쉐도잉 연습: Math Antics - Percents Missing Total - 영상으로 영어 말하기 배우기
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Hi! Welcome to Math Antics. In our last lesson about percents, we learned that there’re three main types of percent problems because there’s three different numbers that could be missing.
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Those three numbers are the ‘part’, the ‘total’, and the ‘percent’.
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They’re just the three variable in the percentage equation.
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The forth number is always 100, since that’s what percent means: per 100.
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In the last two videos, we learned how to solve problems where the ‘part’ was unknown and where the ‘percent’ was unknown.
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In this video, we’re gonna learn how to solve problems where the ‘total’ is unknown or missing.
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With this type of problem, you’ll be told what the percent is, and you’ll be told what part of the total you have.
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But you’ll need to figure out what that total itself is.
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Here’s an example of a problem like that: Your friend has a bag of marbles, and he tells you that 20% of the marbles are red.
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If there’s 7 red marbles, how many marbles does he have altogether?
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Okay, so how do you know that it’s the total that’s missing in this problem?
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Well, the word “altogether” is a big clue because it means almost the same thing as “total”.
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So, if the question has words like, “altogether”, or “in all”, or “total”, or “whole”, or “entire” those can help you know that you need to find the total.
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And another way that we can tell is by the numbers that we ARE given.
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In this problem, we know that the percent is 20, and we’re also told that PART of the marbles are red, so we know that the PART is 7.
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So that means that it must be the total that’s missing!
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Alright then, so how do we figure out what the total is?
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Well, using a little algebra we can re-arrange our percent equation like this: What this new form of the equation tells us is that, if we take the ‘part’ and multiply it by 100, and then we divide that by the ‘percent’, we’ll get the ‘total’.
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That seems simple enough. It’s just two steps!
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Let’s try it out on our word problem about the marbles.
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We know that the ‘part’ is 7, so step one is to just multiply that part by 100.
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7 × 100 is 700.
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And in step two, we take that 700 and divide it by the ‘percent’, which we’re told is 20.
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Okay, 700 divided by 20…. hmmm….
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Well, we could use a calculator to divide, but this doesn’t seem too hard, so I’ll just do the division the long way.
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20 is to big to divide into the first digit so we’ll need to include the digit next to it as well.
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Now we ask, “How many ’20’s does it take to make 70 or almost 70”.
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That would be 3 because 3 × 20 is 60.
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70 minus 60 leaves 10 as the remainder.
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And then we bring down the zero and then we ask, “How many ’20’s will divide into 100?” Ah-ha… 5, because 5 × 20 is 100, so that leaves no remainder.
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So 700 divided by 20 is 35.
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And that means that the total number of marbles is 35.
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And in a problem like this, you can always check your answer by making sure that the fraction of the ‘part’ over the ‘total’ would give you the correct percent.
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For example, in this case, you could make sure that the fraction 7 over 35 would really be 20%.
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Now that wasn’t so tough, was it?
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Let’s see one more example to make sure you’ve got the procedure down before you try some on your own.
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The next problem says: A high school marching band has 12 flute players.
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If 8% of the band members play the flute, then how many members are in the entire band?
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Okay, so the smaller ‘part’ in this problem is 12 since there’s 12 flute players.
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And we’re told that they make up 8 percent of the band, so the ‘percent’ is 8.
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Again, it’s the ‘total’ that’s missing, and to find it, we just need to follow our 2-step procedure.
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For step one, we multiply the ‘part’ by 100: 12 × 100 = 1,200 For step two, we divide that 1,200 by the percent, which is 8.
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1,200 divided by 8 equals 150.
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Great… that means that the total number of band members is 150.
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And again, you can always check your answer the way we did in the last example.
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Alright… that does it for this lesson.
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Remember… the key to getting really good at math is to do it yourself.
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Doing practice problems on your own will help you become a great problem solver.
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Good luck! Thanks for watching Math Antics and I’ll see ya next time.
