“It’s 5,050!”: Seeing the patterns in the numbers – and using them
The teacher wanted to keep a class of third-graders busy. The instructor assigned the kids a problem that seemed guaranteed to keep them grinding away for the hour: adding up all the numbers from 1 to 100.
After a few minutes, little Karl Frederich Gauss raised his hand.
The teacher recognized the kid.
“It’s 5,050!” the eager child exclaimed.
Gauss would distinguish himself as a brilliant mathematician when he grew up. How did he figure this problem out so quickly when but a wee lad?
What is 1 + 100? 101. What is 2 + 99? 101. What is 3 + 98? 101. There are 50 pairs of 101. 50 X 100 = 5,000. 50 X 1 = 50 and together they add up to 5,050.
While his classmates were adding 1 + 2 + 3 + 4 . . . young Gauss apprehended the patterns in the numbers. Much of mathematics – and much of what makes mathematics so interesting and enjoyable – is the understanding of the patterns in numbers and the relationships between numbers.
I myself have been extremely math-phobic and math-challenged throughout most of my life. One of the reasons I’ve been at such odds with this subject is that somehow – I don’t know how – I got the idea early on that figuring a problem out in anything other than a standard manner was somehow “cheating.”
However, the truth is that learning how to see the relationships between numbers is what makes math fascinating and can make it doable for many people for whom it has often been endlessly frustrating. For example, one easy way to multiply a number by 11 is first to multiply by 10 and then add the original number. One easy way to multiply by 9 is to multiply by 10 and then subtract the original number. An easy way to multiply by 5 is to multiply by 10 and divide it in half.
One of the most important things to know about math problems is that they can often be performed in two easy steps rather than one difficult one. This is also a key to finding this subject enjoyable.
Readers, what are some others?
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amfortas said,
Yep, math-phobic.
Or maybe scared of nothing (as in 0s)
July 21, 2008 at 1:47 am
Denise Noe said,
5 X 100 = 5,000.
Yep, math-phobic.
Or maybe scared of nothing (as in 0s)
(Denise) Thank you for pointing that out, editor amfortas. I corrected it to 50 X 100 = 5,000.
July 21, 2008 at 2:45 am