1.Good
Listening in Class
It is
important for you to be a good listener in class. Much of what you will have to
learn will be presented verbally by your teachers. Just hearing what your
teachers say is not the same as listening to what they say. Listening is a
cognitive act that requires you to pay attention and think about and mentally
process what you hear.

- Be Cognitively Ready to Listen When You Come to Class. Make sure you complete all assigned work and readings. Review your notes from previous class sessions. Think about what you know about the topic that will be covered in class that day.
- Be Emotionally Ready to Listen When You Come to Class. Your attitude is important. Make a conscious choice to find the topic useful and interesting. Be committed to learning all that you can.
- Listen with a Purpose. Identify what you expect and hope to learn from the class session. Listen for these things as your teacher talks.
- Listen with an Open Mind. Be receptive to what your teacher says. It is good to question what is said as long as you remain open to points of view other than your own.
- Be Attentive. Focus on what your teacher is saying. Try not to daydream and let your mind wander to other things. It helps to sit in the front and center of the class and to maintain eye contact with your teacher.

- Be an Active Listener. You can think faster than your teacher can speak. Use this to your advantage by evaluating what is being said and trying to anticipate what will be said next. Take good written notes about what your teacher says. While you can think faster than your teacher can speak, you cannot write faster than your teacher can speak. Taking notes requires you to make decisions about what to write, and you have to be an active listener to do this.
- Meet the Challenge. Don't give up and stop listening when you find the information being presented difficult to understand. Listen even more carefully at these times and work hard to understand what is being said. Don't be reluctant to ask questions.
- Triumph Over the Environment. The classroom may be too noisy, too hot, too cold, too bright, or too dark. Don't give in to these inconveniences. Stay focused on the big picture - LEARNING.
2. Identifying Lecture StylesLectures given by your teachers are usually organized in one of the following lecture styles:
Topic-ListThe teacher begins by presenting the topic followed by associated subtopics. Each subtopic includes details and sometimes subdetails. Number words like one or second and transitional words like next and finally indicate that the teacher is using a Topic-List style. The transitional words also indicate a change from one subtopic to another subtopic.Question-AnswerThe teacher begins by introducing a topic that is followed by one or more questions about the topic. Each question is answered after it is introduced. Words such as who, what, where, when, why and how indicate that the teacher is using a Question-Answer style. Phrases such as in what way and how did they react also indicate that this style is being used.Compare-ContrastThe teacher begins by identifying two things that will be compared and contrasted. The teacher then tells how the two things are alike (i.e., compare) and how they are different (i.e., contrast). Words and phrases such as alike, similarly, correspondingly, in parallel, counterpart, equal to, resemble, and just as suggest similarities. Words and phrases such as differently, however, antithesis of, disparity, on the other hand, opposite, and on the contrary suggest differences.Series of EventsThe teacher begins by identifying the topic. Then the teacher describes an initial event, step, or stage related to the topic. Information is then presented about additional events, steps, or stages. The teacher concludes by revealing the final event, step, or stage. Words and phrases such as initially, at the outset, next, followed by, then, later, after, succeeding, intermediate, last, culminating, and finally indicate that the teacher is using a Series of Events style.Cause-EffectThe teacher begins by presenting the cause of something, followed by one or more effects related to the cause. Details are included for some of the effects. Words or phrases such as since, thus, therefore, consequently, for that reason, on account of, owing to, and as a result indicate that the teacher is using a Cause-Effect style.Problem-SolutionThe teacher begins by introducing a problem and explaining why it is a problem. The teacher continues by describing attempts to solve the problem, providing details as needed. Finally, the teacher concludes by identifying the solution to the problem if one has been found or the status of attempts to solve the problem. Words and phrases such as puzzle, issue, point of dispute, enigma, and complication indicate that a problem is being presented. Words and phrases such as solution, explanation, answer, cleared up, and worked out indicate that the problem has been resolved. Words and phrases such as unravel, investigate, clear up, and untangle indicate that an attempted solution is under way. |
3. Notetaking
Tips
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It is
important to take good notes in class. Taking written notes
almost forces you to concentrate on what the teacher is saying. Your notes
will help you prepare for tests and will give you clues as to what your
teacher thinks is most important for you to know. Further, your notes will
contain information that may not be in your textbooks.
Here are some tips that can help you take good notes.
Your class notes are your record of what your teacher covered. Use the tips above to make them as good as possible. |
4. Rewriting
Class Notes
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Teachers
often emphasize the information they provide in class lectures when they
design tests. This means that your class notes are a vital resource when
studying for a test. It is important that your class notes be complete and
accurate.
The best
way to be certain that your class notes are complete and accurate is to
review them in the evening while the information that was covered in class is
still fresh in your mind. At this time you should rewrite your notes,
correcting any errors, filling in any gaps, and adding additional information
as appropriate. Rewriting your class notes also gives you the opportunity to
improve their organization and to make them neater, thereby making your notes
easier to study from. Further, rewriting your class notes reinforces the
information so that you will remember it better.
Here are some tips to consider
when you rewrite your class notes.
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5. Taking
Notes in Class
|
In
classes, your teachers will talk about topics that you are studying. The
information they provide will be important for you to know when you take
tests. You must be able to take good written notes from what your teachers
say.
Taking
good notes is a three-stage process in which there are certain things you
should do before class, during class, and after class.
Here are the three stages of notetaking and what you should do during each
stage.
1. Get
Ready to Take Notes (Before Class)
2. Take
Notes (During Class)
3. Rewrite
Your Notes (After Class)
Having
good class notes will help you to be better prepared for tests.
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6. Using
Abbreviations To Write Notes Quickly
Many of
the questions you find on class tests will be based upon the information your
teachers orally present in class. Therefore, you need to write
class notes that
completely and accurately include the most important information presented by
your teachers. This is hard to do because your teachers can talk faster than
you can write.
It would
be nice if your teachers talked slower so that you could keep up with what
they are saying as you write your notes. This is not realistic though. It is
up to you to write more quickly. One way to do this is to write abbreviations
for words. An abbreviation is a shortened form of a word used when
writing to represent the complete word. You must be able to recognize the
complete word from its abbreviation.
Many words
have a commonly used abbreviation. Here are some examples of words that have
a common abbreviation:
You can
form your own abbreviation for just about any word. Here are three ways you
