Solve Rational Equations

Solve Rational Equations Equations consist of one or more than one unknown variables with different coefficients and constant numbers. Rational equations is an equation which consists of terms in the fraction form i.e. p / q form. Here q cannot equal zero. There are various mathematical operations which are used to simplify and solve the given rational equations. Example 1: Find the solution by simplifying the expression x2/ 21 - x2 / 3? Solution: The given question is on subtracting rational expressions. This question contains adding with the same polynomial x2. The first step of the question is to calculate the LCM of denominators 21 and 3, its 21. Now 1 /21 and 1 /3 can be subtracted with the LCM of the denominators as 21. . This makes the solution x2 / 21 - x2 / 3 = x2 / 21 - 7 x2 / 21 = -6x2 /21. Hence the solution is -2x2 /7. Example 2: Find the solution by simplifying the expression x/6 + 2 x/5? The given question is on Adding rational expressions. This question contains adding with the same polynomial x. The first step of the question is to calculate the LCM of the denominators 6 and 5, its 30. Now 1 / 6 and 2 /5 can be added with the LCM of the denominators as 30. . This makes the solution x/ 6 + 2 x / 5 = 5x/ 30 + 12x / 30 = 17 x / 20. Hence the solution is 17x/ 20.

How To Audition for Solos in Choir Songs in 5 Steps

How To Audition for Solos in Choir Songs in 5 Steps Suzy S. Ready for your time to shine? Get ready for your upcoming choir audition with these tips from Ann Arbor, MI voice teacher  Elaina R Choir songs are all about group mentality. Singing as part of an ensemble, working on blend and teamwork, is very rewarding. But there are also opportunities to get in the spotlight once in a while, and those can be rewarding too. Choir songs with solos provide singers with a chance to sing alone â€" a very different experience than singing as part of an ensemble. If you are thinking about auditioning for a solo in choir, here are a few steps you can take to prepare. 1. Determine if it’s a Good Fit When solos in choir songs come up, it’s natural to jump at the opportunity. But the truth of the matter is that not all solos will fit your voice. The first indicator is your voice part in choir; a tenor solo probably isn’t fit for a bass, for example. However, this is not a hard-and-fast rule, since plenty of people can sing higher or lower than they are called on to do in choir. Do you think you may be a good choice for a solo? Try singing through it, using a keyboard or piano to help you hit the right notes. If the solo feels too high or too low for you, you have your answer. If it feels comfortable, it’s time to go on to Step 2. 2. Learn the Words Once you’ve decided to audition, take a break from singing and look at the words. Are they in English? If so, read through them and make sure you understand them. If not, look up a translation. You can also read up on the background of choir songs, as well as the context of the piece as a whole, to help you get a better idea of how to sing the solo. 3. Learn the Music Next, learn the music itself. To make the process easier, learn the rhythm first. Pay attention to the time signature, and try clapping through it. If there are tricky parts, jot down reminders for yourself. When I encounter difficult rhythms in choir songs (or anywhere else), I write the beats in above the staff. When you’ve mastered the rhythm, play through your part on the keyboard (it’s OK if you aren’t comfortable with the piano as long as you can find your notes). Be sure to note the key signature and play sharps and flats when present. 4. Bring it to a Voice Teacher A voice teacher can help you sing the solo well by coaching you on phrasing, breaths, and other technical details. Many voice teachers are also well-versed in languages and may offer coaching with pronunciation. To really master solos in choir songs, enlisting professional help is a must. 5. Have a Mock Audition Do you get nervous about auditions? Join the club! To help assuage your nerves, ask your voice teacher to conduct a mock audition. Practice walking into the room and singing the piece as if you were in an audition. Your teacher will give you feedback to help you look relaxed and sing well, even under pressure. If you have the opportunity to audition for a choir solo, remember these five steps. See if the solo fits your voice, then learn the words and music. Take the solo to a voice teacher â€" and conduct a mock audition â€" for maximum preparedness. This process fully prepares you for the audition so that you can do your best and, with a little luck, enjoy singing your well-earned solo. Need some  specific  song ideas?  Check out our list of 400+ songs to sing  here! Elaina R. teaches opera voice and  singing in Ann Arbor, MI, as well as through online lessons. She is currently  working on a Master of Music at the University of Michigan, and she has a B.M. from the University of Southern California.  Learn more about Elaina here! Interested in Private Lessons? Search thousands of teachers for local and live, online lessons. Sign up for convenient, affordable private lessons today! Search for Your Teacher Photo  by  AM-Commerce

