 1. Algebra 2. Geometry.

Home schools in Texas have been determined by the Texas courts to be private schools, and private schools are not regulated by the state of Texas. Parents do not have to “register” with the state, and home school students are not required to be “enrolled” in an accredited program. There are no requirements such as teacher certification or curriculum approval. The ruling in the Leeper case states that “a parent or one standing in parental authority” may educate a child. A home school may have whatever curricula the parents decide upon in whatever mode they choose, provided the curricula cover the five basic subjects of reading, spelling, grammar, math, and a study in good citizenship, and that the curricula are followed in a bone fide way. Texas Home School Coalition. Providing excellence in home school education since 1988


. 5 Courses are required + the Citizenship or Bible Teaching Section) Each graduate must have completed at least six electives. These can be things that you have already experienced, or mastered. Such as, playing an instrument or working in construction. Each subject requires that you take part in each “course” for approximately six (6) months each.

From the following list, circle and check all that apply to you. Attach this page to test when you turn it in for grading. Courses:

Accounting: Balancing a check book Check Register Working with numbers Other (Specify):____________

Foreign Language: Spanish French German Italian

Vietnamese Chinese Japanese

Other

(Specify):____________ Work Study: List name of employer on separate sheet of paper Home Economics: Cooking Cleaning Babysitting Fine Arts: Drawing Painting Other (Specify):____________ Music: Guitar  Piano Keyboard Trumpet Saxophone Accordion Other (Specify):____________

Administrative: Typing Data Entry Answering Phones Placing orders Faxing Other (Specify):____________ Computer Programs: Windows 95/98/2000 ME or XP Microsoft Word Excel Power Point, Other (Specify):____________ Mechanics: Car repair Truck repair A/C repair Other (Specify):____________

Physical Education / Sports: Body Building Swimming Exercising Football Soccer Baseball Basketball Tennis Golf Dancing Other (Specify):____________

Providing excellence in home school education since 1988


COURSES


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Providing excellence in home school education since 1988


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English 1

Providing excellence in home school education since 1988


. Contents 1. II.

Order and steps to excellent writing........................................................................................... 15 THE WRITING PROCESS ............................................................................................................ 16

2.

How to begin the writing process ............................................................................................... 16 2.1.

Writing takes time ............................................................................................................... 16

2.2.

Keep the purpose of your writing in mind; Here are some examples .................................. 16

3.

Pre-writing strategies ................................................................................................................. 17 3.1.

4.

Questions to yourself about what your purpose is for writing about the subject. ........................ 18

III.

ACCADEMIC WRITING ............................................................................................................ 18

5.

What is a Text? ......................................................................................................................... 18

6.

Medium of a Text ....................................................................................................................... 18

7.

The Purpose for the text ............................................................................................................ 19 7.1.

Authors’ purposes .............................................................................................................. 19

7.2.

Audiences’ purposes .......................................................................................................... 19

7.3.

The Role of Purposes ......................................................................................................... 20

7.4.

Attitude ............................................................................................................................... 20

8.

The Setting ................................................................................................................................ 20 8.1.

Time ................................................................................................................................... 21

8.2.

Place .................................................................................................................................. 21

8.3.

Community / Conversation ................................................................................................. 21

IV.

HOW TO ESTABLISH AN ARGUMENT .................................................................................... 23

9.

V.

Begin to get fresh new ideas .............................................................................................. 17

Developing a strong position or argument ................................................................................. 23 9.2.

The thesis needs to be narrow ........................................................................................... 23

9.3.

Example of a thesis that is too broad: ................................................................................. 23

9.4.

Example of a narrow or focused thesis: .............................................................................. 24

9.5.

Claims ................................................................................................................................ 24

HOW TO STRUTURE YOUR ESSAY WRITING........................................................................... 25 10.

Logic in Argumentative Writing............................................................................................... 25

11.

On Paragraphs ...................................................................................................................... 26

11.1.

What is a paragraph?...................................................................................................... 26

11.2.

The Basic Rule: Keep one idea to one paragraph ........................................................... 26

11.3.

Elements of a paragraph ................................................................................................. 26

11.4.

A topic sentence ............................................................................................................. 26

11.5.

Adequate development ................................................................................................... 27

11.6.

Some methods to make sure your paragraph is well-developed: .................................... 27

11.7.

When to start a new paragraph? ..................................................................................... 27 Providing excellence in home school education since 1988


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When you begin a new idea or point. .............................................................................. 27

11.9.

To contrast information or ideas. ..................................................................................... 27

11.10.

When your readers need a pause. .................................................................................. 27

Breaks between paragraphs function as a short............................................................................ 27 11.11.

When you are ending your introduction or starting your conclusion. ................................ 27

Your .............................................................................................................................................. 27 11.12. 12.

Transitions and signposts ............................................................................................... 27

Conciseness .......................................................................................................................... 27

12.1.

Replace several vague words with more powerful and specific words............................. 28

12.2.

Examine every word in a sentence ................................................................................. 28

12.3.

Combine Sentences........................................................................................................ 29

12.4.

A Lesson in Writing Concisely ......................................................................................... 29

13.

Sentence Variety ................................................................................................................... 30

13.1.

Vary the rhythm by alternating short and long sentences. ............................................... 30

13.2.

Vary sentence openings. ................................................................................................ 31

14.

Using Appropriate Language ................................................................................................. 32

14.1.

Active and Passive Voice ................................................................................................ 33

14.2.

Using Active Versus Passive Voice ................................................................................. 33

Providing excellence in home school education since 1988


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How to write winning articles, reports and essays

Order and steps to excellent writing In this section you will learn the writing process: pre-writing (invention), developing questions and outlines, composing statements, and proofreading. While the writing process is different for each person and for each unique assignment, the resources contained in this section follow the general work flow of pre-writing, organizing, and revising. This resource will help you find material for the many different kinds of writing tasks you may face in school and in the workplace.

Read the story, or article the entire way through once. This gives you an overall view of what is going on. Underline or circle the portions that you absolutely must know. This information may include due date, research (source) requirements, page length, and format (MLA, APA, CMS). Underline or circle important phrases. You should know your instructor at least a little by now - what phrases does she use in class? Does he repeatedly say a specific word? If these are in the material, you know the instructor wants you to use them in the assignment. Think about how you will address the material. The material contains clues on how to write the assignment. Your instructor will often describe the ideas she wants discussed either in questions, in bullet points, or in the text of the material. Think about each of these sentences and number them so that you can write a paragraph or section of your essay on that portion if necessary. Rank ideas in descending order, from most important to least important. You may find out much more information than you can cover in your assignment, so rank them in the order you think is more important. Ask questions.

After you are finished with the above steps, ask yourself the following questions: What is the purpose of this assignment? Is my purpose to provide information without forming an argument, to construct an argument based on research, or analyze a poem and discuss its imagery? Who is my audience? Is my instructor my only audience? Who else might read this? Will it be posted online? What are my readers' needs and expectations? What resources do I need to begin work? Do I need to conduct literature (hermeneutic or historical) research, or do I need to review important literature on the topic and then conduct empirical research, such as a survey or an observation? How many sources are required?

ď ś For help if you have questions about an assignment condense your questions into shorter formats to email to our Tutoring department: tutoring@esl180.com and attend the Tutoring classes Live On Line. Providing excellence in home school education since 1988


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Your essay should begin with an introduction that includes your topic and indicates 1 the general direction of your argument. You need to have a clear thesis that appears early in your paper. Your conclusion should restate the thesis in different words, 2 and then draw some additional meaningful analysis out of the developments of your argument. Think of this as a "so what" factor. What are some implications for the future, relating to your topic? What does all this mean for society? A good conclusion moves outside the topic in the paper and deals with a larger issue. You should spend at least one paragraph acknowledging and describing the opposing position in a manner that is respectful and honestly representative of the opposition’s 3 views. The counterargument does not need to occur in a certain area, but generally begins or ends your argument. Attempting to prove each aspect of your argument’s structure should comprise the majority of your paper. Ask yourself what your argument assumes and what must be proven in order to validate your claims. Then go step-by-step, paragraph-by-paragraph, addressing each facet of your position. Most important part! Finally, pay attention to readability. Just because this is a research paper does not mean that it has to be boring. Use examples and allow your opinion to show through word choice and tone. Proofread before you turn in the paper.

