Since Ms. Cole's sixth-level math class has 40 students and four times as many students in her fourth-level class, there are 4*40 = <<4*40=160>>160 in her fourth-level math class.

For the two levels, Ms. Cole teaches math to 160+40 = <<160+40=200>>200 students.

If the number of students in her seventh-level math class is twice that in the fourth-level math class, then she teaches 2*160 = <<2*160=320>>320 students in the seventh-level math class.

Ms. Cole teaches 320+200 = <<320+200=520>>520 math students in the school.

# Answer

520
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Ms. Cole teaches math in three levels of classes in her school. There are four times as many students in Ms. Cole's fourth-level math class as in her sixth-level math class. The number of students in her seventh-level math class is twice that in the fourth-level math class.  If Ms. Cole's sixth-level class has 40 students, how many math students does Ms. Cole teach?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
520
Ms. Cole teaches math in three levels of classes in her school. There are four times as many students in Ms. Cole's fourth-level math class as in her sixth-level math class. The number of students in her seventh-level math class is twice that in the fourth-level math class.  If Ms. Cole's sixth-level class has 40 students, how many math students does Ms. Cole teach?
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