1. She likes to jump rope as a warm-up.

2. She likes to skip rope as a warm-up.
3. She likes jump rope as a warm-up.
4. She likes jump roping as a warm-up.
5. She likes skip rope as a warm-up.
6. She likes skip roping as a warm-up.

(Which expressions are grammatical?)

I think sentences 1 and 2 are the best. The others sound contrived and unnatural.

To determine which expressions are grammatical, we can analyze each sentence structure individually:

1. She likes to jump rope as a warm-up. (grammatical)
In this sentence, "to jump rope" functions as an infinitive phrase, and it is grammatically correct.

2. She likes to skip rope as a warm-up. (grammatical)
Similar to the previous sentence, "to skip rope" is used as an infinitive phrase, and it is also grammatically correct.

3. She likes jump rope as a warm-up. (not grammatical)
This sentence lacks the verb "to" before the gerund phrase "jump rope." To make it grammatical, it should be rephrased as "She likes jumping rope as a warm-up."

4. She likes jump roping as a warm-up. (grammatical)
This sentence uses the gerund form "jump roping" correctly, making it grammatically sound.

5. She likes skip rope as a warm-up. (not grammatical)
Similar to sentence 3, this sentence lacks the verb "to" before the gerund phrase "skip rope." It should be revised as "She likes skipping rope as a warm-up."

6. She likes skip roping as a warm-up. (grammatical)
This sentence uses the gerund form "skip roping" accurately, making it grammatically correct.

In conclusion, sentences 1, 2, 4, and 6 are grammatical, while sentences 3 and 5 need to be revised to include the proper "to" before the gerunds.