the difference between showing and checking

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So we had a quiz in math a couple of days ago and I had gotten none of the questions wrong on the quiz. I was very angered to find out that I had been marked down 5 points for not checking my work and it bumped the grade from a 100 to an 83. I went on to say that I did check the answers in my head just to make sure that they were right. He then proceeded to tell me that I didn't have the work written down. I then said that checking and showing are to very different things and that checking means the way for you to make sure that the answer is right. He is still refusing to give me full credit on my quiz. Aren't I correct though on the difereence between checking and showing?

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If your teacher wants you to show your work, show your work. Your teacher can't read what's in your head, only what's on your paper.