THREE -3- Reasons Your Entire Family Needs SAT Math!
MONDAY: Your calculator Tuesday: The Grid Problems Wednesday: Square root-all you need
1) SAT Math questions often follow everyday logic allowing elimination of wrong answers immediately on standardized tests and in life tests, as well.
Using the strategy I use for what I call ‘racecar’ questions is not helpful on most math questions, but eliminating some incorrect answers IS very helpful.
Try a game for the day—with a one-minute timer.
Look at today’s example below for an example.
2) Learning to use a calculator, especially a science and graphing calculator, is a special skill that helps in many other areas of life.
Teacher’s confession: I admit that I have been one of the teachers who felt that calculators can hold you up on tests because so many students I tutor slow down to try to figure out how to use the calculators to do problems they have no idea how to solve—or, worse, they spend too much time using the calculators on problems they already know how to check without help in calculation.
With the help of the Princeton Review, I now believe I have been prejudiced by the fact that I did not use calculators on standardized tests when I was in school and by the fact that I tutor Algebra to students who are studying for standardized tests; but I am, foremost, an English and language arts teacher, and a Gifted, Reading, and Exceptional Ed teacher. My tutoring is about bridging the content areas. I have not ‘played’ with calculators in math classes with teachers who use them daily. But I am going to use this to your advantage by choosing only the top tips and techniques for using calculators. Come back on Monday.
MONDAY: USING YOUR CALCULATOR ON SAT TUESDAY: THE GRID PROBLEMS
3) Spend some time with your family working some problems using logic. Logic is math. Logic is the trail of what is true. If A is true and B is true, C may or may not be a conclusion from these two premises. This is the mathematical way to measure an argument, even a political argument. You may not be able to find what is true, but you will be able to eliminate what is not proved.
For example: You may say: A. Many students drive to school. (A may be true.) B. When a student drives to school, his or her parent can take a different route to work. (B may be true). C. Buying a student a car for school is a family benefit. (This conclusion, while somewhat justifiable by the two premises given and supportable by some popularity—or whatever the case may be—is NOT a mathematical conclusion. Furthermore, the two premises have not been proven by the information here.
But you can prove A and B premises. You can see by these premises and a possible conclusion that public opinion and campaigns—not to mention advertisements—are often based upon so-called ‘logic’—often false logic.
Today’s math question for the point. There is NO REASON TO MISS this question. It is from a past SAT test, and it is featured in the 2010 Princeton Review.
This math question counts one point and so does a question that is many times more difficult. Take a few seconds and get this one right:
If you buy a clothing item that cost 20% more last week when it was not on sale, and you are buying it on sale for $100, how much did it cost before?
A. $140
B. $70
C. $120
D. $125
E. $82
Okay, now did you throw out B and E right away? Hello. It is cheaper now—not more expensive, right. So are you diving to C. Wait up!
It’s
D. Don’t miss this point. Some of the other math is soooo complicated. This is yours.
Maybe a quick use of your calculator is in order here, but I do a lot of taking ten percent and doubling that for twenty percent. I often tip twenty percent—not that my bill would be $80!
But my constant practice helps to visualize in reverse. To be paying $80 after a discount of 20%, the old price was $125. (You should try it next after eliminating the obviously wrong ones because the 100 and 120 are just too enticing 125x.20 =25. So subtract $25 from $125 and you have $100 as the original.
Saturday, March 27, 2010
Wednesday, March 24, 2010
Hey! Don't Miss These SAT QUESTIONS!!! Your TUTOR HERE! MATH? LET'S TALK!
62% Missed the Fastest RACECAR of ALL TODAY!! SAT 62% WRONG! READ YOUR TUTOR!
Keep Reading On To The Last Part—It’s the Math. We Can Do This! We Can Do This!!!
Why did so many people miss today’s SAT question? It is absolutely the fastest one they have had yet!
In fact, I used the math strategy on it, so it is the perfect way to segue into the mathematics strategy instead of the language arts and other test strategies. This question today should be solved WITHOUT ELIMINATING THE INCORRECT ANSWERS—LIKE A MATH QUESTION.
In the movie The Blind Side, Kathy Bates portrays a tutor who teaches the way I teach, one-on-one, across the curriculum. Like ‘Miss Sue’ in the movie, I have my own personal eccentricities, and I expect each of my students to use her or his personal talents to the fullest. Also, like Miss Sue, I have an extremely high success rate with each and every student. Sometimes it IS rocket science, but you can surprise yourself.
