It's important that you remember that "let's" is an imperative form directed to everybody in the situation, therefore it is NOT a question. It proposes an action that includes the speaker and the listener. The meaning of (1a), therefore, is shown in (1b):
(1) a. Let's eat breakfast.
b. I propose that you and I eat breakfast.
This way, the form *Let's eat breakfast? sounds incorrect, since it would be equivalent to saying "Do I propose that you and I eat breakfast?"
Let's is also used in a meaning that is closer to an order or an instruction:
(2) a. Let's bow our heads and be silent to show respect.
b. Let's have a look at your tongue (a medical doctor)
c. OK. It looks like we may have gone too far, so let's take the next exit and and turn around.
d. You all have to draw your superhero. Let's do it, please.
In (2d), the teacher instructs his/her group of children to draw. This use is the one you use a lot in the classroom with your students. It is not meant to be "vamos...?" as used in Portuguese, which is also an order/instruction but made less authoritarian by the use of the rising intonation. "Vamos fazer um desenho?" - clearly, in the classroom context refers to the teacher instructing/giving a command, but the rising intonation used makes it more polite or more inviting. This CANNOT be transfered into English. In English, the simple use of let's (with falling intonation) already constitutes a polite way to frame a command.
In order to make it more inviting or tentative, one can use a tag and rising intonation with let's. This is done by adding ", OK?" after a sentence with let's. An alternative tag form, recognizedly more formal or British sounding can be made with shall at the end.
(3) a. So, let's keep that on, shall we?
b. Let's take turns, ok?
c. Let's not talk about this anymore, shall we/OK?
One can also start the sentence with shall.
(4) a. Shall we go outside now, kids?
b. Shall we talk about this later?
Even though the form with shall sounds a little more formal or slightly British, depending on the context, I still recommend using it in the classroom with our kids to make sure they are exposed to that form in English. Otherwise, the "vamos...? use" will be automatically and incorrectly transfered to English. We should expose our kids to this type of language too.
source consulted: Cowan, R. (2008) The Teacher's Grammar of English. Cambridge.