"I work on weekdays."
Hijacking the top comment to explain this for people in the future: はたらく = "to work". かいしゃ= "office". しごと = "job". In English we typically refer to all of these as "work" which is why it get get frustrating to parse them. This is why we we need a をし when we verb しごと. Because it literally saying "I am jobbing..." which is sounds moronic if done directly.
My dictionary lists it as a noun, but does provide a list of conjugations. I've never heard it used as anything but a noun but given my level there's not a lot that i have heard. It is possible that the Duolingo writers want us to use it as a noun exclusively and follow the standard "noun-to-verb conversion" pattern of ['noun' を し-'masu-ending']. It is possible that this is actually an example of noun-to-verb conversion used solely in order to teach verb conversion.
I think this Youtube video from "Japanese From Zero" provides an explanation for anyone confused about する: https://youtu.be/7ecX6VSSNxQ?t=244, I've timestamped the relevant point for this comment but the whole video seems good.
In the dictionary I'm looking at, it lists しごと (仕事) as a "suru verb"-- "する" can be applied directly to the noun "work" to convert it into the verb "to work", and "します" is the masu form of suru, so しごとします seems correct. That being said, 仕事をします isn't incorrect per say as it also means "do work". So I think both should be correct, AFAIK; which you'd actually use would come down to what's more commonly said in Japan.
See my reply to TomosFrate further up the page. As far as I'm aware: in this case there should be no difference, but if the noun isn't a "suru verb" then you would need to say "をします" or "をする". Even then, there would be a preferred way of saying it in Japanese, but it's seemingly case-by-case for each word.
週末 = しゅうまつ = End of the week / weekend
平日 = へいじつ = Regular day / weekday (not weekend or holiday)
Those two are the most common AFAIK, though there are other words with similar meanings. E.g. 週日 = しゅうじつ = Weekdays, including any holidays (possibly including Saturday?) which seems to be less commonly used.