Táim trí bliana déag d'aois I am thirteen years of age.

Before looking at the numerical adjectives let us count to ten -- just using the numbers themselves:

1 = a haon, 2 = a dó, 3 = a trí, 4 = a ceathair, 5 = a cúig,

6 = a sé, 7 = a seacht, 8 = a hocht, 9 = a naoi, 10 = a deich.

The pronunciation of these is important. Listen carefully here: [ éist ]
Here's some help with learning them. [ Cluiche ]

Since "bliain" is an irregular word, eisceacht, an exception, let us look first at an ordinary word with the Numerical Adjectives Uimhreacha Aidiachtacha. Let us count cats! Note: here we use the singular of the noun; we lenite séimhiú if possible after 2, 3, 4, 5, & 6 and put an eclipse urú if possible after 7, 8, 9, & 10 as before.

1 = cat, one cat, a cat;
2 = dhá chat two cats;
3 = trí chat, three cats;
4 = ceithre chat, four cats;
5 = cúig chat, five cats ;
6 = sé chat, six cats;
7 = seacht gcat, seven cats;
8 = ocht gcat, eight cats;
9 = naoi gcat, nine cats;
10 = deich gcat, ten cats.

This is worth learning well. Copy them into your Leabhar Nótaí Gaeilge Irish Notebook. As you might expect with a vibrant living language that has been out of "academic" control for hundreds of years there are two conventions in common use. One uses the singular of the noun with the Numerical Adjectives Uimhreacha Aidiachtacha. The other uses the plural.

Ag comhaireamh le "Ceann" Counting with "Ceann"
A common word used with numbers is ceann, or more often in the plural cinn where it roughly means of them,and it always follows the second convention, the plural is used with numerical adjectives. What does ceann mean? Don't ask! There are five columns of meanings and examples of its use in Ó Dónaill's dictionary. Have a look. You'll learn lots of good structures there. Among the meanings are head, end, and one. Not the numeral one but ceann can be used when counting things, plants, or animals, much as we use of them in English. To illustrate let's count the cats again using ceann. I give the long version first then the shorter:

1 = ceann amháin (one cat i.e. one unit of cat!);
2 = dhá cheann de chait (two i.e. two units of cats);
3 = trí cinn de chait (three i.e. three units of cats);
4 = ceithre cinn de chait (four i.e. four units of cats);
5 = cúig cinn de chait (five i.e. five units of cats);
6 = sé cinn de chait (six i.e. six units of cats);
7 = seacht gcinn de chait (seven i.e. seven units of cats);
8 = ocht gcinn de chait (eight i.e. eight units of cats);
9 = naoi gcinn de chait (nine i.e. nine units of cats);
10 = deich gcinn de chait (ten i.e. five units of cats);

That's the long version. The short version is:

1 = ceann amháin (one cat i.e. one unit of cat!);
2 = dhá cheann (two i.e. two units, two of them);
3 = trí cinn (three i.e. three units, three of them);
4 = ceithre cinn (four i.e. four units, four of them);
5 = cúig cinn (five i.e. five units, five of them);
6 = sé cinn (six i.e. six units, six of them);
7 = seacht gcinn (seven i.e. seven units, seven of them);
8 = ocht gcinn (eight i.e. eight units, eight of them);
9 = naoi gcinn (nine i.e. nine units, nine of them);
10 = deich gcinn de chait (ten i.e. ten of them);

Daoine a chomhaireamh Counting People
We don't use ceann with people although some people use cloigne especially in the higher numbers i.e. trí cloigne déag de ghasúir scoile thirteen school children . With people we have this special list of words for 1, 2, 3, etc.

1 = duine (amháin) one person (only)
2 = beirt two people
3 = triúr three people
4 = ceathrar four people
5 = cúigear five people
6 = seisear six people
7 = seachtar seven people
8 = ochtar eight people
9 = naonúr nine people
10 = deichniúr ten people

Each of those is a noun in its own right. Cor beirte is a dance; col ceathrair means cousin; and another dance is cor seisear déag, the sixteen hand reel.

Eisceachtaí Exceptions
There are the few exceptions which we have met above: bliain, a year, cloigeann, a head, (sometimes used counting people), fichead, twenty, seachtain, a week, uair, an hour, a time, and ceann. A special plural of these words is used with numeral adjectives i.e. trí bliana, three years; sé seachtaine, six weeks, ceithre fichid, eighty; cúig uaire, five times, and naoi gcloigne, nine heads of people. Don't we say "nine head of cattle" in English?

To count up to ten using the word bliain a year we use a special plural unique to this word. 1 and 2 lenite; 3, 4, 5, 6, make no initial change to the following word, and 7, 8, 9, and 10 cause an eclipse urú on the initial consonant or vowel of the following word.

1 = bliain / aon bhliain amháin, one year only;
2 = dhá bhliain, two years;
3 = trí bliana, three years;
4 = ceithre bliana, four years;
5 = cúig bliana, five years;
6 = sé bliana, six years;
7 = seacht mbliana, seven years;
8 = ocht mbliana, eight years;
9 = naoi mbliana, nine years;
10 = deich mbliana, ten years.

Here you will see that the noun, bliain, itself on its own means one year or a year. Thus the noun on its own conveys the English indefinite article a year. Later on or elsewhere in these notes you will need to consider whether a noun is definite cinnte or indefinite éiginnte to decide whether lenition séimhiú is needed.

Instead of using just the word bliain for one year many people like to say for emphasis "aon bhliain amháin" which means only one year or one year only but learn to use bliain as one year.

Dhá bhliain, two years, dhá chat, two cats, dhá cheann de chait mhóra, two big cats, is referred to in grammar as An Uimhir Dhéach or The Dual Number and you will find the grammarians have a lot to say about it. No need to go into all that here. If you are interested you know what to look for. Suffice to say dhá is always followed by the singular and the initial consonant is lenited if possible: dhá bhliain; dhá cheann; dhá chat.

Regarding the two conventions associated with the numerical adjectives mentioned above I recommend using the singular for ordinary nouns (other than bliain, ceann, cloigeann, fichead, seachtain, and uair, etc. which have a special plural to use with the numerical adjectives) but if your teacher is using the plural for all nouns that is correct also. I think the Official Standard An Caighdeán Oifigiúil also recommends the singular except as outlined above.