What Role did Pythagoras Play in the History of Math

What Role did Pythagoras Play in the History of Math Who is Pythagoras and What is the Pythagoras Formula? ChaptersThe Early Life of PythagorasThe History of the Pythagorean TheoremOther Important Discoveries made by PythagorasThe School of Pythagoreans in the Context of MathematicsEvery year sees new reforms in the sector of education, reforms which strive to fit the changing values and interests of the government and students alike. It is no surprise that, with each new revision, there are some concepts that manage to stay a part of the maths curriculum.One such example is the concepts discovered and expanded by the great, mathematician Pythagoras. While he is most known for the theorem he gave his name to, the Pythagoras theorem, there still remains quite a bit of Pythagoras in our countless other maths exercises. Cosines, trigonometry, reciprocals, square roots, fractions, geometry, arithmetic, tangent, symmetry â€" discover the influence of Pythagoras in the history of maths!If you're interested in other famous Greek philosophers and mathematicians, check out Archimedes of Syracuse! MyriamMaths Teacher 5.00 (13) £20/h1st lesson free!Discover all our tutors MarkMaths Teacher 5.00 (5) £200/h1st lesson free!Discover all our tutors Dr parikhMaths Teacher 5.00 (8) £40/h1st lesson free!Discover all our tutors KamalMaths Teacher 5.00 (9) £30/h1st lesson free!Discover all our tutors PetarMaths Teacher 5.00 (8) £40/h1st lesson free!Discover all our tutors GowsikaMaths Teacher 5.00 (5) £15/h1st lesson free!Discover all our tutors RubenMaths Teacher 5.00 (1) £15/h1st lesson free!Discover all our tutors ConorMaths Teacher 4.75 (4) £30/h1st lesson free!Discover all our tutorsThe Early Life of PythagorasBorn on the Greek island of Samos at the end of the 6th century BCE, Pythagoras is known as one of the greatest mathematicians from antiquity. However, the elements of his history have not been completely proven as no document from his era has survived. While some biographies that include Pythagoras’ life have been found, all were written well after Pythagor as died.Legend has it that some months before his birth, an oracle predicted the birth of a gifted being to Pythagoras’ father. This is how Pythagoras’ name was chosen, signifying “announced by Pythian.”Just as the oracle predicted, Pythagoras proved to be a very gifted child. History tells that at just eighteen years of age, Pythagoras not only participated in the Olympic games of combat, but he won all of the competitions. Athletic and intellectual, the young Pythagoras was interested as a scholar in Greek philosophy, history and the sciences. Some historians have also noted that he was the student of another celebrated mathematicians: Thales.Pythagoras has been the source of inspiration for manyTo continue his studies, the Greek philosopher and mathematician left on a series of journeys would eventually lead him to Egypt. There, he strove to learn from the teachings of the Egyptian priests until 525 BCE, when the Persians invaded the country and took him as a prisoner to Babylon. There, he utilized his time to study the knowledge of the Babylonian scribes.Once he was allowed to return to the island of Samos, Pythagoras started to teach in an amphitheater, but without much success. In fact, it was his attempts at spreading his knowledge that led to his banishment from the city. He decided to flee to Greater Greece in order to fulfill his goal of creating a school, giving lectures and continuing the tradition of Greek philosophers.Pythagoras made it a priority, throughout all of his life, to apply mathematics to philosophical thought. A number of disciples followed him in his experiences and research with the same passion â€" to the point where some have argued if Pythagoras started a sect and not a school.Pythagoras died around 500 BCE, but once again, the circumstances of his death are not well known.Here is a platform to find a motivated maths tutor near me!The History of the Pythagorean TheoremPythagoras has been the bane of many middle and high-s choolers' existence, with many struggling understand Pythagoras’ most seminal concept, the Pythagorean theorem. It must come as surprise, then, to learn that it was not actually discovered by Pythagoras.Engraved tablets of clay, dating back to 1800 BCE, illustrate that the length of triangles and their properties were already well known to the Babylonians, way before the arrival of Pythagoras. However, the reason Pythagoras has gained the credit for this theorem is because he was the first to define it in the way we still earn it today:“For right triangles with the sides a, b and c, the length of the hypotenuse can be calculated by a2 + b2 = c2.”Theorizing this law led Pythagoras to be forever remembered in the annals of history. To thank the gods for having helped him in his discovery, certain accounts hold Pythagoras to have sacrificed a hundred oxen. However, it was not enough to simply form the law into existence, Pythagoras had to prove his theory.The school founded by Py thagoras was in charge of this task, performing many experiments and calculations towards prove this theorem. The work done by these academics inspired countless other scientists, including even the infamous Leonardo de Vinci and Sir Isaac Newton.The Pythagorean theorem has led to many discoveries, such as the Pythagorean tripleWithout numbers, it is possible to also