Today’s SAT question and answer is one of the several styles that I call ‘RACECAR’ SAT Q&A. For my students and other readers, you know I use this term because ‘racecar’ is a palindrome; and I do the language arts questions and answers quickly. Therefore, my usual strategy on the racecar is to check the answer by testing each and every answer to eliminate each incorrect answer. A palindrome is a word that reads the same backwards and forwards, ‘racecar’ is the same backwards and forwards. I check the fast answers backwards and forwards.
For several days now, I have been promising to use today, Wednesday, to describe the difference in the strategies for managing mathematics questions on the SAT and other standardized tests. I have said that the difference is extremely important because you must manage the calculating questions in A COMPLETELY OPPOSITE MANNER from the “racecar” questions.
Helpfully, today’s “racecar” SAT question is the very first SAT style language arts question that I solved using the strategy that I use for a mathematics question. This is the way you need to solve mathematics questions. It is also the way to solve questions that require answers involving calculations and applications of rules.
Here is the difference: Do NOT spend time eliminating the incorrect answers.
Here is why: Eliminating the incorrect answers will take too much time and/or be a confusing procedure.
Here is the way to do this type of question:
MATH
Methodically, write out the problem in a new sentence in your booklet or scratch paper.
Act upon what you know, using resources you have (calculator, formulae in booklet, visual)
Teach yourself as you move through the problem once.
Hit the answer sheet and go.
Summary: The strategy is: Instead of answering and checking by eliminating the wrong answers, you find all you know and restate the problem; solve the problem; look for the answer; mark your answer sheet; move on. You work the problem. If you cannot work the problem, guess and go.
Today’s SAT question worked like a math problem because you need to know how to recognize that a rule is broken. There is not a way to try out different things. The very first word is underlined and the word is ‘Origin.’ The very first verb is NOT underlined. The verb is ‘lie.’ In this sentence, this subject (origin is singular) and this verb (lie) do not agree.
More attempts to eliminate other possibilities will just blur this because ‘Origin’ is underlined, but ‘lie’ is not. If Origin is changed to ‘Origins,’ the sentence can be correct. Otherwise, nothing else will fix the sentence because there is no opportunity given to work on the verb in disagreement.
The origin (has to be “origins”) of amusement parks(could be “lies”—but we don’t have this option) lie in ancient and medieval religious festivals and trade fairs, b where merchants, entertainers, and food sellers c gathered d in order to take advantage of the large crowds. e No error
THE ANSWER HAS TO BE A—Taking time to eliminate the other answers will be counter-productive. This is ONE POINT!!!
There is no other way to make subject-verb agreement!
TAKING THIS TO MATHEMATICS—AND STAYING WITH THIS UNTIL WE CAN DO THIS, TOO!!!!
LET’S JUST DO ONE TO SHOW HOW THIS IS DIFFERENT FROM WHAT WE HAVE BEEN DOING IN THE PAST ON THE ELIMINATION OF WRONG ANSWER QUESTIONS
LOOK AT THE MARCH 16th question:
The first thing I want to say about this question is that it is NOT an easy one. The second thing is that it IS fairly easy to do once you write it in the correct ‘sentence.’ This is a good one to notice how comfortable you are with writing the sentence. Just know this: There WILL be questions like this on the test. Some of those questions will not be this difficult. Do not skip them. Try them. Practice some things about these questions ahead of time.
In a class of seniors, there are boys for every girls. In the junior class, there are boys for every girls. If the two classes combined have an equal number of boys and girls, how many students are in the junior class?
The answers are just short—the answer only. You would be working all day to eliminate each one! No way! The correct way to do this is to form a new statement of what the math problem says and to solve it. After you have done this again and again and again (and again), this becomes as fluid as translating from one language to another. You start ‘thinking’ in those terms. Really.
A. 72 B. 80 C. 84 D.100 E. 120
Okay, after reading that question, look at the hint they gave you. This is one time that I am just putting the SAT hint and explanation right here. I cannot improve on their mathematical sentence for you to see. Here is their hint,
The statement about boys for every girls means that out of every students in the senior class, are boys and are girls. In other words, of the class is boys and is girls. Since there are seniors, of , or , must be boys and of , or , must be girls. Let stand for the total number of juniors and express, in terms of , the number of junior boys and the number of junior girls. Then you can write an equation in to represent the fact that the total number of boys (juniors and seniors) is equal to the total number of girls. Solving for will give the total number of juniors.
What I suggest that you do is to draw this out while you are copying how to solve this. When it says to let x stand for the total number of juniors and express in terms of x the number of junior boys and the number of junior girls—draw what x is representing—with little notes to yourself.