can do this.
1. Write
just the beginning of a long word. Here are some examples of long words
that have been abbreviated by writing just the beginning of the word:
2. Leave
out the vowels when writing a word. Here are some examples of words that
have been abbreviated by leaving out the vowels when writing the word:
3. For words
that have just one syllable, write just the first and last letter of the
word. Here are
some examples of words that have been abbreviated by writing just the first
and last letter of the word:
![]()
Use common
abbreviations of words whenever you recognize them. For other words, form
abbreviations by using one of the three ways you just learned. Use the way
that best fits the word for which you are writing an abbreviation. Do not try
to abbreviate every word you write in your notes. Abbreviate those words that
are important and for which you can quickly form an abbreviation. REMEMBER:
YOU MUST BE ABLE TO RECOGNIZE THE COMPLETE WORD FROM ITS ABBREVIATION.
Knowing the context in which you wrote the word will help you recognize the
complete word from its abbreviation.
Using
abbreviations for words will help you take good notes more quickly. Having
good notes will help you do better on tests.
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ACT Test Taking Tips
The ACT is a widely used college admission standardized test. It has four
mandatory subject tests: English, Reading, Mathematics, and Science. There is
also an optional Writing test which some colleges require.General Tips
- Answer the questions you find easiest first. Come back to the others later.
- Don't spend more than a minute or two on any question.
- As you work on a section, keep track of how much time remains. (It's a good idea to bring a reliable watch.)
- Answer every question. There is no penalty for guessing.
- Be careful to mark only one answer choice per question.
- Write in the test book in any way that will help you.
- Consider all answer choices before you choose one. Use the process of elimination to narrow your choices.
English Section Tips
- Consider the writing style used for each section. The correct answer choice will be the one that works best with the writing style used.
- When asked a question about something that is underlined, consider how the underlined portion fits with the rest of the section.
- Examine each answer choice to see how it differs from the others.
- For items that include "No Change" as an answer choice, choose this as your answer only if you are sure none of the other answer choices are correct.
- Reread the underlined portion with your answer choice to be sure it is correct.
Reading Section Tips
- Read the passage carefully before you read the questions.
- Focus on the main ideas in the passage. Underline these. Don't get lost in the details.
- Try to identify how ideas in the passage are connected.
- Refer to the passage as you answer each question.
Mathematics Section Tips
- Work out the problem before looking at the answer choices. When done, choose the answer choice that matches your answer. If none match, redo the problem.
- Don't overly rely on your calculator. Some problems are best worked out manually. Some don't even require calculation.
- The questions focus much more on reasoning than on calculation. If you find yourself doing complicated calculations, you're probably on the wrong track.
- Make sure your answer choice makes sense. A calculation error can lead you to a wrong answer choice.
- Check your work.
Science Section Tips
- Given the complexity of the passages, it may help to make some simple notes as you read them.
- Cross out irrelevant information.
- Don't be overly concerned with any technical terminology. Technical terms usually have little to do with the correct answer choice.
- Be watchful for conflicting viewpoints in some of the passages.
Writing Section Tips
- Organization of your response is very important. Use a five-paragraph essay that includes an introduction, supporting paragraphs, and a conclusion.
- Plan your response before you begin to write it.
- Stay with the topic throughout your response.
- Vary your sentence structure and word choices.
- Use specific examples wherever possible.
- Write legibly.
- If you have time, check your grammar, usage, punctuation, and spelling.
6. Direction
Words In Essay Test Items
Most essay
test items are not presented in the form of a question. Instead, they are often
presented as a statement that includes a direction word. The direction
word tells you what you should do when you write your answer to the item. Look
for the direction word and be sure to do what it tells you to do.
Here are the
direction words that are most frequently used by teachers when they write essay
test items. The meaning of each direction word is provided and is followed by
an example of an essay test item using that direction word. Get to know what
each of these direction words tells you to do.
- Analyze - Analyze tells you to
break something down into its parts and show how the parts relate to each
other to make the whole.
Analyze the factors that contribute to good health. - Compare - Compare tells you to
show how two or more things are BOTH similar and different.
Compare the forms of government found in the United States and in China. - Contrast - Contrast tells you to
show how two or more things are different.
Contrast the Republican and Democratic political platforms. - Define - Define tells you to
explain the meaning of something in a brief, specific manner.
Define what is meant by "living life to the fullest." - Describe - Describe tells you to
present a full and detailed picture of something in words to include
important characteristics and qualities.
Describe what it was like to live in ancient Rome. - Diagram - Diagram tells you to
illustrate something by drawing a picture of it and labeling its parts.
Diagram a modern commercial jet airplane. - Evaluate - Evaluate tells you to
present both the positive and negative characteristics of something.
Evaluate the impact of rap music on American youth. - Explain - Explain tells you to
provide facts and reasons to make something clear and understandable.
Explain why the American Civil War occurred.
- Justify - Justify tells you to
provide reasons and facts in support of something.
Justify the need for the federal income tax. - List - List tells you to
present information about something as a series of brief numbered points.
List the ingredients needed to bake bread. - Outline - Outline tells you to
present the most important information about something in a carefully
organized manner.
Outline what it takes to be successful in school. - Summarize - Summarize tells you
to present the main points about something in a brief form.
Summarize how Thomas Edison's inventions have made our lives better. - Trace - Trace tells you to
present the order in which something occurred.
Trace the major events that led to America's Declaration of Independence.
Recognizing
these direction words and knowing what they tell you to do will help you do
well when taking an essay test.
8. Studying
for a Multiple-Choice Test
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Essay
tests assess your mastery of things and overall ideas. When you study
for an essay test, your goal should be to recall broad information in an
organized way so that you can produce an answer. Multiple-choice
tests, in contrast, require you to recognize a correct answer
among a set of options. You should study differently for a
multiple-choice test than the way in which you study for an essay test.
Here are some things you should do when studying for a multiple-choice test.
The key to
success when studying for a multiple-choice test is to keep in mind that
success requires recognizing correct information.
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10. Outlining
a Response to an Essay Test Item
Writing a
response to an essay test item is quite different from writing an essay when
you have days or even weeks to plan, research, review, and revise your work.
Your response to an essay test item must be written on the spot and within a
short period of time. The item is based on what you've learned about the course
topics, rather than a topic of interest which you select. Successful essay
responses have three things in common: focus, organization, and support.