show the theorem like this:“The sum of the squares of the lengths of a right triangle are equal to the square of its hypotenuse.”This formula permits for the calculation of the length of one side of a right triangle, and simultaneously to prove that the triangle is a right triangle. In fact, if the square of the longest side is equal to the sum of the squares of the two other sides, the triangle is a right triangle.The theorem of Pythagoras, still taught today, led to the advancement of a particular type of geometry, known as “Euclidean geometry.”Other Important Discoveries made by PythagorasPythagoras was a ver itable genius in many respects, and not just mathematics. According to him, mathematicians should strive to learn other subjects like music, philosophy, astronomy, mysticism. During the course of his life, he and his disciples adopted this mentality and managed to bring to light many mathematical discoveries.Most notably, Pythagoras discovered the link between the length of a vibrating string and the pitch of the note played on that string. His investigations in to music didn’t stop there, he also played with glasses containing different levels of water and found that each level of water represented a distinct musical note. These works were the basis of research of many other scientists and mathematicians, including Rene Descartes.His advancements in mathematics continued to permeate into many different disciplines and took on many different forms. Here are some of his most diverse discoveries.Pythagorean SpiralThe Pythagorean spiral is a tool that allows for the geometric visuali zation of the square roots of consecutive whole numbers.To construct them, it is necessary to start by drawing a right triangle where the sides of the angle should be equal to 1. From this, basing the rest on Pythagoras’ theorem, the next step is to build a new triangle based on the hypotenuse of the first. One of the sides of the right angle of the new triangle has to be on the hypotenuse of the first. The other side of the angle should have the value of 1.The spiral forms by continuing the construction of the next right triangles in the same configuration as the ones proceeding it. Thanks to this tool, and the concept of right angles, we know the square roots of the consecutive whole numbers that are equal to the lengths of the hypotenuses of the right triangles.The Pythagorean Table of OppositesThis table is largely utilized to teach multiplication tables to kids and adults.The Pythagorean table is simple: it deals with a table containing two columns. In the first column, on th e left, values are written. These values are multiplied, added or divided, with the values to the right. The response is put on the intersection of the two values on the table.This table, utilized for multiplication, can also be used when there is a large amount of information that needs to be accounted for visually. Why not use this in your mathematics exercises to prepare for some upcoming exams?The School of Pythagoreans in the Context of MathematicsPythagoras’ life goal was to teach math and to always have a group of people around him to help him in his scientific inquiries. This is why he found in Cortona, in the south of Italy, a school known as the School of Pythagoras. Likened to a sect, the members of this school discussed not only science but also aimed to be astute philosophers, politicians, and even involved in religion. In general, all of Pythagoras’ life centered around mathematics.The Pythagorean school was considered a sect by someFor this school, numbers were th e centre of everything. Pythagoras and his disciples continued to interest themselves in the divisibility of numbers and led to the famous proclamation: “numbers rule the universe.”The school lasted for 150 years and is totalled to have had about 218 members, members who were known as Pythagoreans.Because much of the work was executed as a team, it is impossible to know the exact identities of the real inventors of various formulas and principles we attribute to the Pythagorean school. They placed an emphasis on studying perfect numbers, associated numbers and sacred numbers. These latter were particularly appreciated by the Pythagoreans.For them, sacred numbers were made up of the sum of many exceptional numbers. The number 10, for example, could represent the sum of 4 prime numbers, the sum of a pair of squared prime numbers and one perfect number, or even the sum of the first three prime numbers.Pythagoras’ disciples and Pythagoras himself were sometimes considered as magic ians by people in their epoque. This belief was mostly due to the fact that the Pythagoreans had discovered a way to trace a regular pentagon, a figure whose five sides are equal.To do this, the small team utilized five equilateral triangles that formed one pyramid with five faces. Once made, the scientists traced the base of the pyramid to obtain the pentagon. The pentagon that was traced by the figure was used as their symbol.The school of Pythagoreans was broken up after a dispute between two political factions within the group itself.Pythagoras and his school played a vital role in the evolution of mathematics. Whole numbers, circumferences, quadrilaterals, perpendicular, relative numbers, addition, parallelogram, decimals, sine, conjecture, scale products, fragment, diamond â€" all aspects of the math we learn today passed through the hand of the great mathematician.

