"Say" is transitive in this context, so you need to include an object: Students tend to say things off the top of their heads. And the the second one also needs an adverb of frequency to sound natural: Students sometimes say things off the cuff. Students often say things off the cuff.

I agree with the others. If you don't want to include a direct object you can use TALK instead of SAY.

Neither of these phrases sound natural in this context. The common expressions you're looking for are: 1. Off the top of their heads – This means saying something without giving it much thought, or quickly giving an answer based on what they immediately remember. * Example: "Students tend to speak off the top of their heads." 2. Off the cuff – This also means speaking without preparation or planning, often spontaneously. * Example: "Students speak off the cuff." Both phrases mean saying something without thinking deeply, but "off the top of their heads" is more common in casual contexts like with students.

You're right about what they mean, but they don't sound natural at all. Here's how I would say it: Students tend to speak spontaneously, saying whatever they think off the top of their heads. This "off the top of one's head" idiom is MUCH more common than the "off the cuff" idiom. So I would comfortably use the first one, but I would personally avoid using the second one, because less people will be familiar with it, so less people will understand it. I've only ever seen it used in hyper-formal contexts, by people who are kind of out-of-touch with the common working-class folks these days. Regarding singular vs plural... We could say "off the tops of their heads". We could say "off the top of their head". We could say "off the top of their heads" as I have done here. All three options are grammatically acceptable - the grammar is flexible enough for you to pick whichever way you prefer to say it. The way I've chosen considers what's most commonly said as well as what's most easily understood.