Think Outside The Box With Online Geometry Tutor

Think Outside The Box With Online Geometry Tutor 0SHARESShare Anything visual and creative attracts the eye     and it is more so in the case of different figures and shapes on earth and in the universe -this is what Geometry tries to tell us through its varied applications. Learning Geometry could be interesting and fun, if you understand that it after all deals with shapes, sizes and figures that loom large around us and it is we who need to gauge their beauty and purpose through learning them with academic parameters. Online Geometry Tutor Geometry learning is not an easy task so to say. It demands perfect skills of measurement, an eye for details and visualizing capacities in a student. Accuracy in measuring lines and drawing circles is a necessary aspect in doing Geometry for great results. Hence it would be good that a student understands the importance of Geometry and contacts an online Geometry tutor for excellent outputs in Geometry learning. Learning Geometry-benefits Geometry helps one in understanding the significance of objects that are strewn around him in the universe It motivates visual imagination on the part of the learner and allows him to visualize the beauty of various sizes and shapes that he finds around him You are able to use your brain to the maximum in learning Geometry. With the logical and reasoning functioning of your left brain, you are able to activate the aesthetic sense of your right brain when you do Geometry .You could bring out the artistic element that is inherent in you along with your intellectual acumen-this is what is the specialty of Geometry learning Stay tuned to an online Geometry tutor to obtain the above mentioned benefits while doing the subject. A tutor online is able to connect you to the real world of objects and enhance your visual impact through his multimedia tools and video presentations. His innovative measures to make you understand the formulas and their applications in problems help you improve your scores and gain top notch results in the subject. Tutor Pace provides online Geometry tutor whose expertise in the field renders a great fillip to you and as such you could excel in the subject with ease. [starbox id=admin]

Distance Between 2 Points

Distance Between 2 Points Distance between 2 points can be found by using distance formula. The distance is the amount of space between points, lines etc. In mathematics the distance formula is an expression used to determine the distance between two points in a plane. The distance between two points with coordinates (x1, y1) and (x2, y2) can be represented by a formula Distance = ((x2- x1) ^2 + (y2 y1) ^2) The distance formula is obtained from Pythagorean Theorem. The below two examples illustrate how to find out distance between two points. Problem 1: Calculate the distance between the two points P (2, 1) and Q (3, 2). Solution: According to the question the coordinates of two points are P (2, 1) and Q (-3, 2). = To find out distance between P and Q use distance formula = Distance = ((x2- x1) ^2 + (y2 y1) ^2) = ((-3- 2) ^2 + (2 1) ^2) = ((-5) ^2 + (1) ^2) = Distance = 26 = The distance between PQ = Distance = 26 Problem 2: The distance between the points A (-2, -3) and B (-3, x) is equal to 5. Find value of x. Solution: Given the distance between two points is 5 = Since the distance is known we can use distance formula to set up an equation = Distance = ((x2- x1) ^2 + (y2 y1) ^2) = 5 = ((-3 (-2)) ^2 + (x (-3)) ^2) = 5 = ((-1) ^2 + (x + 3) ^2) = 5^2 = 1 + (x + 3) ^2 = (x + 3) ^2 = 24 = We get 2 solutions for x = -3 2 sqrt (6) and -3+ 2 sqrt (6).

