Answer: Gypsum is sometimes used to amend clay soil, but I would suggest you consult with your local county extension as to the best way to amend the soil in your yard for growing a lawn. In general, adding organic matter in generous quantity is the best approach. But they will be most familiar with your local soil and can tell you more specifically the best way to go about it.
You will also want to check the fertiliy and pH to see how much you need to fertilize and if you need to lime. Your extension should be able to help you with the basic soil testing and interpreting the results as well.
The plugging or core aeration will pull up little plugs or cores of the soil, then your top dressing of compost will work down into the holes. This is easier to do than tilling the entire lawn and starting over from scratch so it might be worth a try.
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