to notice / remark
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to notice
To be able to recognize a certain state (such as tiredness, joy, nervousness) from someone's appearance, behavior, or voice.
Man hat ihr die Nervosität vor der Prüfung deutlich angemerkt.
You could clearly notice her nervousness before the exam.
'Anmerken' (to notice / remark) is a separable verb. In a main clause, the prefix 'an' stands at the end. In subordinate clauses or in the infinitive with 'zu', the verb stays together.
Man merkt ihm seine schlechte Laune sofort an.
You can immediately notice his bad mood.
In this meaning, the verb has a fixed structure: the person in whom something is noticed is always in the dative. What is noticed is in the accusative.
Ich habe meiner Kollegin die Müdigkeit nicht angemerkt.
I did not notice my colleague's tiredness.
When making a comment, 'anmerken' (to remark) is often used with a 'dass' clause or a direct object (the comment).
Ich möchte anmerken, dass wir im Zeitplan liegen.
I would like to remark that we are on schedule.
The phrase 'Ich möchte anmerken, dass...' (I would like to remark that...) is often used in formal contexts such as meetings, discussions, or written language to introduce a thought.
Der Redner merkte an, dass die bisherigen Ergebnisse unzureichend seien.
The speaker remarked that the results so far were insufficient.
to recognize / realize
'erkennen' and 'anmerken' can both mean that you notice something from outward signs. 'erkennen' is more general: you can recognize or identify a person, a thing, a problem, or a state. 'jemandem etwas anmerken' is used especially with people. You see or hear from their behavior, voice, or face how they are doing. Typical examples are noticing someone's tiredness, joy, or nervousness. 'erkennen' describes more the act of perceiving or understanding itself, while 'anmerken' emphasizes the visible or audible signs in a person.
Wegen seiner leisen Stimme merkt man ihm die Unsicherheit an.
Because of his quiet voice, you can tell that he feels unsure.
Am Gesicht der Mutter erkennt das Kind sofort, dass etwas nicht stimmt.
From his mother's face, the child immediately recognizes that something is wrong.