Online Adjectives That Begin With J Tutors Tutorpace

Online Adjectives That Begin With J Tutors Tutorpace Adjectives are the words, phrases which are added to the noun in a sentence to enhance or modify the meaning of the used noun. The letter j is one of the common words in English. There are some useful adjectives which start with the letter j, these adjectives enhance the meaning of the sentences. Following are different adjectives starting with the letter j. Mentioned below is the meaning of the adjective and a suitable example using the adjective starting with the letter j in a sentence. Joyful means cheerful or happy. Sentence: Lydia is a joyful girl and can spread happiness wherever she goes. Here joyful is the adjective and girl is the noun. Jaded means lack of enthusiasm or felling bored Ben had a very jaded day as he was feeling sick. Here jaded is the adjective and day is the noun Judicious means possessing good judgment. Statement: The judge is judicious thats why he is said to be good at his job. Here judicious is the adjective and judge is the noun. Jocose means humor or funny. The birthday party was quite jocose. Everyone seemed to have a very good time. Here jocose is the adjective and birthday party is the noun. Jovial means lively or cheerful. Mr. Smith wants his children to be jovial all the time. Here jovial is the adjective and children is the noun.

How To Draw A Face

How To Draw A Face A Mini Guide to Portrait Drawing ChaptersHow Can I Draw a Realistic Face? What Tools Will I Need?What Proportions Do I Need to Understand in Order to Draw a Face?Tips for Drawing a Human FaceTrust Your EmotionsTips for Drawing a Realistic Portrait  How to Draw Faces: 7 Mistakes to Avoid! “This drawing took me five minutes, but it took me sixty years to get to this point.” â€" Pierre-August Renoir, French painter (1841-1919).Drawing is becoming less and less common as a hobby, with only a small percentage of people saying they draw in their spare time for pleasure these days.Amateur drawers generally think that drawing a face is one of the most difficult drawing exercises.You can take the reins with style and materials! Photo by giveawayboy on Visual HuntWhether you are an apprentice drawer, starting out with drawing classes or at home, a self-taught artist, a caricaturist, a painter, a specialist in drawing female characters, there are loads of techniques to learn.It’s important to learn how to respect proport ions, give your drawing volume with light and shadow, draw expressions and convey attitudes in order to produce a realistic and beautiful piece of art.Drawing a face from various angles, making some marks on the paper to map out the space between the eyes and knowing how to erase sufficiently to shade your drawing correctly are all skills which require a precise and confident control of the pencil.How can you draw the different shapes of a face without making mistakes? It’s a good idea to start with a guide on the basics of drawing.To get to grips with the basics, there are few other alternatives that are as worthwhile as taking an online drawing course and making sure you practise, practise, and practise some more!The fundamental lessons of learning to draw is the not be afraid of making mistakes, not getting frustrated if you’ve failed an attempt, and to always give it another go until it’s right.How can you learn to draw different angles in order to draw in perspective? (Wh ich ground are you drawing in, where is the vanishing point, where is the horizon line?)Let Superprof show you some simple techniques to help you find your feet in the art of portraiture. Whether you want to learn to draw the face of a manga character, design a tattoo or produce a realistic portrait, the basics are the same.It’s all just a question of practise, perseverance and observation.Superprof has put itself in the shoes of an art teacher to show you the drawing techniques you need to learn how to draw faces. FernandoDrawing Teacher 5.00 (8) £30/h1st lesson free!Discover all our tutors EmmaDrawing Teacher 5.00 (5) £75/h1st lesson free!Discover all our tutors DavidDrawing Teacher 4.75 (4) £40/h1st lesson free!Discover all our tutors NatashaDrawing Teacher 5.00 (7) £37/h1st lesson free!Discover all our tutors LorrenDrawing Teacher 5.00 (2) £18/h1st lesson free!Discover all our tutors Julia janeDrawing Teacher 5.00 (5) £60/h1st lesson free!Discover all our tutors Ev elinaDrawing Teacher £20/h1st lesson free!Discover all our tutors ZangmoDrawing Teacher 5.00 (6) £25/h1st lesson free!Discover all our tutorsHow Can I Draw a Realistic Face? What Tools Will I Need?What kind of drawing equipment is needed to easily draw a portrait? What is needed to sketch a manga face and drawings for children?  There are lots of tools for the different elements of a figurative drawing.  