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“Math is All Around Us” By Darian Vander Veen Email: aardvarklearning@gmail.com Perhaps you’ve heard a thousand times that “Math is all around us” but here at Aardvark Learning our Math tutoring program asks for students to stop and think that math is everywhere in life and we use Math everyday. This is what makes Math essential is that understanding and mastering math is the key to understanding and mastering any other subject that you want to learn. Are you into music? Do you like to play an instrument? Have you tried to figure out how to tune your guitar, but find that you are simply unable to figure out exactly where your tuning note is? You can actually hear how far off you are by playing with some sort of sound at your tuning note, and I can explain exactly how that works with math. Sound Waves and Sinusoidal Functions Sound travels in waves. If you look at the graphs on the right (and you’re familiar with sinusoidal functions), you’ll be able to see exactly what’s being plotted. Let’s imagine the red wave is the wave you’re trying to tune to. The blue wave is what your instrument is playing. The green wave is the combination of the two, as you can see on the left if you’re familiar with function notation(if not, don’t despair, the lightbulb moment comes soon). The green wave is also the important one, so let’s look at it alone: Can you see how the wave pulses? The really important part here, is that you can hear these pulses. The sounds of the two sources combined will pulse maybe 4-15 times a second, depending on how bad you’re out of tune. The secret lies within that 0.95. For the blue wave, the magic number is 0.95. For the red wave, it’s 1. The closer the two magic numbers are together, the less pulses you’ll hear, and the closer to in tune you’ll be. You can duplicate this on www.desmos.com and check it out for yourself by changing that 0.95. If you make it 1 like the red wave, the pulses will disappear If you’re tuning your guitar, and you hear the pulses sort of disappear, you’re now in tune, and this is why. If you understand this, you’ll be able to tune your instruments, even if you don’t have an ear for it. This is how I tune, because I can’t tell you if my guitar is flat or sharp to save my life. Math & Sports: What is the best way to strike a ball? Sports appear to be as far apart from math as possible, there’s no way math could help with your game, right? Wrong. Sometimes in sports, you have to hit an object as far as you can. You may notice that hitting it into the air helps, but what’s the best way to do it? If you hit it straight upwards, sure, it will go high, but it won’t go forward. So maybe you just want to kick it outwards. However, it’ll hit the ground before it goes anywhere. The best way to hit it is somewhere in the middle as the Math in the Graph shows: From this graph, you can see that “the middle” I’m talking about is at 45 degrees. And this is where math is handy, because you probably wouldn’t come to this conclusion just by kicking a ball over and over. Maybe you’d kick it with less speed sometimes, and more speed other times. Perhaps you can’t see what angle you’re kicking it at(neither can I), and you can’t really tell what the best angle is just by kicking the ball. But now, you can see the angle, and aim for it next time you’re practice soccer, or golf, or whatever. But where’s the math? Or you might not ask that, you may be content with the result and leave. If you’re interested, however, I’ll give you the formula for how far the ball will go, and we’ll be able to see how the math is applied to reach it. Ouch. That’s a doozy. We can make this easier, though. R is how far the ball will go, so that’s simple enough. v02 is the initial velocity squared. Basically, the harder we kick it, the farther it will go. Let’s just pretend we’re always kicking our hardest, because we want to get the ball as far away as possible. Then we can ignore it. g is the force of gravity. You can’t kick a ball as far on Jupiter, because gravity is heavier there, but you can kick a ball way farther on the moon. However, on Earth, gravity is basically always the same, so we can ignore that as well. Now we’re left with something like R = sin (2θ) That funny symbol is the Greek letter theta. It’s just the angle we’re kicking at. Now, if you plot this using www.desmos.com, you’ll find that the highest it reaches is 1, at 45 degrees. Again, this is the result we came to earlier, and now you have the mathematics behind it. If you’re familiar with sinusoidal graphs, you can take this a step further by seeing that the high point of sin (θ) is 1 at 90 degrees. What’s the point, you ask? Well, if sinθ reaches a maximum at 90 degrees, sin2θ will reach its maximum at half that, 45 degrees, because 2 times 45 is 90. If you understand that, then you don’t even need a graph to understand all of this math behind kicking a ball. You can see that now you have something to aim for when you’re trying to master the surprisingly complex art of kicking a ball as far as you can. Perhaps you like to play video games instead. Video games run off a series of formulas. Maybe they calculate something that’s random chance. Maybe the formulas work together to calculate how much damage you deal in a situation. There’s also that range of a projectile formula, that could be used in a sports video game, or rather, any game in which something is launched into the air somehow. So let’s consider these formulas. What’s the advantage to learning about them? For those of you who don’t play video games, I’d wager you’ve still heard of Pokemon somehow. You know, the game where you catch small animals in balls and have them fight for you? Morality issues aside, let’s look at the formula for catching a Pokemon, shall we? Simple, right? And how do you figure that out? Simple. By understanding the math behind it. You can start by checking out this video. It’s just over a minute long, but in that short time, it has a lot of interesting visuals, connections, and yes, math. https://www.youtube.com/watch?v=whYqhpc6S6g
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By Kayo Hawkins, Owner and Second language learner