THE WRITING PROCESS

How to begin the writing process Writing takes time Write out a plan of action. This may seem irrelevant to the writing process, but it's not. Writing is a process. Even the best professional writers don't just sit down at a computer, write, and call it a day. The quality of your writing will reflect the time and forethought you put into the assignment. Plan ahead for the assignment by doing pre-writing: this will allow you to be more productive and organized when you sit down to write. Also, schedule several blocks of time to devote to your writing; then, you can walk away from it for a while and come back later to make changes and revisions with a fresh mind. Keep the purpose of your writing in mind; Here are some examples Summarizing: Presenting the main points or essence of another text in a condensed form Arguing/Persuading: Expressing a viewpoint on an issue or topic in an effort to convince others that your viewpoint is correct Narrating: Telling a story or giving an account of events Evaluating: Examining something in order to determine its value or worth based on a set of criteria.

Providing excellence in home school education since 1988


. Analyzing: Breaking a topic down into its component parts in order to examine the relationships between the parts. Responding: Writing that is in a direct dialogue with another text. Examining/Investigating: Systematically questioning a topic to discover or uncover facts that are not widely known or accepted, in a way that strives to be as neutral and objective as possible. Observing: Helping the reader see and understand a person, place, object, image or event that you have directly watched or experienced through detailed sensory descriptions.

Pre-writing strategies Once you have thesis statement just start writing! Don't worry about spelling, grammar, or writing in complete sentences. Brainstorm and write down everything you can think of that might relate to the thesis and then reread and evaluate the ideas you generated. It's easier to cut out bad ideas than to only think of good ones. Once you have a few useful ways to approach the thesis you can use a basic outline structure to begin to think about organization. Remember to be flexible; this is just a way to get you writing. If better ideas occur to you as you're writing, don't be afraid to refine your original ideas. Begin to get fresh new ideas Gather as many good and bad ideas, suggestions, examples, sentences, false starts, etc. as you can. Perhaps some friends can join in. Jot down everything that comes to mind, including material you are sure you will throw out. Be ready to keep adding to the list at odd moments as ideas continue to come to mind. Talk to your audience, or pretend that you are being interviewed by someone — or by several people, if possible (to give yourself the opportunity of considering a subject from several different points of view). What questions would the other person ask? You might also try to teach the subject to a group or class. See if you can find a fresh analogy that opens up a new set of ideas. Build your analogy by using the word like. For example, if you are writing about violence on television, is that violence like clowns fighting in a carnival act (that is, we know that no one is really getting hurt)?

Tips     

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Take a rest and let it all percolate. Summarize your whole idea. Tell it to someone in three or four sentences. Diagram your major points somehow. Make a tree, outline, or whatever helps you to see a schematic representation of what you have. You may discover the need for more material in some places. Write a first draft. Then, if possible, put it away. Later, read it aloud or to yourself as if you were someone else. Watch especially for the need to clarify or add more information. You may find yourself jumping back and forth among these various strategies.

Providing excellence in home school education since 1988


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You may find that one works better than another. You may find yourself trying several strategies at once. If so, then you are probably doing something right.

Questions to yourself about what your purpose is for writing about the subject. There are many "correct" things to write about for any subject, but you need to narrow down your choices. For example, your topic might be "hospital food." At this point, you and your potential reader are asking the same question, "So what?" Why should you write about this, and why should anyone read it? Do you want the reader to pity you because of the intolerable food you have to eat there? Do you want to analyze large-scale institutional cooking? Do you want to compare City Hospital food to that served at The Baptist Hospital? Ask yourself how you are going to achieve this purpose. How, for example, would you achieve your purpose if you wanted to describe some movie as the best you've ever seen? Would you define for yourself a specific means of doing so? Would your comments on the movie go beyond merely telling the reader that you really liked it?

ACCADEMIC WRITING Here you will examine the types of writing you may encounter while in writing assignments, such book reports, and research papers. Here are some factors that contribute to strong, wellorganized writing. This presentation is suitable for the assignment of a writing project in any class.

What is a Text? Usually, the word “text” refers to a written or typed document. In terms of a rhetorical situation, however, “text” means any form of communication a person can create. Whenever we engage in any act of communication, a text is what we use to communicate. Three basic factors affect the nature of each text: the medium of the text, the tools used to create the text, and the tools used to decipher the text.

Medium of a Text Texts can appear in any kind of mechanism for communicating. The plural of medium in this sense is media. Various media affect the ways that authors and audiences communicate. Consider how these different types of media can affect how and what authors communicate to audiences in various rhetorical situations: hand-written, typed, computer-generated, audio, visual, spoken, verbal, non-verbal, graphic, pictorial, tactile, with words, or without words (there are many others, of course). Some varied specific examples of media could include a paper, a speech, a letter, an advertisement, a billboard, a presentation, a poster-board, a cartoon, a movie, a painting, a sculpture, an email, a Twitter tweet, a Providing excellence in home school education since 1988


. Facebook post, graffiti, a conversation (face-to-face, on a cell phone, via text messages) ... Tools to Make a Text Every text is made with tools that affect the structure and content of a text. Such tools could be physical tools that range from very basic (such as, teeth, lips, and tongue necessary for verbal communication) to very complex (such as a laptop computer with software). Tools to translate and understand a Text Likewise, audiences have varied tools for reading, viewing, hearing, or otherwise appreciating various texts. These could be actual physical tools that would likewise range from very basic (like the eyes and reading glasses necessary to read) to very complex (like a digital projector and screen to view a PowerPoint presentation).

The Purpose for the text Authors and audiences both have a wide range of purposes for communicating. The importance of purpose cannot be overstated. It is the varied purposes that determine how an author communicates a text and how audiences receive a text. Rarely is there only one purpose. Authors and audiences tend to bring their own purposes (and often multiple purposes each) to a rhetorical situation, and these purposes may conflict or complement each other depending on the efforts of both authors and audiences. Authors’ purposes Most texts written in college or in the workplace often fill one of two broader purposes: to be informative or to be persuasive. Under each of these two broad purposes, they identify a host of more specific purposes. The following table show some of the purposes authors could easily have purposes that are not listed on this table. Author Purposes Informative to inform to describe to define to review to notify to instruct to advise to announce to explain to demonstrate to illustrate

Persuasive to persuade to convince to influence to argue to recommend to change to advocate to urge to defend to justify to support

Audiences’ purposes The audiences’ purposes may range from more passive purpose to more active purposes. Audience Purposes More Passive Purposes to receive notice to feel reassured

More Active Purposes to examine to quantify Providing excellence in home school education since 1988


. to feel a sense of unity to be entertained to receive instruction to enjoy to hear advice to be inspired to review to understand to learn

to assess to make informed decisions to interpret to evaluate to judge to resist change to criticize to ridicule to disprove

The Role of Purposes Authors’ and audiences’ purposes in communicating determine the basic rationale behind other decisions both authors and audiences make (such as what to write or speak about, or whom to listen to, or what medium to use, or what setting to read in, among others). An author’s purpose in communicating could be to instruct, persuade, inform, entertain, educate, startle, excite, sadden, enlighten, punish, console, or many, many others. Like authors, audiences have varied purposes for reading, listening to, or otherwise appreciating pieces of communication. Audiences may seek to be instructed, persuaded, informed, entertained, educated, startled, excited, saddened, enlightened, punished, consoled, or many, many others. Authors’ and audiences’ purposes are only limited to what authors and audiences want to accomplish in their moments of communication. There are as many purposes for communicating as there are words to describe those purposes.

Attitude Attitude is related to purpose and is a much-overlooked element of rhetorical situations. But attitude affects a great deal of how a rhetorical situation unfolds. Consider if an author communicates with a flippant attitude as opposed to a serious attitude, or with drama as opposed to comedy, or calmly as opposed to excitedly. Depending on authors’ purposes, audiences’ specific qualities, the nature of the context, and other factors, any of these attitudes could either help or hinder authors in their efforts to communicate depending on the other factors in any given rhetorical situation. Like authors, audiences bring diverse attitudes to how they appreciate different pieces of communication. The audience’s attitude while reading, listening, observing, or whatnot affects how they receive and process the communication they receive.

The Setting The time and location in which a story takes place is called the setting. For some the setting is very important, while for others it is not. There are several aspects of a story's setting to consider when examining how setting contributes to a story (some, or all, may be present in a story): a) place - geographical location. Where is the action of the story taking place? b) time - When is the story taking place? (historical period, time of day, year, etc) c) weather conditions - Is it rainy, sunny, stormy, etc? d) social conditions - What is the daily life of the characters like? Does the story contain local colour (writing that focuses on the speech, dress, mannerisms, customs, of a particular place)?

