werten
to evaluate
To judge or assess the value, quality, or significance of something or someone.
Die Lehrerin muss die Aufsätze aller Schüler fair werten.
The teacher has to evaluate all the students' essays fairly.

to evaluate
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to evaluate
To judge or assess the value, quality, or significance of something or someone.
Die Lehrerin muss die Aufsätze aller Schüler fair werten.
The teacher has to evaluate all the students' essays fairly.

The verb 'werten' (to evaluate) is derived directly from the noun 'der Wert' (value). So it literally means assigning a value to a thing or an action.
Es ist schwer, die Arbeit von Künstlern objektiv zu werten.
It is difficult to evaluate artists' work objectively.
In the meaning 'interpretieren' (to interpret), 'werten' (to interpret) is almost always used with the preposition 'als' (as). The fixed structure is: 'etwas als etwas werten' (to interpret something as something).
Er wertete ihre Nachricht als klares Zeichen des Interesses.
He interpreted her message as a clear sign of interest.
To specify the type of assessment, 'werten' (to evaluate) is often combined with adverbs such as 'positiv' (positively), 'negativ' (negatively), 'hoch' (highly), or 'niedrig' (low).
Die Kritiker werteten den neuen Film überwiegend positiv.
The critics evaluated the new film mostly positively.
The verb 'werten' (to evaluate/score) is very often used in the context of sports, competitions, or exams when a performance is judged according to fixed criteria.
Im Eiskunstlauf werden die Sprünge und die Choreografie getrennt gewertet.
In figure skating, the jumps and the choreography are scored separately.
to estimate / appreciate
'schätzen' and 'werten' can both mean that you form a judgment about something. 'schätzen' is often used when you do not know an exact number and say approximately how large, expensive, or much something is. It can also mean that you guess something. 'werten' more often means that you judge the quality, significance, or effect of something, or understand something as a sign of something else. Learners may confuse the words because both have to do with assessment. For approximate numbers, 'schätzen' usually fits. For an evaluation or interpretation, 'werten' is more appropriate.

Nach der Besprechung wertet Moritz die lange Pause als schlechtes Zeichen.
After the meeting, Moritz interprets the long pause as a bad sign.
Meine Mutter schätzt im Supermarkt, dass der Einkauf etwa vierzig Euro kostet.
At the supermarket, my mother estimates that the groceries will cost about forty euros.