跟讀練習: Math Antics - Percents Missing Total - 通過影片學習英語口語
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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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上下文與背景
在這段影片中，主持人歡迎觀眾來到數學課堂，討論關於百分比的問題。這一課主要關注在解決含有缺失總量的百分比問題。通過具體的例子，如朋友的彈珠袋和高中樂隊的情況，講解思路使得複雜的數學概念變得易於理解。掌握這些概念不僅可以幫助觀眾解決數學難題，還能提升他們的邏輯思維能力。
日常溝通的五個關鍵短語
- 總計 (altogether)
- 部分 (part)
- 百分比 (percent)
- 全部 (total)
- 如何解決 (how to figure out)
逐步跟讀指南
在學習如何解決缺失總量的百分比問題時，您可以遵循以下步驟，這將有助於您提高英語口語能力，特別是通過shadow speech技術來增強語言的流暢性：
- 收聽與理解: 觀看影片時，務必全神貫注，試圖理解每個數學概念如何關聯到實際問題。
- 分段跟讀: 使用shadow speak技巧，暫停影片，模仿影片中的語調與節奏，臨摹彼此的表達方式。
- 分析問題: 在影片講解後，練習分解相似的數學題，嘗試自己找出總量。在這種情況下可以使用shadowspeak技巧來反覆練習。
- 重複與自主練習: 反覆觀看這個影片並嘗試解答類似的問題，以加深理解。同時，可使用看YouTube學英語的方式學習更多相關內容。
- 自我檢查: 最後核對您的答案是否正確，習得解決問題的思維方式，掌握數學與語言的結合。
通過這樣有條理的學習方式，不僅可以提高數學能力，還能在口語表達上獲得質的提升，成為更加自信的英語學習者。提升您的技能，歡迎您訪問相關的shadowing site，獲取更多資源！
影片中的語法
說話人最常用的結構，並附上影片中的原話：
| 結構 | 影片中的用法 |
|---|---|
| 被動語態 be + 過去分詞 — 強調發生了什麼，而不是誰做的 | be told · ARE given |
| “will” 表將來 will + 動詞 — 決定、承諾或預測 | you'll be · you'll need · we'll get |
| 義務：must / have to / need to 表示某事是必要的 | need to figure · need to find · need to include |
什麼是跟讀法？
跟讀法 (Shadowing) 是一種有科學依據的語言學習技巧，最初開發用於專業口譯員的培訓，並由多語言者Alexander Arguelles博士普及。這個方法簡單而強大：您在聽英語母語原聲的同時立即大聲重複——就像是一個延遲1-2秒緊跟說話者的影子。與被動聽力或語法練習不同，跟讀法強迫您的大腦和口腔肌肉同時處理並模模擬實的講話模式。研究表明它能顯著提高發音準確性，語調，節奏，連讀，聽力理解和口語流利度——使其成為雅思口語備考和真實英語交流最有效的方法之一。