Translation:There are three tables.
@Crazy_plant_lady: I'm familiar with the rule, though like many "rules" in English, this one has many exceptions.
Firstly, 三わ would always be pronounced "san wa"; your teacher probably told you that 三
羽 would be pronounced "sam ba".
However, that wasn't the main problem; it's whether the pronunciation of 羽 changes from わ to ば. I did a little further research into this and it looks like 三羽 is generally pronounced "san wa", though technically it's supposed to be "sam ba" and in certain set phrases, such as 三羽烏, it's always pronounced "sam ba". Source1, source2, source3.
I confirmed this with my partner (a native Japanese speaker) by asking her to read "三羽" without giving her any context about it, and she said "san wa".
@Joshua: my Japanese sensei told us it would be pronounced "samba", the same way えんぴつ would be pronounced empitsu or the way that しんぶん is pronounced shimbun. In Japanese, the ん is pronounced as m when followed by b, p or wa. The closest equivalent to this rule I can find is the grammatical rule of shondhi in the Bengali language (an Indian language) but I don't think there is a similar rule in English, so I can't provide an example of it which would be familiar to an English speaker, but this is a grammatical rule in Japanese.
Good suggestions, but 一口 isn't really a counter. It's a phrase meaning "a mouthful, a small bite/sip of food/drink". You would count how many 一口's ("up to three mouthfuls" = 一口を三回まで), rather than increment the 一.
Also, you're right about 一箱, but when the counter is paired with 三, you get 三箱 (sanhako) so つ and 日 are still the only counters that use the irregular pronunciation for 三.
There should have been tips to this lesson to teach people about counters and introduce native numbers.
To clarify further, in Japanese, you use counters with everything. Different things have different counters, such as small round objects, machines, etc. Think of it the way we sometimes say in English "Five heads of cattle" or "three strands of hair" except Japanese use it all the time.
It's acceptable if you don't know or want to use the specific counter, to just use native Japanese numbers from 1 to 10 (hitotsu, futatsu, mittsu...) without a counter (they don't go above 10). Those are different from the previously taught Sino-Japanese numbers (ichi, ni, san...). You can't do that however with counting money, time, or people.
The native Japanese numbers that are used in this lesson are as follows (expressed as hiragana (romaji) kanji):
Number- Sino-Japanese / native
1- いち (ichi) 一 / ひとつ (hitotsu) 一つ
2- に (ni) 二 / ふたつ (futatsu) 二つ
3- さん (san) 三 / みっつ (mittsu) 三つ
4- し、よん (shi, yon) 四 / よっつ (yottsu) 四つ
5- ご (go) 五 / いつつ (itsutsu) 五つ
6- ろく (roku) 六 / むっつ (muttsu) 六つ
7- しち、なな (shichi, nana) 七 / ななつ (nanatsu) 七つ
8- はち (hachi) 八 / やっつ (yattsu) 八つ
9- く、きゅう (ku, kyuu) 九 / ここのつ (kokonotsu) 九つ
10- じゅう (juu) 十 / とう (tou) 十
Hope this helps.
Anything that has to do with quantity goes right before the verb, for example: 公園に多い木があります (kouen ni ooi ki ga arimasu) (= in the park there are many trees) is WRONG The CORRECT sentence is: 公園に木が多いあります。(kouen ni ki ga ooi arimasu) Similarly, if you want to say I bought three apples: ''mittsu ringo wo kaimashita'' it's wrong ''ringo wo mittsu kaimashita'' would be the correct one.
There is no ichi or itsu in this sentence...
teeburu ga mitsu arimasu
(tables) (subject) (three of them) (exist)
三 "san" is read with its native Japanese reading "mi" when used with the counter つ
If you're thinking of ー that is the katakana long vowel mark, not the kanji for one 一 which would be "ichi"
Yes, ～つ (and all other counters) are cardinal numbers, as in one, two, three.
Ordinal numbers, e.g. first, second, third, are a bit trickier. You can use the suffix 番 (ばん) instead. The pronunciation is actually very regular for these: 一番 (いちばん), 二番 (にばん), 三番 (さんばん), etc.
Or you can also use the suffix 目 (め), but this is simply attached to the end of your counter 三つ目 (みっつめ the third thing).
Here 三つあります is used. They are not simply interchangeable.
In Japanese, there is a class of words called "counters" which are used when counting (duh) or enumerating things. Each counter is specific to one or more types of things, for example 羽【わ】is specifically used when counting birds (or rabbits), while 匹【ひき】is specifically for small animals.
There are many, many different counters, and while it's a good idea to learn as many common ones as you can, Japanese makes things a little easier for you by providing a "generic counter" which you can use if you don't know the specific counter for something or there isn't a commonly used specific option for an object. That "generic counter" is つ (the specific counter for tables is actually 台【だい】).