Question

Round to estimate the sum of all the numbers in 14.

Answer 1

So you want the sum of 1+2+3+....+12+13+14.

Well, there are 14 numbers. Divide them in half at 7, divide them again at 3 1/2 and 10 1/2

so 1/4 of the numbers are closest to zero, 1/2 of the numbers are closest to 7, and 1/4 of the numbers are closest to 14

Sum= 1/4*14*1+1/2*14*7+ 1/4*14*14
= 3.5+49+49=102 about

This is not 3rd grade, I had this method in highschool.

Now here is another method, a college method, call the sum of arithemetic series..

Sum= 14/2 *(1+14)=7*15=105

So the estimate was not far off.