How would you translate
I'm planning to do that next week
Ich habe vor, das nächste Woche zu machen.
Does it sound strange to put "das" after the comma?
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That's perfect. It's actually a quite common mistake among native speakers to misspell the das as dass in a situation like this. But no, it doesn't sound strange at all.
Technically it's not wrong but I'd say it sounds a bit stiff.
The sentence may be affected by the previous one as the context could determine which part of the sentence should get more focus.
Take a look at these examples
Das plane ich, nächste Woche zu machen. (focus on action, you may not be sure if you will get around to it)
Nächste Woche habe ich vor, das zu machen. (focus on time when talking about several future plans)
Das nehme ich mir nächste Woche vor. (action focus, more natural and a tiny bit ambitious)
The translation is fine but it feels a bit clunky to me. I think I would leave out the whole machen-part all together because it doesn't add any information. It is just grammatical filler.
Ich habe mir das für nächte Woche vorgenommen.
Das steht nächste Woche an/auf dem Plan/auf meiner Agenda.
Or the more straight forward way using "wollen"
Das will/wollte ich nächste Woche machen.
Note, that the use of past in this situation does not mean that you don't plan that anymore. There is the same phrasing in English.
The dishes? Oh I was planning on doing those next week.