And it scales with multiplication too. 9*7 is (7-1) and whatever adds to 9, so 63. This breaks down for larger numbers, but works really well up to 9*10. I don’t know what “common core” teaches for that, but you can’t change the 9 to a 10 for multiplication (well, you could, but you’d need to subtract 7 from the answer).
Treating 9s special makes math a lot easier. Doing the “adjust numbers until they’re multiples of 10” works for more, but it’s also more mental effort. 9s show up a lot, so learning tricks to deal with them specifically is nice. I just memorized the rest instead of doing “common core” math to adjust things all the time.
That said, I do the rounding thing for large numbers. If I’m working with lots of digits, I’ll round to some clean multiple of 10 that divides by 3 (or whatever operation I need to do) nicely. For example, my kid and I were doing some mental math in the car converting fractional miles to feet (in this case 2/3 miles to feet). I used yards in a mile (1760) because it’s close to a nice multiple of three (1800), and did the math quickly in my head (1800 - 40 yards -> 6002 yards - 40 yards to ft * 2/3 -> 1200 yards - 120 ft2/3 -> 3600 ft - 80 ft -> 3520 ft). I calculated both parts of the rounding differently to make them divisible cleanly by 3. I don’t know what common core math teaches, but I certainly didn’t learn this in school, I just came up with it by combining a few tricks I learned largely on my own (i.e. if the digits add to 3, it’s divisible by 3) through years of trying to get faster at math drills. If I wasn’t driving, I would have done long division in my head, but I needed to be able to pause at stop signs to check for traffic and whatnot, and just remembering two numbers w/ units is much easier than remembering the current state of long division.
I was very competitive in school like this, wanted to finish things first. I think maybe you make a good point about wanting to solve things faster leading to these types of tricks developing. Sort of puts math competitions in a new light.
And it scales with multiplication too.
9*7is(7-1) and whatever adds to 9, so 63. This breaks down for larger numbers, but works really well up to9*10. I don’t know what “common core” teaches for that, but you can’t change the 9 to a 10 for multiplication (well, you could, but you’d need to subtract 7 from the answer).Treating 9s special makes math a lot easier. Doing the “adjust numbers until they’re multiples of 10” works for more, but it’s also more mental effort. 9s show up a lot, so learning tricks to deal with them specifically is nice. I just memorized the rest instead of doing “common core” math to adjust things all the time.
That said, I do the rounding thing for large numbers. If I’m working with lots of digits, I’ll round to some clean multiple of 10 that divides by 3 (or whatever operation I need to do) nicely. For example, my kid and I were doing some mental math in the car converting fractional miles to feet (in this case 2/3 miles to feet). I used yards in a mile (1760) because it’s close to a nice multiple of three (1800), and did the math quickly in my head (1800 - 40 yards -> 6002 yards - 40 yards to ft * 2/3 -> 1200 yards - 120 ft2/3 -> 3600 ft - 80 ft -> 3520 ft). I calculated both parts of the rounding differently to make them divisible cleanly by 3. I don’t know what common core math teaches, but I certainly didn’t learn this in school, I just came up with it by combining a few tricks I learned largely on my own (i.e. if the digits add to 3, it’s divisible by 3) through years of trying to get faster at math drills. If I wasn’t driving, I would have done long division in my head, but I needed to be able to pause at stop signs to check for traffic and whatnot, and just remembering two numbers w/ units is much easier than remembering the current state of long division.
I was very competitive in school like this, wanted to finish things first. I think maybe you make a good point about wanting to solve things faster leading to these types of tricks developing. Sort of puts math competitions in a new light.