The key to
writing a good response to an essay test item is to construct an outline for
your response. Begin by reading the essay item carefully. Underline the key
words and make sure you know exactly what you're being asked to do. Then
construct an outline as follows. The number of main points to be covered and
the number of supporting details for each will vary depending on the specific
item.
- Introduction
- Background information that provides context for your response. This is where you'll demonstrate your general knowledge of the topic. Try not to exceed three sentences.
- A statement that includes the main points you will cover in your response. Three main points is usually sufficient.
- Main point one
- A topic sentence that introduces the first main point.
- Supporting detail that provides evidence for this main point.
- Supporting detail that provides evidence for this main point.
- Supporting detail that provides evidence for this main point.
- Main point two
- A topic sentence that introduces the second main point.
- Supporting detail that provides evidence for this main point.
- Supporting detail that provides evidence for this main point.
- Supporting detail that provides evidence for this main point.
- Main point three
- A topic sentence that introduces the third main point from the thesis.
- Supporting detail that provides evidence for this main point.
- Supporting detail that provides evidence for this main point.
- Supporting detail that provides evidence for this main point.
- Conclusion
- Synthesize your points to draw a conclusion.
Once you
have constructed your outline, go through it and ask yourself the following
questions. Is each of your main points directly related to what is being asked
on the test item? Have you provided sufficient supporting details for each of
your main points? Is everything in your outline necessary to respond to the
item? Have you omitted any main points or details? You want to be sure that
your outline is tightly focused on what is being asked in the test item.
Once your
outline is completed, consider how you want to organize your ideas when writing
your response. Do you want to order your ideas chronologically? In order of
importance? In order of complexity? Once you've decided on your organization
strategy, consider which transitional words and phrases you'll use to move from
one paragraph to another. Transitions will help your teacher understand your
thought process and follow the essay. Remember that your teacher must
understand what you're saying and why you're saying it in order to give you
maximum credit for your response.
Creating a
strong and focused outline is actually the hardest part of responding to an
essay test item. If your outline is well-developed, writing your response will
be relatively easy. In general, about half your time should be spent writing
your outline, and the other half to expanding the outline into a full written
response. Try to reserve a little to proofread your response for possible
errors in writing mechanics.
Writing a
good outline is the key to writing a good response to an essay test item.
11. Studying for an Essay Test
Tests such
as multiple-choice
tests and true/false
tests assess
specific factual knowledge. When you study for these tests, your goal should be
to recognize facts.
Essay tests assess your mastery of themes and
overall ideas. When you study for essay tests, your goal should be to recall
broad information in an organized way. Your studying for essay tests should be
related to this goal.
Here are the
steps to follow when studying for an essay test.
- Assemble the materials that contain the information that will be covered on the test. This includes your textbook, your textbook notes, and your class notes.
- Read these materials to identify themes and overall ideas. Each time you identify one, label an index card with the name of that theme or overall idea. You will often find the same theme or overall idea in one or more places, but use just one card to represent it.
- For each card you prepare in Step 2, carefully review your textbook, textbook notes, and class notes and add written details about the theme or overall idea to the card.
- Once you have completed Step 3 for each card, review your cards several times. Doing this will give you a working familiarity with the information that is most likely to be the basis of questions on the test.
- Now is the time to think like your teacher. Try to predict the questions your teacher will ask on the test. Write each question on its own index card. When writing the questions, include direction words often used by teachers, such as explain or compare.
- For each card you prepared in Step 5, write a response to the question on that card (write on the back of the card and on additional cards if necessary). Use the cards you developed in Step 3 to help you answer each question. When you complete Step 6, you will have a set of study cards, each containing a possible test question and a written response to that question.
- Carry the study cards you developed in Step 6 with you so that you can review them frequently. Be sure to review these cards the evening before the test.
Essay tests
can be scary. Take the scare out of them by following the study steps above.
True/false tests seem easy. All you have to do is read a statement and
decide whether the statement is true or false. At the very worst, you have a
50-50 chance of being right. But would you be pleased with a test grade of 50?
Of course you wouldn’t.True/false tests are a lot more difficult than they seem to be. They test very specific factual knowledge. Nothing can replace having the knowledge. But even if you do have the knowledge, there are some guidelines you should follow to make sure you demonstrate your knowledge.
12. Guidelines When Taking True/False Tests
Here are some guidelines that will help you correctly answer true/false items.
1. Choose
True for an item only when you are certain that the entire statement is true. This is especially important
when the item contains more than one "fact."


