Is it correct to say "times" in this context?
Solution 1:
In Standard English, this usage of the word times is considered an error. It is often used by children and students when speaking of multiplication, for exactly the reason that you indicate: the formula X times Y equals Z has spawned the creation of a verb to times meaning to multiply.
However, using this in any kind of formal context is considered an error, and I have only ever encountered this usage from children. I would avoid it in writing altogether, and discourage students from using it.
Solution 2:
Most dictionaries will tell you times is a preposition, though it is closer to an interposition, which some might call a conjunction. It could be seen as a noun with "ten times four" meaning "four, ten times", or by parsing "Learn your three times table." Alternatively, twice is seen as an adverb.
Personally I would accept times as a verb if that is how somebody wanted to use it, for example if they said "Times the decimal fraction by 100 to get a percentage", though I would more often use multiply in that context.
Solution 3:
When I was a child in primary school, anyone using "times" as a verb would be corrected by the teacher. The modern fashion is not to correct children's mistakes as it stresses them, or lowers their self esteem. So what once were considered errors become common usage, and rabble-pandering "authorities" like OED eventuallt accept this misuse of language as correct. You multiply two numbers together: you do not "times" them
Solution 4:
Times comes from the idea of repetition!
Q. The pirate put five coins into the bag. If he did this ten times then how many coins would the bag contain?
A. The bag contains ten times five coins (fifty)
Mathematically, times belongs between two numbers (and belongs to the first one if you see what I mean)
Hearing "You times that number by that other number" makes me want to vomit!
Junior math(s) teachers will often say "times means multiply", but the two are not always interchangeable.