Translation:The pupil is looking for the definition in a dictionary.
I think your version should translate to "sprawdza definicję".
First he is looking for it (searching for it), and when he finally finds it, he looks it up (reads it = checks it).
Hm, I'd rather disagree, because 'look up' does not imply that the action is completed and, from my points of view, there is no real difference between those two sentences (with 'look for' and 'look up') in English. No idea about Polish, of course.
a link to a (rather short) discussion: https://hinative.com/en/questions/45927
Hm, on the other hand, http://www.oxforddictionaries.com/definition/english/look defines 'to look up' as 'to search for and find'.
"Look up" is the whole process. For us, "I'll look it up in the dictionary" and "I'll look for it in the dictionary" are pretty well synonymous. The former is probably more common, the latter might suggest that you're not sure you'll find it in the dictionary - "irregardless", perhaps.
But of course "look for" is of course closer to "szukać.