<p>^ As an aside, I remember by 3rd grader indignantly showing us her grade for a homework.
[mom] Your teacher marked it wrong because you were supposed to estimate the answer
[DD] Why would I put down a wrong answer when I can work it out in my head??</p>
<p>The next year she got into the advanced math taught by the Principal who had a math PhD. In that she learned all kinds of shortcuts and tricks to check calculations.</p>