5 Reasons Learning Barre Chords Is Easier Than You Think

5 Reasons Learning Barre Chords Is Easier Than You Think Suzy S. Learning guitar barre chords, or chords created while clamping down all six strings with your index finger, intimidates many guitar students. However, these new chords dont need to be so scary! Austin guitar teacher Samuel B. breaks down five reasons why learning barre chords is not so bad I maintain little to no doubt that learning guitar barre chords is the most challenging advance for a student. Along the way there, I recommend practicing chords such as F (which involves holding down two strings at a time) as well as conditioning in the form of scales before the introduction of relevant chords (as in the video on my profile). Despite the hefty work in store for your left hand (no, I cant sugarcoat this), some key facts are worth considering as what youre learning to do is probably simpler than you think. 1. Youll Begin By Learning To Play An Alternate Version Of A Familiar Chord When its time to begin barring, youll begin doing so on the fifth fret (in sixth position to be exact) as I find it the most accommodating place to start. For one thing, the E formation youll be transposing will be an A (based on the fourth note of the E scale as you will have learned while playing first-position chords in that key). Your first barre chord, in other words, will compliment the base (1st) chord of the last first-position key you will have learned to play (which is E). Put simpler, youll be learning another version of something you already know. 2. You Will Have Learned To Play Triads In The Same Position Just as I preface chord knowledge with scale knowledge, I always teach abbreviated variations of the E and B7 formations in the middle of the neck before I introduce barre chords. The E formation looks like this: E|||| B|||| G||-O-|| D|-O-||| A|||| E|-O-||| The B7th one looks like this: E|||| B|||| G||-O-|| D|-O-||| A||-O-|| E|||| Both chords are easily transposable anywhere on the neck and serve as the basis for introducing jazz tinges into familiar standards. 3. Conditioning Your Index Finger To Hold Down Six Strings At Once Is Really Just A Matter of Clamping Your thumb and your index finger are doing the most work here. You will have to practice holding them together tightly on the neck, but this is a mere matter of strengthening your grip. 4. All Barre Chords Are Based On Two Basic First-Position Formations E and A Though variations such as minor, seventh, and augmented will be introduced down the line, all youre really learning to do is play E and A with your third, fourth, and fifth (as opposed to your index, third, and fourth) fingers. 5. The Most Important Thing To Learn To Do Is Switch Smoothly Between The Two At this point in the curriculum, I condense as much instruction as possible (without creating drudgery) into having you play the barred E formation and the barred A one back and forth. The goal here is to create a see-saw effect. Once this has happened, youll be ready to learn to play whole songs with guitar barre chords only. Samuel B. teaches beginner  guitar lessons in Austin, TX. He teaches lessons face-to-face without sheet music, which is his adaptation of Japanese instruction (involving a call-and-response method).  Learn more about Samuel 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  stimpsonjake

