Ah! Speeding Through SAT Completion is Still a Favorite!
Rocketcat Racecar (palindrome) strategy is at peak performance today!
First, you read the sentence filling in the shortest, best word to have the right connotation. Then, you use your two words to match against the pairs in the answers for two matching connotations.
Gwendolyn Brooks’ character Maud Martha appears ______ (calm?) but feels great rage; she _____(masks?) her emotions with a mask of compliance.
We went all the way to the semicolon before choosing ‘calm’ because we see this ‘Maude Martha’ ‘appearing’ (indicating what something seems but is not)—aha! ‘but feels great rage;
Okay,she looks like ______ but feels rage. We choose ‘calm’
Reading on…she ______ her emotions (we already know she covers up so I am thinking ‘masks’ )
Okay, that second word is going to be a coverup word.
Let’s try them: calm word first…cover-up word second
A. Responsive (calm?so-so but no)….echoes (no…an echo repeats)
B. Nonchalant (okay)….exposes (NO—opposite of a cover-up word)
C. Docile (yes…) camouflages (yes)—MARK THE ANSWER SHEET NOW, PLEASE. It is C.
Now ‘race over D&E just to make sure nothing is ‘better’ than this one.
D. Uncontrolled (no)…belies (unh-uh)
E. Invincible (NO)….catapults (NO!)
PACING: You want to get these but use the speed to move on to the ones that take longer.
IF YOU ARE FEELING TIME PINCH, GO ON TO THE NEXT QUESTION WHEN YOU FIND AND MARK THE ANSWER. Eliminate at least one of the other answers to make sure you are answering what is asked.
Friday, April 23, 2010
Thursday, April 22, 2010
Rocketcat Visualizes SAT Shapes With Sapphire and Emerald Eyes
April 21st Math SAT Question: What’s the area of the triangle?
This column contains at least five strategies that are fast and accurate to get points for you on the math test. These tips are all about visualizing—starting with multiplying the low numbers while looking at the triangle.
Guess what? This was a RACECAR Q&A for Rocketcat. We did this one right behind the blue eye and the green eye. 2.5 x 3 =7.5!
Notice that the official explanation is much different—and, yet, not so different! The SAT Board advocates multiplying the sides (b)(h) or (5)(3)=15 and dividing by 2 =7.5.
This is such a nice drawing—no warnings, as on some problems, that it is not to scale!
Here is a lovely triangle on a graph. You are asked: What’s the area?
No problem. The numbers were so low that Rocketcat used the RACECAR strategy that we only use in math when we can zoom forwards—and then backwards (palindrome style) and get the same answer (like the word RACECAR).
Guess what? This was a RACECAR Q&A for Rocketcat. We did this one right behind the blue eye and the green eye. 2.5 x 3 =7.5! (Rocketboy,Rocketcat’s hero, also had one sapphire eye and one emerald eye.)
We love the visual stuff—like the graph and the triangle.
Here is a strategy from a ‘non-math’ teacher who teaches math often: If you do have a page on a standardized test with formulae, keep that marked to glance over when you encounter a formulae-based problem. But just let it remind you. Learn the formulae with your own visual flashcards or PowerPoint displays—with pictures. ‘See’ these visuals in your mind when working on problems.
Do visualize area as a rug over the area. Do visualize perimeter and circumference as fences around an area. Do visualize a cylinder as a can of soup. Visualize taking off the label and seeing that it is a rectangle around the can, and the top and bottom of the can are circles. To find the area of a cylinder, you have to get the area of those can ends AND the label around the can. Visualize how the actual can can be pulled apart into two circles and a rectangle.
Know the formula for the area of a triangle by putting this on your list of a few things to know before taking a math test. In fact, this is one of the things to put on your sheet for the last day or so.
Here is something funny that ‘real’ math teachers never mention. I think it is because they are so used to this. Visualize what I am saying here for a minute.
What if you are ready to do a problem using a formula, and you forget what ‘b’ and ‘h’ are? What if you have not done circles for a while and you forget that r is radius and d is diameter in some versions of the formulae?
Take today’s question, for example. Under test conditions, you may forget that ‘b’ is base and ‘h’ is height. What you need to know is: Wow! Look at this great graph and right angle triangle. I know all about this figure! What do you want to know? Oh, well to get the number to make a rug to cover this area, we take one-half of that 5 side (2.5) and multiply it by the vertical (height) side (3) because to get the area of a triangle, you take ½ of the base and multiply that number times the height or A=1/2 bh.
Here is a neat thing about the College Board style explanation—PEMDAS—First you multiply. Then, you divide.
Just to be sure Rocketcat did not ‘get’ this one in a fluke way, he tried out some more possibilities for the base and height measurements. It works out just fine to take ½ of the base and to multiply that figure times the height. We get it!!!judiethcarol&RocketcatApril2010
This column contains at least five strategies that are fast and accurate to get points for you on the math test. These tips are all about visualizing—starting with multiplying the low numbers while looking at the triangle.
