7 ms·

I've been using a less strict version of this method to multiply in my head since I was a kid. Nice to know there's a name for it. You can also take advantage

I've been using a less strict version of this method to multiply in my head since I was a kid. Nice to know there's a name for it. You can also take advantage of multiples of 5 and 10. For example: 115 x 37 = (100 + 10 + 5) x 37 = 3700 + 370 + 370/2 = 3700 + 370 + 300/2 + 70/2 = 3700 + 370 + 150 + 35 = 4255

ricardobeat 9y ago
That's exactly how I do multiplication in my head! I wonder why school never taught something like this, I find the standard right-to-left-and-carry-over method impossible to keep track of without paper.
- pbhjpbhj 9y ago
  They teach this method in my kids UK school, I'm pretty sure it's part of the standard curriculum.
  - ricardobeat 9y ago
    Wouldn't that be the 'grid multiplication' method? https://en.m.wikipedia.org/wiki/Grid_method_multiplication https://en.m.wikipedia.org/wiki/Grid_method_multiplication
lancebeet 9y ago
In this case I would do 115 x 37 = 115 x (40-3) = 460 x 10 - 3 x 115 = 4600 - 345 = 4255 Since 15 x 3 and 15 x 4 are trivial calculations the only caveat is the subtraction which isn't too bad.
smallnamespace 9y ago
Somewhat surprisingly, this is how Common Core arithmetic is taught nowadays. Some parents are making a fuss because 'that's not how they learned arithmetic' [1], but actually anyone who is good with mental math uses these sort of tricks, particularly taking advantage of commutativity and distributivity. In fact this builds far stronger intuition for the properties of numbers and is a good way to prepare for algebra and proof-based approaches later on. Same sort of mental shortcuts for two-digit squaring: 52² = (50 + 2)² = (5 ⋅ 10)² + 2 * (50 ⋅ 2) + 4² = 5² ⋅ 10² + 200 + 4 = 2500 + 200 + 4 = 2604 [1] https://www.salon.com/2015/11/28/youre_wrong_about_common_core_math_sorry_parents_but_it_makes_more_sense_than_you_think/ https://www.salon.com/2015/11/28/youre_wrong_about_common_co...
- romwell 9y ago
  >Somewhat surprisingly ..to people who learn about Common Core from the rants of the parents who don't get it, quite sadly.
  - Xeoncross 9y ago
    I disliked Common Core from the homework children brought to me. Looked nothing like the good example above GP showed.
    - fjsolwmv 9y ago
      You disliked Pearson worksheets. That's different from Common Core.
  - pdx 9y ago
    I don't like Common Core because it attempts to solve a problem that does not exist. The way we learned math was sufficient to enable us to build atomic bombs and go to the moon, all with slide rules for the most part. It has a proven history of working and working well. The math shown in this article as well as much common core does not provide the user/student with understanding. Instead, they are taught incantations and rituals to get to an answer. This is a recipe for a society of math illiterates. Who is pushing this and why do they want such a society? Common Core is not a better system than the one taught for a hundred years in this country. If you disagree, I would love to see the evidence. I'm sure before such a huge change was made to our educational system, there must be MOUNTAINS of such evidence that was presented. No? Not really?
    - chiaro 9y ago
      gf is an English teacher. This is some of the research underpinning the instructional changes in CCSS for English specifically: Bonfiglio, C. M., Daly, E. J., Persampieri, M., & Andersen, M. (2006). An experimental analysis of the effects of reading interventions in a small group reading instruction context. Journal of Behavioral Education, 15, 93- 109. Burns, M. K. (2007). Reading at the instructional level with children identified as learning disabled: Potential implications for Response-to-Intervention. School Psychology Quarterly, 22, 297-313. Burns, M. K., Dean, V. J., & Foley, S. (2004). Preteaching unknown key words with incremental rehearsal to improve reading fluency and comprehension with children identified as reading disabled. Journal of School Psychology, 42, 303–314. Carney, J.J., Anderson, D., Blackburn, C., & Blessing, D. (1984). Preteaching vocabulary and the comprehension of social studies materials by elementary school children. Social Education, 48(3), 195-196. Daly, E., & Martens, B. (1994). A comparison of three interventions for increasing oral reading performance: Application of the instructional hierarchy. Journal of Applied Behavior Analysis, 27,459-469. Eckert, T. L., Ardoin, S. P., Daisey, D. M., & Scarola, M. D. (2000). Empirically evaluating the effectiveness of reading interventions: The use of brief experimental analysis and single-case designs. Psychology in the Schools, 37, 463-474. Faulkner, H. J., & Levy, B. A. (1999). Fluent and nonfluent forms of transfer in reading: Words and their message. Psychonomic Bulletin and Review, 6, 111-116. Gickling, E. E., & Armstrong, D. L. (1978). Levels of instructional difficulty as related to on-task behavior, task completion, and comprehension. Journal of Learning Disabilities, 11,559-566. Hall, K. M., Sabey, B. L., & McClellan, M. (2005). Expository