How Is A Pilates Class Organized

How Is A Pilates Class Organized How To   Learn Pilates As A Beginner ChaptersWhat Is The Pilates Method?What You Need To StartPilates Class EtiquetteBefore The Pilates ClassIn The Pilates ClassAfter The Pilates ClassChanges That You May Notice From Regular Pilate TrainingGetting ready for your first Pilates class can be an exciting and daunting experience. The benefits of Pilates speak for themselves, and with regular practise, these benefits are easily within your grasp. One thing is sure that you will love this heart pumping full body workout. CarleyYoga Teacher 5.00 (5) £100/h1st lesson free!Discover all our tutors GenYoga Teacher £45/h1st lesson free!Discover all our tutors JulieYoga Teacher £30/h1st lesson free!Discover all our tutors LynnYoga Teacher 4.89 (9) £35/h1st lesson free!Discover all our tutors AliceYoga Teacher £20/h1st lesson free!Discover all our tutors LauraYoga Teacher 5.00 (6) £70/h1st lesson free!Discover all our tutors UndramYoga Teacher £25/h1st lesson free!Discover all our tutors LottieYoga Teacher £10/h1st lesson f ree!Discover all our tutorsWhat Is The Pilates Method?Pilates was invented around the time of the first world war by Joseph Pilates who wanted to create a minimal equipment exercise program that used the mind to control the body consciously.Pilates is a complete full body workout that uses resistance training, alignment and holistic awareness to strengthen the body. Using the breath, spine and the core muscles to empower the practice and promote wellness in the body.The results of practising Pilates are incredible, some of which include body awareness, body sculpting, high energy, improved flexibility, fat burning, improved Posture, strengthened mind and body connection. These benefits are available for Pilates beginners, intermediate or advanced practitioners. No matter what your background, fitness level or style of Pilates you choose to practise, huge benefits await you.It is vital to drink lots of water after your class to rehydrate. Photo Source: UnsplashWhat You Need To StartW hen planning your first Pilates workout, it is essential to make sure that you are fully equipped and ready to learn. As a new student, you will need a few things to get started. Some of the things are necessary, and some of the items are encouraged. But generally, there is almost no Pilates equipment needed as studios provide all essential apparatus.The EssentialsYou must have an open mind and be ready to learn. To really learn something new we must leave our preconceptions at the door and open ourselves up mentally and physically to make some new changes in our lives. This means leaving habits like bad posture, laziness, self-judgment and know-it-all-ness outside.Money to pay the Pilates teacher for the classThe BasicsYou need a good Pilates mat or a yoga mat to support you when doing Pilates exercises. This serves to support you during your practise, helping you to keep your balance, providing resistance and cushioning your body from the hard floor. A good yoga mat is at least 6m m thick (the thicker it is, the more padding) and is highly resistant to slipping. Very important for a Pilates mat class.Wearing comfortable clothing is also very important while practising. Your fitness wear should give you the opportunity to move freely with the full range of motion. While being supportive and wicking away sweat from your body. A simple t-shirt with leggings is very acceptable, but if you can invest in some stretchy sweat-wicking gym clothing, you will be thankful later.Choose stretchy breathable fabrics for your work outTry to select simple form-fitting clothing over baggy fitness outfits. To teach you well the Pilates teacher will need to see your body to be sure about your alignment.You don’t need trainers, Pilates is done barefootDon’t use anything that has adornments such as drawstrings, belts, tassels, buckles, ties or buttons as they may be uncomfortable if you lie on top of them and they also damage equipment.Don’t wear shorts if you can help it, as many positions require you to be upside down and you don’t want them to ride up or expose you.With most Pilates sessions being around an hour to 90 minutes long you will need to rehydrate. Nothing does this better than a good drink of water. Make sure to bring a litre of water to sip throughout the lesson. Keeping your body hydrated and flushing the toxins from your body is a key part of reaping the benefits of Pilates quickly. If you can invest in a refillable water bottle, you will also be helping the environment.Check out  yoga London  now.Encouraged ItemsResistance bands are great if you have limited mobility in some parts of your body. They are stretchy bands that can support your flexibility and they can also add strength training to the workout.A cushion is a perfect accompaniment for those who have any issues with alignment. It can be used to support any part of your body while practising, lying down or working with on the floor postures. A cushion can also support your a lignment when you need to sit in class.Pilates Class EtiquetteAn important part of taking any group fitness class is knowing just how to behave to ensure you are not hindering anyone else’s progress. A