Guess what? This was a RACECAR Q&A for Rocketcat. We did this one right behind the blue eye and the green eye. 2.5 x 3 =7.5!
Notice that the official explanation is much different—and, yet, not so different! The SAT Board advocates multiplying the sides (b)(h) or (5)(3)=15 and dividing by 2 =7.5.
This is such a nice drawing—no warnings, as on some problems, that it is not to scale!
Here is a lovely triangle on a graph. You are asked: What’s the area?
No problem. The numbers were so low that Rocketcat used the RACECAR strategy that we only use in math when we can zoom forwards—and then backwards (palindrome style) and get the same answer (like the word RACECAR).
Guess what? This was a RACECAR Q&A for Rocketcat. We did this one right behind the blue eye and the green eye. 2.5 x 3 =7.5! (Rocketboy,Rocketcat’s hero, also had one sapphire eye and one emerald eye.)
We love the visual stuff—like the graph and the triangle.
Here is a strategy from a ‘non-math’ teacher who teaches math often: If you do have a page on a standardized test with formulae, keep that marked to glance over when you encounter a formulae-based problem. But just let it remind you. Learn the formulae with your own visual flashcards or PowerPoint displays—with pictures. ‘See’ these visuals in your mind when working on problems.
Do visualize area as a rug over the area. Do visualize perimeter and circumference as fences around an area. Do visualize a cylinder as a can of soup. Visualize taking off the label and seeing that it is a rectangle around the can, and the top and bottom of the can are circles. To find the area of a cylinder, you have to get the area of those can ends AND the label around the can. Visualize how the actual can can be pulled apart into two circles and a rectangle.
Know the formula for the area of a triangle by putting this on your list of a few things to know before taking a math test. In fact, this is one of the things to put on your sheet for the last day or so.
Here is something funny that ‘real’ math teachers never mention. I think it is because they are so used to this. Visualize what I am saying here for a minute.
What if you are ready to do a problem using a formula, and you forget what ‘b’ and ‘h’ are? What if you have not done circles for a while and you forget that r is radius and d is diameter in some versions of the formulae?
Take today’s question, for example. Under test conditions, you may forget that ‘b’ is base and ‘h’ is height. What you need to know is: Wow! Look at this great graph and right angle triangle. I know all about this figure! What do you want to know? Oh, well to get the number to make a rug to cover this area, we take one-half of that 5 side (2.5) and multiply it by the vertical (height) side (3) because to get the area of a triangle, you take ½ of the base and multiply that number times the height or A=1/2 bh.
Here is a neat thing about the College Board style explanation—PEMDAS—First you multiply. Then, you divide.
Just to be sure Rocketcat did not ‘get’ this one in a fluke way, he tried out some more possibilities for the base and height measurements. It works out just fine to take ½ of the base and to multiply that figure times the height. We get it!!!judiethcarol&RocketcatApril2010
Tuesday, April 20, 2010
Rocketcat Wins with RACECAR AGAIN! Don't MISS these!
Rocketcat’s Racecar Strategy wins in UNDER a minute tonight. The statistics today are surprising to us: only 50% correct out of over a hundred thousand responders.
Watch the speeding rocket in his RACECAR (forward now…) He Never misses these.
Rocketcat’s patent RACECAR strategy:
First, go forward. Speed out but keep the wheels on the road on every part of the title, the directions, and the sentence.
Your brain is already practiced with these instructions, right?
Still, you use seconds to snap on the parts of your aptitude to make connections, to eliminate predictable errors, to choose the answer, to mark the answer.
Breathe deeply; and move through the title, the directions, and the sentence like a RACECAR gliding over black pavement at night. Consider the routine part as the white line on the pavement, guiding.
Title: This question is about improvement.
Directions: There is only one underlined portion to improve. If no improvement, choose A. to stay.
Now, you are looking for improvement: You are riding in a finely tuned RACECAR, moving surely.
Read the sentence noticing whether any predictable issues in the underlined portion.
But do NOT read for whether it ‘sounds’ right or ‘looks’ right.
Read to notice any predictable standard error—signaled by extra words, awkward introductory phrases, misused verb tense…
They use light that is 100 million times dimmer than the midday sun, and tropical nocturnal sweat bees leave their nests to forage for food.
A. (this one is the same as the original)
B. By using light that is 100 million times dimmer than midday, (This is ‘of interest’ because the introductory phrase does properly modify –after taking out the underlined ‘and’); but the sentence is in need of ‘sun’)
C. (Oh, here it is: MARK YOUR ANSWER AS C) In light that is 100 million times dimmer than the midday sun, tropical nocturnal sweat bees leave their nests to forage for food.