text comprehension: Helping primary-grade teachers use expository texts to full advantage. Reading Psychology, 26,211-234. Levy, B. A., Nicholls, A., & Kohen, D. (1993). Repeated readings: Process benefits for good and poor readers. Journal of Experimental Child Psychology, 56, 303-327. McComas, J. J., Wacker, D. P. & Cooper, L. J. (1996). Experimental analysis of academic performance in an academic setting. Journal of Behavioral Education, 6,191-201. Neill, K. (1979). Turn kids on with repeated reading. Teaching Exceptional Children, 12, 63-64. O’Shea, L. J., Sindelar, P. T., & O’Shea, D. J. (1985). The effects of repeated readings and attentional cues on reading fluency and comprehension. Journal of Reading Behavior, 17, 129-142. Pany, D., & McCoy, K. M. (1988). Effects of corrective feedback on word accuracy and reading comprehension of readers with learning disabilities. Journal of Learning Disabilities, 21, 546-550. Rasinski, T. V. (1990). Effects of repeated reading and listening-while-reading on reading fluency. Journal of Educational Research, 83, 147-150. Reitsma, P. (1988). Reading practice for beginners: Effects of guided reading, reading-while-listening, and independent reading with computer-based speech feedback. Reading Research Quarterly, 23, 219-235. Rose, T. L., & Beattie, J. R. (1986). Relative effects of teacher-directed and taped previewing on oral reading. Learning Disability Quarterly, 9, 193-199. Sanford, A. K., & Horner, R. H. (2013). Effects of matching instruction difficulty to students with escapemaintained problem behavior. Journal of Positive Behavior Interventions, 15, 79-89. Sindelar, P. T., Monda, L. E., & O’Shea, L. J. (1990). Effects of repeated readings on instructional- and masterylevel readers. Journal of Educational Research, 83, 220-226. Smith, D. D. (1979). The improvement of children’s oral reading through the use of teacher modeling. Journal of Learning Disabilities, 12 (3), 39-42. Stoddard, K., Valcante, G., Sindelar, P., O’Shea, L., & Algozzine, B. (1993). Increasing reading rate and comprehension: The effects of repeated readings, sentence segmentation, and intonation training. Reading Research and Instruction, 32, 53-65. Taylor, N. E., Wade, M. R., & Yekovich, F. R. (1985). The effects of text manipulation and multiple reading strategies on the reading performance of good and poor readers. Reading Research Quarterly, 20, 566-574. Turpie, J. J., & Paratore, J. R. (1995). Using repeated reading to promote success in a heterogeneously grouped first grade. In K. A. Hinchman, D.J. Leu, & C.K. Kinzer (Eds.), Perspectives on literacy research and practice: Forty-fourth yearbook of the National Reading Conference (pp. 255-263). Chicago: The National Reading Conference. VanWagenen, M. A., Williams, R. L., & McLaughlin, T. F. (1994). Use of assisted reading to improve reading rate, word accuracy, and comprehension with ESL Spanish-speaking students. Perceptual and Motor Skills, 79, 227-230. Weinstein, G., & Cooke, N. L. (1992). The effects of two repeated reading interventions on generalization of fluency. Learning Disability Quarterly, 15, 21–28. Wixson, K.K. (1986). Vocabulary instruction and children’s comprehension of basal stories. Reading Research Quarterly, 21(3), 317-329.
infodroid 9y ago
> ... using a less strict version... Nice to know there's a name for it. Using distributivity for creative simplification of a hard multiplication problem is a useful skill... It's a mental shortcut, like Russian Peasant Multiplication. But it isn't the same as, or just a "less strict" version of it. The latter is an algorithm, and relies on binary arithmetic and the "simple" operations of doubling, halving, and summation.
xster 9y ago
ya, surprised too. I always thought this is just how everyone informally does multiplications in their head.
knowThySelfx 9y ago
Divide and conquer, in a way :D
reacweb 9y ago
I do it quite differently, because I am good at operations, but I have a bad memory. 37 x 110 -> 4070 (mentally I visualize 3700+370 . This is not fully obvious because of the carry), then I try to remember this number so that I can add 185 (when I see 37x5, I see 18.5x10 without other intermediate step) to it and remember the result. The "normal" way is 30 x 115 -> 3450 (easy because I can see 3x15->45, so it is as if there was no carry), then 7 x 115 -> 805 (not obvious because of 2 carries), then I have forgotten the 3450, I recompute it while trying to remember 805. For me, the aim of all these tricks is to cope with a bad memory.
- reacweb 9y ago
  I also likes the table of 37, but this works better for smaller numbers. This gives: 37 x 115 -> 37 x 3 + (114 / 3) + 37. I know that 37x3=111. With some efforts, I can see that 114 / 3 -> 38. I am still memory free to perform the difficult 111x38 -> 3800+380+38 = 4180+38 = 4218 that I pain to remember to add 37. In this case, the table of 37 is not very effective.
underwoodley 9y ago
This is a pretty standard way of doing mental multiplication. The interesting thing about the method in the article is that it involves binary not base 10.