Providing excellence in home school education since 1988


. e) mood or atmosphere - What feeling is created at the beginning of the story? Is it bright and cheerful or dark and frightening? Time “Time” in this sense refers to specific moments in history. It is fairly common knowledge that different people communicate differently depending on the time in which they live. Americans in the 1950s, overall, communicate differently than Americans in the 2000s. Not that they necessarily speak a different language, but these two groups of people have different assumptions about the world and how to communicate based on the era in which they live. Different moments in time can be closer together and still affect the ways that people communicate. Certainly, scientists discussed physics somewhat differently the year after Einstein published his theory of relativity than they did the year before Einstein published his treatise. Also, an author and audience may be located at different times in relation to one another. Today, we appreciate Shakespeare’s Hamlet a bit differently than the people who watched it when it first premiered four hundred years ago. A lot of cultural norms have changed since then. Place Similarly, the specific places of authors and their audiences affect the ways that texts are made and received. At a rally, the place may be the steps of a national monument. In an academic conference or lecture hall or court case, the place is a specific room. In other rhetorical situations, the place may be the pages of an academic journal in which different authors respond to one another in essay form. And, as mentioned about authors’ and audiences’ backgrounds, the places from which audiences and authors emerge affect the ways that different texts are made and received. Community / Conversation In various rhetorical situations, “community” or “conversation” can be used to refer to the specific kinds of social interactions among authors and audiences. Outside of speaking about rhetorical situations, “community” usually means specific groups of people united by location and proximity like a neighborhood; “conversation” usually refers to fairly intimate occasions of discussion among a small number of people. But in regard to rhetorical situations, both of these terms can have much larger meanings. In any given rhetorical situation, “community” and “conversation” can refer to the people specifically involved in the act of communication. For instance, consider Pablo Picasso who used cubism to challenge international notions of art at the time he painted. Picasso was involved in a worldwide “community” of artists, art critics, and other appreciators of art many of whom were actively engaged in an extended “conversation” with differing assumptions about what art is and ought to be. Sometimes, authors and audiences participate in the same community and conversation, but in many instances, authors may communicate in one community and conversation (again, think of Shakespeare four hundred years ago in England) while audiences may participate in a different community and conversation (think of scholars today in any other country in the world who discuss and debate the nature of Shakespeare’s plays).

Read this example of a famous speech and identify its components: “I Have a Dream” Speech A lot of what was covered above may still seem abstract and complicated. To illustrate how diverse kinds of texts have their own rhetorical situations, consider the following examples.

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. First, consider Dr. Martin Luther King’s famous “I Have a Dream” speech. Because this speech is famous, it should be very easy to identify the basic elements of its particular rhetorical situation. Text The text in question is a 17-minute speech written and delivered by Dr. King. The basic medium of the text was an oral speech that was broadcast by both loudspeakers at the event and over radio and television. Dr. King drew on years of training as a minister and public speaker to deliver the speech. He also drew on his extensive education and the tumultuous history of racial prejudices and civil rights in the US. Audiences at the time either heard his speech in person or over radio or television broadcasts. Part of the speech near the end was improvised around the repeated phrase “I have a dream.” [Print Version of the speech] Author Dr. Martin Luther King, Jr. was the most iconic leader of the American Civil Rights Movement in the 1950s and 1960s. He was an African-American Baptist minister and prominent civil rights activist who campaigned to end segregation and racial discrimination. He gained inspiration from Howard Thurman and Mahatma Gandhi, and he drew extensively from a deep, rich cultural tradition of African-American Christian spiritualism. Audience The audiences for “I Have a Dream” are extraordinarily varied. In one sense, the audience consisted of the 200,000 or so people who listened to Dr. King in person. But Dr. King also overtly appealed to lawmakers and citizens everywhere in America at the time of his speech. There were also millions of people who heard his speech over radio and television at the time. And many more millions people since 1963 have heard recordings of the speech in video, audio, or digital form. Purposes Dr. King’s immediate purposes appear to have been to convince Americans across the country to embrace racial equality and to further strengthen the resolve of those already involved in the Civil Rights Movement. Audiences’ purposes are not as easily summarized. Some at the time may have sought to be inspired by Dr. King. Opponents to racial equality who heard his speech may have listened for the purpose of seeking to find ways to further argue against racial equality. Audiences since then may have used the speech to educate or to advocate for other social justice issues. Setting The initial setting for the speech was on the steps of the Lincoln Memorial in Washington, DC on August 28, 1963. The immediate community and conversation for the speech was the ongoing Civil Rights Movement that had gained particular momentum with the 1955 Montgomery Bus Boycott, which Dr. King helped direct. But the enduring nature of Dr. King’s speech has broadened the setting to include many countries and many people who have since read or listened to his speech. Certainly, people listening to his speech for the first time today in America are experiencing a different mix of cultural attitudes toward race than as present in America in 1963. Analysis Dr. King’s speech is an example of a rhetorical situation that is much bigger than its initial text and audience. Not many rhetorical situations are as far reaching in scope as Dr. King’s “I Have a Dream” speech. The following example of a research paper may be more identifiable to students reading this resource. Providing excellence in home school education since 1988


. HOW TO ESTABLISH AN ARGUMENT

Developing a strong position or argument The thesis statement2 or main claim must be debatable An argumentative or persuasive piece of writing must begin with a debatable thesis or claim. In other words, the thesis must be something that people could reasonably have differing opinions on. If your thesis is something that is generally agreed upon or accepted as fact then there is no reason to try to persuade people.

Examples: Example of a non-debatable thesis statement: Pollution is bad for the environment. This thesis statement is not debatable. First, the word pollution means that something is bad or negative in some way. Further, all studies agree that pollution is a problem; they simply disagree on the impact it will have or the scope of the problem. No one could reasonably argue that pollution is good. Example of a debatable thesis statement: At least 25 percent of the federal budget should be spent on limiting pollution. This is an example of a debatable thesis because reasonable people could disagree with it. Some people might think that this is how we should spend the nation's money. Others might feel that we should be spending more money on education. Still others could argue that corporations, not the government, should be paying to limit pollution. Another example of a debatable thesis statement: America's anti-pollution efforts should focus on privately owned cars. In this example there is also room for disagreement between rational individuals. Some citizens might think focusing on recycling programs rather than private automobiles is the most effective strategy. The thesis needs to be narrow Although the scope of your paper might seem overwhelming at the start, generally the narrower the thesis the more effective your argument will be. Your thesis or claim must be supported by evidence. The broader your claim is, the more evidence you will need to convince readers that your position is right. Example of a thesis that is too broad: Drug use is detrimental to society. There are several reasons this statement is too broad to argue. First, what is included in the category "drugs"? Is the author talking about illegal drug use, recreational drug use (which might include alcohol and cigarettes), or all uses of medication in general? Second, in what ways are drugs detrimental? Is drug use causing deaths (and is the author equating deaths 2

A thesis statement is a short statement that summarizes the main point or claim of an essay, research paper, etc., and is developed, supported, and explained in the text by means of examples and evidence. Providing excellence in home school education since 1988


. from overdoses and deaths from drug related violence)? Is drug use changing the moral climate or causing the economy to decline? Finally, what does the author mean by "society"? Is the author referring only to America or to the global population? Does the author make any distinction between the effects on children and adults? There are just too many questions that the claim leaves open. The author could not cover all of the topics listed above, yet the generality of the claim leaves all of these possibilities open to debate. Example of a narrow or focused thesis: Illegal drug use is detrimental because it encourages gang violence. In this example the topic of drugs has been narrowed down to illegal drugs and the detriment has been narrowed down to gang violence. This is a much more manageable topic. We could narrow each debatable thesis from the previous examples in the following way: Narrowed debatable thesis 1: At least 25 percent of the federal budget should be spent on helping upgrade business to clean technologies, researching renewable energy sources, and planting more trees in order to control or eliminate pollution. This thesis narrows the scope of the argument by specifying not just the amount of money used but also how the money could actually help to control pollution. Narrowed debatable thesis 2: America's anti-pollution efforts should focus on privately owned cars because it would allow most citizens to contribute to national efforts and care about the outcome. This thesis narrows the scope of the argument by specifying not just what the focus of a national anti-pollution campaign should be but also why this is the appropriate focus. Qualifiers such as "typically," "generally," "usually," or "on average" also help to limit the scope of your claim by allowing for the almost inevitable exception to the rule. Claims Claims typically fall into one of four categories. Thinking about how you want to approach your topic, in other words what type of claim you want to make, is one way to focus your thesis on one particular aspect of your broader topic. Claims of fact or definition: These claims argue about what the definition of something is or whether something is a settled fact. Example: What some people refer to as global warming is actually nothing more than normal, long-term cycles of climate change.. Claims of cause and effect: These claims argue that one person, thing, or event caused another thing or event to occur. Example:The popularity of SUV's in America has caused pollution to increase. Claims about value: These are claims made of what something is worth, whether we value it or not, how we would rate or categorize something. Example: Global warming is the most pressing challenge facing the world today. Claims about solutions or policies: These are claims that argue for or against a certain solution or policy approach to a problem. Example: Instead of drilling for oil in Alaska we should be focusing on ways to reduce oil consumption, such as researching renewable energy sources. Providing excellence in home school education since 1988