Some people favour using charcoal, whilst others prefer working with ink or pencil. In all cases, the material used depends on the desired results, but also on the mastery of different drawing techniques.Try not to be too concerned with a budget for drawing equipment, because unfortunately, artistic activities are always quite costly.Here’s a list of drawing materials necessary for a beginner learning to draw faces:Soft type B pencils (2B, 4B, etc.): this model of graphite pencil is very useful for shading. By pressing with varying pressures, these pencils will give a uniform g radient throughout your workHard type H pencils (2H, 4H, etc. up to 10H)An eraser: a rubber is absolutely essential for correcting pencil mistakes and erasing initial pencil sketches.A putty eraser: this is an indispensable accessory, especially useful for working with light and shadows. It allows for softening and lightening pencils and even charcoal. Putty erasers are malleable and can therefore be modelled for working with small or large surfaces and with small detailsA blending stump: this tool will help you shade your drawing and avoid blurring lines with a cloth or your finger â€" an absolute essential for drawing!Bristol paper: strong textured paper especially for artistic useYou could also use some modern tools and technology to create 3D portraits.Expert drawers use varied tools to draw a portrait. Generally, to create a portrait, you will need:Charcoal: thanks to the varying drawing techniques of charcoal drawing, it’s possible to make very precise sketches, but also to apply it in think lines for bolder sketching. This technique can add textured effects to the drawing, and can create shading for graduated or blurred effects.Sanguine: there are chalks and pencils available in sanguine, which is a range of orangey-red to beige colours. Sanguine is commonly used for portraits because it offers a great range of volume to the drawing.Sanguine is a great colour scale for showing depth and volume in your portrait. Photo by L'art au présent on VisualhuntWhat Proportions Do I Need to Understand in Order to Draw a Face?Above all other things, in order to learn to draw a face step by step, it’s crucial to have some reliable points of reference.What are the proportions of a face?How can you place the mouth, nose and eyes in the right spot?Here are some simple tips to help you draw a realistic portrait.Some general points for drawing faces:Every face has its own characteristics (thin, round, long, square, etc.). But in order to draw a portrait, you must be able to use your points of reference to trace an oval shape, then divide that into four parts.This is the preparatory step taught to young children when teaching them to draw men’s and women’s faces.To do this, trace what are commonly known as the division lines: one vertical line through the middle of the oval, then the horizontal lines.Drawing the nose:The first line drawn horizontally must correspond with where the eyes will go, but this is for later on. First of all, concentrate on the second horizontal line which splits the oval into two parts.It’s at this point of intersection with the vertical line that you must draw the base of the nose: place a nostril on either side of the vertical line.Drawing the mouth:The mouth will be located on a third axis drawn horizontally so that the lower part of the oval circle is divided into two.The bottom of the lower lip must meet this new line: draw the separation line of the two lips, then draw the upper lip and finally the lower lip .Drawing the eyes:  At the level of the first horizontal line - in the middle of the oval - draw two large circles on either side of the line: these are the eye sockets.Briefly mark out the eyebrows at the top of these two circles, then draw two small almonds inside each of them: the space between the eyes should be the width of a third eye.Draw each iris and then the pupil, each time in the centre of each circle and on the axis of the eyes. Colour each pupil in black in order to mark out the white of the eye.Then move on to the eyelids: try to make a second almond within the first, going around the iris.Drawing ears, hair, neck, and details:The bottom of each ear should be at the same level as the base of the nose. The upper point of the ears should be at the same level as the eyebrows.After this, you must draw the hair and neck, and add some small basic details: some shading, some definition on and around the nose, the chin, adding expression to the face.When sketching, the drier, stiffer and more pronounced the lines are, the older the face will look. To create a younger-looking character, you should try to make the lines more rounded and flexible.Once these marks are drawn, we will be able to refine the shape of the face, and especially of the chin. You could also go a bit further and even add the shoulders and clothes!Here are some good drawing classes for you. FernandoDrawing Teacher 5.00 (8) £30/h1st lesson free!Discover all our tutors EmmaDrawing Teacher 5.00 (5) £75/h1st lesson free!Discover all our tutors DavidDrawing Teacher 4.75 (4) £40/h1st lesson free!Discover all our tutors NatashaDrawing Teacher 5.00 (7) £37/h1st lesson free!Discover all our tutors LorrenDrawing Teacher 5.00 (2) £18/h1st lesson free!Discover all our tutors Julia janeDrawing Teacher 5.00 (5) £60/h1st lesson free!Discover all our tutors EvelinaDrawing Teacher £20/h1st lesson free!Discover all our tutors ZangmoDrawing Teacher 5.00 (6) £25/h1st lesson free!Discover a ll our tutorsTips for Drawing a Human FaceGet a sketchbook and practise basic sketches to get a feel for proportion and perspective. Photo by stenz on Visual huntFor drawing an imaginary character for comic books, it’s the creativity of the drawer which comes into play and must be drawn upon.On the other hand, if the goal is to do a portrait of a live model or a photo, it becomes a question of very close observation to reproduce the elements and maintaining the right proportions of the original.Observe and draw grids to reproduce a faceIt’s the same process as drawing a hand: the illustrator who wants to draw a hand will very carefully observe the shape of the fingers and nails, the colour and pigments of the skin, etc., before drawing the lines and contours with confidence.  