1. They made a pose like a model.

2. They made poses like models.
*2-1. They made poses like a model.
*2-2. They made a pose like models.

3. They made a mistake.
4. They made mistakes.

5. They made a card for Mom.
6. They made cards Mom.
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(Can we use all the expressions above? I have written down explanations for each sentence above as follows? Are my explanations plausible?)

1. They made only one pose. All of them made one pose like their favorite model.

2. They made their own poses. Their poses were different.

3. They made only one mistake. They were working together.

4. They made various mistakes.
Each of them made mistakes.

5. They made only one card for Mom.

6. Each of them made a card for Mom.
They made several cards.

Rather than saying/writing "made a pose" you need to simply use the verb form: they posed.

3, 4, 5, and 6 are fine, and so are your explanations for them.

1. They made a pose like a model.

2. They made poses like models.
*2-1. They made poses like a model.
*2-2. They made a pose like models.

3. They made a mistake.
4. They made mistakes.

5. They made a card for Mom.
6. They made cards for Mom.

They posed like models.

3 - 6 are fine.

Your explanations for the sentences are generally plausible, but there are a few clarifications that can be made.

1. They made a pose like a model.
- Your explanation is correct, indicating that they all made one pose resembling a favorite model.

2. They made poses like models.
- Your explanation is partially correct, mentioning that they made their own poses, but it doesn't clarify whether their poses were similar or different. It is possible that they made poses resembling multiple models.

2-1. They made poses like a model.
- This sentence is grammatically incorrect, as the subject "poses" is plural, while the article "a" is singular. It should be "like models" to match the plural subject.

2-2. They made a pose like models.
- This sentence is also grammatically incorrect. It should be "like models" to match the plural subject.

3. They made a mistake.
- Your explanation is correct, stating that they made only one mistake while working together.

4. They made mistakes.
- Your explanation is partially correct, stating that each of them made mistakes. It could also mean that collectively, they made multiple mistakes.

5. They made a card for Mom.
- Your explanation is correct, indicating that they made one card for their mother.

6. They made cards Mom.
- This sentence is grammatically incorrect. It should be "They made cards for Mom" or "They made multiple cards for Mom" to convey that they made several cards for their mother.