لم يأخذ المتطوع القفازات المطاطية.

Because لم is the normal MSA particle for negating a past action.

After لم, Arabic uses the imperfect verb form, but that verb takes jussive mood and the whole expression has a past meaning.

So:

• أخذَ = he took
• لم يأخذْ = he did not take

This is very common in Arabic, even though it feels unusual to English speakers at first.

It becomes jussive.

The regular form is:

• يأخذُ = he takes / he is taking

After لم, it becomes:

• يأخذْ

In normal unvoweled Arabic writing, both are spelled the same way, so you usually do not see the change unless the text is fully vocalized.

So grammatically, the sentence contains:

• لم + imperfect jussive

That is the standard pattern for did not ... in MSA.

In this sentence, word order helps a lot.

Arabic very often uses verb–subject–object order:

• لم يأخذ = did not take
• المتطوع = the volunteer → subject
• القفازات المطاطية = the rubber gloves → object

So the first noun after the verb is normally understood as the subject, and the next noun phrase is the object.

If the sentence were fully vocalized, the case endings would also show this clearly:

• المتطوعُ = nominative, so it is the subject
• القفازاتِ = accusative, so it is the direct object

In Arabic, adjectives normally come after the noun they describe.

So Arabic says:

• القفازات المطاطية

not the equivalent of the rubber gloves with the adjective first.

Also, adjectives in Arabic match the noun in definiteness. Since القفازات is definite, the adjective must also be definite:

• القفازات المطاطية = the rubber gloves

Compare:

• قفازات مطاطية = rubber gloves / some rubber gloves

So the repeated الـ is completely normal.

Because non-human plurals in MSA usually take feminine singular adjectives and pronouns. This is a very important rule.

So even though القفازات is plural, it is non-human, so the adjective is:

• المطاطية = feminine singular

This is called deflected agreement.

So:

• القفازات المطاطية is correct

A human plural would usually take a true plural adjective, but non-human plurals usually do not.

Because القفازات is a sound feminine plural in form.

For this type of plural, the case endings work like this:

• nominative: -اتُ
• accusative: -اتِ
• genitive: -اتِ

So even though القفازات is the direct object of the verb and therefore accusative, its ending is still -اتِ, not a regular fatḥa.

That means the fully vocalized object would be:

• القفازاتِ

This is one of the forms English-speaking learners often need time to get used to.

They both negate the verb, but they refer to different time frames.

• لم يأخذ = he did not take → past
• لا يأخذ = he does not take / he is not taking → present or habitual

So in this sentence, لم is specifically telling you that the action did not happen in the past.

Yes, that is also correct.

The original sentence:

• لم يأخذ المتطوع القفازات المطاطية

uses the common verb-first order.

If you say:

• المتطوع لم يأخذ القفازات المطاطية

you are putting more focus on the volunteer as the topic.

Both are grammatical. The difference is mainly one of style, emphasis, and information structure, not basic meaning.

المتطوع is an active participle meaning the volunteer or the person who volunteers.

It comes from the verb:

• تطوّعَ = to volunteer

From that verb, Arabic forms:

• مُتَطَوِّع = volunteer / volunteering person

Then with الـ:

• المتطوع = the volunteer

So this word is not just a random noun to memorize; it belongs to a very common word-formation pattern in Arabic.