Lessons · Teaching · estimation, and catching your own wrong answer
Estimation, and catching your own wrong answer
Before working a question out, decide roughly what the answer should be. Afterwards, check it against that estimate and against the units. Almost every arithmetic error is an order of magnitude out, a sign flipped, or an answer in the wrong kind of unit, and all three are visible to an estimate.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
In beta. This lesson was written for Hone and has not yet been checked by a state certification officer. Practice material, not professional advice. What that means.
What it is for
You cannot mark your own work by redoing it, because you will make the same mistake the same way. An estimate is an independent second opinion, and it is the habit that separates candidates who get the marks they deserve from candidates who lose two or three to slips.
How to think about it
Round every number to one significant figure and do the sum in your head first. Write the estimate down. Then work exactly, and compare. If the exact answer is not near the estimate, one of the two is wrong and you now know to look. Check the unit last, because it is free.
Worked example
812 / 4: estimate 800 / 4 = 200, so an answer of 23 is caught immediatelyThe estimate costs three seconds and saves the mark.
18 per cent of 52: estimate 20 per cent of 50 = 10, so expect about 9The exact answer is 9.36, which is close enough to the estimate to trust.
An answer of 1.5 children, or a negative length, is wrong whatever the arithmetic saidSense-checking against the situation catches what estimation does not.
On CBEST there is no calculator, so estimation is not a check, it is a methodSeveral questions are answerable from the estimate alone once the options are seen.
Your turn
Name what to round each number to for a quick estimate.
Round each number to one figure
Solve one, graded on the server
The trap
Checking by redoing the same calculation the same way. You will repeat the mistake and gain confidence in it. The check has to be a different route to the same place, which is what an estimate is.