Another technique is to draw a grid on your drawing paper to realistically reproduce the face’s shape and proportions.Whichever technique you choose to draw your portrait, the important thing here is to find a way of faithfully respecting the proportions of the model and every individual part of the face.Some essential elements to observe:The width of the mouth in relation to the noseThe positioning of the eyes in relation to the mouthThe characteristics and the position of the eyebrows on the face.Amongst these useful tips, it’s important to make sure that:The spacing of the two eyes corresponds with the width of a third imaginary eye in between the twoThe base of the nose is aligned with the inner corner of the eyesThe corners of the mouth are aligned with the inner edge of the iris.The initial proportions are fairly general, but being attentive to the smaller details makes it possible to mark out the right reference points with the first pencil strokes. After that, all that remains is to refine the lines in order to reproduce all the details you’ve observed.Trust Your EmotionsWhen drawing, it’s important to disconnect the left half of the brain â€" that of reason â€" so th at you can give free rein to feeling and expression.To achieve this, you will be guided purely by your perceptions, which comes from the right side of the brain.The idea is not to seek meaning as such, but rather to reproduce exactly what one sees in a descriptive, sensory way. Remember that portraiture is not an exercise in symmetry. You will realise pretty quickly, by studying models in close detail, that no face is perfectly symmetrical.The most important thing to achieve when aiming for an accurate drawing is to bring the face to life with three-dimensional drawing. It is therefore important to make your markings accurately according to the model you are observing and stick to them closely.The nose may not be quite straight, the smile crooked, eyebrows misaligned, but that doesn’t mean the drawing is inaccurate - the hand must draw whatever the eye sees!Tips for Drawing a Realistic Portrait  So here it is, the first sketch has been made!From now on, you should work on the smal l details so that you can transform your drawing into a realistic portrait which resembles the model as closely as possible.To work on the resemblance, each element counts. There are many important points that shouldn’t be neglected in drawing, not least the facial features such as the mouth, nose, hair and especially the eyes.In each case, try to observe your model as closely as possible so that you can faithfully reproduce what you see, particularly the facial expression. After all, the facial expression is one of the most complex elements to draw. It’s not just necessary to respect the shapes of the eyes, but it’s also crucial that you pay attention to the eyelids, the iris and pupil, the eyelashes, and also the eyebrows.The main difficulty lies in having to focus on each eye individually, whilst ensuring that there is a consistency between the two eyes at the same time.These are the particular details that allow you to capture the facial expression. In order for a portrait to be a success, you must learn to draw a vivid and expressive look.To get started, you should observe all the details (not forgetting light reflections), but you should also learn how to use empty spaces. The empty spaces in drawing are very important, because they create a cohesive whole - so it’s crucial not to neglect them!Do you need to design a logo based on an eye or other facial feature? Having great observation skills and an eye for detail is the key to success.Those who have trouble drawing the outline of the eye can, for example, focus on the white of the eye and the iris. By drawing these elements one by one, the drawer’s hand will naturally reproduce the shape of the whole eye. The thickness of the eyelids is another important point to consider.For a portrait to be truly complete, you must also observe the shadows and reproduce them as accurately as possible.This will give volume to the parts of the face, and will make your drawing more realistic. This is why it’ s key to learn how to work with gradients and play with light and shadow, adding a new dimension to the portrait.Finally, the thickness of the features will influence the final result.When you start to draw, you usually tend to focus on the contours by making stronger lines. This can result in mistakes and inaccuracies, which should be avoided.For example, contrary to the common temptation to draw the contours of the lips, the most important line for drawing a mouth must be the one that separates the lower lip from the upper lip.The contours of the lips will form with lots of lighter lines rather than more pronounced, heavy lines. This is also an example of where shading will help to give the lips their definitive form and give the mouth its volume.It’s important to take into account the lighting of the face to produce an accurate