few simple rules will ensure you get the maximum out of the class and support your fellowPilates practitioner Etiquette List.Always be aware of attending on timeWarm up before class to avoid any injuries.Tell the Pilates instructor about any existing injuriesDon’t chat in class, remain present and focused.If it hurts stop immediately, safely come out of the pose and raise your hand for some help.Tie your hair back off your faceBring a towel to wipe down any shared surfaces and equipment CarleyYoga Teacher 5.00 (5) £100/h1st lesson free!Discover all our tutors GenYoga Teacher £45/h1st lesson free!Discover all our tutors JulieYoga Teacher £30/h1st lesson free!Discover all our tutors LynnYoga Teacher 4.89 (9) £35/h1st lesson free!Discover all our tutors AliceYoga Teacher £20/h 1st lesson free!Discover all our tutors LauraYoga Teacher 5.00 (6) £70/h1st lesson free!Discover all our tutors UndramYoga Teacher £25/h1st lesson free!Discover all our tutors LottieYoga Teacher £10/h1st lesson free!Discover all our tutorsBefore The Pilates ClassBefore you attend your class make sure you know which kind of class it is that you have signed up for. If you attend a Pilates Mat class then you will need to bring your yoga mat with you but if you if you are going to be using the Pilates reformer machine then you may only need to take yourself and a bottle of water. To ensure you don’t get any surprises, just be aware of what class you are attending.Remember that Pilates isn’t going to tire your muscles in the same way that a similar aerobic, cardio or high-intensity workout would. It is focused primarily on working your muscles and core strength in a precise and controlled way, your breath becomes the rhythm of the movement. You will be encouraged to be present an d aware of yourself for precision in your poses and mindful practise.Don’t book yourself in for daily yoga classes near me until you have tried your first class.Remember that Pilates isn’t going to tire your muscles in the same way that cardio would. Photo Source: UnsplashIn The Pilates ClassMake sure to arrive at the studio on time, the Pilates instructor will likely be there a few minutes early. It is a great time to introduce yourself and let them know that you are a beginner and of any injuries or restrictions that you may have during the session. This is important so that the teacher can watch over you and give you additional help during the class. Also so that she can provide you with any modifications should they be needed.When you enter the class as a beginner take a place in the second row rather than the first, often more experienced students sit in the front. Sitting a bit further back gives you additional people to model during the practise. Try not to be too worried in your first class about getting it perfect, just be very observant and do your best. The Pilates teacher will likely come to support you if they notice you need additional help with your alignment.As you progress through the class, you are going to become aware of your body and muscles. Although you are moving with a slow, purposeful precision in the session, you will often feel your muscles burning. This is a good thing. As long as you are not in actual pain, you should try to resist stopping and complete the set for maximum results.After The Pilates ClassImmediately after class make sure rehydrate properly, even if you feel you didn’t sweat that much your body would have lost a lot of water and vital nutrients during your practise. Replenishing these lost nutrients and water will help your body to recover and repair.In the following few days after the Pilates class, you are likely to feel a little bit sore. This is normal and happens when the muscles have been worked hard in new ways, and they are responding to that workout. Despite how your body feels, practising Pilates regularly will move you towards your fitness goals and to a more balanced body. Although your body will need a few days to recover, you should book your next class right away so that you don’t lose momentum.Pilates is a complete full body workout that uses resistance training. It can be adapted to suit everybody of every level. Photo Source: UnsplashChanges That You May Notice From Regular Pilate TrainingRegular Pilates sessions can make you feel top notch, here are a few of the improvements that you can expect.A stronger whole bodyNew muscle groups that you didn’t know existedReduced body weightBetter concentrationDefined muscle toneImproved staminaA lifted bootyFeeling more energizedSpeed up your metabolic rate and burn fatMinimise stress and anxietyPilates is a lifelong practise that has no limits as to what you can achieve, it can even complement other forms of exercise. It is a well-developed training program with teachers who follow a very regimented Pilates teacher training program to become qualified to teach.Therefore you can guarantee that the quality of any class that you choose will be of a high standard and reward you with the best benefits. I hope that this list will help you to keep your eye on your personal goals and keep you motivated to keep going. Pilates is such a useful method, and when paired with a proper diet you will notice and feel the health benefits from head to toe.

