Welcome to the second unit, Objects, Math, School, and Telling Time. This title is pretty self-explanatory, so I won't go into much detail. In this unit, we will cover correct naming of objects based on distance, telling time from both a 12-hour and 24-hour time system, typical school life in Japan, and basic Japanese Math vocabulary. Please be aware that vocabulary from Unit 1 may well be used in this and following Units, so I hope you studied!!
Objects
When identifying objects, it is important to keep distance in mind. How far you are from an object is important. The distance the person(s) you are speaking to is/are from the object must also be taken into consideration. This is also true in English, so don't think that I am teaching new material. For instance, you wouldn't say, "That is my glass." if you were holding the glass at the time; you would say, "This is my glass."
Objects that are close to you are identified with kore, which means "this". Objects that are a distance from you (not close, but not far away, either) are labeled as sore, or "that". This also applies to objects that are not close to you,but are close to whoever you are talking to. Finally, objects that are far away from both you and the person(s) you are speaking with are labeled as are, which basically means "that (far away) thing over there". The uses of these words is shown below, using the below diagram (sorry for the ridiculous nature of the diagram):

Mark-san: Kore wa ore no BOORU desu. *points to Object 1*
Mark: This is my ball.
Sayoko-san: Sou desu ka? Jaa, sore wa? *points to Object 2*
Sayoko: Is that right? Then, how about that?
Mark-san: Iie, sore wa ore no BOORU dewa arimasen. Are wa dare desu ka? *points at Object 3*
Mark: No, that is not my ball. Who's that over there?
Sayoko-san: Are wa Tateishi-san desu.
Sayoko: That's Tateishi-san (over there).
Differing from kore, sore, areand dore, kono, sono, ano and dono cannot be used alone. While you can say, Kore wa nan desu ka, you cannot say Kono wa nan desu ka. This is because the -ono's, as I will call them, show possession. In other words, while one uses kore to mean "this", one uses kono to mean "this (something)". The same goes for the other object words.
Example of difference between kore and kono, with the object in possession underlined:
Mark-san: Kore wa ore no hon desu.
Mark: This is my book.
Mark-san: Kono hon wa ore no desu.
Mark: This book is mine.
So, you can see that when using an -ono word, you have to be specific about what you're talking about. You need to add a specific object after the -ono word. This rule does not apply for slang, however (We'll get into slang later on).
Math (and Numbers)
Before we get into anything else, something that I would like to make known is that one does not add an "s" to the end of a word to make it plural. There are no "s"'s in Japanese. This is why you call one Pikachu "Pikachu" and call forty Pikachus "Pikachu" as well. You might be confused now because I used the word "Pikachus" in the last sentence. This is because English does have "s"'s. While you say "kimonos" in English, you would say "kimono" in Japanese no matter how many kimonos there are. Other words in a conversation should tip one off about whether a person is talking about one or several items.
Now let's get into Math. I'm not going to cover very much material in this unit because I don't think it is very relevant to being able to converse in Japanese. Unless you are a mathmetician, scientist, or other type of professional and you really want to be able to discuss mathematical terms with Japanese people, I don't think that it is really necessary to fully delve into the realm of Math in Japanese right now. Math terms are very easy to memorize if you speak English: MAINESU means "minus" and PURASU means "plus." So, 1 + 1 = 2 in Japanese is ichi PURASU ichi wa ni desu, and 2 - 1 = 1 in Japanese is ni MAINASU ichi wa ichi desu. Not very hard, is it? Now I'll teach you how to count in Japanese.
The way that I was taught the numbers one to ten in Japanese was to simply say the words one after the next. The sequence has a rhythm to it and some people find it easy to remember if they say it out loud. One to ten in Japanese is: Ichi, ni, san, yon, go, roku, shichi, hachi, kyuu, jyuu. Say it over and over, emphasizing each word*, and you'll probably notice the rhythm. I may put up a .wav of this later.
*The way to say this is something like this: "Ichi, nii, sann, yonn, go, roku, shichi, hachi, kyuu, jyuu."
After ten, things get pretty simple. If you can remember one through ten, there's not much more to learn in regards to Japanese numbers. The way to say numbers greater than ten is different than in English (i.e: the order of the words is different), though. Eleven is made up of the words "ten" and "one," so you would say Jyuuichi. This is also sometimes written Jyuu-ichi to make the word clearer. This order is the same throughout the numbering system: Multiple of ten, multiple of one. So, twelve is "ten-two," Jyuu-ni, and fifteen is "ten-five," Jyuu-roku.
Now for multiples of ten: When you want to say "twenty," thirty," etc., you have a new word order. This one is: Number of tens, ten. In other words, twenty is "two-ten(s)," ni-jyuu, and sixty is "six-ten(s)," roku-jyuu. When you say twenty-five, simply combine the two previous orders: Number of tens, ten, multiple of one. Therefore twenty-five is "two-ten(s)-(and) five," or ni-jyuu-go. Similarly, forty-two is "four-ten(s)-(and) two," or yon-jyuu-ni.
In Japanese there is sometimes more than one way to say a number. This can be somewhat confusing. The word for "four," yon, can also be pronounced shi, which means "death." This is a very unlucky number in Japanese, and Japanese people tend to be very superstitious about it. Therefore yon is used to make it more pleasant. This is also the reason why there are no Room 4's in Japanese hospitals, and why there are sometimes no 4th Floor buttons in Japanese elevators. Seems weird, but it's the superstition of many Asian cultures. Another number that can be said two different ways is nine, or kyuu. Depending on the context, one might use either kyuu or ku. Also another word for "seven" or shichi is nana.
The word for "hundred" is "hyaku," the word for "thousand" is sen, and the word for "ten thousand" is man. In Japanese (as well as Chinese), there is a specific "ten thousand" unit. They do not say "one hundred thousand" like we do in English. Rather, they say, "ten ten thousand(s)." Sound a little weird, but that's how it works. One million, then, is "one hundred ten thousand(s)." So 1,000 is ichi-sen, 10,000 is ichi-man, 100,000 is jyuu-man, and 1,000,000 is hyaku-man.

School
Telling Time