It’s not that 人 becomes plural (Japanese largely doesn’t distinguish between singular and plural) it’s that 一人 and 二人 are exceptions – after that, it’s にん all the way. さんにん, よにん, ごにん, ろくにん. 七人 can be read as both しちにん and ななにん, because 七 is a weird one in that its readings are fairly interchangeable, though at least in the case of counting people, しちにん tends to be a bit more common.

Joel is correct the first 2 counters are exceptions to the rule.

Mostly there are 2 different counting systems in Japan one is the traditional counting system, and the second is the Chinese counting system imported along with Kanji.

So 一人 and　二人　use the traditional Japanese counting system. Where as the rest use the Chinese counting System.

The Japanese counting system is used for small items such as food or beverages in a restaurant, pub or my personal favorite festival food booths.

一つ　(ひとつ）、　二つ　（ふたつ）、　三つ　（みっつ）、　
四つ　（よっつ）,　五つ　（いつつ）　、 六つ　（むっつ）、　
七つ　（ななつ）、　八つ　（やっつ）、　九つ　（ここのつ）、　
十　（とお）。

I’m only covering the counters through ten. For further study [1].

[1]
http://en.wikipedia.org/wiki/Japanese_numerals

I know your question has already been answered but now you know why they are exceptions to the rule.
　

• This reply was modified 9 years, 8 months ago by  Devon Lazzari.
• This reply was modified 9 years, 8 months ago by  Devon Lazzari.
• This reply was modified 9 years, 8 months ago by  Devon Lazzari.

七 is a weird one in that its readings tend to be fairly interchangeable. I have heard ななにん used for 七人, but I think しちにん is more common.

That said, 七人 is not seven “things” but seven people. When he says “things” he means generic items without a specific counter word. これを七つください = “seven of these, please” uses ななつ.

That said, 七 tends to veer towards なな rather than しち when attached to counter words – 人 just happens to be one of the ones that goes the other way more often than not. Your children would be 七歳 = ななさい = seven years old.