(2) Ken looked up her number.
(3) Ken looked up her dress.

A little scrutiny will show that up does not have the same function in both sentences. For example, while we can create a cleft sentence with up her dress, we can't do the same thing with up her number:

(2a) *Up her number is what Ken looked.
(3a) Up her dress is where Ken looked.

Also, we can move up to the end of the first sentence, but not the second:

(2b) Ken looked her number up.
(3b) *Ken looked her dress up.

Both these rearrangements demonstrate that up her dress forms a constituent, but up her number does not.

Additionally, we can replace up her dress with other phrases that indicate direction:

(4) Ken looked across the courtyard.
(5) Ken looked under his bed.
(6) Ken looked away from the accident.

But we cannot do the same thing with up in (2) and still have the verb mean the same thing. In other words, the meaning of looked up as a compositional unit differs from that of looked by itself.

Finally, sentence (3) allows right/straight modification, but sentence (2) does not:

(2c) *Ken looked right up her number.
(3c) Ken looked right up her dress.

All of these differences indicate that up in in (3) behaves like a typical preposition, but in sentence (2) it does not. Words that function in this unusual way are called . A particle forms a one-word phrase that can, but doesn't have to, appear between the verb and the direct object. Historically, most particles derive from prepositions, but their behavior is so different from ordinary prepositions that we will classify them separately. Particles usually combine with the verb to produce a specific idiomatic meaning that is different from a verb and a prepositional phrase.

Because up her number in sentence (2), does not constitute a single constituent, we analyze her number as a direct object, which makes look a transitive verb. Thus we will diagram the sentence like this:

If the particle follows the verb, the diagram looks like this:

These diagrams imply that we consider particles to be separate constituents within the verb phrase. Some grammar books call verb + particle combinations "multiword verbs." That name implies that the particle is actually part of the verb. We won't use that terminology—the particle isn't actually part of the verb. The fact that it can appear after the direct object demonstrates that. But we still must be able to distinguish verbs with particles from free combinations of verbs and prepositional phrases. Fortunately, the test is relatively straightforward. If the sentence can be transformed so that the word appears after the object, it's a particle:

(7a) The bank turned down the Johnsons
(7b) The bank turned the Johnsons down.

Notice that if the object is an unstressed pronoun, the particle cannot appear between the verb and the direct object. In this case, it must come after the object:

(7c) The bank turned them down
(7d) *The bank turned down them.

If you can create a cleft sentence by moving the word along with the noun phrase, then it's a prepositional phrase:

(8a) I put my socks in the drawer.
(8b) In the drawer is where I put my socks.

This test, though, is not definitive. If you can move the phrase, it is a PP, but some verbs are followed by prepositional phrases that cannot be moved:

(9a) Jane disposed of the remaining objections.
(9b) *It was of the remaining objections that Jane disposed.

We continue to call of the remaining objections a prepositional phrase because of cannot be moved like true particles:

(9c) *Jane disposed the remaining objections of.