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First the weather has to be warm and dry (ever mown the grass in the rain?)
The combine harvester both cuts and threshes the wheat. During threshing, the grain is separated from the stalk and chaff and collected in a tank, which is periodically emptied into a grain truck. The leftover bits are dropped back onto the field among the 'little standing up stalks'.
Then a baling machine comes along and gathers the stalks into straw bales, which are used mostly for animal bedding. (Hay is grown in its own right, rather than a by-product, and is more nutritious than wheat stalks, which become straw.)
Finally the last bits of stalk are tilled back into the ground.... and the 'short standing-up stalks' (stubble) are now 'lying down'.
The wheat crop was the most obvious, as it was being currently worked on, but we have also been driving, walking and riding bikes through fields of corn, rye and oats. Today we picked a sample of each of the cereal crops and then went home and looked in our cupboards for things that were made from these plants.