How to Plan Your Economics Tutor Jobs

How to Plan Your Economics Tutor Jobs Planning For Economics Tutoring ChaptersWho is Your Audience?What is Your Methodology?Creating a Lesson PlanFinal Notes on Lesson PlanningLet us say you have mastered economic theory: you are well-versed in the laws of supply and demand, you know all about international economics and what factors drive the economy.You have a particular fascination for economic models; how they shape politics and public policy... and you want to share that awe with students of all stripes.That is both noble and commendable.You should know that, more so than for any teacher in any formal institute of learning, a tutor's viability is predicated on his/her reputation, which is based on several factors:knowledge of your subject matterteaching methodologyaccessibility â€" how amenable and engaging you areorganisation: how your lessons are structured and sequencedWhich student hasn't experienced a teacher who, when posed a question, answered we'll cover that later  or worse: read your book; your answer is in there?Simply having earned a d octorate in Economics does not a first-rate teacher make.Knowing how to plan and organise your wealth of knowledge such that your pupils will rave about you to their friends and classmates, and even write testimonials about your style of instruction is, quite literally, putting your money where your mouth is.Obviously, doing everything off the cuff runs counter to the very idea of efficiency. Planning your economics lessons is a vital step toward them coming off without a hitch.Let us give you a few pointers on creating Economics lesson plans that our most successful tutors have passed on to us.Discover more about becoming an economics tutor.Be knowledgeable: your tutee may place emphasis on a facet of economics that you perhaps are not wholly familiar with.Should that be the case, you may have to do a bit of studying yourself, prior to giving lessons!Be patient: no matter what is currently boiling in your kitchen, your students deserve every bit of tolerance and forbearance you hav e at your disposalBe kind: Although the student him/herself has expressed a motivation to learn about economics, where that motivation comes from could be a different source altogether.It is quite possible that family pressure could be the prime motivator behind a student's decision to major in economics, even though s/he may or may not have a love for it, or even any aptitude.If that is the case, you surely have plenty of teaching resources and ways to encourage recalcitrant students into exploring economics as a career field.What does all of this have to do with formulating lesson plans?Your intro to economics lesson plans may incorporate simple math concepts Source: Pixabay Credit: RuddinCreating a Lesson PlanJust as a roadmap shows different routes to reach a destination, a well-crafted lesson plan permits flexibility and spontaneity in teaching.The analogy of a lesson plan being a map is apt in more ways than one: such a document should be a guide linking past sessions with the upcoming one.One of the most vital aspects of a lesson plan is its time breakdown.Suppose your session lasts 50 minutes: how will you spend them?The negligent tutor would advocate: Eh, we've got almost an hour; surely we'll cover a bunch of stuff!You, the conscientious mentor, would plan down to the last minute.Warm UpHow's your week been? Were you able to finish last week's assignment? Did you hear about America's new sanctions on Iran? What do you think of them?Warm-ups should comprise of a greeting and some manner of gearing your student's thoughts toward economics.Talking about current events, perhaps even listening to a relevant  podcast segment would work well.Your warm-up should last perhaps 5 minutes, and you have the greatest control over the session at this point.IntroductionThis is where you present new information; ideally, your warm-up topic of discussion will segue neatly into the development of new material study.Here, you will do most of the talking. However, you sh ould remain vigilant for signs that your student isn't following your speech; perhaps fidgeting or frowning.Asking questions along the way is not a bad idea, but please nothing so generic as are you with me so far? or You understand?Perhaps looking for a tie-in with already known facts, or asking your student to paraphrase and put the new knowledge into context would work well.Around 10 minutes should be sufficient for expounding on new material.At any point during this segment, you may have to pause in order to allow your student more time to organise his/her thoughts, or for you to widen a limited perspective.Be prepared for discussion, but keep your eye on the clock.PracticeAt this point in the lesson, your student should be prepared to work on his/her own, but with supervision.You may have worksheets prepared that s/he can work on, or you might task him/her to analyse a graph or equation.If you are teaching a group of students, you may plan an activity in which collaboration is key.You should allow 15 minutes for this portion of the lesson, which includes time for questions and answers.ProductionHere your student(s) works on his/her own, and it should be active work: writing formulas, answering questions in writing, or perhaps outlining an essay or a simulation of an economic condition that s/he will turn in next week.During this phase, there should be little talking, either by you or your student.This segment should take up to 15 minutes; the perfect time for you to draft next week's lesson plan!ReviewFinal questions, notes and perhaps a summary quiz rule this last segment.You may impose extra work during this time, or provide a preview of the next lesson.Most importantly: make sure your student is comfortable with the just-learned material. If there is a measure of uncertainty, you may provide extra study links in the form of videos or websites.This portion should wrap up the lesson, possibly providing material for next week's warm-up.Build time into you r lesson plan to be sure your student is at least conversant on complex economics equations Source; Pixabay Credit: Free-PhotosFinal Notes on Lesson PlanningThe strategies of an educator are predicated on many variables, not the least of which are the subject and teaching materials s/he has to work with.Determining the students' objective is of prime consideration to organizing the flow and progression of tutoring sessions.New material presentations may include charts and graphs, podcasts, news articles and Powerpoint; simply relying on textbooks could limit your and your students' productivity.You should be cognizant at all times of students' comprehension, to the point of interrupting the lesson to ensure understanding.Unlike math or language arts, which are common core subjects with wide applications, economics is a relatively narrow field which demands a concrete understanding of fundamentals before moving on to other concepts.Writing lesson plans is a critical step in your prep aration, prior to starting instructional activities:to give you teaching ideasto provide a guideline for teachers and students â€" what worked well, what did not, and how the student respondedalso to measure if the cumulative lessons' trajectory is aligned with students' objectivesto assess pupils' progressto keep a timeline of what economics concept has already been taught, and its degree of mastery.Ideally, you should try out several templates before settling on the lesson plan template that works well for you.You will also find several sample lesson plans online, should you be at a loss on how to organize your sessions.In a classroom setting, the main purpose of a daily lesson plan is so that, should the teacher be absent, a substitute teacher could step right in without wondering what to teach that day.As a freelance Economics instructor, nobody will be looking over your shoulder, nor is it likely that anyone would cover your lessons for you.Still, you should incorporate lesson planning into your teaching activities to demonstrate your professionalism, and to illustrate your methodical mind.Your students will see you as a primary source of leadership while they learn to master economics concepts.You have a duty to provide them with the very best example, and that starts with planning your lessons well!See here about pricing your lessons.