Read the
following statement:
Milk, cheese, and butter are all in the dairy food group.
This statement is true because all three of these foods are part of the dairy food group.
Now read this changed statement:
Milk, lettuce, and butter are all in the dairy food group.
This statement is false because while milk and butter are in the dairy food group, lettuce is not.
Milk, cheese, and butter are all in the dairy food group.
This statement is true because all three of these foods are part of the dairy food group.
Now read this changed statement:
Milk, lettuce, and butter are all in the dairy food group.
This statement is false because while milk and butter are in the dairy food group, lettuce is not.
2. Be
very careful when a statement contains a negative word such as not
or a negative prefix such as un as in the word
unfriendly. A negative word or prefix completely changes the
meaning of a statement.
Read the
following two statements:
Directions given by teachers should be very clear.
Directions given by teachers should be very unclear.
The first statement is true, while the second is false. At a quick glance, these two statements might seem the same. It is always important to read a statement carefully. It is especially important to do this when the statement contains a negative word or prefix.
Directions given by teachers should be very clear.
Directions given by teachers should be very unclear.
The first statement is true, while the second is false. At a quick glance, these two statements might seem the same. It is always important to read a statement carefully. It is especially important to do this when the statement contains a negative word or prefix.
3. When
a statement contains two negative words and/or prefixes, cross out both. Two negatives typically make a
positive, but in a very confusing way.