. Which type of claim is right for your argument? Which type of thesis or claim you use for your argument will depend on your position and knowledge of the topic, your audience, and the context of your paper. You might want to think about where you imagine your audience to be on this topic and pinpoint where you think the biggest difference in viewpoints might be. Even if you start with one type of claim you probably will be using several within the paper. Regardless of the type of claim you choose to utilize it is key to identify the controversy or debate you are addressing and to define your position early on in the paper.

HOW TO STRUTURE YOUR ESSAY WRITING

Logic in Argumentative Writing This resource covers using logic within writing— logical vocabulary, logical fallacies, and other types of logos-based reasoning. It is designed to help writers develop and use logical arguments in writing. This handout helps writers analyze the arguments of others and generate their own arguments. However, it is important to remember that logic is only one aspect of a successful argument. Non-logical arguments, statements that cannot be logically proven or disproved, are important in argumentative writing—such as appeals to emotions or values.Illogical arguments, on the other hand, are false and must be avoided. Logic is a formal system of analysis that helps writers invent, demonstrate, and prove arguments. It works by testing propositions against one another to determine their accuracy. People often think they are using logic when they avoid emotion or make arguments based on their common sense, such as "Everyone should look out for their own self interests" or "People have the right to be free." However, unemotional or common sense statements are not always equivalent to logical statements. To be logical, a proposition must be tested within a logical sequence. The most famous logical sequence, called the syllogism, was developed by the Greek philosopher Aristotle. His most famous syllogism is: Premise 1: All men are mortal. Premise 2: Socrates is a man. Conclusion: Therefore, Socrates is mortal. In this sequence, premise 2 is tested against premise 1 to reach the logical conclusion. Within this system, if both premises are considered valid, there is no other logical conclusion than determining that Socrates is a mortal. This guide provides some vocabulary and strategies for determining logical conclusions.

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On Paragraphs The basic instruction and advice regarding the creation of understandable and coherent paragraphs. The purpose of this handout is to give some basic instruction and advice regarding the creation of understandable and coherent paragraphs. What is a paragraph? A paragraph is a collection of related sentences dealing with a single topic. Learning to write good paragraphs will help you as a writer stay on track during your drafting and revision stages. Good paragraphing also greatly assists your readers in following a piece of writing. You can have fantastic ideas, but if those ideas aren't presented in an organized fashion, you will lose your readers (and fail to achieve your goals in writing). The Basic Rule: Keep one idea to one paragraph The basic rule of thumb with paragraphing is to keep one idea to one paragraph. If you begin to transition into a new idea, it belongs in a new paragraph. There are some simple ways to tell if you are on the same topic or a new one. You can have one idea and several bits of supporting evidence within a single paragraph. You can also have several points in a single paragraph as long as they relate to the overall topic of the paragraph. If the single points start to get long, then perhaps elaborating on each of them and placing them in their own paragraphs is the route to go. Elements of a paragraph To be as effective as possible, a paragraph should contain each of the following: Unity, Coherence, A Topic Sentence, and Adequate Development. As you will see, all of these traits overlap. Using and adapting them to your individual purposes will help you construct effective paragraphs. ELEMENTS (COMPONENTS) OF PARAGRAPHS The entire paragraph should concern itself with a single focus. If it begins Unity with one focus or major point of discussion, it should not end with another or wander within different ideas. Coherence is the trait that makes the paragraph easily understandable to a reader. You can help create coherence in your paragraphs by creating logical bridges and verbal bridges.

Coherence

Logical bridges

• The same idea of a topic is carried over from sentence to sentence • Successive sentences can be constructed in parallel form

Verbal bridges

• • • •

Key words can be repeated in several sentences Synonymous words can be repeated in several sentences Pronouns can refer to nouns in previous sentences Transition words can be used to link ideas from different sentences

A topic sentence A topic sentence is a sentence that indicates in a general way what idea or thesis the paragraph is going to deal with. Although not all paragraphs have clear-cut topic sentences, and despite the fact that topic sentences can occur anywhere in the paragraph (as the first sentence, the last sentence, or somewhere in the middle), an easy way to make sure your reader understands the topic of the paragraph is to put your topic sentence near the beginning of the paragraph. (This is a good general rule for less experienced writers, although it is not the only way to do it). Regardless of whether you include an explicit topic sentence or not, you should be able to easily summarize what the paragraph is about. Providing excellence in home school education since 1988


. Adequate development The topic (which is introduced by the topic sentence) should be discussed fully and adequately. Again, this varies from paragraph to paragraph, depending on the author's purpose, but writers should be wary of paragraphs that only have two or three sentences. It's a pretty good bet that the paragraph is not fully developed if it is that short. Some methods to make sure your paragraph is well-developed:  Use examples and illustrations  Cite data (facts, statistics, evidence, details, and others)  Examine testimony (what other people say such as quotes and paraphrases)  Use an anecdote or story  Define terms in the paragraph  Compare and contrast  Evaluate causes and reasons  Examine effects and consequences  Analyze the topic  Describe the topic  Offer a chronology of an event (time segments)

When to start a new paragraph? You should start a new paragraph when: When you begin a new idea or point. New ideas should always start in new paragraphs. If you have an extended idea that spans multiple paragraphs, each new point within that idea should have its own paragraph. To contrast information or ideas. Separate paragraphs can serve to contrast sides in a debate, different points in an argument, or any other difference. When your readers need a pause. Breaks between paragraphs function as a short "break" for your readers—adding these in will help your writing more readable. You would create a break if the paragraph becomes too long or the material is complex. When you are ending your introduction or starting your conclusion. Your introductory and concluding material should always be in a new paragraph. Many introductions and conclusions have multiple paragraphs depending on their content, length, and the writer's purpose. Transitions and signposts Two very important elements of paragraphing are signposts and transitions. Signposts are internal aids to assist readers; they usually consist of several sentences or a paragraph outlining what the article has covered and where the article will be going. Transitions are usually one or several sentences that "transition" from one idea to the next. Transitions can be used at the end of most paragraphs to help the paragraphs flow one into the next.

Conciseness This resource will help you write clearly by eliminating unnecessary words and rearranging your phrases. Providing excellence in home school education since 1988


. The goal here is to use the most effective words. Concise writing does not always have the fewest words, but it always uses the strongest ones. Writers often fill sentences with weak or unnecessary words that can be deleted or replaced. Words and phrases should be deliberately chosen for the work they are doing. Like bad employees, words that don't accomplish enough should be fired. When only the most effective words remain, writing will be far more concise and readable. This resource contains general conciseness tips followed by very specific strategies for pruning sentences.

Replace several vague words with more powerful and specific words. Often, writers use several small and ambiguous words to express a concept, wasting energy expressing ideas better relayed through fewer specific words. As a general rule, more specific words lead to more concise writing. Because of the variety of nouns, verbs, and adjectives, most things have a closely corresponding description. Brainstorming or searching a thesaurus can lead to the word best suited for a specific instance. Notice that the examples below actually convey more as they drop in word count.

EXAMPLES Wordy: The politician talked about several of the merits of after-school programs in his speech (14 words) Concise: The politician touted after-school programs in his speech. (8 words) Wordy: Suzie believed but could not confirm that Billy had feelings of affection for her. (14 words) Concise: Suzie assumed that Billy adored her. (6 words) Wordy: Our Web site has made available many of the things you can usefor making a decision on the best dentist. (20 words) Concise: Our website presents criteria for determining the best dentist. (9 words) Wordy: Working as a pupil under someone who develops photos was an experience that really helped me learn a lot. (20 words) Concise: Working as a photo technician's apprentice was an educational experience. (10 words) Examine every word in a sentence Check every word to make sure that it is providing something important and unique to a sentence. If words are dead weight, they can be deleted or replaced. Other sections in this handout cover this concept more specifically, but there are some general examples below containing sentences with words that could be cut.

