Learn how to solve math problems
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| INTRODUCTION |
| John: Hi everyone, and welcome back to DanishClass101.com. This is Intermediate Season 1 Lesson 24 - Doing the Math in Denmark. John here. |
| Nana: Hej I'm Nana. |
| John: In this lesson, you’ll learn how to solve math problems. The conversation takes place in a classroom. |
| Nana: It's between Carsten and Mia. |
| John: The speakers are a teacher and student. Okay, let's listen to the conversation. |
| DIALOGUE |
| Carsten: Mia, kan du reducere følgende stykke? Hvis du starter med at læse udtrykket igennem. |
| Mia: Okay. 3 + (8 - 2x) - (x + 3y) + 4y - 5. |
| Carsten: Godt. Hvad vil du gøre først? |
| Mia: Først vil jeg ophæve de to parenteser. Den første kan jeg ophæve med det samme. |
| Carsten: Og hvorfor kan du det? |
| Mia: Fordi det er en plusparentes. Så skal jeg ikke gøre noget. |
| Carsten: Ja, og hvad så med den anden parentes? |
| Mia: Der skifter alle fortegnene, fordi det er en minusparentes. Så plusset bliver til et minus. |
| Carsten: Ja, og hvad står der så nu? |
| Mia: 3 + 8 - 2x - x - 3y + 4y - 5. Og så skal jeg sortere leddene, ikke? |
| Carsten: Præcis! Tallene for sig, leddene med x for sig og leddene med y for sig. |
| Mia: Okay, så det vil sige 3 + 8 - 5 - 2x - x - 3y + 4y. |
| Carsten: Ja, så nu skal du bare lægge de forskellige ting sammen. |
| John: Listen to the conversation with the English translation. |
| Carsten: Mia, kan du reducere følgende stykke? Hvis du starter med at læse udtrykket igennem. |
| Carsten: Mia, can you reduce the following problem? If you would start by reading through the expression. |
| Mia: Okay. 3 + (8 - 2x) - (x + 3y) + 4y - 5. |
| Mia: Okay. 3 + (8 - 2x) - (x + 3y) + 4y - 5. |
| Carsten: Godt. Hvad vil du gøre først? |
| Carsten: Good. What will you do first? |
| Mia: Først vil jeg ophæve de to parenteser. Den første kan jeg ophæve med det samme. |
| Mia: First, I will remove the two parentheses. I can remove the first one straight away. |
| Carsten: Og hvorfor kan du det? |
| Carsten: And why can you do that? |
| Mia: Fordi det er en plusparentes. Så skal jeg ikke gøre noget. |
| Mia: Because it is preceded by a plus sign. Then I don't have to do anything. |
| Carsten: Ja, og hvad så med den anden parentes? |
| Carsten: Yes, and what about the other parenthesis then? |
| Mia: Der skifter alle fortegnene, fordi det er en minusparentes. Så plusset bliver til et minus. |
| Mia: All the signs change because it is preceded by a minus sign. So the plus sign becomes a minus sign. |
| Carsten: Ja, og hvad står der så nu? |
| Carsten: Yes, so what does it say now? |
| Mia: 3 + 8 - 2x - x - 3y + 4y - 5. Og så skal jeg sortere leddene, ikke? |
| Mia: 3 + 8 - 2x - x - 3y + 4y - 5. And then I'm going to sort the terms, right? |
| Carsten: Præcis! Tallene for sig, leddene med x for sig og leddene med y for sig. |
| Carsten: Exactly! The numbers for themselves, the terms with x for themselves, and the terms with y for themselves. |
| Mia: Okay, så det vil sige 3 + 8 - 5 - 2x - x - 3y + 4y. |
| Mia: Okay, so that means 3 + 8 - 5 - 2x - x - 3y + 4y. |
| Carsten: Ja, så nu skal du bare lægge de forskellige ting sammen. |
| Carsten: Yes, so now you only have to add the different things. |
| POST CONVERSATION BANTER |
| John: I think I’m having a nightmare. |
| Nana: Why? |
| John: I just heard some math equations... |
| Nana: Math isn’t that bad! Don’t overreact! |
| John: I thought I was learning Danish, not math! |
| Nana: You can learn both! There have been many famous Danish mathematicians. |
| John: Like who? |
| Nana: Harald Bohr. His greatest contribution was his theory on almost periodic functions, dating back to 1925. |
| John: Anyone else? |
| Nana: Bohr published a textbook with fellow mathematician Johannes Mollerup on mathematical analysis. The Bohr-Mollerup theorem, characterizing the gamma function, is named after the two. |
| John: I think I remember that one from my college days. |
| Nana: There is also Johan Jensen, who contributed the Jensen's inequality and Jensen's formula. Both form important statements. |
| John: Okay, so maybe we can learn both at the same time. But now onto the vocab! |
| VOCAB LIST |
| John: Let’s take a look at the vocabulary from this lesson. The first word is... |
| Nana: reducere [natural native speed] |
| John: to reduce |
| Nana: reducere [slowly - broken down by syllable] |
| Nana: reducere [natural native speed] |
| John: Next we have... |
| Nana: stykke [natural native speed] |
| John: piece, slice, problem (math) |
| Nana: stykke [slowly - broken down by syllable] |
| Nana: stykke [natural native speed] |
| John: Next we have... |
| Nana: udtryk [natural native speed] |
| John: expression, look, phrase, term |
| Nana: udtryk [slowly - broken down by syllable] |
| Nana: udtryk [natural native speed] |
| John: Next we have... |
| Nana: ophæve [natural native speed] |
| John: to remove, to lift, to abolish, to annul, to cancel |
| Nana: ophæve [slowly - broken down by syllable] |
| Nana: ophæve [natural native speed] |
| John: Next we have... |
| Nana: plusparentes [natural native speed] |
| John: parenthesis preceded by a plus sign |
| Nana: plusparentes [slowly - broken down by syllable] |
| Nana: plusparentes [natural native speed] |
| John: Next we have... |
| Nana: fortegn [natural native speed] |
| John: preceding sign |
| Nana: fortegn [slowly - broken down by syllable] |
| Nana: fortegn [natural native speed] |
| John: Next we have... |
| Nana: minusparentes [natural native speed] |
| John: parenthesis preceded by a minus sign |