Introduction Aardvark Learning Academy offers excellent language programs - French, Japanese, and English as a second language. Learning a language with an Instrutor is the best and closest way to improve your skills to communicate effectively in the language under study. At Aardvark, we have excellent teachers and our existing students are highly motivated to study a new language. There is one common denominator that every Aardvark student tells us why they want to study with our instructors. Our students’ want to have someone to speak with and get immediate feedback on their language development. Nowadays, you can easily find tools available to self-teach a new language such as textbooks, Language Apps, Youtube, movies and songs. Most of our students had already tried these FREE media before calling us for specific help and language teaching. Currently, Aardvark Learning Academy has serious language learners whom realized that they want to try their skills to actually carry a conversation, not to just repeat the sound or to fill in the textbook. There is nothing more motivating than speaking effectively, socializing in your second language, easily and with natural humour that happens when you study another language. Summary The reason why learning a new language with an actual teacher / person is because the connection between the language and you happens. With an instructor, you can practice talking about your real life situation; about yourself, about your work and school, about your interest. Being able to express yourself is more fun and meaningful than talking about Mary and John going to the movies in the textbooks. The Instructor automatically introduce a new grammar and vocavulary that would be useful in your situation to gain the ability to say more different topics in appropriate ways. Moreover, it's just simply fun. We will help you achieve your goals whether it's for passing the test, doing better at school, business or preparing for a trip in the future. French : Grade 3 - adults , Online Japanese : Grade 4- adults, Online and in-person English as a second language: Adults, Online and in-person Contact us for a free Consultation on ZOOM, aardvarklearning@gmail.com By Kayo Hawkins email: aardvarklearning@gmail.com September schooling in 2020 is a new experience from what it used to be, whether you are in person at school, learning virtually online, or taking homeschooling. Aardvark Learning Academy is here to support all students (Grades 1-12) that want to enjoy learning, develop new skills and gain confidence from challenging yourself and succeeding. Aardvark Learning Academy has started new POD Math & English programs for Grades 1-4 students learning at home / homeschooling. Both students and parents understand that it can be a struggle to be engaged in learning when you are at home every day. Instead, why not try making one day a week available for tutoring that can improve the attitude at home and motivate your child in the learning process. Learning is a joy and students should know firsthand that it is not just a job to complete in 75-minute blocks. Rather students should also be switched ON in your mind, enjoying the learning process and discovering something new and interesting each day 😊. Small Group Tutoring in the morning is perfect for primary students Grades 1-4 who are staying home via online or homeschooling. Each student has an opportunity to interact with our experienced OCT (Ontario College of Teachers) Instructor and cooperate together to learn in small group of like-minded peers. Morning tutoring is the best time for younger minds to be active! See your child smile after learning Math & English at Aardvark!!! POD 25$ per hour!!! Tuesdays: Grade 3/4: 10:00-12:00 English and Math (1 spot left in October) Thursdays: Grade 1/2: 10:00-11:30 Early Literacy and Math (2 spots left in October) Each group has a maximum of 4 students. Spots are limited! Contact us to start today: aardvarklearning@gmail.com Group Fees 25$ per hour x 6 = 150$ Registration fee (one time only) = 50$ Monthly Materials fee = 10$ Total: 210$ Identifying and comparing data on a chart Some texts include statistics and data in graphical form. To understand this information, first identify:
The bar chart below gives information about the percentage of the population living in urban areas in different parts of the world. Summarise the information by selecting and reporting the main features, and make comparisons where relevant. Write at least 150 words. Source: United Nation Model answer The graph compares the growth in the percentage of the population living in urban areas in six different regions of the world. According to the chart, between 1950 and 2007 the percentage of the population living in cities in Latin America and the Caribbean almost doubled, from 42% to 76%, whereas in Europe it only increased by 21%. However, in Europe over half the people already lived in cities in 1950. When we compare the projected increases in Asia and Europe by 2050 we see that in Asia the percentage will continue to grow at the same speed, with a further increase of 25%, whereas in Europe the change will be slower than before, increasing by only 12%. By 2050, the vast majority (around 90%) of people in Latin America, the Caribbean and North America will live in cities. Even in Africa, more than half the population (62%) will live in urban areas by then. (155 words) EXAMPLE B: TASK 1 The diagrams below show the main reasons workers chose to work from home and the hours males and females worked at home for the year 2019. Summarise the information by selecting and reporting the main features, and make comparisons where relevant. Write at least 150 words. Model answer The bar chart illustrates the reasons men and women chose to work from home in 2019. Overall, saving money was the main reason for both males and females (45% and 42% respectively). In contrast, approximately a quarter of males put productivity as a reason, which was twice as high as the female response (24% and 11% respectively). For childcare, the pattern was different again with almost a quarter of females giving this reason compared to very few males (4%). The table shows the hours men and women worked from home in 2019. The vast majority of males worked over 30 hours per week (81%) contrasting with a minority of females (6%) doing similar hours. This pattern is reversed when examining the under ten hours category with almost three quarters of females working this amount compared to only 3% of males. The 10 to 30 hours per week category shows fewer marked differences. To sum up, it can be seen that men and women do not always give the same reasons for home working and, in general, men work longer hours from home. (182 words) July 8, 2020: CELPIP OR IELTS Preparation?
Do we offer CELPIP in addition to IELTS preparation? The answer is resoundingly YES because we teach the underlying test strategies that empower you; our adult students to succeed in Reading, Writing, Listening and Speaking on any given academic or general test. Driving a car has different road rules and regulations in every country, nation around the globe. But those that already know how to drive will be able to succeed in Driving in any car (Subaru, Tesla, Porche) or nation around the globe. CELPIP and IELTS are similar in the sense that once you know the strategies, its easy to do well on the test. Nowadays, CELPIP and IELTS are being held online but the test skills you need to be successful are the focus of study at Aardvark Learning Academy. Already we have had several adult students achieve their Goals on Academic IELTS and general CELPIP. We can definitely help you develop your English language skills. Just contact us and get started today! Experienced teacher that has taught ESL to international ESL-Adults since 1999. Try out 6 hours and you can see for yourself that everything we do is 1000% for real. |
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