portrait of your model.And why not attempt to design your future tattoo based on a face?How to Draw Faces: 7 Mistakes to Avoid!When getting started on t he first page of your sketchbook, a novice sketcher will usually seek to overdo the lines and details, when just gently scribbling would be enough.Or instead, we tend to start by drawing the eyes before marking out the rest of the head â€" but think about the human skull, the eyes are important, but they are not the first thing you should draw, far from it in fact!We’re exaggerating a bit â€" but to sketch out a beautiful portrait, you should start by getting rid of bad habits and avoiding common mistakes. And even if you are not planning to draw realistically -for example, when designing logos - it's important to understand the basics!Draw parallel linesIt’s crucial to always ensure that the dividing lines of the face are parallel to each other. Good distances will result in a good symmetry of the face.Making uneven lines runs the risk of the distances between the elements of the face being completely inaccurate, and you’d have to start all over again.Don’t neglect the cont ours of the human skullDon't forget the structure of the skull when drawing you face and head. Photo on Visual huntknowing how to draw a face also means taking into account the outline of the skull: a face too fine will give the impression of lacking structure, or being too flat.If the top of the head is too low it will be hard to add hair accurately later on: a flattened skill truncates the shape of the hair, preventing your ability to achieve a realistic portrait.Adding the right amount of detail to the sketchOur brain can play tricks on us, and sometimes we lose sight of the bigger picture when we focus too early on the fine details. This is a common mistake among beginner: adding too much detail from the beginning.This is a mistake, and actually creating outlines and building shapes saves time in the long run. So give priority to light sketch and to outlines of shapes without too much precision, and once you’ve got all the structure in place, you can start detailing.We start o ut by sketching out the three major parts of the face: the eyes, the nose and the mouth.Don’t rush it!  Make sure you don’t make rash moves with your drawing: taking your time and not taking shortcuts is the best strategy to bypass the temptations you might feel to hurry your portrait along, but you must learn to control erratic pencil strokes.If you feel blocked by a particular obstacle, continuing regardless would be a mistake because the consequences of doing so will affect the overall results of your work. Aim to tackle every obstacle head on until you’re happy with the result.Taking your time also helps you to properly observe your model, their expression and the structure of their face. And then keep at it until it looks perfect!Don’t neglect perspectiveUnderstanding the concept of perspective is a fundamental part of drawing. The most common mistakes when it comes to drawing faces are:An inaccurate depth to the noseAn inaccurate distance between the eyesFlat eyes and eye socketsIgnoring the thickness of the eyelidsThe eyes are incredibly important in a portrait â€" in the same way that the mouth is â€" because they are the features which give the most expression on the face. But amateur drawers easily fall into the trap of drawing what they see as flat.It’s equally important to draw with a three-quarter view (between profile and face-on): the nose should hide the space of the eye in the background to create the illusion of perspective that the eye in the foreground is further from the base of the nose.The left side of the face must therefore be smaller than the right side, seen in the foreground.Suggest depth with your drawing The neck is in the background on a three-quarter facial view. To create this depth, a small trick is to use the shadows and the outline of the neck. The most common mistake is to connect the jawline with the neck line, but these two lines should normally be on different planes.To avoid falling into this trap, the drawer must make a small shift in the contour of the neck to stop it joining directly into the jawline.Correctly position the earsThe last mistake that is very commonly made is where to put the ears.When drawing a face in profile, an ear can be difficult to place â€" is it nearer the eyes, or the mouth? How far between the two?Drawing an ear too close to the face will make it look too long, but if it is too far away it will make the skull look misshapen.Placing the ear on the head requires measuring the distance between the eye and the chin, and then the measurement of the eye to the ear: we get an isosceles triangle, with the optimal location of the upper ear in line with the eye. Finally, even if it varies widely from person to person, the ear will generally be in line with the eyebrows and the base of the nose.In conclusion:To learn how to draw a woman's or man's face, it’s best is to take up drawing lessons with a real tutor in portrait drawing.To learn to draw and to acquire good dr awing techniques, don’t hesitate to consult drawing blogs and draw inspiration from online drawing tutorials.In any case, it’s crucial to practise and persevere! Once you feel more at ease, you can easily draw beautiful portraits, manga characters or master the art of caricature!

