As I was wrapping up my previous post on skip counting, I realized there was something I wanted to emphasize about mental math, particularly the math of mental addition.
When my sons were counting those seats in the movie theater  where the middle section had rows of 8 seats and the side sections had rows of 6 seats  they came up with a total of something like 96 seats in the middle section, with 72 seats on the left and another 66 seats on the right. Because of an enrichment book we were using on mental math, they had learned that with mental addition, it's easier to add the larger place value numbers first. In other words, while pencilandpaper addition is done righttoleft (starting with the ones place, then the tens place, then the hundreds place, etc.), mental addition is much easier when done lefttoright (starting in this case with the tens place first, then the ones place afterward).
So their mental addition in this situation (96 + 72 + 66) was, "90 + 70 is 160, then 160 + 60 is 220, then 220 plus the 6 [from the 96] is 226, then the 226 plus the 2 [from the 72] is 228, then the 228 plus the 6 [from the 66] is 234."
Another quick example: 347 + 225. The mental math would be like this, "300 + 200 is 500 [hold that number mentally for a moment]; then 40 + 20 is 60, so now we're at 500 + 60 which is 560 [hold that number mentally for a moment]; then 7 + 5 is 12, so now we're at 560 + 12, which is 572."
The point here is that with mental addition, it's easier  far easier  to start with the largest place value on the left and work rightward to the smallest place value. This process is easier to track mentally, since the bigger place value sums are numbers that always end in at least one zero.
Also, this process more closely approximates estimation. Using the above example, if the exact, precise sum is not all that important, then after adding the hundreds (for a total of 500) and then the tens (for a subtotal of 60), one might just stop at that point and say, "Okay, so there's 560 plus a few more, so about maybe 570..." This is because in estimation, the larger place value places (the hundreds, or the thousands) are the digits that dominate the eventual sum.
Hope this helps!
Bob Hazen
mental addition: DON'T start with the ones place!!!
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I noticed my 2nd grade daughter is just starting to learn this method. Unknowingly, I already taught her the way I learned (ones, then tens, etc.) while she was in 1st grade. She is comfortable w/ my method and she is resisting this "backward" method (as she calls it). Hopefully she will start buying into this method since it seems much easier!
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