What it means
ましょうか is a polite way to suggest doing something together or to offer to do something for someone. It is formed with a verb stem followed by ましょうか. The familiar equivalent uses the plain volitional form followed by か. Depending on the context, it can mean “Shall we...?” or “Shall I...?”.
Usage note
The context determines whether the suggestion includes the listener or is an offer by the speaker to help. Do not confuse ましょうか with a simple question about the listener’s intention, such as “Will you...?”.
How to use it
映画を見に行きましょうか。
Shall we go watch a movie?
映画を見に行こうか。
Shall we go watch a movie?
Example sentences
荷物が重そうですね。私が持ちましょうか。
Your luggage looks heavy. Shall I carry it?
駅まで一緒に歩きましょうか。
Shall we walk to the station together?
昼休みに公園でお弁当を食べましょうか。
Shall we eat our boxed lunches in the park during lunch break?
窓を開けましょうか。
Shall I open the window?