Why you shouldnt take test prep advice from Homer Simpson

Why you shouldnt take test prep advice from Homer Simpson Homer Simpson provides test prep advice you should not follow!Depending on how familiar you are with the Simpsons oeuvre, you might remember an episode where Mr. Burns decides that he needs a male heir in order to pass on his fortune.  Naturally, Homer encourages Bart to audition for the part of Burns’ heir.  Bart, relying on Homer’s inept guidance, bungles the audition and misses out on the chance to inherit the fortune.  As the Simpson family walks out afterwards, Homer passes on some fatherly advice: “Kids, you tried your best, and you failed miserably.  The lesson is, never try.”Of course, no one is looking to Homer Simpson for test prep advice.  But the reality is that many students fall into the “Homer mindset”: I really tried my best on that homework/practice test/actual test and didn’t do well, so game over.  I’m never going to do better on the SAT!Where does failure occur during the process of test preparation?  It can happen during a tutoring session no matter how the tutor tries to explain that tricky algebra concept, the student just doesn’t get it.  It can happen on a homework assignment the student understood the reading comprehension strategy during the tutoring session, but can’t focus and complete the reading section at home.  It can happen on a practice test time runs out and the student only got through half of the math section.And of course, failure can happen on the big kahuna the actual test.  Anxiety got the best of her; he forgot how subject-verb agreement works; her calculator batteries died during the math section.  You try your best and just don’t get the score you want.So what do you do when you’re confronted with failure during test prep?  You see failure correctly for what it is: a learning opportunity.Many students are practically allergic to making mistakes in front of their tutors, preferring instead to maintain the illusion of perfection.  This attitude is typical of the “fixed mindset ”.  Carol Dweck, the pioneer of mindset thinking, defines the fixed mindset as one in which “students believe their basic abilities, their intelligence, their talents, are just fixed traits.  They have a certain amount and that’s that, and then their goal becomes to look smart all the time and never look dumb.”Here at AJ Tutoring, we do everything in our power to break down the fixed mindset in our students.  The fixed mindset is the enemy of true learning and improvement on the SAT or ACT.  The fixed mindset denies students the chance to take risks, learn from mistakes, and experience the satisfaction that comes from working hard and mastering a skill.  In the end, you will only improve your SAT score if you’re willing to get questions wrong and then figure out how to get them right.Theorizing about failure in a blog post is one thing, but what do we tell our students when they fail?  How do we reconceptualize failure so our students can see it as a good thing?  Le t’s revisit the “failure points” during test preparation.Failure to understand a concept during the tutoring session.When a student has a hard time understanding a concept during a tutoring session, it usually comes down to one of two things: either they’re weak on fundamentals, or they’re terrified of “looking dumb” in front of their tutor.  If the student is weak on fundamentals ( for example, they can’t solve a system of equations because they don’t know how to solve one equation for one variable), the tutor can usually diagnose this issue quickly.  The sooner a student “fails” on a problem, the easier it is for their tutor to figure out the true issue and backtrack to the more elementary concept.  And if the student doesn’t want to miss a problem and look dumb, this too is helpful information.  It tells the tutor something about the student’s mindset towards failure and allows the tutor to take appropriate steps to change that mindset.This could lea d to your greatest success.Failure on a homework assignment.Sometimes a student understands a concept during the tutoring lesson, but can’t execute on the homework assignment.  Failure on a homework assignment tells us something important too either the student didn’t understand the concept as well as we thought they did (in which case, time to review), the student rushed through the assignment, or the student didn’t apply the correct strategies on the assignment.  In all of these cases, failure tells us more about the student’s approach to SAT prep when he’s on his own.   