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. Wordy: The teacher demonstrated some of the various ways and methods for cutting words from my essay that I had written for class. (22 words) b) Concise: The teacher demonstrated methods for cutting words from my essay. (10 words) a)

Wordy: Eric Clapton and Steve Winwood formed a new band of musicians together in 1969, giving it the ironic name of Blind Faith because early speculation that was spreading everywhere about the band suggested that the new musical group would be good enough to rival the earlier bands that both men had been in, Cream and Traffic, which people had really liked and had been very popular. (66 words) d) Concise: Eric Clapton and Steve Winwood formed a new band in 1969, ironically naming it Blind Faith because speculation suggested that the group would rival the musicians’ previous popular bands, Cream and Traffic. (32 words) c)

e)

f)

Wordy: Many have made the wise observation that when a stone is in motion rolling down a hill or incline that that moving stone is not as likely to be covered all over with the kind of thick green moss that grows on stationary unmoving things and becomes a nuisance and suggests that those things haven’t moved in a long time and probably won’t move any time soon. (67 words) Concise: A rolling stone gathers no moss. (6 words)

Combine Sentences. Some information does not require a full sentence, and can easily be inserted into another sentence without losing any of its value. a) Wordy: Ludwig's castles are an astounding marriage of beauty and madness. By his death, he had commissioned three castles. (18 words) b) Concise: Ludwig's three castles are an astounding marriage of beauty and madness. (11 words) Wordy: The supposed crash of a UFO in Roswell, New Mexico aroused interest in extraterrestrial life. This crash is rumored to have occurred in 1947. (24 words) d) Concise: The supposed 1947 crash of a UFO in Roswell, New Mexico aroused interest in extraterrestrial life. (16 words) c)

A Lesson in Writing Concisely Steps and exercises to eliminate wordiness at the sentence level. Editing your writing using the following methods will make your prose easier to read. Sentences that are easy to read are more persuasive and easier to understand. Professional writers understand the need for clear, concise prose. An industry standard for helping workplace writers achieve user-centered, persuasive, and clear prose reducing your word count by eliminating unnecessary words and by eliminating passive voice and redundancies. . Follow the seven steps below to improve the readability of your sentences. 1. 2. 3. 4. 5.

Circle the prepositions (of, in, about, for, onto, into) Draw a box around the "is" verb forms Ask, "Where's the action?" Change the "action" into a simple verb Move the doer into the subject (Who's kicking whom) 6. Eliminate any unnecessary slow wind-ups 7. Eliminate any redundancies. Providing excellence in home school education since 1988


. EXAMPLES 1. The point I wish to make is that the employees working at this company are in need of a much better manager of their money. 2. It is widely known that the engineers at Sandia Labs have become active participants in the Search and Rescue operations in most years. 3. After reviewing the results of your previous research, and in light of the relevant information found within the context of the study, there is ample evidence for making important, significant changes to our operating procedures.

Examples of Concise Solutions: 1. Employees at this company need a better money manager. (Original word count: 26. New word count: 10). 2. In recent years, engineers at Sandia Labs have participated in the Search and Rescue operations. (Original word count: 24. New word count: 16). 3. After reviewing the results of your research, and within the context of the study, we find evidence supporting significant changes in our operating procedures. (Original word count: 36. New word count: 25).

Sentence Variety This resource presents methods for adding sentence variety and complexity to writing that may sound repetitive or boring. Sections are divided into general tips for varying structure, a discussion of sentence types, and specific parts of speech which can aid in sentence variety. Adding sentence variety to prose can give it life and rhythm. Too many sentences with the same structure and length can grow monotonous for readers. Varying sentence style and structure can also reduce repetition and add emphasis. Long sentences work well for incorporating a lot of information, and short sentences can often maximize crucial points. These general tips may help add variety to similar sentences. Vary the rhythm by alternating short and long sentences. Several sentences of the same length can make for bland writing. To enliven paragraphs, write sentences of different lengths. This will also allow for effective emphasis. Example: The Winslow family visited Canada and Alaska last summer to find some native American art. In Anchorage stores they found some excellent examples of soapstone carvings. But they couldn't find a dealer selling any of the woven wall hangings they wanted. They were very disappointed when they left Anchorage empty-handed. Revision: The Winslow family visited Canada and Alaska last summer to find some native American art, such as soapstone carvings and wall hangings. Anchorage stores had many soapstone items available. Still, they were disappointed to learn that wall hangings, which they had especially wanted, were difficult to find. Sadly, they left empty-handed.

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. Example: Many really good blues guitarists have all had the last name King. They have been named Freddie King and Albert King and B.B. King. The name King must make a bluesman a really good bluesman. The bluesmen named King have all been very talented and good guitar players. The claim that a name can make a guitarist good may not be that far-fetched. Revision: What makes a good bluesman? Maybe, just maybe, it's all in a stately name. B.B. King. Freddie King. Albert King. It's no coincidence that they're the royalty of their genre. When their fingers dance like court jesters, their guitars gleam like scepters, and their voices bellow like regal trumpets, they seem almost like nobility. Hearing their music is like walking into the throne room. They really are kings.

Vary sentence openings. If too many sentences start with the same word, especially The, It, This, or I, prose can grow tedious for readers, so changing opening words and phrases can be refreshing. Below are alternative openings for a fairly standard sentence. Notice that different beginnings can alter not only the structure but also the emphasis of the sentence. They may also require rephrasing in sentences before or after this one, meaning that one change could lead to an abundance of sentence variety. Example: The biggest coincidence that day happened when David and I ended up sitting next to each other at the Super Bowl. Possible Revisions: 

Coincidentally, David and I ended up sitting right next to each other at the Super Bowl.

In an amazing coincidence, David and I ended up sitting next to each other at the Super Bowl.

Sitting next to David at the Super Bowl was a tremendous coincidence.

But the biggest coincidence that day happened when David and I ended up sitting next to each other at the Super Bowl.

When I sat down at the Super Bowl, I realized that, by sheer coincidence, I was directly next to David. Providing excellence in home school education since 1988


. 

By sheer coincidence, I ended up sitting directly next to David at the Super Bowl.

With over 50,000 fans at the Super Bowl, it took an incredible coincidence for me to end up sitting right next to David.

What are the odds that I would have ended up sitting right next to David at the Super Bowl?

David and I, without any prior planning, ended up sitting right next to each other at the Super Bowl.

Without any prior planning, David and I ended up sitting right next to each other at the Super Bowl.

At the crowded Super Bowl, packed with 50,000 screaming fans, David and I ended up sitting right next to each other by sheer coincidence.

Though I hadn't made any advance arrangements with David, we ended up sitting right next to each other at the Super Bowl.

Many amazing coincidences occurred that day, but nothing topped sitting right next to David at the Super Bowl.

Unbelievable, I know, but David and I ended up sitting right next to each other at the Super Bowl.

Guided by some bizarre coincidence, David and I ended up sitting right next to each other at the Super Bowl.

Using Appropriate Language Major issues with appropriate language use: levels of language formality, deceitful language and euphemisms, slang and idiomatic expressions; using group-specific jargon; and biased/stereotypical language. When writing, it is very important to use language that fits your audience and matches purpose. Inappropriate language uses can damage your credibility, undermine your argument, or alienate your audience. This handout will cover some of the major issues with appropriate language use: levels of language formality, deceitful language and Euphemisms, slang and idiomatic expressions; using group-specific jargon; and biased/stereotypical language. The following is a short overview of the different aspects of using appropriate language. Review the other sections of this handout for a more complete discussion. 1. Levels of Formality: Writing in a style that your audience expects and that fits your purpose is key to successful writing. 2. In-Group Jargon: Jargon refers to specialized language used by groups of like-minded individuals. Only use in-group jargon when you are writing for members of that group. You should never use jargon for a general audience without first explaining it. 3. Slang and idiomatic expressions: Avoid using slang or idiomatic expressions in general academic writing. 4. Deceitful language and Euphemisms: Avoid using euphemisms (words that veil the truth, such as "collateral damage" for the unintended destruction of civilians and their property) and other deceitful language. 5. Biased language: Avoid using any biased language including language with a racial, ethnic, group, or gender bias or language that is stereotypical. Providing excellence in home school education since 1988


. Active and Passive Voice This section helps you to know the difference between active and passive voice in writing. We give examples of both, and shows how to turn a passive sentence into an active one. Also, it explains how to decide when to choose passive voice instead of active. Using Active Versus Passive Voice In a sentence using active voice, the subject of the sentence performs the action expressed in the verb.