D. NOW RACECAR backwards (racecar is the same word backwards and forwards—a palindrome).
With the light being (nope—It is difficult to defend ‘with…being’)
E.When the light is 100 times as dim as with the midday sun…awkward comparative (See ‘dimmer than’ not ‘as dim as.’ The racecar is at the finish line. Rocketcat wins again!
You chose the correct answer right away by the forward speed, covering the full routine. Because the process is fast, you need to check all possibilities to be sure that you answered the correct question. The question here is whether you will notice that making a connection about how the bees use the light with the introductory preposition is superior to the two complete thoughts: They use the light. They leave their nests to forage. No, there’s a connection ‘In light…bees leave nests.
Remember: Mark the answer. Go back and eliminate the others. This is for the faster format. Most math questions will not require eliminating all the incorrect answers. There are other ways to check. However, about every fifth or sixth problem can be a ROCKETCAR--We mean RACECAR. Read it left to right or right to left. Rocketcat is my pal, and racecar is a palindrome. When you RACECAR math questions, be sure to answer the right question.
I always use the example in my mind of those questions you do in math when a bag is filled with blue, green, and red marbles. There are several questions one can ask. Notice which one the test designer DID ask.
Let me know if you ARE in the smaller group getting these answers!! So many missed this one! Why oh why did they miss the Rocketcat special style of question? He has not missed ONE—EVER. judiethcarol&rocketcatApril2010c
Watch the speeding rocket in his RACECAR (forward now…) He Never misses these.
Rocketcat’s patent RACECAR strategy:
First, go forward. Speed out but keep the wheels on the road on every part of the title, the directions, and the sentence.
Your brain is already practiced with these instructions, right?
Still, you use seconds to snap on the parts of your aptitude to make connections, to eliminate predictable errors, to choose the answer, to mark the answer.
Breathe deeply; and move through the title, the directions, and the sentence like a RACECAR gliding over black pavement at night. Consider the routine part as the white line on the pavement, guiding.
Title: This question is about improvement.
Directions: There is only one underlined portion to improve. If no improvement, choose A. to stay.
Now, you are looking for improvement: You are riding in a finely tuned RACECAR, moving surely.
Read the sentence noticing whether any predictable issues in the underlined portion.
But do NOT read for whether it ‘sounds’ right or ‘looks’ right.
Read to notice any predictable standard error—signaled by extra words, awkward introductory phrases, misused verb tense…
They use light that is 100 million times dimmer than the midday sun, and tropical nocturnal sweat bees leave their nests to forage for food.
A. (this one is the same as the original)
B. By using light that is 100 million times dimmer than midday, (This is ‘of interest’ because the introductory phrase does properly modify –after taking out the underlined ‘and’); but the sentence is in need of ‘sun’)
C. (Oh, here it is: MARK YOUR ANSWER AS C) In light that is 100 million times dimmer than the midday sun, tropical nocturnal sweat bees leave their nests to forage for food.
D. NOW RACECAR backwards (racecar is the same word backwards and forwards—a palindrome).
With the light being (nope—It is difficult to defend ‘with…being’)
E.When the light is 100 times as dim as with the midday sun…awkward comparative (See ‘dimmer than’ not ‘as dim as.’ The racecar is at the finish line. Rocketcat wins again!
You chose the correct answer right away by the forward speed, covering the full routine. Because the process is fast, you need to check all possibilities to be sure that you answered the correct question. The question here is whether you will notice that making a connection about how the bees use the light with the introductory preposition is superior to the two complete thoughts: They use the light. They leave their nests to forage. No, there’s a connection ‘In light…bees leave nests.
Remember: Mark the answer. Go back and eliminate the others. This is for the faster format. Most math questions will not require eliminating all the incorrect answers. There are other ways to check. However, about every fifth or sixth problem can be a ROCKETCAR--We mean RACECAR. Read it left to right or right to left. Rocketcat is my pal, and racecar is a palindrome. When you RACECAR math questions, be sure to answer the right question.
I always use the example in my mind of those questions you do in math when a bag is filled with blue, green, and red marbles. There are several questions one can ask. Notice which one the test designer DID ask.
Let me know if you ARE in the smaller group getting these answers!! So many missed this one! Why oh why did they miss the Rocketcat special style of question? He has not missed ONE—EVER. judiethcarol&rocketcatApril2010c
ROCKETCAT'S RACECAR STRATEGY WINS TODAY ON SAT!
Rocketcat's patent RACECAR strategy wins again on the SAT queToday’s SAT Is Back to Rocket cat’s PATENT RACECAR STRATEGY
Our favorite questions: Language Arts!By judieth&Rocketcat (NOTE—Read to the end for a mini-lesson re irony and humor that will also win points on standardized tests.)
Rocketcat says: Use the RACECAR strategy on the short and sweet ride through a sentence that tells you the answer on the way.
Sentence completion means that you are COMPLETING the sentence in tone so pay attention to the connotation of every clue. Connotation=feeling, emotion, implication of the words
RACECAR –a palindrome—the same word forwards and backwards.