Read the
following statement:
Eating a balanced diet is not unhealthy.
This statement is true, but in a confusing way.
Now read the same statement with the negatives crossed out.
Eating a balanced diet isnot unhealthy.
The statement has now become:
Eating a balanced diet is healthy.
It is now a much easier statement to understand as true.
Eating a balanced diet is not unhealthy.
This statement is true, but in a confusing way.
Now read the same statement with the negatives crossed out.
Eating a balanced diet is
The statement has now become:
Eating a balanced diet is healthy.
It is now a much easier statement to understand as true.
4. An
absolute statement is usually false.
An absolute statement contains words such as the following: all, none,
always, every, never, only, and no.
Each of these words suggests that there are no exceptions.
Read the
following statement:
The official language of all the countries in South America is Spanish.
This statement is false because of the absolute word all. Spanish is the official language of 9 of the 13 countries in South America. The exceptions are Brazil (Portuguese), French Guiana (French), Guyana (English), and Suriname (Dutch).
The official language of all the countries in South America is Spanish.
This statement is false because of the absolute word all. Spanish is the official language of 9 of the 13 countries in South America. The exceptions are Brazil (Portuguese), French Guiana (French), Guyana (English), and Suriname (Dutch).
5. A
qualified statement is usually true.
A qualified statement contains words such as the following: some, many,
usually, most, sometimes, may, and often.
These words allow for exceptions.
Read the
following statement:
The official language of most of the countries in South America is Spanish.
This statement is true because of the qualified word most.
The official language of most of the countries in South America is Spanish.
This statement is true because of the qualified word most.
6. If
you are uncertain whether a statement is true or false, take your best guess
unless there is a penalty for wrong answers. If you have absolutely no clue, choose True as your
answer. Research has shown that true/false tests typically contain more true
statements than false statements. This is because teachers typically use tests
not only to assess what you have learned, but to reinforce what you have
learned.
True/false tests can be tricky. Use these guidelines to do your
best.13. Writing an Essay Test Answer
An essay
test item requires you to recall and organize information and to communicate
the information in an extended writing form. Your response to any essay test
item should be:
- Focused. Write specifically to the question. Think about what you want to convey before you begin to write your answer. Don't pad your answer with all kinds of information in the hope that some of the information will be relevant to the question.
- Organized. Plan what you want to write before you actually begin to write your answer. Don't write your answer in a haphazard "think-as-you-go" manner. It is very helpful to prepare an outline that contains all the necessary points you want to have in your answer. Following the outline will help you produce a fluid answer that is easy for your teacher to follow.
- Supported. Do more than just state your points. Provide evidence for what you write. Using examples is an excellent way to bring your points across.
Here are
some tips that will help you do your best when responding to an essay test
item:
- Look to see if there is a direction word that tells you what you need to do to respond to the item.
- Write your answer legibly so that you do not have to waste time rewriting it.
- Budget your time if the test includes more than one item that must be answered. Don't spend so much time on one item that you have to rush to respond to the remainder of the test. In general, spend the most time on the items that count for the most points.
- Don't give your personal opinion unless the item calls for it.
- Use an approximation if you are not sure about an exact date or number. For example, rather than "1748," you could write "in the middle of the 18th century."
- Cross out anything you write but want to delete. This is faster and neater than trying to erase it.
- If you have time left after answering everything required, proofread your work quickly to correct any errors in spelling and mechanics, or any factual errors.
Most
important of all, study well to master the information you need to know for the
test.
See our article "Studying for Essay Tests."
See our article "Studying for Essay Tests."
14. Preparing to Study: A Good Study Place
You need a
good study place to be prepared to study. You should be able to answer YES to
all of the following questions:
- Is my Study Place available to me whenever I need it?
Your Study Place does you little good if you cannot use it when you need
it. If you are using a Study Place that you must share with others for any
reason, work out a schedule so that you know when you can use it.
- Is my Study Place free from interruptions?
It is important to have uninterrupted study time. You may have to hang a
DO NOT DISTURB sign on the door or take the phone off the hook.
- Is my Study Place free from distractions?
Research shows that most students study best in a quiet environment. If
you find that playing a stereo or TV improves your mood, keep the volume low.
- Does my Study Place contain all the study materials I need?
Be sure your Study Place includes reference
sources and
supplies such as pens and pencils, paper, ruler, calculator, and whatever else
you might need. If you use a computer for your schoolwork, it should be in your
Study Place.
- Does my Study Space contain a large enough desk or table?
While working on an assignment or studying for a test, use a desk or
table that is large enough to hold everything you need. Allow enough room for
writing and try to avoid clutter.
- Does my Study Place have enough storage space?
You need enough room to store your study materials. Be sure you have
enough storage space to allow you to keep your desktop or other work surface
clear of unnecessary materials that can get in the way.
- Does my Study Place have a comfortable chair?
A chair that is not comfortable can cause discomfort or pain that will
interfere with your studying. A chair that is too comfortable might make you
sleepy. Select a chair in which you can sit for long periods while maintaining
your attention.
- Does my Study Place have enough light?
The amount of light you need depends on what you are doing. The important
thing is that you can clearly see what you need to see without any strain or
discomfort.
- Does my Study Place have a comfortable temperature?
If your Study Place is too warm, you might become sleepy. If it is too
cold, your thinking may slow down and become unclear. Select a temperature at
which your mind and body function best.
Having a
good Study Place is important for good studying.
16. Math Vocabulary
Mathematics (math) is the study of numbers, quantities, shapes, and space using mathematical processes, rules, and symbols. There are many branches of mathematics and a large vocabulary associated with this subject.Here are some math words and terms you will likely come across but may not know their precise meanings. Any word or term shown in bold is defined in the following alphabetical list of math words and terms.
Algorithm A step-by-step mathematical procedure used to find an answer.
Coefficient A number that multiplies a variable. For example, 9 is the coefficient in 9x.
Denominator The bottom number in a fraction. The denominator represents the number of parts into which the whole is divided. For example, 6 is the denominator in the fraction
Equation A mathematical statement used to show that two expressions are equal. It contains an equals sign. For example, 16 - 9 = 7 (the expression 16 - 9 and the expression 7 are equal).
Greatest Common Factor (greatest common divisor) The largest number that will divide two or more other numbers equally. For example, the greatest common factor of 32 and 48 is 16.
Improper Fraction (mixed fractions) A fraction that has a larger numerator than denominator. For example,
Inverse Operations Opposite or reverse operations. Addition and subtraction are inverse operations, as are multiplication and division.
Negative Number A number that is less than zero. A minus sign is used to show that a number is negative. For example, -12 is a negative number.
Numerator The top number in a fraction. The numerator represents the number of parts of the whole. For example, 5 is the numerator in the fraction
Ordinal Number A number that shows place or position, as in 2nd place.
Positive Number A number that is greater than zero. While a minus sign is used to signify a negative number, the absence of a minus sign signifies a positive number.
Prime Number A number that can be divided evenly only by itself and 1. For example, 7 is a prime number.
Square Number A number that results from multiplying another number by itself. For example, 49 is the square of 7 (7 x 7 = 49).
Square Root of a Number A number that is multiplied by itself to produce a square number. For example, 7 is the square root of 49. It is designated by the symbol √.
Variable A quantity that can change or vary, taking on different values. It is typically represented by a letter of the alphabet. For example x is the variable in 9x (x can be any number that is being multiplied by 9).
These are just some of the many words and terms found in mathematics. It is important to know the meanings of words and terms you will encounter as you progress through the study of math.
17. The RQWQCQ Strategy for Solving Math Word Problems
RQWQCQ is a
good strategy to use when solving math word problems. Each of the letters in RQWQCQ
stands for a step in the strategy.
Read
Read the entire problem to learn what it is about. You may find it helpful to read the problem out loud, form a picture of the problem in your mind, or draw a picture of the problem.
Read the entire problem to learn what it is about. You may find it helpful to read the problem out loud, form a picture of the problem in your mind, or draw a picture of the problem.
Question
Find the question to be answered in the problem. Often the question is directly stated. When it is not stated, you will have to identify the question to be answered.
Find the question to be answered in the problem. Often the question is directly stated. When it is not stated, you will have to identify the question to be answered.
Write
Write the facts you need to answer the question. It is helpful to cross out any facts presented in the problem that are not needed to answer the question. Sometimes, all the facts presented in the problem are needed to answer the question.
Write the facts you need to answer the question. It is helpful to cross out any facts presented in the problem that are not needed to answer the question. Sometimes, all the facts presented in the problem are needed to answer the question.
Question
Ask yourself, "What computations must I do to answer the question?"
Ask yourself, "What computations must I do to answer the question?"
Compute
Set up the problem on paper and do the computations. Check your computations for accuracy and make any needed corrections. Once you have done this, circle your answer.
Set up the problem on paper and do the computations. Check your computations for accuracy and make any needed corrections. Once you have done this, circle your answer.
Question
Look at your answer and ask yourself: "Is my answer possible?" You may find that your answer is not possible because it does not fit with the facts presented in the problem. When this happens, go back through the steps of RQWQCQ until you arrive at an answer that is possible.
Look at your answer and ask yourself: "Is my answer possible?" You may find that your answer is not possible because it does not fit with the facts presented in the problem. When this happens, go back through the steps of RQWQCQ until you arrive at an answer that is possible.
Use RQWQCQ
to help you correctly solve math word problems.
18. Basic Number Properties
There are four basic properties of numbers: commutative, associative, distributive, and identity. You should be familiar with each of these. It is especially important to understand these properties once you reach advanced math such as algebra and calculus.
Commutative Property
a. Addition. When two numbers are added, the sum is the same regardless of the order in which the numbers are added.
3 + 5 =
8 or 5
+ 3 = 8
b. Multiplication. When two
numbers are multiplied together, the product is the same regardless of the
order in which the numbers are multiplied.
3 x 5 =
15 or 5
x 3 = 15
Associative Property
a. Addition. When three or more numbers are added, the sum is the same regardless of the way in which the numbers are grouped.
6 + (4 +
3) = 13 or (6 + 4) + 3 = 13
b. Multiplication. When
three or more numbers are multiplied, the product is the same regardless of the
way in which the numbers are grouped.
6 x (4 x
3) = 72 or (6 x 4) x 3 = 72