Inequalities on a number line

Inequalities on a number line A number line is representing the numbers on a straight line. On the number line the numbers are written from left to right in an ascending order, smaller on the left and greater on the right. This helps to identify which number is greater and smaller. A number line can be used to represent an inequality. A greater that sign is represent by and a smaller than sign can be represented by . In an inequality two sides of the equation are not the same which leads to comparison of greater than or lesser than. Example 1: What inequality does the following number line show? Solution: Given here is a number line. The filled circle includes the number on the number line. An open circle represents not including the number on the number line. Now the blue underlined line represents a set of points, which can represented as an inequality. For the inequality a variable x can be taken. Here the shaded line starts from 3 (including 3) and covers all the points less than 3. So the inequality will be x is lesser than or equal to 3. Hence the solution is x 3. Question: Multiple choice question (Pick the correct option.) Which of the following point is not included in the following number line? a) 1 b) 5 c) 10 d) None of these. Correct answer: option a. The inequality covers all point greater than 1. Hence, the number line represents the inequality x 1. The inequality doesnt include the point 1 as it has an open circle.

Dealing with Difficult Reading Passages on the SAT and ACT

Dealing with Difficult Reading Passages on the SAT and ACT ACT SAT Prep and College Admissions Blog The SAT and the ACT are not designed to be fun tests. That’s probably really obvious to you already! These tests takes forever, have a billion questions, and will turn you into a zombie for the rest of your Saturday. One of the most evil parts of these tests is consistently that one passage on the Reading section that was written two- or three-hundred years ago. Lots of test-takers find these passages more boring than usual (and yes, the people who write these tests intentionally choose boring passages), if not significantly harder to understand thanks to a confusing, older style of English writing. Many students also really hate passages about science topics. Don’t panic! You may dread these passages every time you sit down to take a test, but there are plenty of ways to wrap your head around what’s important in the text and, more importantly, to answer questions confidently. That’s right: even if you don’t reallyunderstand a passage, you can still answer questions about it with confidence. There are only ever one or two questions for a given passage that talk about the passage overall, such as main idea, author’s intent, or tone questions. The remainder simply ask about specific parts of the passage. You don’t have to understand any part of the passage until a question specifically asks you about it. Rest assured, if you have a good strategy for tackling these questions, you’ll be able to pick up enough of them to boost your overall Reading score. Okay, But What If The Passage Just Doesn’t Make Sense? It’s always a good idea to read a passage through before you start answering questions, but you’ll want to approach reading a little differently if you feel like the passage is either boring or hard to understand. Start, as you always should, by reading the blurb right before the passage. This will give you some rough ideas about who is writing it, what era it’s from, and, based on the title, the general idea of the passage. There might be another sentence in there that gives you some clues too. The blurb is a great place to refer back to when answering a main idea question, by the way. Next, read through the passage and make a mental road map as you go.Even if you don’t quite get what the passage is talking about, you want to be able to walk away with a rough understanding along the lines of: “Ok, in the beginning it’s introducing a theory, it talks about turtles, later on there’s something about Bermuda, and at the end it says there’s something wrong with the theory.” Now, when a question talks about turtles but doesn’t give you a set of lines to look back to, you know where to go and re-read. Don’t Answer Questions in Order Really, don’t. On the SAT and ACT alike, the test writers tend to put a bigger picture question such as author’s intent or main idea as the very first question. Those types of questions are going to be much easieronce you’ve completed all of the questions that ask about specific parts of the passage (such as line or paragraph reference-based questions) since you’ll end up re-reading a bunch of little chunks of the passage and come away with a much better understanding of what’s going on here on a bigger picture level. Answer all line reference questions first.Go back to the important lines and re-read them. Maybe read a sentence before and sentence after too. Once again, you don’t have to understand any part of the passage until a question asks about it. But now is the time to understand a small chunk of it well enough to answer a question. Only once those are all completed, complete the bigger picture questions.You might realize you have a better understanding of the passage now that you’ve done those other questions, and you can use that to your advantage. Always use process of elimination.Whether you like the passage or not, identifying answers that are bad is always going to be easier than identifying the one that seems right. Worst case scenario, if you can eliminate some answer choices theDon you have a significantly better chance of randomly guessing correctly on a hard question within a hard passage. It always helps to have a little bit of an idea of what a right answer will look like before actually looking at the answer choices. So, even when passages seem difficult to comprehend or boring, stick with it. Take notice of the blurb at the beginning and make an outline in your head of what the passage talks about and in what order things happen when you do the initial read through. Don't feel compelled to answer questions in order. First, complete the line reference questions, which will also give you a better grasp of the overall passage and then use process of elimination to increase your chances of choosing the right answer on the more difficult questions. About the Author Mike S. is one of our most experienced test prep tutors. For more information on our SAT and ACT prep packages, click here.