Once you have done the above, followed this ‘hint,’ you have to do the following:Among the seniors, there are boys for every girls, so of the seniors, or , are boys and , or , are girls. Among the juniors, are boys and are girls. If stands for the total number of juniors, then are boys and are girls. The total number of senior and junior boys is . The total number of senior and junior girls is . The question states that these quantities are equal, so . Solving this gives , or .
The answer is D. 100. This looks complicated. I KNOW it does to more than a few because many of the responding test-takers missed this one. However, this is NOT as complicated as it looks on this page. If we were sitting next to each other like Michael and Miss Sue, this would even be fun. Come back.judiethcarol&rocketcatmarch2010
Keep Reading On To The Last Part—It’s the Math. We Can Do This! We Can Do This!!!
Why did so many people miss today’s SAT question? It is absolutely the fastest one they have had yet!
In fact, I used the math strategy on it, so it is the perfect way to segue into the mathematics strategy instead of the language arts and other test strategies. This question today should be solved WITHOUT ELIMINATING THE INCORRECT ANSWERS—LIKE A MATH QUESTION.
In the movie The Blind Side, Kathy Bates portrays a tutor who teaches the way I teach, one-on-one, across the curriculum. Like ‘Miss Sue’ in the movie, I have my own personal eccentricities, and I expect each of my students to use her or his personal talents to the fullest. Also, like Miss Sue, I have an extremely high success rate with each and every student. Sometimes it IS rocket science, but you can surprise yourself.
Today’s SAT question and answer is one of the several styles that I call ‘RACECAR’ SAT Q&A. For my students and other readers, you know I use this term because ‘racecar’ is a palindrome; and I do the language arts questions and answers quickly. Therefore, my usual strategy on the racecar is to check the answer by testing each and every answer to eliminate each incorrect answer. A palindrome is a word that reads the same backwards and forwards, ‘racecar’ is the same backwards and forwards. I check the fast answers backwards and forwards.
For several days now, I have been promising to use today, Wednesday, to describe the difference in the strategies for managing mathematics questions on the SAT and other standardized tests. I have said that the difference is extremely important because you must manage the calculating questions in A COMPLETELY OPPOSITE MANNER from the “racecar” questions.
Helpfully, today’s “racecar” SAT question is the very first SAT style language arts question that I solved using the strategy that I use for a mathematics question. This is the way you need to solve mathematics questions. It is also the way to solve questions that require answers involving calculations and applications of rules.
Here is the difference: Do NOT spend time eliminating the incorrect answers.
Here is why: Eliminating the incorrect answers will take too much time and/or be a confusing procedure.
Here is the way to do this type of question:
MATH
Methodically, write out the problem in a new sentence in your booklet or scratch paper.
Act upon what you know, using resources you have (calculator, formulae in booklet, visual)
Teach yourself as you move through the problem once.
Hit the answer sheet and go.
Summary: The strategy is: Instead of answering and checking by eliminating the wrong answers, you find all you know and restate the problem; solve the problem; look for the answer; mark your answer sheet; move on. You work the problem. If you cannot work the problem, guess and go.
Today’s SAT question worked like a math problem because you need to know how to recognize that a rule is broken. There is not a way to try out different things. The very first word is underlined and the word is ‘Origin.’ The very first verb is NOT underlined. The verb is ‘lie.’ In this sentence, this subject (origin is singular) and this verb (lie) do not agree.
More attempts to eliminate other possibilities will just blur this because ‘Origin’ is underlined, but ‘lie’ is not. If Origin is changed to ‘Origins,’ the sentence can be correct. Otherwise, nothing else will fix the sentence because there is no opportunity given to work on the verb in disagreement.
The origin (has to be “origins”) of amusement parks(could be “lies”—but we don’t have this option) lie in ancient and medieval religious festivals and trade fairs, b where merchants, entertainers, and food sellers c gathered d in order to take advantage of the large crowds. e No error
THE ANSWER HAS TO BE A—Taking time to eliminate the other answers will be counter-productive. This is ONE POINT!!!
There is no other way to make subject-verb agreement!
TAKING THIS TO MATHEMATICS—AND STAYING WITH THIS UNTIL WE CAN DO THIS, TOO!!!!
LET’S JUST DO ONE TO SHOW HOW THIS IS DIFFERENT FROM WHAT WE HAVE BEEN DOING IN THE PAST ON THE ELIMINATION OF WRONG ANSWER QUESTIONS
LOOK AT THE MARCH 16th question:
The first thing I want to say about this question is that it is NOT an easy one. The second thing is that it IS fairly easy to do once you write it in the correct ‘sentence.’ This is a good one to notice how comfortable you are with writing the sentence. Just know this: There WILL be questions like this on the test. Some of those questions will not be this difficult. Do not skip them. Try them. Practice some things about these questions ahead of time.