We use this strategy on the short passages, completion sentences, and underlined portions –all of the formats of the language arts section plus some of the formats in other sections.
When we do NOT use this strategy is when time is wasted in eliminating all the incorrect answers. That is true of many math questions. Once solved, you can check the math question itself rather than eliminating all the other wrong answers. Even in the math section, eliminating two of the other answers will be a quick way to check that you are answering the correct question. Answering the correct question is a key element in the mathematics section of the test.
Here’s the RACECAR strategy as it works smoothly:
Read the title and instructions quickly—to put your brain into the mode of this type of question.
You are looking for ‘SENTENCE COMPLETION’ (Title) and you will:
(DIRECTIONS): Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole.
Okay, what is the SAT measuring here? Your aptitude for completing a sentence with the BEST word is being measured. The measurement is of your ability to solve the logic of the question.
Now, read the sentence thinking of what word, in the simplest form you can imagine, YOU would fill in:
Because he felt intimidated in his new position,
VISUAL: Cast a male actor: This male (he) felt (emotion) intimidated (emotion-fear-timid) in his new (unknown—fear of unknown) position (he has a new job—either new where he works or in a different position where he works)—FEEL IT!!!—and SEE the movie of this sentence in your mind…Here is a man who is feeling fear or anxiety in a new position…
Because he felt intimidated in his new position, he was ________ divulging his frank opinions of company proposals.
I would put ‘wary of’ in this spot. I’m looking for a word that describes being cautious and reserved before blurting out every opinion of the company’s policies.
Now, I look for a word like the one I think goes there:
A. Scurrilous about (Nope—This is negative enough but it reflects upon his own character rather than his concerns about policy…We don’t have any reason to think our man is ‘scurrilous’
B. Candid in—(Nope—our new guy on the job has no space to be ‘candid’ yet. He’s not feeling outspoken.)
C. Chary of—(Yes, I’m not familiar with this word; but it has the right connotations plus the correct form. My choice was wary of…chary sounds cautious, too)
MARK THIS ANSWER ON THE ANSWER SHEET.
We have already eliminated A&B. Now, RACECAR, to eliminate the other wrong answers—the part we only do on the fast answer questions:
D. Fervid about-(No, he is intimidated, so he is not feeling ‘fervid’ about ranting on about his opinions.
E. Precipitate in (No, this just does not make sense).
A. No. B. No. C.YES D.No E. No
Whether you are Nancy Drew, a Hardy Boy, or a scientist in the field, detection uses all your sensory powers and your emotional intellect. Make the connections to your clues about the feelings behind words. The connotation leads to the correct answers.
Here’s a little poem by Dorothy Parker. Dorothy Parker had a certain type of wit. On a past GED (graduation equivalency diploma) test, the test-takers were asked which of the following words best describes the overall mood of the speaker in this poem. Is the ‘mood of the speaker’: embarrassed, sarcastic, romantic, angry, or sad?
Let me show you how it speeds things up if you know the type of writer Dorothy Parker was, which I do. I am looking for this poem to turn in tone or mood. Watch this happen:
One Perfect Rose
A single flow’r he sent me, since we met.
All tenderly his messenger he chose;
Deep-hearted, pure, with scented dew still wet—
One perfect rose.
I knew the language of the floweret;
“My fragile leaves,” it said, “his heart enclose.”
Love long has taken for his amulet
One perfect rose.
Why is it no one ever sent me yet
One perfect limousine, do you suppose?
Ah no, it’s always just my luck to get
One perfect rose.
Dorothy Parker, “One Perfect Rose,” from Collected Poetry, 1926
Mood?
1. Embarrassed
2. Sarcastic
3. Romantic
4. Angry
5. Sad
Note: This is the way the answers are on the official test question that was used. In general, though, learn that this could even be called ‘ironic’ in literary terms. Literature questions often involve passages of irony: 1) dramatic irony –the reader or audience knows something the characters on the stage do not know; 2) situational irony—the woman sells her long fine hair to buy her beloved a chain for the watch he pawned to buy combs for her hair (Gift of the Magi by O’Henry); and 3) verbal (see above poem)judiethcarol&rocketcatApril2010c.
stion for the day. The RACECAR is fast, sleek, smooth, and correct!
Our favorite questions: Language Arts!By judieth&Rocketcat (NOTE—Read to the end for a mini-lesson re irony and humor that will also win points on standardized tests.)
Rocketcat says: Use the RACECAR strategy on the short and sweet ride through a sentence that tells you the answer on the way.
Sentence completion means that you are COMPLETING the sentence in tone so pay attention to the connotation of every clue. Connotation=feeling, emotion, implication of the words
RACECAR –a palindrome—the same word forwards and backwards.
We use this strategy on the short passages, completion sentences, and underlined portions –all of the formats of the language arts section plus some of the formats in other sections.