School Volunteering - Sashas Story

School Volunteering - Sasha's Story The Tutorfair Foundation helps children who can't afford private tuition by organising school volunteering placements for top tutors. Not all placements take place during the school day. Medical student and maths tutor Sasha tells us about volunteering at an after school club. For the past few months Sasha, has been volunteering with Stretch Academy after school club, at Woodberry Down Primary School. At Stretch, Sasha  supports children with learning 11+ style content. He helps with all the material, “particularly aiming to help out with the tricky maths and non-verbal sections.” As a big believer in social mobility, he was drawn to the Foundation. Sasha says,  â€œit's massively important that access to one-on-one (or similar out-of-school) teaching is available to all children, not just those who can afford to pay privately.” How does a working medic find the time to volunteer? Sasha tells us he wanted to do some volunteering last year, “but unfortunately my medical school timetable was unrelenting. None of the sessions were at times I could do. This year I'm free on Thursday afternoons, so I signed-up straightaway! Woodberry Down is also very close to my home, so it was ideal!” School Volunteering Stretch Despite having years of tutoring experience Sasha, like many of our volunteers, was nervous to begin with. He tells us, “I was a little daunted, to be honest! It'd been a while since I'd last done any classroom-based work, let alone in a primary school.  So I guess I was also unsure of exactly what to expect. Thankfully Alex is an exceptional teacher and all of the students in the group were so engaged and hard-working. It all fell into place and I was really enjoying helping out by the end.” Fast forward to several months in and the nerves are all gone. Sasha says it's relaxed as, “the students all know me, by now, and are much more confident in asking questions, and making the most of the time. This is great, as it means Alex has more time to focus on other students and make sure everyone can contribute and learn to the best of their ability! The class are really fun and welcoming, too, so I always feel at ease and really enjoy helping with the work.” School Volunteering  positives Each day has different positives, Sasha’s favourite session so far was, “when the topic was codes, using algebra. Maths has always been my favourite subject to teach (despite its general reputation!) and it was so rewarding to see the kids racing through the worksheet with bright smiles. Some actually volunteered to take unfinished work home to do as homework! That's not something you see everyday.” As well as the joy of seeing children develop a love of maths, volunteering has had personal benefits for Sasha. He has found it “a real pleasure teaching the children at Woodberry Down, particularly given our similarities in background. It so inspiring and motivating to see these children staying in school, and working until 5pm on a Thursday, just to stretch themselves that bit further and expand their education. I'm glad they've been offered this opportunity. I'm all the more glad that they seem to be grasping it with both hands!” School Volunteering Stretch Though it is fun and inspiring now it was challenging to begin with. Sasha remembers finding it tricky, “adapting to the new students, particularly to teaching in a large-group environment. Everyone has their own style and way of understanding things, so you just have to be really patient and make sure that you're using the best explanation for that particular student.” One thing that helped in getting ready for the placement was the training day. Sasha tells us, “Alex actually led the Primary session, on the training day, and it was largely based around the way he delivers the Stretch Academy sessions. It was an excellent insight into the way he teaches and the way he covers certain topics, so I at least felt prepared for that, on my first day!” Are you low on time but thinking of volunteering? Let Sasha encourage you to get involved: “I'd highly recommend it! There's such a great range of volunteering opportunities, across various subjects and age groups, and it really is such a satisfying and rewarding way to spend an hour (or more!) of your week. It's also an excellent chance to work with brilliant students who otherwise may never have the opportunity to ask those extra questions, or seek that bit more help.” You can book  Sasha on Tutorfair

New Private STD Testing Service Geared Towards Students Launched

New Private STD Testing Service Geared Towards Students Launched pexels.com “Our research shows consumers believe that the ability to purchase certain tests and receive results would facilitate better communication with their physicians and improve their health. Greater access to accurate testing, diagnoses, and treatment is particularly critical in sexual and reproductive health, where medications can often quickly cure many common STDs,” said Cathy Doherty, senior vice president and group executive, clinical franchise solutions and marketing, Quest Diagnostics. “With these services, Quest is meeting consumers where they are, empowering them to access and take actions from diagnostic insights to improve their health.” Part of the issue that Quest Diagnostics is trying to combat is the stigma surrounding STD’s that make young adults hesitant or uncomfortable to discuss STD’s or get tested for them by medical professionals. “Too many people are not being screened for STDs, and one reason is a reluctance to discuss risk with healthcare providers,” said Damian “Pat” Alagia, III, MD, FACOG, FACS, an OB/GYN and medical director of woman’s health for Quest Diagnostics. “Services that empower individuals to access STD testing extend physician-based care so more people can receive the evaluation and treatment they need.” To get more information about the service, check out QuestDirect.QuestDiagnostics.com.