In a class of seniors, there are boys for every girls. In the junior class, there are boys for every girls. If the two classes combined have an equal number of boys and girls, how many students are in the junior class?
The answers are just short—the answer only. You would be working all day to eliminate each one! No way! The correct way to do this is to form a new statement of what the math problem says and to solve it. After you have done this again and again and again (and again), this becomes as fluid as translating from one language to another. You start ‘thinking’ in those terms. Really.
A. 72 B. 80 C. 84 D.100 E. 120
Okay, after reading that question, look at the hint they gave you. This is one time that I am just putting the SAT hint and explanation right here. I cannot improve on their mathematical sentence for you to see. Here is their hint,
The statement about boys for every girls means that out of every students in the senior class, are boys and are girls. In other words, of the class is boys and is girls. Since there are seniors, of , or , must be boys and of , or , must be girls. Let stand for the total number of juniors and express, in terms of , the number of junior boys and the number of junior girls. Then you can write an equation in to represent the fact that the total number of boys (juniors and seniors) is equal to the total number of girls. Solving for will give the total number of juniors.
What I suggest that you do is to draw this out while you are copying how to solve this. When it says to let x stand for the total number of juniors and express in terms of x the number of junior boys and the number of junior girls—draw what x is representing—with little notes to yourself.
Once you have done the above, followed this ‘hint,’ you have to do the following:Among the seniors, there are boys for every girls, so of the seniors, or , are boys and , or , are girls. Among the juniors, are boys and are girls. If stands for the total number of juniors, then are boys and are girls. The total number of senior and junior boys is . The total number of senior and junior girls is . The question states that these quantities are equal, so . Solving this gives , or .
The answer is D. 100. This looks complicated. I KNOW it does to more than a few because many of the responding test-takers missed this one. However, this is NOT as complicated as it looks on this page. If we were sitting next to each other like Michael and Miss Sue, this would even be fun. Come back.judiethcarol&rocketcatmarch2010
Tuesday, March 23, 2010
Back to Tutor Racecars-Critical Reading-Check SAT
Today's question was missed by 20%, so you have to be checking them to make sure you keep your points.The strategy for this style of question--as opposed to mathematical questions with calculations--is to eliminate every incorrect answer after you choose the correct answer.
STEP ONE: Read the question noticing every clue, realizing that the writer of the question is including clues to lead you to choose a best answer that is strongly supported by the clear definitions of the words. The first word is 'confident.' For the first blank, I am seeking a word that indicates that the candidate is expecting to win, despite some surge of popular opinion in favor of an opponent. Therefore, for the second blank, I am not expecting the word to be a tragic or defeatist word. This candidate is 'confident.'
The only two possible first words in the pairs to fit the connotation needed in the first blank are 'strengthen' and 'prevail'--so A,D,and E are eliminated. I try:
Confident that her own political platform would prevail at election time, the mayor considered her opponent's sudden popularity less a threat than a distraction.
(I'm thinking: Yes, that fits. I was thinking that 'distraction' would have been something like 'aberration' but let's see if that other possibility is something that fits better for some reason.)
Confident that her own political platform would strengthen at election time, the mayor considered her opponent's sudden popularity less a threat than a calamity. Nope, that is NOT it. She would not be thinking the opponent's sudden popularity is a calamity (awful, terrible happening) if she is so confident.
So it IS C. I'm right. But I have to check it by eliminating everything. I just have to move in a quick, orderly, planned, methodical way. This is how I get the big score on this part of the test!
Tomorrow, we will talk about the difference in how to work on the math questions. Come back, please.
STEP ONE: Read the question noticing every clue, realizing that the writer of the question is including clues to lead you to choose a best answer that is strongly supported by the clear definitions of the words. The first word is 'confident.' For the first blank, I am seeking a word that indicates that the candidate is expecting to win, despite some surge of popular opinion in favor of an opponent. Therefore, for the second blank, I am not expecting the word to be a tragic or defeatist word. This candidate is 'confident.'
The only two possible first words in the pairs to fit the connotation needed in the first blank are 'strengthen' and 'prevail'--so A,D,and E are eliminated. I try:
Confident that her own political platform would prevail at election time, the mayor considered her opponent's sudden popularity less a threat than a distraction.
(I'm thinking: Yes, that fits. I was thinking that 'distraction' would have been something like 'aberration' but let's see if that other possibility is something that fits better for some reason.)
Confident that her own political platform would strengthen at election time, the mayor considered her opponent's sudden popularity less a threat than a calamity. Nope, that is NOT it. She would not be thinking the opponent's sudden popularity is a calamity (awful, terrible happening) if she is so confident.