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Learn more at www.mathantics.com
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맥락 및 배경
이번 비디오에서는 퍼센트 문제 해결에 대한 기초를 배우고 있습니다. 발표자는 퍼센트 문제를 해결하는 데 필요한 세 가지 주요 숫자, 즉 '부분', '총합', 그리고 '퍼센트'를 설명합니다. 이러한 컨셉은 초급자가 수학적 사고를 개선하고, 더 나아가 영어 회화 연습을 위해 필수적인 소양을 기르는 데도 큰 도움이 됩니다. 발표자는 이해를 돕기 위해 실제 예제를 통해 퍼센트의 총합을 찾는 방법을 설명하고 있습니다. 이를 통해 학습자는 문제 해결 능력을 배양하고, IELTS 스피킹과 같은 시험에서도 유리한 점수를 받을 수 있습니다.
일상 대화를 위한 5가지 핵심 구문
- “What is the total?” - 총합이 무엇인지 물어볼 때 유용하게 사용할 수 있습니다.
- “How many are there in all?” - 전체가 몇 개인지 확인할 때 쓰는 표현입니다.
- “If 20% are red, how many marbles do I have?” - 퍼센트를 기반으로 하고 있는 구체적 질문입니다.
- “Let’s check the answer.” - 답을 확인할 때 사용하는 표현입니다.
- “I need to figure out the percentage.” - 퍼센트를 계산해야 할 때 표현하는 방법입니다.
단계별 쉐도우 스피치 가이드
이 비디오의 내용을 습득하는 데 있어 shadow speech 기법이 매우 유익합니다. 다음 단계를 따라 해보세요:
- 듣기: 비디오를 한 번 듣고 전체적인 맥락을 이해합니다.
- 문장 반복: 중요한 구문을 개별적으로 반복해 보세요. 발표자가 말하는 방식을 주의 깊게 따라 하여 shadowspeaks를 연습합니다.
- 예제 활용하기: 비디오 속 문제를 해보며 직접 수치를 계산해 보세요. 문제 해결 과정에서 설명된 절차를 따라 해, 언어적 표현과 수리적 사고를 동시에 발전시킬 수 있습니다.
- 자기 점검: 스스로 문제를 해결한 후, 얼만큼 이해했는지 확인합니다. 이 과정에서 IELTS 스피킹 시험에서 통할 수 있는 표현력을 기를 수 있습니다.
꾸준함이 명확한 이해를 가져다 주므로, 여러 번 반복하며 연습하는 것이 중요합니다. 이러한 방법들은 여러분의 영어 회화 연습뿐만 아니라 총체적인 문제 해결 능력 향상에 크게 기여할 것입니다.
이 영상의 문법
화자가 가장 많이 쓰는 문형을 영상 속 실제 표현과 함께 정리했습니다.
| 문형 | 영상 속 표현 |
|---|---|
| 수동태 be + 과거분사 — 누가 하는지보다 무슨 일이 일어나는지에 초점 | be told · ARE given |
| “will” 미래 will + 동사 — 결정, 약속 또는 예측 | you'll be · you'll need · we'll get |
| 의무: must / have to / need to 어떤 일이 필요하다고 말할 때 | need to figure · need to find · need to include |
쉐도잉이란? 영어 실력을 빠르게 키우는 과학적 방법
쉐도잉(Shadowing)은 원래 전문 통역사 훈련을 위해 개발된 언어 학습 기법으로, 다언어 학자인 Dr. Alexander Arguelles에 의해 대중화된 방법입니다. 핵심 원리는 간단하지만 매우 강력합니다: 원어민의 영어를 들으면서 1~2초의 짧은 지연으로 즉시 소리 내어 따라 말하는 것——마치 '그림자(shadow)'처럼 화자를 따라가는 것입니다. 문법 공부나 수동적인 청취와 달리, 쉐도잉은 뇌와 입 근육이 동시에 실시간으로 영어를 처리하고 재현하도록 훈련합니다. 연구에 따르면 이 방법은 발음 정확도, 억양, 리듬, 연음, 청취력, 말하기 유창성을 크게 향상시킵니다. IELTS 스피킹 준비와 자연스러운 영어 소통을 원하는 분들에게 특히 효과적입니다.