Logarithm Worksheet Express The Equation In Logarithmic: Fill & Download for Free

I like to compare a calculator in math to an automatic translator when learning a foreign language.Automatic translators get you to the translation quickly and easily, but there are three major problems:You are completely dependent on the translator.The translator doesn't always understand the subtleties of translation, and will sometimes give the wrong result.And... well... YOU NEVER LEARN THE LANGUAGE.You can't speak it, and unless you really have to, you'll never use it.A calculator is an invaluable tool in the math classroom, but one that can easily sabotage learning if used improperly.Calculators swiftly removes the motivation behind math concepts, and the intuition from math students.I'll use the topic of logarithms as an example. I think it is fairly understood that "in the real world" no one calculates logarithms without a calculator. (Except for that hold-out slide rule guy.) So why bother learning to calculate them by hand?Well, for starters, when would you ever use a logarithm?*crickets*If you don't understand what a logarithm is used for and how it's calculated, you'll never use it. That will be one of many buttons that sits unused on your calculator because you never knew the why.Once you realize that logarithms "undo" exponentiation, and turn multiplication into addition, the logarithm gains meaning, and not only can you solve logarithmic expressions, but more importantly: you can write them!I like to take my math students onto http://www.wolframalpha.com and show them how far calculators have come. I tell them, "Hey! This can solve any of the equations we're going to learn in this class. So why are we bothering to learn all this crap?" They give me a look like "Beats me."Then I give them a word problem and ask them to put it into Wolfram Alpha. They discover that the smartest computer has huge difficulties with word problems. It's up to them to translate their problem into the language of math, calculate, and translate their answer back into the language of the everyday. This translation requires them to know what's going on with their calculations, not just "the answer."Finally I want to spend a little time talking about what good calculator use in the classroom looks like.Calculators do two things very well. The first is establishing patterns that are difficult to see without them. Not only can they destroy intuition, calculators can be used to build intuition.For example: I gave my students a worksheet with a long list of exponentials with fraction exponents. Their first job was just to put these in the calculator. Their next job was to find the pattern and answer some similar problems without the calculator. By the end of the assignment, almost all of the students could tell me the what the pattern was.This still didn't answer *why* fraction exponents behave the way they do, but it established a rudimentary understanding that could be built upon. And importantly, they built that understanding on their own.The second good use of calculators in the classroom is to allow students to focus on problem solving rather than arithmetic. It also allows them to work on real data that is not practical to do by hand.This is well documented in a ton of educational studies. Students solve problems better when they have calculators available. It doesn't matter if the calculations were actually easy or not. Just knowing they could fall back on the calculator allowed the students to keep their focus on solving the problem rather than "doing the math." I use quotes here because the real math is the problem solving, not the arithmetic.Can you imagine consistently doing regression problems in statistics without a calculator? Having to solve 8 quadratics to do a single problem? These are all doable, but in the process you lose focus on the application.In summary, teaching a kid calculations with a calculator first is like teaching a kid to drive before you teach them to walk.Obviously driving is important, but so is walking. If you have to jump in a car every time you want to go 5 feet, lets face it, you won't do it. Just like you won't sit there with an automatic translator to communicate with someone in another language. You could, but you won't.People who don't understand calculations choose not to do them.

