One actor: a purpose infinitive
An um ... zu group has no separately expressed subject. In the introductory pattern, the person doing the main action also performs the intended action.
Nora fährt zum Markt, um Gemüse zu kaufen.
Nora goes to the market to buy vegetables.
Another actor: damit
A finite purpose clause can name its own subject. That lets you distinguish the person taking an action from the person expected to benefit or do something afterwards.
Nora liest laut, damit Ben sie hört.
Nora reads aloud so that Ben hears her.
The same subject can also use damit
Do not treat damit as forbidden when both subjects match. A shared subject often allows a shorter infinitive alternative, but the finite version is still possible.
Nora notiert den Termin, damit sie ihn nicht vergisst.
Nora notes the appointment so that she does not forget it.
Watch the verb form at the end
Use an infinitive in the um ... zu group and a conjugated verb in the damit clause. With a modal in the latter, the action infinitive precedes the finite modal.
Nora schickt den Plan, damit wir früher anfangen können.
Nora sends the plan so that we can start earlier.
A goal is not a guaranteed result
A purpose states what someone intends to achieve. A reason clause instead gives grounds for the action. Weil der Kurs bald beginnt is a reason; um besser Deutsch zu sprechen describes a goal.
Nora übt, um sicherer zu sprechen.
Nora practises in order to speak more confidently.
Practise this pattern
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References
Original teaching prose and examples, informed by these grammar references. A2 placement is an editorial curriculum choice, not a CEFR certification.