Spotlight on Checking Your Work
Since Math grades are dependent on exams, it is extremely beneficial to check one's work. Taking a test is a learning opportunity that goes beyond the content --identifying and correcting errors strengthens thinking processes and attention to detail.
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Casting Out Nines
Learning how to check work in elementary school can help students later when studying Algebra -- both the actual process of checking and the development of a mindset for self-reflection.
Checking multiplication can involve long division or we can use Casting Out Nines -- a technique that compares the sum of the digits
in the alleged answer with the product of the sum of the digits in the problem.
Wikipedia on Casting Out Nines = Sanity Check
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Brain Teaser
Solve for a, b, c, d, and e.
a (b + c + d + e) = 128
b (a + c + d + e) = 155
c (a + b + d + e) = 203
d (a + b + c + e) = 243
e (a + b + c + d) = 275
Answer to January's Brain Teaser:
First, solve a simpler problem. To add the consecutive numbers 1- 10, sum the smallest(1) with the largest(10) and then 2 + 9 and so on. You will end up with 5 pairs of 11 and 5 x 11 = 55.
There are 5000 even numbers 2 through 10000. So there are 2500 pairs of 10002 -- 2500 x 10002 = 25005000. |