When we do NOT use this strategy is when time is wasted in eliminating all the incorrect answers. That is true of many math questions. Once solved, you can check the math question itself rather than eliminating all the other wrong answers. Even in the math section, eliminating two of the other answers will be a quick way to check that you are answering the correct question. Answering the correct question is a key element in the mathematics section of the test.
Here’s the RACECAR strategy as it works smoothly:
Read the title and instructions quickly—to put your brain into the mode of this type of question.
You are looking for ‘SENTENCE COMPLETION’ (Title) and you will:
(DIRECTIONS): Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole.
Okay, what is the SAT measuring here? Your aptitude for completing a sentence with the BEST word is being measured. The measurement is of your ability to solve the logic of the question.
Now, read the sentence thinking of what word, in the simplest form you can imagine, YOU would fill in:
Because he felt intimidated in his new position,
VISUAL: Cast a male actor: This male (he) felt (emotion) intimidated (emotion-fear-timid) in his new (unknown—fear of unknown) position (he has a new job—either new where he works or in a different position where he works)—FEEL IT!!!—and SEE the movie of this sentence in your mind…Here is a man who is feeling fear or anxiety in a new position…
Because he felt intimidated in his new position, he was ________ divulging his frank opinions of company proposals.
I would put ‘wary of’ in this spot. I’m looking for a word that describes being cautious and reserved before blurting out every opinion of the company’s policies.
Now, I look for a word like the one I think goes there:
A. Scurrilous about (Nope—This is negative enough but it reflects upon his own character rather than his concerns about policy…We don’t have any reason to think our man is ‘scurrilous’
B. Candid in—(Nope—our new guy on the job has no space to be ‘candid’ yet. He’s not feeling outspoken.)
C. Chary of—(Yes, I’m not familiar with this word; but it has the right connotations plus the correct form. My choice was wary of…chary sounds cautious, too)
MARK THIS ANSWER ON THE ANSWER SHEET.
We have already eliminated A&B. Now, RACECAR, to eliminate the other wrong answers—the part we only do on the fast answer questions:
D. Fervid about-(No, he is intimidated, so he is not feeling ‘fervid’ about ranting on about his opinions.
E. Precipitate in (No, this just does not make sense).
A. No. B. No. C.YES D.No E. No
Whether you are Nancy Drew, a Hardy Boy, or a scientist in the field, detection uses all your sensory powers and your emotional intellect. Make the connections to your clues about the feelings behind words. The connotation leads to the correct answers.
Here’s a little poem by Dorothy Parker. Dorothy Parker had a certain type of wit. On a past GED (graduation equivalency diploma) test, the test-takers were asked which of the following words best describes the overall mood of the speaker in this poem. Is the ‘mood of the speaker’: embarrassed, sarcastic, romantic, angry, or sad?
Let me show you how it speeds things up if you know the type of writer Dorothy Parker was, which I do. I am looking for this poem to turn in tone or mood. Watch this happen:
One Perfect Rose
A single flow’r he sent me, since we met.
All tenderly his messenger he chose;
Deep-hearted, pure, with scented dew still wet—
One perfect rose.
I knew the language of the floweret;
“My fragile leaves,” it said, “his heart enclose.”
Love long has taken for his amulet
One perfect rose.
Why is it no one ever sent me yet
One perfect limousine, do you suppose?
Ah no, it’s always just my luck to get
One perfect rose.
Dorothy Parker, “One Perfect Rose,” from Collected Poetry, 1926
Mood?
1. Embarrassed
2. Sarcastic
3. Romantic
4. Angry
5. Sad
Note: This is the way the answers are on the official test question that was used. In general, though, learn that this could even be called ‘ironic’ in literary terms. Literature questions often involve passages of irony: 1) dramatic irony –the reader or audience knows something the characters on the stage do not know; 2) situational irony—the woman sells her long fine hair to buy her beloved a chain for the watch he pawned to buy combs for her hair (Gift of the Magi by O’Henry); and 3) verbal (see above poem)judiethcarol&rocketcatApril2010c.
stion for the day. The RACECAR is fast, sleek, smooth, and correct!
3 math concepts to study for numerous points on SAT and other standardized tests
READ AND STUDY THESE THREE MATH CONCEPTS TO SOLVE NUMEROUS PROBLEMS
by judiethcarol&rocketcat
Three concepts to learn to reap many, many more points on every standardized math test--including the SAT:
1. slope (the graph, the ratio, the formula, the terms--and even the letter that is usually used to indicate the unknown number for slope:m)
2. order of operations (use the most common mnemonic to remember the order: PEMDAS (parentheses, exponents, mulitiplication, division, addition, subtraction)
3. Pythagorean theorem (Greek name and square roots, even names for the sides of the right angle triangle) This is a favorite for standardized test because the visualization, and the codes are standardized already. This is all about a triangle that has a right angle (90 degrees) and the longest side of the 3 sides of the triangle is across from that right angle.