Distributive Property
The sum of two numbers times a third number is equal to the sum of each addend times the third number.
5 x (7 +
2) = 45 or 5 x 7 + 5 x 2 = 45
Identity Property
a. Addition. The sum of any number and zero is that number.
12 + 0 =
12
b. Multiplication, The
product of any number and one is that number.
18 x 1 =
18
Knowing these properties of numbers will improve your
understanding and mastery of math.19. Measurement Units
A measurement system is a set of units which can be used to specify anything which can be measured. There are various measurement systems used across the world. The system used in the United States is the U.S. customary system. Here are the common units used in this system along with examples to give you a frame of reference.Length
Inch (in): The distance between the knuckles on your index finger is approximately one inch.Foot (ft): One foot equals 12 inches. An official professional football is about one foot long.
Yard (yd): One yard equals three feet. A baseball bat is about one yard long.
Mile (mi): One mile equals 5,280 feet. A mile is approximately the distance a championship distance runner can run in just under four minutes.
Weight
Ounce (oz): A slice of bread usually weighs a little less than one ounce.Pound (lb): One pound equals 16 ounces. A loaf of white bread usually weighs a little more than one pound.
Ton (T): A ton is 2,000 pounds. The famous Liberty Bell in Philadelphia weighs about one ton.
Capacity
Cup (c): A standard baby bottle holds about one cup of juice.Pint (pt): One pint equals two cups. A pint of ice cream is just about right for four people to share.
Quart (qt): One quart equals two pints. Motor oil typically comes in a quart-sized container.
Gallon (gal): One gallon equals four quarts. A large container of milk contains one gallon.
Knowing these measurement units will help you in school and in everyday life.
20. Temperature Scales
Temperature is the level of heat in a gas, liquid, or solid. Three scales are commonly used for measuring temperature. The Celsius and Fahrenheit scales are the most common. The Kelvin scale is primarily used in scientific experiments.Celsius Scale
The Celsius scale was invented in 1742 by the Swedish astronomer, Anders Celsius. This scale divides the range of temperature between the freezing and boiling temperatures of water into 100 equal parts. You will sometimes find this scale identified as the centigrade scale. Temperatures on the Celsius scale are known as degree Celsius (ºC).Fahrenheit Scale
The Fahrenheit scale was established by the German-Dutch physicist, Gabriel Daniel Fahrenheit, in 1724. While many countries now use the Celsius scale, the Fahrenheit scale is widely used in the United States. It divides the difference between the melting and boiling points of water into 180 equal intervals. Temperatures on the Fahrenheit scale are known as degree Fahrenheit (ºF).Kelvin Scale
The Kelvin scale is named after William Thompson Kelvin, a British physicist who devised it in 1848. It extends the Celsius scale down to absolute zero, a hypothetical temperature characterized by a complete absence of heat energy. Temperatures on this scale are called Kelvins (K).Converting Temperatures
It is sometimes necessary to convert temperature from one scale to another. Here is how to do this.
1. To convert from ºC to ºF, use the
formula: ºF = ºC x 1.8 + 32.
2. To convert from ºF to ºC, use the
formula: ºC = (ºF-32) ÷ 1.8.
3. To convert from K to ºC, use the
formula: ºC = K – 273.15
4. To convert from ºC to K, use the
formula: K = ºC + 273.15.
5. To convert from ºF to K, use the
formula: K = 5/9 (ºF – 32) + 273.15.
6. To convert from K to ºF, use the
formula: ºF = 1.8(K – 273.15) + 32.
Comparing Temperatures
Here are some common comparisons between temperatures on the Celsius and Fahrenheit scales.
TEMPERATURE
|
ºC
|
ºF
|
Boiling
point of water
|
100
|
212
|
Freezing
point of water
|
0
|
32
|
Average
human body temperature
|
37
|
98.6
|
Comfortable
room temperature
|
20 to
25
|
68 to
77
|
22. Building Vocabulary: Using Context Clues to Learn Word Meaning
When authors write, they often include context clues to the meaning of words they use but think that some of their readers may not know. The context clue is usually presented in the sentence or paragraph in which the word occurs. Sometimes a visual such as a picture is provided.Here are six types of context clues used by authors to help the reader understand the meanings of words. An example is provided for each.
1. Definition context clue
The author includes a definition to help the reader understand the meaning of a word. In the following example, "tainted" is defined as having a disease.
The people of the town were warned not to eat the
tainted fish. The local newspaper published a bulletin in which readers were
clearly told that eating fish that had a disease could be very dangerous. This
was especially true for fish caught in Lake Jean.
2. Synonym context clue
The author includes a synonym to help the reader understand the meaning of a word. A synonym is a word that means the same as or nearly the same as another word. In the following example, the synonym "pity" helps the reader understand the meaning of "compassion."
After seeing the picture of the starving children, we
all felt compassion or pity for their suffering.
3. Antonym context clue
The author includes an antonym to help the reader understand the meaning of a word. An antonym is a word that means the opposite of another word. In the following example, the antonym "eager" helps the reader understand the meaning of "reluctant."
Joe was reluctant to take on the position of captain of
the basketball team. He was afraid that the time it would take would hurt his
grades. On the other hand, Billy was eager for the chance to be captain. He
thought that being captain of the team would make him very popular in school.
4. Description context clue
The author includes one or more descriptions to help the reader understand the meaning of a word. In the following example, descriptions of President Kennedy as having charm, enthusiasm, and a magnetic personality help the reader understand the meaning of "charismatic."
John Fitzgerald Kennedy, our 35th president, improved
human rights and equal rights for all people. He was a very charismatic president.
People were attracted to his charm and enthusiasm. His personality was
described as magnetic.
5. Summary context clue
The author makes a number of statements that help the reader understand the meaning of a word. In the following example, statements about being rude, showing no respect, having poor manners, and being impolite help the reader understand the meaning of "impertinent."
Andrea was a very impertinent young lady. She was so
rude that she talked while her teacher was explaining a lesson. She showed no
respect for other students. Her manners were very poor. Even her parents
thought that Andrea was impolite.

