シャドーイング練習: Math Antics - Percents Missing Total - 動画で英語スピーキングを学ぶ
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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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このレッスンについて
このレッスンでは、パーセントを用いた数学の問題を解く方法に焦点を当てます。特に「合計」が不明な場合の問題の解き方を学びます。問題の中で与えられた「パート」と「パーセント」を使用して、未知の「合計」を導き出す工程を理解することが目標です。このレッスンを通じて、英語を使った数学の表現に親しむこともでき、英語のスピーキング能力を高める助けとなります。
重要な語彙とフレーズ
- パート (part): 具体的な数値の一部を示す。
- 合計 (total): 完全な数量を示す。
- パーセント (percent): 百分率を示す数値。
- 全て (altogether): 合計と同じ意味を持つ表現。
- 計算する (to calculate): 数値を操作する行為。
- 確認する (to check): 答えが正しいかどうか確かめること。
- 数学の問題 (math problem): 数学に関する課題。
- 練習問題 (practice problems): 学習のための問題。
練習のコツ
このレッスンにおける数理的なプロセスをマスターするためには、何度も繰り返し練習することが重要です。shadow speechの技術を活用しいることで、スピーチのスピードやトーンに慣れる助けになります。特にYouTubeで英語学習動画を観ながら、発音やリズムに注意を払いながら声に出してみてください。声に出して練習することで、英語の発音を良くすることができます。
練習する際には、まずは動画の音声に合わせて声を重ねることから始め、次第に自分自身で考えながら解答してみましょう。このプロセスを繰り返すことで、IELTS スピーキング対策にも効果が期待できます。確かな理解を得るために、解き終わった後は自分の答えを確認し、どの部分が間違っていたのかを見直すことも大切です。
この動画の文法
話し手がよく使っている文型を、動画の実際の表現とともに紹介します。
| 文型 | 動画での表現 |
|---|---|
| 受動態 be + 過去分詞 — 誰がするかより、何が起きるかに焦点を当てる | be told · ARE given |
| 「will」の未来表現 will + 動詞 — その場の決定、約束、予測 | you'll be · you'll need · we'll get |
| 義務：must / have to / need to 何かが必要であることを伝える | need to figure · need to find · need to include |
シャドーイングとは？英語上達に効果的な理由
シャドーイング（Shadowing）は、もともとプロの通訳者養成プログラムで開発された言語学習法で、多言語習得者として知られるDr. Alexander Arguelles によって広く普及されました。方法はシンプルですが非常に効果的：ネイティブスピーカーの英語を聞きながら、1〜2秒の遅延で声に出してすぐに繰り返す——まるで「影（shadow）」のように話者を追いかけます。文法ドリルや受動的なリスニングと異なり、シャドーイングは脳と口の筋肉が同時にリアルタイムで英語を処理・再現することを強制します。研究により、発音精度、抑揚、リズム、連音、リスニング力、そして会話の流暢さが大幅に向上することが確認されています。IELTSスピーキング対策や自然な英語コミュニケーションを目指す方に特におすすめです。