Please see my comment above. I'm new here and typed my response in the wrong location.

Use "amount of" before uncountable nouns such as "Homework, water, money,..." a substantial amount of money use "a great deal of..." before uncountable nouns "A great deal of effort" "Big effort" is not wrong but informal. Use Number before countable nouns such as " people, animals, pens,..." A large number of people rushed into the street....... or " The number of people interested in Facebook is increasing"

I would not split hairs over this question. You could go a life time without using the expression "a great deal." As in Spanish, there are regional differences as well as age differences in the frequency of expressions. I have rarely used the term "a great deal." I typically say " a lot of" or as you said perfectly "they put a big effort". In the USA, what you said would not be a "big deal." :)

When they used "great deal" it was meant to add more emphasis on the amount of work that was done. When you're talking about quantity you want to use the number.