The arrow points from the subject performing the action (the dog) to the individual being acted upon (the boy). This is an example of a sentence using the active voice.

Sample active voice sentence with the subject performing the action described by the verb.

The active voice sentence subject (watching a framed, mobile world) performs the action of reminding the speaker of something. Each example above includes a sentence subject performing the action expressed by the verb. Active Verb Tenses Simple Present Present or Action Condition

General Truths

I hear you. Here comes the bus.

There are thirty days in September.

Non-action; Habitual Action

Future Time

I like music. I run on Tuesdays and Sundays.

The train leaves at 4:00 p.m.

Present Progressive Activity in Progress I am playing soccer now.

Verbs of Perception He is feeling sad. Simple Past

Completed Action

Completed Condition

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. We visited the museum yesterday.

The weather was rainy last week.

Past Progressive Past Action that took place over a period of time

Past Action interrupted by another

They were climbing for twenty-seven days.

We were eating dinner when she told me.

Future With will/won't — Activity or event that will or won't exist or happen in the future I'll get up late tomorrow. I won't get up early

With going to — future in relation to circumstances in the present I'm hungry. I'm going to get something to eat.

Present Perfect With verbs of state that begin in the past and lead up to and include the present He has lived here for many years

To express habitual or continued action He has worn glasses all his life.

With events occurring at an indefinite or unspecified time in the past — with ever, never, before Have you ever been to Tokyo before? Present Perfect Progressive To express duration of an action that began in the past, has continued into the present, and may continue into the future David has been working for two hours, and he hasn't finished yet. Past Perfect To describe a past event or condition completed before another event in the past When I arrived home, he had already called.

In reported speech Jane said that she had gone to the movies.

Future Perfect To express action that will be completed by or before a specified time in the future By next month we will have finished the job. He won't have finished his work until 2:00.

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Mathematics

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Math Fundamentals Part 1 This Math section will help you build foundational math skills. Our carefully paced, guided instruction and interactive tools effectively present math skills and the conceptual understanding you need to bridge, with confidence, to upper level math courses.

Part 1 Part 1 includes review of the real number system including rational numbers, rules for combining and multiplying real numbers, order of operations, connecting words and numbers through expressions, developing a plan to solve a problem , combining like terms, definition and examples of ordered pairs, grids, quadrants, abscissa, defining linear equations, graphing equation systems, three-variable equations, matrix multiplication, transformation, point and matrix transformations, polynomial types, zero as an exponent, finding higher variables, factoring numerators, and solving complex rationals. Algebra Part 2 This covers the review of square roots, radicals, complex pure and imaginary numbers, solving and factoring, identifying and evaluating the discriminant of a quadratic equation, rewriting equations, solving problems with number lines, graphing parabola, circle parts and formulas, hyperbola, graphing quadratic relations and inequalities, inverse functions, compound interest problems, sequences of numbers, identification of sigma, examples and definition of common ratios, finite series, and solving factorial problems.

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. Glossary absolute value

The value of a number without regard to its sign.

Additive Inverse Property

States that every real number added to its additive inverse (or opposite) will equal zero: For all real numbers a, a + (-a) = 0; also called Inverse Property of Addition.

Coefficient

A number that multiplies a variable.

common denominator

A number that is a multiple of all of the denominators in a group of fractions.

Distributive Property

States that the product of a number and a sum equals the sum of the individual products of the number and the addends: for all real numbers a, b, and c, a(b + c) = ab + ac.

Equation

A statement that describes the equality of two expressions by connecting them with an equals sign.

formula

A type of equation—usually reserved for multi-variable equations that describe a well-known or often repeated calculation.

inverse operations

Operations that undo or cancel one another, such as addition/subtraction and multiplication/division.

Multiplicative Inverse Property

States that any number multiplied by 1 over that number equals 1: For all real numbers a, a 

1  1 ; also called Inverse Property of a

Multiplication. multi-step equation

An equation that requires more than one step to solve.

numeric constant

A quantity that has a known, fixed value.

operation

A mathematical procedure, such as addition, subtraction, multiplication, and division

Property of Equality

States that the equality of an equation is maintained when both sides have the same value added, subtracted, multiplied, or divided.

variable

A symbol that represents an unknown value.

To see these and all other available Instructor Resources, visit the NROC Network.

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Unit 3 – Functions and Patterns First Edition Lesson 1 – Working with Patterns

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. 11.1.2 Multiplying and Dividing Rational Expression Learning Objective(s) 1 Multiply and divide rational expressions and simplify.

Introduction Just as we can multiply and divide fractions, we can multiply and divide rational expressions, or fractions that include polynomials. In fact, we use the same processes for multiplying and dividing rational expressions as we use for multiplying and dividing numeric fractions. Objective 1

Multiplication of Rational Expressions There are two ways to go about multiplying fractions: We can multiply the numerators and the denominators and then simplify the product:

4 9 36 9  =  5 8 40 10 Or we can factor and simplify the fractions before performing the multiplication:

4 9 4  3 3 4 3  3 9 33 =  = 1 =  =  5 8 5 2 4 4 5 2 5  2 10 The same two approaches can be applied to rational expressions. In the following examples, we'll try both techniques: multiply, then simplify; and simplify, then multiply. An important  fractions  and rational expressions, though,  is that we must identify any difference between values for the variables that would result in division by 0 since this is undefined. These excluded values must be eliminated from the domain, the set of all possible values of the variable. First, we'll multiply and then simplify: Example Problem

Solve

5a 2 7  14 10a 3 10a3 = 0



a=0

The domain is all a  0

35a 2 140a 3

Determine if there are excluded values, values of a which result in 0 as a denominator—14 cannot equal 0, 10a3 can. Multiply the numerators together, and multiply the denominators together

 inding a counterexample doesn't call for despair—we may be able to use the new information to revise our conjecture.



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. Example Problem

Deshawn looked at the x, x2, and x3 values below and decided that x ≤ x2 ≤ x3 for all real numbers. Find counterexamples and refine Deshawn's conjecture.

2

X

x2

x3

1

1

1

2

4

8

3

9

27

4

16

64

5

25

125

3

2

3

x

x

x

x≤x ≤x?

0.5

0.25

0.125

No

1.5

2.25

3.375

Yes

-1

1

-1

No

-1.5

2.25

-3.375

No

-0.5

0.25

-0.125

No

The table only includes natural numbers for x, but Deshawn overgeneralized the results to all real numbers. The conjecture is true for some rational numbers (such as x=1.5), but not all of them (such as x = 0.5). It doesn't appear to be true for any negative numbers. To get a good look at when this inequality is true, graph the functions, y = x (in red), y = x2 (in blue), and y = x3 (in green).

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. The inequality says the red should be below both the blue and green, and the blue should be below the green. Find the areas where this is true. The red is below the blue when x < 0 and x > 1. However, the green is below (or touches) the blue when x < 1. So the only values when x < x2 < x3 is x > 1. Answer

Counterexamples: x = 0.5, x = -0.5, and x = -1. Revised conjecture: x ≤ x2 ≤ x3 for all real numbers of x ≥ 1.

Since Deshawn's conjecture included x = x2 = x3, the value x = 1 can be included in the revision.

Objective 1

Identifying Inductive Reasoning

Because conjectures based on inductive reasoning may or may not be true, it's important to recognize when inductive reasoning is being used to make a conjecture. Then we can think more about whether the conjecture is reasonable based on the observations, whether the conjecture overgeneralizes those observations, and whether there may be counterexamples that we should look for.

Example Problem

Jeanne's birthday was on a Wednesday one year. She noticed that the next year it would fall on a Thursday, and it would fall on a Friday in two years. Without checking, she said, "My birthday will be on a Wednesday again in seven years." Is she using inductive reasoning? Why or why not? Whether or not Jeanne is using inductive reasoning depends on the process she uses, not whether she is correct or not. Jeanne has:  Noticed similarities and differences in the day her birthday falls each year. For the three years she observed, she noticed that the day of the week was one later each year.  Generalized her observations, assuming that the pattern Providing excellence in home school education since 1988


. would continue. Formed a conjecture. Although she didn't state it, exactly, her conjecture was: If my birthday is x years after my last birthday, it will fall x days later in the week than my last birthday did. Notice that she even applied the conjecture to make a prediction (though that's not a necessary part of the inductive reasoning process). ď&#x20AC;­

Answer

Yes, she used inductive reasoning. She made a conjecture about a longer pattern by generalizing some specific observations.