That side of a right angle triangle has its own name. The longest side of a triangle with a 90 degree angle is the hypotenuse. This is generally the side with the label c. The other two sides have the name 'legs' in these right angle triangles. They generally have the labels: a and b. Even though the formula is usually written with a,b, and c. You need to remember that these are labels for the unknown numbers in this type of triangle. The letters could be different. They stand for particular sides of the triangle. On a standardized test they are probably going to call these sides a,b, and c with c being the longest side, the hypotenuse.
I'm not sure what makes my post disappear when I have been composing, but this has happened before.
Instead of talking so much about the classic problem about slope that is in today's example, let me tell you that there WILL be problems about slope. Part of what you can predict and learn before the mathematics test is in relation to problems about slope. Visualize the graphs, the steepness of skateboard ramps as opposed to the stretched out manageability of a wheelchair ramp.
Learn that the answer is a ratio. Use this concept to understand the formula and to remember the formula. Look at the same problem as a graph problem. The ratio is made up of the relationship of two coordinated points on a graph of the 'hill' or 'ramp' or 'mountain' you envision. The slope is the steepness--How steep is it? What you are finding, with slope, is the steepness ratio based upon how high UP you go vertically in relation to how FAR OUT you go on the horizon (the x axis).
VISUALIZE: Put a crossbar on top of the drawing of your hill or ramp. The measurement of how high is up and down, the y axis. The measurement of right and left (I sometimes call it east and west in my mind) is the distance you are going out (the 'run') to make the slope easier to manage (think wheelchair ramp). The ratio of the point up the y axis (rise) to the point you go out on the x axis (run) is the slope (m).
Maybe the fact that I had to start over in composing this because my graph and symbols for the formula was whisked away by the blog blotter is better anyway, as what you need to do for mathematics questions on the SAT is: to realize that so much is predictable that you need to be working on the obvious questions right now. Visualize EVERYTHING. Jot down little pictures to do this.
You can gain many more points in the medium and difficult level portions of the SAT in math if you use a few minutes a day for a few days to learn how to do the following types of questions:
1) There will be questions about slope involving ratios (because slope IS a ratio) and graphs. The formula to find the slope (steepness) of a ramp (think steep for skateboard and stretched out to make a manageable ramp for wheelcairs (run).
The more a steep (rise) ramp is stretched out (run), the less difficulty in climbing.
Slope questions will sometimes have coordinates on a graph (Yesterday's SAT is a nice, classic drawing!) SAT slope questions will sometimes just check if you can use the formula.
Now that we have talked about slope, come back to see me about some of the OTHER types of problems you will have on the SAT and other standardized tests in the math section. They include:
2) There will be questions checking whether you understand Order of Operations. Some of the questions will have only a couple of steps and still require that you notice the correct sequence. Remember: Doing the actual arithmetic incorrectly can still lose points for you--even if you understand a strange and difficult concept. The thing is: You will be tested to use proper order of operations with tiny problems and with big 'family' problems.
3) There will be mathematical questions that require your understanding of the Pythagorean Theorem. This looks fancy because it has that Greek name and it says that c squared is equal to a squared plus b squared. But what it is really about is a right angle triangle. So look up these problems with right angle triangles--and the terms used for the lines making these triangles (2 shorter sides are 'legs' and the longer side across from the right angle is the hypotenuse. A right angle is 90 degrees. If you are given any 'leg' or line length of the sides of the triangle, you can square the amounts and then find more answers by taking square roots.
Let's say, for example, that a squared plus b squared equals c squared. If a is 4 and b is 6, what is c?
Okay, we have 16 +36 = 42 Therefore, c is the square root of 42. What if your possible answers from which you were choosing were: 16, 4, or 12.20.
Please realize that if you need some quick help with your multiplication tables when you are in the middle of a problem about slope, you can quickly jot down the low numbers and figure while visualizing or you can use your calculator on the multiplication. This is an instance that jotting down will save you time so you can visualize the answer you are looking for by seeing what is too big and what is too small. But you have to know your mulitplication tables. If you have trouble remembering the multiplication tables while doing problems on a test, learn how to check your calculations quickly on the calculator. Use this as why using your pencil and paper on a standardized test can be faster. You can sometimes be more accurate using pencil and paper to figure because of the visualization going on in your mind.
You could eliminate all of these answers because the square root of 42 is going to be more than 4 and less than 16. You know this without doing anything, right, because if square 4 (4x4 )you get 16; but when you multiply 16 x 16--It's too big to be the square root of 42. You don't have to multiply it because you already know that even 12 is too big, right? How do you know? 12 x 12 =144. so the answer is not 16, a bigger number than 12! In fact, the square root of 42 is not something neat like the square root of 16 or the square root of 144 because you know that it is not 6 because 6x6 is 36; then the next number is 7. But 7x7=49. So the square root of 42 is going to be a number between 6 and 7. It will be 6 with a decimal portion (a fraction).