Speaking as an aspiring mathematician, on a more ideological level, mathematics is not taught how a mathematician would do it. Mathematics is presented in a very dull and boring manner. The purpose of mathematics is not to simply solve problems, but understand them. Something which our education system does not seem to value.This isn't helped by a culture which assumes that it's okay to be bad at math. People say it almost pridefully! Imagine if people said with pride “oh yeah I SUCK at reading!” — somehow it's okay to say this for mathematics.Mathematics is truly about logic and creativity. The current public school system has taken it upon themselves to remove both components from a math education. Most students never get to see the beauty of simple geometry, or the amazing symmetries that elementary group theory models so well.Instead, students are left to solving polynomials, with no clue why they are doing it, and no clue why the method they have been taught works. They are not taught abstraction and reasoning skills. The concept of a proof does not exist. Yet since proofs are central to mathematics, what then are they learning? Equation solving. The mathematical education of the US is equation solving. There's not much else but a brief and disconnected stint in geometry, which entirely never fails to disappoint the student, as it becomes the subject of proving obscure results whose significance is never understood.As the mathematician Edward Frenkel says,“What if at school you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of Leonardo da Vinci and Picasso? Would that make you appreciate art? Would you want to learn more about it? I doubt it...Of course this sounds ridiculous, but this is how math is taught.”How truly sad our mathematics education is! Our mathematical education “becomes the mental equivalent of watching paint dry.”One mathematician, Paul Lockhart, has given a very detailed criticism of the mathematical education system in the US in a document titled “A Mathematician's Lament” which can be found athttps://www.google.com/url?sa=t&source=web&rct=j&url=https://www.maa.org/external_archive/devlin/LockhartsLament.pdf&ved=2ahUKEwjfqoik59TbAhWpuVkKHeRPD1UQFjAOegQIABAB&usg=AOvVaw1-8EksPe3CjESJf4g-GoVETowards the end, he gives a paraphrase of the US math education. I will include it here, as it is quite clear:“LOWER SCHOOL MATH. The indoctrination begins. Students learn that mathematics is not something you do, but something that is done to you. Emphasis is placed on sitting still, filling out worksheets, and following directions. Children are expected to master a complex set of algorithms for manipulating Hindi symbols, unrelated to any real desire or curiosity on their part, and regarded only a few centuries ago as too difficult for the average adult. Multiplication tables are stressed, as are parents, teachers, and the kids themselves.MIDDLE SCHOOL MATH. Students are taught to view mathematics as a set of procedures, akin to religious rites, which are eternal and set in stone. The holy tablets, or “Math Books,” are handed out, and the students learn to address the church elders as “they” (as in “What do they want here? Do they want me to divide?”) Contrived and artificial “word problems” will be introduced in order to make the mindless drudgery of arithmetic seem enjoyable by comparison. Students will be tested on a wide array of unnecessary technical terms, such as ‘whole number’ and ‘proper fraction,’ without the slightest rationale for making such distinctions. Excellent preparation for Algebra I.ALGEBRA I. So as not to waste valuable time thinking about numbers and their patterns, this course instead focuses on symbols and rules for their manipulation. The smooth narrative thread that leads from ancient Mesopotamian tablet problems to the high art of the Renaissance algebraists is discarded in favor of a disturbingly fractured, post-modern retelling with no characters, plot, or theme. The insistence that all numbers and expressions be put into various standard forms will provide additional confusion as to the meaning of identity and equality. Students must also memorize the quadratic formula for some reason.GEOMETRY. Isolated from the rest of the curriculum, this course will raise the hopes of students who wish to engage in meaningful mathematical activity, and then dash them. Clumsy and distracting notation will be introduced, and no pains will be spared to make the simple seem complicated. This goal of this course is to eradicate any last remaining vestiges of natural mathematical intuition, in preparation for Algebra II.ALGEBRA II. The subject of this course is the unmotivated and inappropriate use of coordinate geometry. Conic sections are introduced in a coordinate framework so as to avoid the aesthetic simplicity of cones and their sections. Students will learn to rewrite quadratic forms in a variety of standard formats for no reason whatsoever. Exponential and logarithmic functions are also introduced in Algebra II, despite not being algebraic objects, simply because they have to be stuck in somewhere, apparently. The name of the course is chosen to reinforce the ladder mythology. Why Geometry occurs in between Algebra I and its sequel remains a mystery.TRIGONOMETRY. Two weeks of content are stretched to semester length by masturbatory definitional runarounds. Truly interesting and beautiful