| Nana: minusparentes [slowly - broken down by syllable] |
| Nana: minusparentes [natural native speed] |
| John: Next we have... |
| Nana: sortere [natural native speed] |
| John: to sort, to sort out |
| Nana: sortere slowly - broken down by syllable] |
| Nana: sortere [natural native speed] |
| John: Next we have... |
| Nana: led [natural native speed] |
| John: term, link, joint, gate |
| Nana: led [slowly - broken down by syllable] |
| Nana: led [natural native speed] |
| John: And last... |
| Nana: sig [natural native speed] |
| John: himself, herself, itself, oneself, themselves |
| Nana: sig [slowly - broken down by syllable] |
| Nana: sig [natural native speed] |
| KEY VOCAB AND PHRASES |
| John: Let's have a closer look at the usage of some of the words and phrases from this lesson. The first phrase is... |
| Nana: følgende stykke |
| John: meaning "following problem." Shall we break down this expression? |
| Nana: Let’s. The first word is følgende, |
| John: an adjective meaning "following." |
| Nana: And the second word is stykke, |
| John: In this case, it means "problem," as in a mathematical problem. How’s this phrase used? |
| Nana: Although there’s no definite article introducing the phrase, the English equivalent is "the following problem.” |
| John: So it’s used when talking about math problems. |
| Nana: Sometimes the definite article det will be present, but the meaning stays the same. Remember det as a definite article means "the." |
| John: Can you give us an example using this phrase? |
| Nana: Sure. For example, you can say, Vi fandt fejl i følgende stykker. |
| John: ...which means "We found errors in the following problems." |
| John: Okay, what's the next phrase? |
| Nana: ophæve parentes |
| John: Meaning "to remove parenthesis." What can you tell us about this phrase.? |
| Nana: This phrase consists of the regular verb ophæve, |
| John: which has several meanings such as "to abolish," |
| Nana: and the common gender noun parentes, which means "parenthesis." |
| John: The meaning of this one is pretty easy to figure out. And, it’s another one that you’ll hear when talking about math. |
| Nana: Yes. The verb ophæve is sometimes used interchangeably with the very similar regular verb hæve. Hæve also has several meanings. |
| John: Can you give us an example using the original phrase? |
| Nana: Sure. For example, you can say, De er klar til at ophæve parenteserne. |
| John: ...which means "They are ready to remove the parentheses." |
| John: Okay, what's the next phrase? |
| Nana: for sig |
| John: Meaning "for oneself, separately." What can you tell us about this phrase? |
| Nana: The first word for is the preposition "for." The second word, sig, is a pronoun that covers “himself.” “herself,” “oneself.” things like that. |
| John: This is used when talking about how something is separate from something else. |
| Nana: If you put a noun in front of the phrase, you can show what is separate. |
| John: That’s easy. |
| Nana: Also, when talking about the way of sorting something, the pronoun hver is added at the front of the phrase. |
| John: Can you give us an example using the phrase? |
| Nana: Sure. For example, you can say, Arkene er i en bunke for sig. |
| John: ...which means "The sheets are in a pile for themselves." |
| John: Okay, now onto the lesson focus. |
Lesson focus |
|---|
| John: In this lesson, you'll learn about solving math problems. |
| Enter Lesson Focus section here. |
| John: Back to math? |
| Nana: First, let’s look at the present tense and future tense. |
| John: In Danish, it’s very common to use the present tense as the future tense as well. The present tense is often used with adverbs of time that refer to the future. |
| Nana: It’s also used in subordinate clauses of time that begin with the conjunction når, which means “when,” or the conjunction hvis, which means “if. |
| John: How do we conjugate verbs into present tense? |
| Nana: You usually add -r to the infinitive verb. But, there are some irregular verbs. |
| John: There is a table of these in the lesson notes. But first, let’s look at some sample sentence. |
| Nana: Læreren kommer senere i dag. |
| John: “The teacher will come later today.” |
| Nana: De laver lektierne, hvis de får tidligere fri end normalt. |
| John: “They will do the homework, if they finish school earlier than usual.” |
| Nana: In the last lesson, we talked about the modal verb skulle. It can also be an auxiliary verb when used with another verb in infinitive form. |
| John: How do you use this verb in future tense? |
| Nana: When conjugating skulle in present tense, you can use it with a verb in infinitive form to express the future tense. |
| John: Again, let’s see some examples. |
| Nana: Han skal forberede opgaverne. |
| John: “He is going to prepare the exercises.” |
| Nana: Jeg skal have kage som belønning senere. |
| John: “I am going to have cake as a reward later.” |
| Nana: You can also use ville with a verb in infinitive form to make the future tense. |
| John: It differs from the previous pattern, because you express what you think will happen. You’re predicting the future. Can we have an example? |
| Nana: Eleverne vil feste efter eksamenen. |
| John: “The students will party after the exam.” |
| Nana: Hendes lærer vil være på kontoret klokken 11. |
| John: “Her teacher will be at the office at 11 AM.” |
Outro |
| John: Okay, that’s all for this lesson. Thank you for listening everyone, and we’ll see you next time! Bye! |
| Nana: Hej hej! |
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