(By the way, Jeanne's conjectu re is incorrect . A leap year occurs every four years and throws

the pattern off.) Self Check B When trying to graph y = |-x|, Benny reasoned this way: Absolute value just makes the value positive or zero. So, the result of |-x| is the positive version of x, or 0 if x = 0. But the result of |x| is also the positive version of x, or 0 if x = 0. That means |-x| = |x|. So the graph of y = |-x| is the same as the graph of y = |x|. Is Benny using inductive reasoning? A) No B) Yes

Summary Inductive reasoning is a kind of logical reasoning which involves drawing a general conclusion, called a conjecture, based on a specific set of observations. In this process, specific examples are examined for a pattern, and then the pattern is generalized by assuming it will continue in unseen examples. Conjectures and predictions can then be made. Conjectures may not be true, especially if a pattern has been overgeneralized, that is, applied to a larger set of circumstances than the observations support. If counterexamples to a conjecture are found, it may be possible to revise it so that it becomes always true.

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. 12.1.3 Self Check Solutions Self Check A Consider this sequence of numbers: 100, 97, 94, 91, 88, … Make a conjecture: What is the 10th term of this sequence? What is the nth term? The 10th term of the sequence is probably 73. The nth term of the sequence would be 103 − 3n. (Note: It’s not likely you found a different answer, but other answers are possible. They would require much more difficult algebraic expressions, though! If you think you found another correct answer, carefully find the 10th term and check that you’re correct.) Each term is 3 less than the one before it. Another 5 terms would be 15 less than the 5th term, 88, which gives 73. Notice that this means you multiply the difference in term numbers by 3 and subtract the result from the earlier term. In general, this means you will multiply the term number by 3 and subtract it from some value. If you multiply 1 by 3 and subtract it from another number to get 100 (the value of the first term), you must be subtracting from 103, so the nth term is 103 − 3n.

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. Self Check B When trying to graph y = |-x|, Benny reasoned this way: Absolute value just makes the value positive or zero. So, the result of |-x| is the positive version of x, or 0 if x = 0. But the result of |x| is also the positive version of x, or 0 if x = 0. That means |-x| = |x|. So the graph of y = |-x| is the same as the graph of y = |x|. Is Benny using inductive reasoning? A) No B) Yes Benny was not using inductive reasoning. When using inductive reasoning, you use specific examples and generalize them to a broader set of examples. In this case, Benny's observations are already general. If he were to use inductive reasoning, he might notice specific examples like |-2| = 2, |-0.25| = 0.25, and |-(-3)| = |3|. From that he could generalize that the absolute value of the opposite of a value is either the value itself or its opposite, and then he could make the conjecture |-x| = |x|. Notice that a general caseâ&#x20AC;&#x201D;the variable xâ&#x20AC;&#x201D;is not used until the end of the process, while Benny used the variable throughout his reasoning.

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. 12.1.4 Deductive Reasoning Learning Objective(s) 1 Use properties of numbers to construct simple logical arguments. 2 Identify and provide examples of deductive reasoning.

Introduction Deductive reasoning is probably the most used process in all of mathematics. Anyone who has solved a logic puzzle like a Sudoku puzzle has used deductive reasoning. When we reason deductively, we use known facts to make logical conclusions that we know must be true. (We deduce one fact by putting together other facts.) This is different from inductive reasoning, which generalizes and conjectures based on observations rather than logic. Mathematicians (and all the rest of us, too) often use both inductive reasoning and deductive reasoning together. Objective 1

Deductive versus Inductive Reasoning

Imagine we have recorded the results of experiments or observations, and decide that we see a pattern in the data. Or, imagine we have a problem to solve but aren't sure where to start, so we try to plug in some possible solutions to see what kinds of results we get. In these cases, we are reasoning inductively, making generalizations based on a limited number of observations. The trouble is, our generalizations might not be correct. Even with a lot of examples, it can be difficult if not impossible to be sure that there isn't at least one counterexample we just haven't found yet. For that reason, mathematicians, scientists, researchers, and other people who make conjectures will often follow up inductive reasoning with some deductive reasoning. They try to justify the conjectures they made based on their observations. That is, they try to provide a logical argument, a series of verifiable statements that explains why their conjecture is always true. Deductive reasoning is helpful when inductive reasoning is not appropriate, or there aren't enough examples to generalize from. Consider puzzles like Sudoku. In a Sudoku puzzle, each row, column, and 3-by-3 box must be filled with the digits from 1 to 9. A digit can't be used more than once in any single row, column, or box.

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. Inductive reasoning is no help in figuring out this puzzle. We could look at the solutions for other puzzles, and see where the digits were placed in each one. But if we generalize this to mean that we should fill the numbers in the same way every time, we won't be able to solve many puzzles! What we can do instead is figure out the specific placements for this puzzle based on the rules of the game and the numbers that are given. In the top row of 3 X 3 boxes in the puzzle above, the left and middle boxes already have a 1. The 1 in the right box can't be in the first or second rows, because they already have 1s. So the 1 for the right box has to be in the third row, and there's only one place for that. Deductive reasoning has revealed the location of the 1 in the right box!

Even without Sudoku, we've all used deductive reasoning a lot. Every time we work with an equation or mathematical expression to arrive at a conclusion or answer, we are using deductive reasoningâ&#x20AC;&#x201D;following the general principles of mathematics to find a specific solution that must be true.

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. Example Terry does the following to factor the expression 3x3 + 6x2 + 3x.

Problem

• First he factors out 3x using the distributive property: 3x3 + 6x2 + 3x = 3x(x2 + 2x + 1) • Then he recognizes that the second factor is in the form a2 + 2ab + b2, and remembers that a2 + 2ab + b2 = (a + b)2 • Finally, he rewrites the second factor as the square of a binomial: 3x(x2 + 2x + 1) = 3x(x + 1)2 Is this inductive or deductive reasoning? Terry used the distributive property and other known facts to create a series of new facts about the expression 3x3 + 6x2 + 3x. This is deductive reasoning Answer

Deductive reasoning

Self Check A Lucretia remembered this rule from arithmetic: To tell if fractions

a c and are equal, “cross multiply” to find ad and bc. b d

If ad = bc, then the fractions are equal.





She thought about whether this always works, and she made the following argument:  



Say we know that ad = bc. Divide both sides of the equation by bd—which we can do if b ≠ 0 and d ≠ 0—and simplify:

ad bc  bd bd a d b c    b d b d a c  b d

 

So it’s true if b and d are not 0. If we’re starting with the fractions, then b and d can’t be 0, so this “crossmultiplication” rule works. What kind of reasoning is Lucretia using? A) Inductive reasoning B) Deductive reasoning

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. Objective 2

Building a Logical Argument

The end result of deductive reasoning is often a logical argument. Most of the arguments we come across are polished, final arguments. We don't usually see the rough drafts, the mistakes, the lines of reasoning that went nowhere. We don't see that a writer started in a completely different place than the finished argument starts, and we can't tell when someone worked his argument out backwards because it was easier to figure it out from the conclusion than from the hypothesis! The point? Don't worry when it's hard to find a good argument right away. Deductive reasoning often takes some creativity and persistence. Time and practice will make it easier to sort out the dead ends from the promising leads. The example below provides one way to approach building an argument: Example Problem

Frank has three siblings, and they all like to chip in to buy lottery tickets. Whenever there's a big jackpot, he wonders if it could be evenly divided among the four of them, just in case they win. Frank has noticed that when a number formed by the last two digits of a whole number is divisible by 4, the whole number itself is divisible by 4. For example, 293,212 is divisible by 4 and 12 is divisible by 4. How can he use deductive reasoning to justify the truth of this divisibility test?

Answer

First, let's write a general example of the conjecture. That is, this example has to represent many examples, not just one. In this case, we want to talk about the last two digits of a whole number. Hereâ&#x20AC;&#x2122;s a trick that can be helpful when working with digits: Use place values to write the number as a sum with addends that are products of powers of 10. In this case, since Frank is interested in the last two digits of a larger number, we can separate those digits from the rest of the number. For example, 236 can be written as 200 + 36, or 2(100) + 36. The number 72,915 can be written as 72,900 + 15, or 729(100) + 15. Any whole number can be written as 100a + b, where a and b are whole numbers and b < 100.

