Big children means big problems.

[Clark]

Is the sentence grammatically correct?

"Means" - 3 person singular, as I understand it as an elliptical sentence : "Having big children means having big problems".

Is "big" lexically OK here?

[David L.]

"Having big children means having big problems".
...is fine, to achieve the humourous effect.

But what do you mean by "Means" - 3 person singular,?

[Clark]

By 3rd person singular I mean that verbs in the present simple tense take the suffix -s/es in that person:
I take
You take
He, she, it takes

As 'children' in my original sentence (Big children - big problems) is used in the plural I thought I should justify the agreement with the form 'means'.

[hanky]

By 3rd person singular I mean that verbs in the present simple tense take the suffix -s/es in that person:
I take
You take
He, she, it takes

As 'children' in my original sentence (Big children - big problems) is used in the plural I thought I should justify the agreement with the form 'means'.

the subject of your sentence is "having ..." and it is singular.

ex: having many replies means you are lucky.

[philadelphia]

the subject of your sentence is "having ..." and it is singular.

ex: having many replies means you are lucky.

Firstly, I am unfortunately not a teacher and I agree with what Hanky and David have typed thus far

That being said, it is the fact of having big children, which means having big problems(, which means...). This is not an academic sentence, but I find it useful to make someone understand better

[David L.]

That being said, it is the fact of having big children, which means having big problems(, which means...). This is not an academic sentence, but I find it useful to make someone understand better

I for one am not sure how this either disagrees with or clarifies what Hanky has posted.

In one construction, 'that' not 'which' should be used, which means rephrasing:
We need big children to grow into adults to look after us in our old age. It is the fact of having big children in your home that means one will have big problems in life, so put them up for adoption as soon as they are starting to grow out of the cute and lovable stage.

or something akin to

Having big children causes me big problems, which means I suffer constant stress.