So it IS C. I'm right. But I have to check it by eliminating everything. I just have to move in a quick, orderly, planned, methodical way. This is how I get the big score on this part of the test!
Tomorrow, we will talk about the difference in how to work on the math questions. Come back, please.
Monday, March 22, 2010
20th and 21st SAT are RACECAR questions for this TUTOR
The 20th and the 21st SAT Questions for the day are back to ‘RACECAR’ questions. These are the ones to use the strategy of eliminating all of the possible answers. I favor the language arts questions because of my own ability to solve them rapidly. For the same reason, however, I am wary of the pitfalls inherent in rushing. Therefore, my strategies for the questions relating to improving sentences and to choosing words to fill in blanks include the admonishment to pace appropriately; to be sure to answer the question asked; and to eliminate all of the other possibilities.
These strategies to CHECK your answer once you feel you know the answer are my ways to make sure you do not skim the ‘RACECAR’ questions too rapidly, as I have done, on occasion. I know that each correct answer on the SAT test counts one point. I know some students miss answers they know because they are too casual on those questions.
However, you have to understand, too, that the way you work on the type of questions and answers that you understand and all of the ones you can check rapidly—such as the questions and answers I call ‘RACECAR’ questions and answers—are quite different from most mathematics questions. Most of the mathematics questions and answers cannot be solved quickly enough to allow you to eliminate all of the other answers.
In short: As I have noted many times: Do not use the same ‘elimination’ strategy in the math portions of the test that you use in the language arts and some other portions of the test.
Pacing does not allow you the time to work the problems to eliminate the wrong answers in the mathematics section and in some other sections of the test.
The correct strategy to use when you have calculations to do is:
1) Figure out what you need to know. Read the problem while visualizing it.
2) Notice what you do know. BE AWARE THAT YOU HAVE MORE INFO THAN YOU NEED TO ANSWER THE QUESTION.
3) Write down the question as simply as you can.
4) Calculate carefully to find the answer—making notes and pictures.
5) Look for the answer in the multiple choice list.
6) Mark the answer on your answer sheet and mark the booklet to come back; and
7) Move on.
The catch in mathematics is that you have extra information. This is where the scholastic aptitude test kicks in to find out if you are able to pace yourself and to move on while you are still aware that you have not used everything you can do.
You will find that you have more information, but you still do not know what to do with it sometimes. Jot down what you know. Make some predictions and guesstimates—Guess about an answer, and mark the problem to come back. Do not keep doodling with it. You have too much information if you do not know the answer.
Come back to this column, and we will talk about the math problems on Wednesday. There are some helpful things to do about the mathematics section that will help you—if you are a whiz in math or even if you are not a whiz in math.
These strategies to CHECK your answer once you feel you know the answer are my ways to make sure you do not skim the ‘RACECAR’ questions too rapidly, as I have done, on occasion. I know that each correct answer on the SAT test counts one point. I know some students miss answers they know because they are too casual on those questions.
However, you have to understand, too, that the way you work on the type of questions and answers that you understand and all of the ones you can check rapidly—such as the questions and answers I call ‘RACECAR’ questions and answers—are quite different from most mathematics questions. Most of the mathematics questions and answers cannot be solved quickly enough to allow you to eliminate all of the other answers.
In short: As I have noted many times: Do not use the same ‘elimination’ strategy in the math portions of the test that you use in the language arts and some other portions of the test.
Pacing does not allow you the time to work the problems to eliminate the wrong answers in the mathematics section and in some other sections of the test.
The correct strategy to use when you have calculations to do is:
1) Figure out what you need to know. Read the problem while visualizing it.
2) Notice what you do know. BE AWARE THAT YOU HAVE MORE INFO THAN YOU NEED TO ANSWER THE QUESTION.
3) Write down the question as simply as you can.
4) Calculate carefully to find the answer—making notes and pictures.
5) Look for the answer in the multiple choice list.
6) Mark the answer on your answer sheet and mark the booklet to come back; and
7) Move on.
The catch in mathematics is that you have extra information. This is where the scholastic aptitude test kicks in to find out if you are able to pace yourself and to move on while you are still aware that you have not used everything you can do.
You will find that you have more information, but you still do not know what to do with it sometimes. Jot down what you know. Make some predictions and guesstimates—Guess about an answer, and mark the problem to come back. Do not keep doodling with it. You have too much information if you do not know the answer.
Come back to this column, and we will talk about the math problems on Wednesday. There are some helpful things to do about the mathematics section that will help you—if you are a whiz in math or even if you are not a whiz in math.
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