To put it in general terms, a large number can be written as 100 times a number plus a second number that is less than 100. This is a general, known statement.

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. If b is divisible by 4, then 100a + b is divisible by 4.

We can also write Frank's conjecture using algebraic expressions. Now we need to find a way to connect the general example to the conclusion. This may take several steps.

 100a  b  425a  

b   4 

In this case, we want 100a + b to be divisible by 4. So let’s factor the 4 out of the expression. What does it mean for the number to be divisible by 4? It means the quotient is a whole number,



so we want 25a 

b to be a whole number. How 4

can we show that it is? Since a is a whole number, 25a is also a whole number.

We can use the hypothesis here. We defined a to  be a whole number, so 25a has to also be a whole number.

Since b is divisible by 4,

The hypothesis is that b is divisible by 4, so that

b is a whole number. 4 b That means 25a  is 4 a whole number.



Since

  100a  b  425a  

gives us information about

b . Combine that with 4

the information about 25a.



b  , 4 

Conclude the argument.

we know that



100a  b b  25a  . 4 4 b Since 25a  is a 4



whole number, 100a + b is divisible by 4.

 Here are some tips for building an argument. None of them will work every time, and we may need to try them all before we find an argument that works.

Use the hypothesis of the logical statement as a starting place.

Use the conclusion of the logical statement as a starting place.

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. ď&#x201A;ˇ

Start with something related to either the hypothesis or conclusion that is already known to be true. For example, with an inequality using absolute value, perhaps start with the fact that |x| â&#x2030;Ľ 0 for all real numbers x.

Self Check B Build a logical argument to explain why a two-digit number is divisible by 3 if the sum of its digits are divisible by 3. Hint: Write the two-digit number as 10x + y, and notice that 10x = 9x + x.

Summary Deductive reasoning is a process of making conclusions by putting known facts together to provide a reasoned argument for a new fact. Deductive reasoning can be used to justify a conjecture arrived at through inductive reasoning. It's also helpful at times when inductive reasoning isn't appropriate, such as when there aren't enough examples to generalize from.

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. 12.1.4 Self Check Solutions Self Check A Lucretia remembered this rule from arithmetic: To tell if fractions

a c and are equal, “cross multiply” to find ad and bc. b d

If ad = bc, then the fractions are equal.





She thought about whether this always works, and she made the following argument:  



 

Say we know that ad = bc. Divide both sides of the equation by bd—which we can do if b ≠ 0 and d ≠ 0—and simplify:

ad bc  bd bd a d b c    b d b d a c  b d So it’s true if b and d are not 0. If we’re starting with the fractions, then b and d can’t be 0, so this “crossmultiplication” rule works.

What kind of reasoning is Lucretia using? A) Inductive reasoning B) Deductive reasoning A) Incorrect. When using inductive reasoning, you use specific examples and generalize them to a broader set of examples. In this case, Lucretia’s observations are already general, and she uses known facts to arrive at her final statement. If she were to use inductive reasoning, she might notice specific examples like 15 = 5 • 12, and

4 12 and 4 •  5 15

2 3  and 2 • 4 ≠ 3 • 3. From several examples like that, she could 3 4

generalize that the equality of the fractions and the products found by cross multiplication are the same for all pairs of fractions, and then she can make the conjecture that the fractions are equal if those products are equal.



B) Correct. Lucretia uses known facts to arrive at her final statement in a logical way, which is deductive reasoning. Self Check B Providing excellence in home school education since 1988


. Build a logical argument to explain why a two-digit number is divisible by 3 if the sum of its digits are divisible by 3. Hint: Write the two-digit number as 10x + y, and notice that 10x = 9x + x. You may have a different argument than the one given here. That doesn’t mean your argument is wrong. However, you should read this argument to understand how it works. (You can learn a lot about building arguments by understanding how finished ones work.) A two-digit number with tens digit x and ones digit y is equal to 10x + y. (For example, in 36, x = 3 and y = 6, so 36 = 10(3) + 6.) The general statement of the conjecture is: “If x + y is divisible by 3, then 10x + y is divisible by 3.”

10x  y 9x x  y xy    3x  3 3 3 3 xy If x + y is divisible by 3, is a whole number. Since x is a digit, 3x is a whole 3 xy number, so 3x is a whole number. That means the original number 10x + y is 3 10x + y = 9x + x + y, so

divisible by 3.





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. 12.2.1 Events and Outcomes (Counting) Learning Objective(s) 1 Use the Fundamental Counting Principle to determine the size of the sample space for simple and compound events. 2 Determine the probability of simple and compound events.

Introduction Random situations are those which cannot be predicted with certainty. However, by using probability, a measure of how likely it is that a random situation will turn out a particular way, we may still be able to make some predictions about those situations. For example, many games use dice or spinners to generate numbers randomly. If we understand how to calculate probabilities, we can make thoughtful decisions about how to play these games by knowing the likelihood of various outcomes. Objective 2

Defining Events

First we need to introduce some terms. When working with probability, a random action or series of actions is called a trial. An outcome is the result of a trial, and an event is a particular collection of outcomes. Events are usually described using a common characteristic of the outcomes. Let's apply this language to see how the terms work in practice. Some games require rolling a die with six sides, numbered from 1 to 6. (Dice is the plural of die.) The chart below illustrates the use of trial, outcome, and event for such a game: Trial

Rolling a die

Outcomes There are 6 possible outcomes: {1, 2, 3, 4, 5, 6}

Events Rolling an even number: {2, 4, 6} Rolling a 3: {3} Rolling a 1 or a 3: {1, 3} Rolling a 1 and a 3: { } (Only one number can be rolled, so this is impossible. The event has no outcomes in it.)

Notice that a collection of outcomes is put in brackets and separated by commas. A simple event is an event with only one outcome. Rolling a 1 would be a simple event, because there is only one outcome that works: 1! Rolling more than a 5 would also be a simple event, because the event includes only 6 as a valid outcome. A compound event is an event with more than one outcome. For example, in rolling one six-sided die, rolling an even number could occur with one of three outcomes: 2, 4, and 6. When we roll a six-sided die many times, we should not expect any outcome to happen more often than another. The outcomes in a situation like this are said to be equally likely. It's very important to recognize when outcomes are equally likely when calculating probability. Since each outcome in the die-rolling trial is equally likely, we would expect to get each outcome

1 of 6

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ď&#x201A; ď&#x20AC; 


. 1 1 1 the rolls. That is, we'd expect of the rolls to be 1, of the rolls to be 2, of the rolls to be 3, 6 6 6 and so on. Example

 Problem





Tori is flipping a pair of coins and noting how many heads she gets. What are the outcomes in this trial? Are they equally likely? A single coin can turn up heads (H) or tails (T). Tori can flip two heads, two tails, or one of each. There are 3 outcomes: 0 heads, 1 head, or 2 heads. These outcomes are not equally likely. This might be surprising, but think about it this way: Imagine one coin is a nickel and the other is a dime. The possible ways to flip the coins are: Nickel

Dime

H H T T

H T H T

Number of Heads 2 1 1 0

Notice that there are two ways to get only 1 head, but only one way to get 2 heads and one way to get 0 heads. Tori should expect to get 1 head on ½ of the flips, 0 heads on ¼ of the flips, and 2 heads on ¼ of the flips. Answer There are 3 outcomes, but they are not equally likely.

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. Self Check A When this spinner is spun, the arrow points to one of the colors. Are the outcomes equally likely?

A) Yes, they are equally likely. B) No, they are not equally likely.

Probability of Events The probability of an event is how often it is expected to occur. When all the possible outcomes for a trial are equally likely, the probability is the ratio of the size of the event space (the outcomes in the event) to the sample space (all the possible outcomes for the trial). The probability of an event E is usually written P(E).

P( E ) 

size of the event space number of outcomes in the event  size of the sample space total number of possible outcomes

Notice that an event is often described using common characteristics of the outcomes, if possible—such as rolling an even number on a die. The event space, however, is a list of all the  outcomes in the event—such as {2,4,6}. The sample space is all possible outcomes, not just the ones in the event. Example Problem

A game requires rolling a six-sided die numbered from 1 to 6. What is the probability of rolling an even number?

Sample space = {1, 2, 3, 4, 5, 6} Event space = {2, 4, 6}

First, find the sample space and the event space. The sample space is all the possible outcomes, and the event space is the outcomes in the event. In this case, the event is “rolling an even

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. number.â&#x20AC;?

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