6. Visual context clue
The author includes a picture, drawing, chart, graph, or other type of visual to help the reader understand the meaning of a word. In the following example, the picture and its caption that is close to the sentence helps the reader understand that "exultant" means great joy.
Peggy had an exultant look on her face.
Using the context clues provided by authors can help you learn
the meaning of many new words.22. Confusing Pairs of Words
Many pairs
of words sound alike or nearly alike, but each has a different meaning. For
example, affect means to influence something, while effect means
the result of something. Words like these can be easily confused with each
other.
You must be
careful to use the correct word from a pair of such confusing words when you
are writing and speaking. If not, you may express something different than what
you mean to express.
For example,
suppose you are writing about the importance of a good marriage. You write that
martial bliss is a wonderful thing. The word martial refers to
war. You should have written that marital bliss is a wonderful thing.
The word marital refers to marriage.
You wouldn't
want to embarrass yourself by addressing a letter to the administrator of your
school as "Dear Principle." The word principle means a
fundamental truth. You should write "Dear Principal." The word
principal refers to the head of a school.
Here are
some word pairs that are commonly confused. Learn the meanings of each of the
words so that you use them correctly.
Accept - to take something that is given
to you
Except - to leave out
Except - to leave out
Altar - a raised place used in religious
services
Alter - to change
Alter - to change
Ascent - to climb
Assent - to agree
Assent - to agree
Brake - a device for stopping or slowing
a vehicle
Break - to come apart
Break - to come apart
Cite - to document
Site - a place
Site - a place
Coarse - rough
Course - moving from one point to the next
Course - moving from one point to the next
Complement - something that makes a thing
whole or perfect
Compliment - to praise
Compliment - to praise
Conscience - a sense of right and wrong
Conscious - state of being awake
Conscious - state of being awake

Descent - coming from a higher place to a
lower one
Dissent - to disagree
Dissent - to disagree
Desert - a dry, hot, sandy area
Dessert - the sweet final part of a meal
Dessert - the sweet final part of a meal
Device - something made for a certain
purpose
Devise - to invent something or develop a plan
Devise - to invent something or develop a plan
Elicit - to bring out
Illicit - illegal
Illicit - illegal
Eminent - famous or well respected
Imminent - about to happen
Imminent - about to happen
Faint - weak
Feint - a movement meant to deceive
Feint - a movement meant to deceive

Forth - forward
Fourth - an ordinal number
Fourth - an ordinal number
Here - at or in a place
Hear - to receive sound through one's ears
Hear - to receive sound through one's ears
Hoard - to save and store away
Horde - a very large group
Horde - a very large group
Hole - an opening through something
Whole - an entire thing
Whole - an entire thing
Loath - reluctant
Loathe - greatly dislike
Loathe - greatly dislike
Palate - the roof of the mouth
Palette - an artist's board for mixing paints
Palette - an artist's board for mixing paints
Peace - absence of fighting
Piece - a portion of something
Piece - a portion of something
Plain - clearly seen, heard, or
understood
Plane - a flat surface
Plane - a flat surface
Pore - a very small opening in the skin
Pour - to cause something to flow
Pour - to cause something to flow
Precede - to come before
Proceed - to go forward
Proceed - to go forward
Shear - to cut the wool off a sheep
Sheer - so thin you can see through it
Sheer - so thin you can see through it
Stationary - to stand still
Stationery - writing paper
Stationery - writing paper
Waist - the part of the human body
between the ribs and the hips
Waste - to use or spend carelessly
Waste - to use or spend carelessly
Weak - without strength
Week - a period of seven days
Week - a period of seven days
Don't be
CONFUSED! Learn the meanings of these words to use them correctly.
23. Writing a Five Paragraph Essay
As you progress through school, you will be required to write essays. An essay is a written composition in which you express a certain idea and back it up with statements that support the idea. Most frequently, you will be required to write your essay in a five paragraph essay format.As its name implies, a five paragraph essay consists of five paragraphs. However, the essay itself consists of three parts: an introduction, a body, and a conclusion.
Introduction
The first paragraph of a five paragraph essay is the introduction. You should begin this paragraph with a statement that captures the reader's interest so that the reader will want to continue to read your entire essay. Make your first sentence as interesting as possible. Follow with several sentences that clarify your opening statement. Conclude the paragraph with a thesis statement in which you present what you believe and intend to prove. A good thesis statement takes a stand and is very specific.Body
The body of a five paragraph essay consists of three paragraphs. Each paragraph should be limited to one main idea that supports your thesis statement. The first paragraph of the body should contain your strongest argument in support of your thesis. Begin this paragraph by stating your idea. Then follow with two or three sentences containing supporting evidence or examples. Conclude this paragraph with a sentence that sums up what you discussed in the paragraph.The second paragraph of the body should follow the same format as the first paragraph of the body. This paragraph should contain your second strongest argument in support of your thesis statement. The third paragraph of the body follows the same format and contains your third strongest argument. In addition to summing up what you have discussed in the paragraph, the last sentence should also indicate that the paragraph contains the final argument you are raising.
Conclusion
The fifth and final paragraph of the essay contains the conclusion. This concluding paragraph should repeat your thesis statement in slightly different words than used in your introductory paragraph. It should summarize the three arguments you presented in the body of your essay. Your final sentence should signal that your essay has come to an end. In essence, your concluding paragraph should make it clear to the reader that you believe you have proven what you set out to prove.Writing essays becomes increasingly important as you progress through school. Following the format presented above will help you write good essays.
25. Reading Comprehension: The REDW Strategy for Finding Main Ideas
REDW is a
good strategy to use to find the main idea in each paragraph of a reading
assignment. Using this
strategy will help you comprehend the information contained in your assignment.
Each of the letters in REDW stands for a step in the strategy.
Read
Read the entire paragraph to get an
idea of what the paragraph is about. You may find it helpful to whisper the
words as you read or to form a picture in your mind of what you are reading.
Once you have a general idea of what the paragraph is about, go on to the next
step.
Examine
Examine each
sentence in the paragraph to identify the important words that tell what the
sentence is about. Ignore the words that are not needed to tell what the
sentence is about. If you are allowed to, draw a line through the words to be
ignored. For each sentence, write on a sheet of paper the words that tell what
the sentence is about.
Decide
Reread the
words you wrote for each sentence in the paragraph. Decide which sentence
contains the words you wrote that best describe the main idea of the paragraph.
These words are the main idea of the paragraph. The sentence that contains
these words is the topic sentence. The other words you wrote are the supporting
details for the main idea.
Write
Write the
main idea for each paragraph in your notebook. This will provide you with a
written record of the most important ideas you learned. This written record
will be helpful if you have to take a test that covers the reading assignment.
Use REDW
to help you understand the information in your reading assignments.
26. Useful
Spelling Rules
Correct
spelling is very difficult for many students because the spellings of many
words do not follow rules.