phenomena, such as the way the sides of a triangle depend on its angles, will be given the same emphasis as irrelevant abbreviations and obsolete notational conventions, in order to prevent students from forming any clear idea as to what the subject is about. Students will learn such mnemonic devices as “SohCahToa” and “All Students Take Calculus” in lieu of developing a natural intuitive feeling for orientation and symmetry. The measurement of triangles will be discussed without mention of the transcendental nature of the trigonometric functions, or the consequent linguistic and philosophical problems inherent in making such measurements. Calculator required, so as to further blur these issues.PRE-CALCULUS. A senseless bouillabaisse of disconnected topics. Mostly a half-baked attempt to introduce late nineteenth-century analytic methods into settings where they are neither necessary nor helpful. Technical definitions of ‘limits’ and ‘continuity’ are presented in order to obscure the intuitively clear notion of smooth change. As the name suggests, this course prepares the student for Calculus, where the final phase in the systematic obfuscation of any natural ideas related to shape and motion will be completed.CALCULUS. This course will explore the mathematics of motion, and the best ways to bury it under a mountain of unnecessary formalism. Despite being an introduction to both the differential and integral calculus, the simple and profound ideas of Newton and Leibniz will be discarded in favor of the more sophisticated function-based approach developed as a response to various analytic crises which do not really apply in this setting, and which will of course not be mentioned. To be taken again in college, verbatim.***And there you have it. A complete prescription for permanently disabling young minds— a proven cure for curiosity. What have they done to mathematics!”… Sigh…***EDIT***To address some of the remarks with regards to the importance of calculus and unimportance of more mathematicians, Lockhart does address this in his paper:“How many students taking literature classes will one day be writers? That is not why we teach literature, nor why students take it. We teach to enlighten everyone, not to train only the future professionals. In any case, the most valuable skill for a scientist or engineer is being able to think creatively and independently. The last thing anyone needs is to be trained.”—“But don’t we need people to learn those useful consequences of math? Don’t we need accountants and carpenters and such?How many people actually use any of this “practical math” they supposedly learn in school? Do you think carpenters are out there using trigonometry? How many adults remember how to divide fractions, or solve a quadratic equation? Obviously the current practical training program isn’t working, and for good reason: it is excruciatingly boring, and nobody ever uses it anyway. So why do people think it’s so important? I don’t see how it’s doing society any good to have its members walking around with vague memories of algebraic formulas and geometric diagrams, and clear memories of hating them. It might do some good, though, to show them something beautiful and give them an opportunity to enjoy being creative, flexible, open-minded thinkers— the kind of thing a real mathematical education might provide.”—“But don’t you think that if math class were made more like art class that a lot of kids just wouldn’t learn anything?They’re not learning anything now! Better to not have math classes at all than to do what is currently being done. At least some people might have a chance to discover something beautiful on their own.”

1) Khan Academy(http://www.youtube.com/user/khanacademy?gl=CA)Undoubtedly one of the most famous YouTube channels for education, the Khan Academy (a quasi-MOOC) offers thousands of clips for different disciplines, such as math, physics, biology, social science, to name a few. Founded by Salman Khan in 2006, the Khan Academy lives by its commitment: “providing high quality education for everyone and anyone.” True to its objective, the channel is filled with videos that can help you learn math the fun and easy way. Famous clips include matrix introduction, matrix addition and subtraction, scalar multiplication, and expression for combined area of triangle and square, among many others.2) YouTube Teachers(www.youtube.com/user/teachers)YouTube Teachers is a collection of more than 700,000 videos, which focus on mathematics and other disciplines. Created by experienced teachers, this channel is a storehouse of information for learners and educators alike. Its videos for elementary students include numbers, cardinality and counting, solving for the surface area and perimeter, as well as geometry and quadrant graphing.Videos for middle school students include geometry, variables, expressions, linear inequalities and equations, while high school students can learn from clips on algebra, polynomial functions, and creating equations, to name a few.3) Patrick JMT Free Math Videos(http://www.youtube.com/user/patrickJMT)Patrick JMT’s Free Math Videos is one of the most popular educational channels in YouTube, boasting a total of more than 150,000 subscribers and about 58 million views. The host, Patrick JMT, is a community college mathematics professor who wishes to share his knowledge so that the viewers