So, I'm currently putting together a lesson about the Aztecs for high schoolers, but there's some gaps about the economic situation of the empire that the books I'm using don't address. The claim that I've often seen repeated is that the Aztec farmer had to give away what he did not consume himself to the ruler/state. This prompts the following questions (if it is true):
what did the ruler/state do with these resources? Distribute them to the nobles? Supply armies? Save for times of famine?
what did commoners who didn't farm but were craftsmen give?
How did this interact with markets? We know the market at Tlatelolco was very busy with all kinds of products, including farmers selling their produce. Was a certain amount of the produce that the farmers could keep meant to be traded away?
Can I ask what sources are telling you that " the Aztec farmer had to give away what he did not consume himself to the ruler/state?" Because this does not jibe with what I know about the agricultural economy of the Aztecs.
Land was owned semi-communally under the Nahua system, with the land technically belonging to a particular calpulli (neighborhood). Working that land, however, gave de facto ownership of the land and its products to the family residing on and farming the soil. Surpluses, or even specifically grown cash crops, would be sold at regular (every 5 days) markets.
There was also a system of taxation in place, which could include households or calpultin rendering up a portion of their harvest. Again though, this did not mean any surplus was obligated to state granaries, and did not preclude personal storehouses. A Mexica superstition around the New Fire ceremony, in fact, involves women being hidden away in granaries for a portion of the night, lest they transform into ravaging monsters.
Michael Smith's "The Aztecs Paid Taxes, Not Tribute" is a concise overview of the tax system. Hirth's The Aztec Economic World is a much more comprehensive look at your question. Kellogg's Law and the Transformation of Aztec Society might also be helpful, as it spends a lot of time looking at how Indigenous land ownership was litigated in Spanish courts.