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One of the difficulties in teaching order of  operations to students is that one of the most often used shortcuts actually causes student confusion.  Most students know that they should use PEMDAS when deciding what math operation to do first.  The problem with PEMDAS is that often students think that multiplication has to come before division and addition before subtraction. Instead, teach students to think of the operations as "levels." Just like on an elevator, you have to do one level before you can get to the next.  Be sure to start at the bottom - just like the first floor of a building.