Summary: Practice these types of problems, in various formats of words, graphs, and symbols:
rocketcat&judiethApril2010x
by judiethcarol&rocketcat
Three concepts to learn to reap many, many more points on every standardized math test--including the SAT:
1. slope (the graph, the ratio, the formula, the terms--and even the letter that is usually used to indicate the unknown number for slope:m)
2. order of operations (use the most common mnemonic to remember the order: PEMDAS (parentheses, exponents, mulitiplication, division, addition, subtraction)
3. Pythagorean theorem (Greek name and square roots, even names for the sides of the right angle triangle) This is a favorite for standardized test because the visualization, and the codes are standardized already. This is all about a triangle that has a right angle (90 degrees) and the longest side of the 3 sides of the triangle is across from that right angle.
That side of a right angle triangle has its own name. The longest side of a triangle with a 90 degree angle is the hypotenuse. This is generally the side with the label c. The other two sides have the name 'legs' in these right angle triangles. They generally have the labels: a and b. Even though the formula is usually written with a,b, and c. You need to remember that these are labels for the unknown numbers in this type of triangle. The letters could be different. They stand for particular sides of the triangle. On a standardized test they are probably going to call these sides a,b, and c with c being the longest side, the hypotenuse.
I'm not sure what makes my post disappear when I have been composing, but this has happened before.
Instead of talking so much about the classic problem about slope that is in today's example, let me tell you that there WILL be problems about slope. Part of what you can predict and learn before the mathematics test is in relation to problems about slope. Visualize the graphs, the steepness of skateboard ramps as opposed to the stretched out manageability of a wheelchair ramp.
Learn that the answer is a ratio. Use this concept to understand the formula and to remember the formula. Look at the same problem as a graph problem. The ratio is made up of the relationship of two coordinated points on a graph of the 'hill' or 'ramp' or 'mountain' you envision. The slope is the steepness--How steep is it? What you are finding, with slope, is the steepness ratio based upon how high UP you go vertically in relation to how FAR OUT you go on the horizon (the x axis).
VISUALIZE: Put a crossbar on top of the drawing of your hill or ramp. The measurement of how high is up and down, the y axis. The measurement of right and left (I sometimes call it east and west in my mind) is the distance you are going out (the 'run') to make the slope easier to manage (think wheelchair ramp). The ratio of the point up the y axis (rise) to the point you go out on the x axis (run) is the slope (m).
Maybe the fact that I had to start over in composing this because my graph and symbols for the formula was whisked away by the blog blotter is better anyway, as what you need to do for mathematics questions on the SAT is: to realize that so much is predictable that you need to be working on the obvious questions right now. Visualize EVERYTHING. Jot down little pictures to do this.
You can gain many more points in the medium and difficult level portions of the SAT in math if you use a few minutes a day for a few days to learn how to do the following types of questions:
1) There will be questions about slope involving ratios (because slope IS a ratio) and graphs. The formula to find the slope (steepness) of a ramp (think steep for skateboard and stretched out to make a manageable ramp for wheelcairs (run).
The more a steep (rise) ramp is stretched out (run), the less difficulty in climbing.
Slope questions will sometimes have coordinates on a graph (Yesterday's SAT is a nice, classic drawing!) SAT slope questions will sometimes just check if you can use the formula.
Now that we have talked about slope, come back to see me about some of the OTHER types of problems you will have on the SAT and other standardized tests in the math section. They include:
2) There will be questions checking whether you understand Order of Operations. Some of the questions will have only a couple of steps and still require that you notice the correct sequence. Remember: Doing the actual arithmetic incorrectly can still lose points for you--even if you understand a strange and difficult concept. The thing is: You will be tested to use proper order of operations with tiny problems and with big 'family' problems.
3) There will be mathematical questions that require your understanding of the Pythagorean Theorem. This looks fancy because it has that Greek name and it says that c squared is equal to a squared plus b squared. But what it is really about is a right angle triangle. So look up these problems with right angle triangles--and the terms used for the lines making these triangles (2 shorter sides are 'legs' and the longer side across from the right angle is the hypotenuse. A right angle is 90 degrees. If you are given any 'leg' or line length of the sides of the triangle, you can square the amounts and then find more answers by taking square roots.
Let's say, for example, that a squared plus b squared equals c squared. If a is 4 and b is 6, what is c?
Okay, we have 16 +36 = 42 Therefore, c is the square root of 42. What if your possible answers from which you were choosing were: 16, 4, or 12.20.
