This is a great video on how to get cleaning contracts with schools. Most schools are dealing with labor problems just like all businesses nowadays. This can make them a great target for commercial cleaning, carpet, tile and janitorial services.
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First question is the school public government run school or private, charter school. This question is specific to your area. Most public schools have in house union employees for daily janitorial services.
But, some areas of the country do contract that out. If they do have in house cleaners then the focus would be in specialty cleaning services. Including carpet, hard tile, disinfecting, furniture and floor care.
Private schools are hit and miss. They can contract out everything, one service or multiple services. Best tactic is to first qualify what they hire out for and then rotate services.