All of these problems are correctable given enough time.Failure on a practice test.Students (and parents) often expect great improvement on practice tests.  Sometimes students get a solid score improvement on a practice test, and sometimes they don’t.  As part of AJ Tutoring’s SAT and ACT prep process, we ask students to take at least 3 practice tests, and then we review those results with stude nts in their next tutoring session.  Reviewing practice tests with students is instructive it allows us to see exactly what happened if a student “failed”.  I had a frustrating situation with an ACT student last year whose practice test scores kept going down, even though he was doing great in our sessions.  After the third declining practice test score, he and I sat down for a serious discussion.  It turned out that the student was staying up late and then had a hectic morning of driving his siblings around before coming to our office for his test.  By having that discussion during his prep, we made sure that he didn’t repeat the same pattern on test day.  Sure enough, he got sleep the night before the actual test, and his ACT score went up by 5 points!Failure on the actual test.This is the scenario that strikes fear into the hearts of students and parents everywhere.  How is it possible to turn a test day failure into a net positive?  For starters, almost all studen ts take the SAT and ACT more than once.  It’s rare that students get the score they’re looking for on the first try.  Every time you take the test, even if you don’t achieve your goal score, you get a little more test-taking experience and you learn more about how you operate on test day.  And once you get your scores back, you know which sections and concepts you need to review for future tests.Do you see the common thread here?  Failure gives us more information.  Rather than seeing failure as a reflection of your intelligence, try to see failure as a diagnostic tool that helps you do better on the next homework assignment or test.Paul Tough’s book How Children Succeed is a worthwhile read on the factors that influence success in school.  Chapter 3 looks at the unorthodox teaching methods of a middle school chess teacher in Brooklyn, Elizabeth Spiegel, who is able to lead her team to unexpected success.  Spiegel’s teaching method is so unusual because she focuses on her students’ failures, analyzing wrong moves and bad games with the class until they deeply understand the right moves.Spiegel tries to lead her students down a narrow and difficult path: to have them take responsibility for their mistakes and learn from them without obsessing over them or beating themselves up for them. How Children SucceedWhen interviewed for the book, Spiegel noted, “It’s uncomfortable to focus so intensely on what you’re bad atIf you really want to get better at chess, you have to look at your games and figure out what you’re doing wrong.”The same thing is true in test prep if you really want a higher score on the SAT or ACT, you have to confront your failures head-on and figure out what you’re doing wrong.  For the student who is brave enough to do this, the rewards are many a higher test score, yes, but also the confidence to take risks, to sometimes fail, and to learn from that failure and do better the next time.[Note: Many adults have a hard time with failure, let alone high school students.  Failing well is a learned skill!  Our SAT and ACT tutors are happy to help guide your student toward testing success.  Please reach out to us for more information!]

Global Endowment Management Sponsors Heart at Westerly Hills - Heart Math Tutoring

Global Endowment Management Sponsors Heart at Westerly Hills - Heart Math Tutoring Global Endowment Management Sponsors Heart at Westerly Hills Global Endowment Management Sponsors Heart at Westerly Hills December 21, 2015 Heart Math Tutoring at Westerly Hills Academy was made possible by a generous $40,000 grant from  Global Endowment Management (GEM Foundation) in December 2014. Eight GEM team members also joined Heart as tutors this year. This grant allows 56 students at Westerly Hills Academy to receive  one hour of structured one-on-one math tutoring per week from September to May. This valuable resource would not be available to Westerly Hills otherwise.  Students work with their tutors to build foundational math skills and academic confidence. Students, parents and tutors gathered last week to celebrate  student progress with food and fun at the Westerly Hills  Holiday Breakfast. Thank you for your support!