can improve their grades in school. Patrick JMT’s free math channel features numerous playlists, such as that of inverse trigonometric functions, derivatives, optimization problems, integrals and anti-derivatives, linear equations, linear inequalities, exponents, polynomials, quadratic equations, quadratic inequalities, rational inequalities, logarithms and functions.4) Ted-Ed(www.youtube.com/user/TEDEducation)Ted-Ed is an online library of short and interesting videos that focus on mathematics, science, and other studies. As one of the best educational channels in YouTube, Ted-Ed features educational videos that have already gained more than 17 million views. In terms of mathematics, the go-to sub-channel at Ted-Ed is the “Math in Real Life,” which features 16 informative clips about math problems. Videos include how to organize, Add and Multiply Matrices by Bill Shilito, Scalars and Vectors by Michelle Buchanan, Estimating Enormous Numbers by Michael Mitchell, Proving a Mathematical Theory by Scott Kennedy, Algorithms by Kevin Slavin, and Fractals by Benoit Mandelbrot.5) Video Math Tutor(http://www.youtube.com/user/videomathtutor)If you’re looking for a great channel that provides math tutorials, then switch to Video Math tutor Resources and Information. features a comprehensive series about basic math, which cover inequalities and equalities, operations and properties of numbers, multiples and divisibility’s, to name a few. Its algebra channel, on the other hand, consists of geometry formulas, linear equations and linear inequalities, among many others. The channel also features video flash cards, calculator tips, tips for teachers, as well as tips for students that can help them pass exams with flying colors. Apart from math videos, the Video Math Tutor also features brain teasers and funny clips that provide pure entertainment to its more than 10,000 subscribers.READ Top 10 Learning Techniques: Ranking From Best to Worst6) Numberphile(www.youtube.com/user/numberphile)Created by Brady Haran and his team of fellow math wizards, Numberphile is all about making learning mathematics fun and more interesting. With almost 400,000 subscribers, Numberphile features colorful, graphic videos about Pi, prime numbers, Graham’s number, even the games Rubik’s Cube and Yahtzee. With the channel’s simple approach to mathematics, viewers can definitely learn a lot of concepts about math the sweat-free way.7) Mathademics(http://www.youtube.com/user/Mathademics)Are you in need of some math lessons? You do not have to look for a tutor anymore as you can access high-quality educational clips for free at YouTube’s Mathademics channel. Founded in 2010, Mathademics features 8 playlists, including fractions and decimals, algebra and functions, data analysis and probability, geometry, measurement and conversion, and arithmetic. The playlist titled Number Sense, meanwhile, teaches tips such as finding multiples of a number, subtracting integers, prime factorization, to name a few. The problem solvers category, on the other hand, deals with logical reasoning, logic puzzles and money problems, among many others.8) Math TV(http://www.youtube.com/user/MathTV)Math TV is a collection of videos hosted by a math expert who has been teaching the subject and writing numerical textbooks for three decades already. Math TV has a total of 119 videos, all of which are meant to simplify complicated subjects and topics. Educational clips listed in the Math TV channel include solving analytic geometry and trigonometry equations, finding Pascal’s triangle, as well as the Fibonacci sequence, integrals and derivatives. Apart from helping students, Math TV also has clips that are highly beneficial for teachers, especially those who have just started in their profession.9) Math Mammoth(http://www.youtube.com/user/MathMammoth)Math Mammoth is all about providing assistance to students to learn math the unconventional way. With data extracted from the Math Mammoth book, the clips feature a helpful instructor with a handy dandy whiteboard at her back. With more than 2,000 subscribers, the channel has already gained a whopping 1.2 million views. Truly a mammoth of information, the channel is brimming with helpful clips, such as scaling figures, proportional relationships, time units, solving proportions, measuring temperatures, adding and subtracting fractions and decimal arithmetic.These videos really come in handy for students who have missed the math lecture at school, as well as those who learn lessons through mere repetition.10) Ten Marks(http://www.youtube.com/user/TenMarksInstructor/videos?view=1)Ten Marks is a YouTube educational channel that aims to help students learn and master different mathematical concepts. Ten Marks enables viewers to grasp concept at a time with its helpful video lessons, hints, and worksheets. With its easy-to-follow lessons, the channel has gained more than 2,000 subscribers and about 2.3 million hits on YouTube.Ten Marks’ playlist has a wealth of choices for videos about circles, similarity and congruence, quadrilaterals and polygons, lines, angles and triangles, transformations and similarities, units of measurement, area and perimeter, volume and surface area, functions, graphs and sequences, number theory and divisibility, fractions and decimals, number operations, percent and algebraSource: 10 Great Youtube Channels to Learn Math