Even when
rules apply to the spellings of words:
- There are many rules to be learned.
- Many of the rules are very complicated.
- Many of the rules apply to a small number of words.
- Almost every rule has exceptions.
Still, there
are some rules that apply to the spellings of words with few exceptions and
that are not difficult to learn and remember. Learning and using these rules
can improve your spelling.
Here are
eight spelling rules you should learn and use.
- A word that ends with the sound
of "v" is spelled with the letters "ve" at its end.
*Examples: shave, above, effective - The letter "i" comes
before "e" except after "c."
*Examples: believe, field, tried (but not receive) - When a word ends with
"y" preceded by a consonant, form the plural of the word by
changing the "y" to "i" and adding "es."
*Examples: countries, carries, ladies

- Drop the final silent
"e" when adding a suffix that begins with a vowel.
*Examples: changing, notable, nervous - Keep the final silent
"e" when adding a suffix that begins with a consonant.
*Examples: useful, lovely, hopeless - When a one-syllable word ends
in a vowel followed by a consonant, double the final consonant when adding
a suffix.
*Examples: topped, swimmer, hitting - The letter "q" in a
word is followed by "u."
*Examples: quick, antique, equation - Do not change the spelling of a
word when adding a prefix to it.
*Examples: remove, triangle, misspell
While some
of these rules have exceptions, learning and using them will help you correctly
spell many words.
27. Capitalization Rules
There are
many times when a word or words must be capitalized. Here are ten
capitalization rules you should know and use. An example is shown for each
rule.
- Capitalize the first word of a
sentence.
It is important to know when a word must be capitalized. - Capitalize the pronoun
"I."
Do you think I should study for another hour? - Capitalize proper nouns (names
of specific people, places, events, and organizations).
I believe that George Washington was our greatest president. - Capitalize days of the week,
holidays, and months of the year.
We usually go on vacation during July and August. - Capitalize the first word in a
quote.
I was pleased when my teacher said to me, "You are a wonderful student." - Capitalize the name of a
language.
Next year I will study Spanish literature. - Capitalize the official title
of a person when used with that person's name.
My friend told me that Dr. Hawkins is a great chemistry teacher. - Capitalize initials in
someone's name.
My favorite author is J. R. R. Tolkien. - Capitalize the first word of a
salutation or closing.
With warmest regards,
Amanda Warren - Capitalize the first word and
last words and each important word in the title of a book, movie, etc. Do
not capitalize short words within a title (e.g.,a, an, and, as, if, for,
or, the). Also, do not capitalize prepositions.
I was very moved when I read To Kill a Mockingbird.
There are
many capitalization rules. Knowing and using these ten rules is a good start.
28. Spelling Long Words: The Syllable-Building Strategy
A long
word is a word that has more than one syllable (i.e., multisyllabic). A
syllable is a word or part of a word that is spoken with a single sound of the
voice. Using the Syllable-Building Strategy will help you spell long
words such as democratic.
Here is how
a student named William used the steps in the Syllable-Building Strategy to
learn to spell democratic. He came across this word while reading his
social studies textbook.
- Step 1. William carefully copied the word into his notebook. He checked what he wrote to be sure that he had spelled the word correctly. Here is what he wrote.
- Step 2. William then located the word democratic in his dictionary.
- Step 3. William used the phonetic respelling of democratic in the dictionary to help him pronounce the word. William knew that if he could still not pronounce democratic, he could ask his teacher for help.
- Step 4. From the dictionary, William learned that democratic was a four-syllable word. William wrote democratic leaving a space between each syllable. Here is what he wrote.
- Step 5. William wrote the first
syllable of democratic three times. He pronounced this syllable
each time he wrote it. Here is what he wrote.



William then covered what he had written and wrote the first syllable of democratic from memory. Here is what he wrote.

He looked to see if he had spelled the first syllable correctly and found that he had. William then wrote the first two syllables of democratic together three times. He pronounced the two syllables together as he wrote them. Here is what he wrote.



He covered what he had written and wrote the first two syllables from memory. Here is what he wrote.

William
then looked to see if he had spelled the first two syllables correctly and
found that he had not. Therefore, he once again wrote the first two
syllables of democratic three times, pronouncing them as he did so.
Here is what he wrote.



William covered what he had written and wrote the first two syllables from memory. Here is what he wrote.

He looked to see if he had spelled the first two syllables correctly and found that he had.
William continued this procedure for the first three syllables of democratic and then for the entire word. - Step 6. Once William had correctly spelled the entire word from memory, he wrote democratic on his personal spelling list. He wrote both the entire word and the word broken into syllables.
- Step 7. William periodically reviewed the spelling of democratic using the following Spell and Say Review Procedure:
- He pronounced democratic aloud.
- He pronounced and spelled aloud each syllable.
- He spelled the entire word aloud.
- He wrote democratic three times.








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