Yes, your teaching, side gig is a source of self-employment and the income does qualify for Sect 199A treatment; it is Qualified Business Income. The tax credit is worth up to 20% of your business income.
You will report your self-employment income and expenses on Schedule C and TurboTax will include it with your Form 1040.
The material participation question is only asking about your involvement with the teaching income. Since you are the one doing the teaching, and assuming you don't have employees, you do 100% of that work (even if it is a small amount of your total income), you want to answer YES to the material participation question.
How do I report income from self-employment?
What self-employed expenses can I deduct?
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