Please realize that if you need some quick help with your multiplication tables when you are in the middle of a problem about slope, you can quickly jot down the low numbers and figure while visualizing or you can use your calculator on the multiplication. This is an instance that jotting down will save you time so you can visualize the answer you are looking for by seeing what is too big and what is too small. But you have to know your mulitplication tables. If you have trouble remembering the multiplication tables while doing problems on a test, learn how to check your calculations quickly on the calculator. Use this as why using your pencil and paper on a standardized test can be faster. You can sometimes be more accurate using pencil and paper to figure because of the visualization going on in your mind.
You could eliminate all of these answers because the square root of 42 is going to be more than 4 and less than 16. You know this without doing anything, right, because if square 4 (4x4 )you get 16; but when you multiply 16 x 16--It's too big to be the square root of 42. You don't have to multiply it because you already know that even 12 is too big, right? How do you know? 12 x 12 =144. so the answer is not 16, a bigger number than 12! In fact, the square root of 42 is not something neat like the square root of 16 or the square root of 144 because you know that it is not 6 because 6x6 is 36; then the next number is 7. But 7x7=49. So the square root of 42 is going to be a number between 6 and 7. It will be 6 with a decimal portion (a fraction).
Summary: Practice these types of problems, in various formats of words, graphs, and symbols:
- Use the Order of Operations, mnemonic: PEMDAS.
- Use the formula and graph to find slope. Remember the answer is in the form of a ratio. Thre are two styles to write the RATIO.
- Use the Pythagorean theorem to solve problems relating to square roots
rocketcat&judiethApril2010x
Monday, April 19, 2010
Slope, Skateboard Ramps, and SAT
Rocketcat &judiethcarolApril2010c
Rocketcat says: I like skateboards. I'm a jumper myself, but a skateboard can be exciting. The ramp may be steep. How steep is the ramp? This is slope. There is a formula; and it is easy. It looks harder than it is. Let me tell you that there is an easier way than today's explanation on the SAT to see the answer to today's question. But, first, you MUST become aware of how problems look that deal with slope.
When you do today's problem, draw it on a piece of paper. The formula is simple. The questions on the SAT will have low numbers like this one. You are looking for a 6 over a 4 to be the same as 3 over 2. Notice that the 3 over 2 is bigger than 1. It is a mixed number 1 1/2. The bigger number on top tips you that you are looking for a numerator and denominator (numerator is the number on top and denominator-d for down--is the number on the bottom) with a larger numerator. Note: Because the number for slope is a ratio, you may fare better calling the top number the 'rise' and the bottom number the run.
Visualizing the rise --going up the y axis on a graph in a ratio to the run --going across the horizon on the x axis--can help you on all of the slope problems.
The only reason you can jot down a little outline of what you are doing (SEE THE FORMULA FOR SLOPE) and visualize the answer is that you have a feeling for what slope is measuring and how to plug in numbers.
Come back tomorrow for more about SLOPE. Prediction: There will be problems, perhaps more than one, on the SAT about slope. The questions about slope will challenge more than your understanding of the formula; but once you know the formula and practice with a few problems on graphs, you will be unstoppable about slope. Check back in a few hr to www.coolrocketschool.org -- Math tips are healthy. Look at the percentage of people who missed today's question. You can do better than half the people on this test by making a little effort to learn how to do what you know will be on the SAT test.
judiethcarol&rocketcatApril2010
Rocketcat says: I like skateboards. I'm a jumper myself, but a skateboard can be exciting. The ramp may be steep. How steep is the ramp? This is slope. There is a formula; and it is easy. It looks harder than it is. Let me tell you that there is an easier way than today's explanation on the SAT to see the answer to today's question. But, first, you MUST become aware of how problems look that deal with slope.
When you do today's problem, draw it on a piece of paper. The formula is simple. The questions on the SAT will have low numbers like this one. You are looking for a 6 over a 4 to be the same as 3 over 2. Notice that the 3 over 2 is bigger than 1. It is a mixed number 1 1/2. The bigger number on top tips you that you are looking for a numerator and denominator (numerator is the number on top and denominator-d for down--is the number on the bottom) with a larger numerator. Note: Because the number for slope is a ratio, you may fare better calling the top number the 'rise' and the bottom number the run.
Visualizing the rise --going up the y axis on a graph in a ratio to the run --going across the horizon on the x axis--can help you on all of the slope problems.
The only reason you can jot down a little outline of what you are doing (SEE THE FORMULA FOR SLOPE) and visualize the answer is that you have a feeling for what slope is measuring and how to plug in numbers.
Come back tomorrow for more about SLOPE. Prediction: There will be problems, perhaps more than one, on the SAT about slope. The questions about slope will challenge more than your understanding of the formula; but once you know the formula and practice with a few problems on graphs, you will be unstoppable about slope. Check back in a few hr to www.coolrocketschool.org -- Math tips are healthy. Look at the percentage of people who missed today's question. You can do better than half the people on this test by making a little effort to learn how to do what you know will be on the SAT test.
judiethcarol&rocketcatApril2010
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