ricardobeat 9y ago

That's exactly how I do multiplication in my head! I wonder why school never taught something like this, I find the standard right-to-left-and-carry-over method impossible to keep track of without paper.

pbhjpbhj 9y ago
They teach this method in my kids UK school, I'm pretty sure it's part of the standard curriculum.
- ricardobeat 9y ago
  Wouldn't that be the 'grid multiplication' method? https://en.m.wikipedia.org/wiki/Grid_method_multiplication https://en.m.wikipedia.org/wiki/Grid_method_multiplication

lancebeet 9y ago

In this case I would do 115 x 37 = 115 x (40-3) = 460 x 10 - 3 x 115 = 4600 - 345 = 4255 Since 15 x 3 and 15 x 4 are trivial calculations the only caveat is the subtraction which isn't too bad.

smallnamespace 9y ago

Somewhat surprisingly, this is how Common Core arithmetic is taught nowadays. Some parents are making a fuss because 'that's not how they learned arithmetic' [1], but actually anyone who is good with mental math uses these sort of tricks, particularly taking advantage of commutativity and distributivity. In fact this builds far stronger intuition for the properties of numbers and is a good way to prepare for algebra and proof-based approaches later on. Same sort of mental shortcuts for two-digit squaring: 52² = (50 + 2)² = (5 ⋅ 10)² + 2 * (50 ⋅ 2) + 4² = 5² ⋅ 10² + 200 + 4 = 2500 + 200 + 4 = 2604 [1] https://www.salon.com/2015/11/28/youre_wrong_about_common_core_math_sorry_parents_but_it_makes_more_sense_than_you_think/ https://www.salon.com/2015/11/28/youre_wrong_about_common_co...

romwell 9y ago
>Somewhat surprisingly ..to people who learn about Common Core from the rants of the parents who don't get it, quite sadly.
- Xeoncross 9y ago
  I disliked Common Core from the homework children brought to me. Looked nothing like the good example above GP showed.
  - fjsolwmv 9y ago
    You disliked Pearson worksheets. That's different from Common Core.
- pdx 9y ago
  I don't like Common Core because it attempts to solve a problem that does not exist. The way we learned math was sufficient to enable us to build atomic bombs and go to the moon, all with slide rules for the most part. It has a proven history of working and working well. The math shown in this article as well as much common core does not provide the user/student with understanding. Instead, they are taught incantations and rituals to get to an answer. This is a recipe for a society of math illiterates. Who is pushing this and why do they want such a society? Common Core is not a better system than the one taught for a hundred years in this country. If you disagree, I would love to see the evidence. I'm sure before such a huge change was made to our educational system, there must be MOUNTAINS of such evidence that was presented. No? Not really?
  - chiaro 9y ago
    gf is an English teacher. This is some of the research underpinning the instructional changes in CCSS for English specifically: Bonfiglio, C. M., Daly, E. J., Persampieri, M., & Andersen, M. (2006). An experimental analysis of the effects of reading interventions in a small group reading instruction context. Journal of Behavioral Education, 15, 93- 109. Burns, M. K. (2007). Reading at the instructional level with children identified as learning disabled: Potential implications for Response-to-Intervention. School Psychology Quarterly, 22, 297-313. Burns, M. K., Dean, V. J., & Foley, S. (2004). Preteaching unknown key words with incremental rehearsal to improve reading fluency and comprehension with children identified as reading disabled. Journal of School Psychology, 42, 303–314. Carney, J.J., Anderson, D., Blackburn, C., & Blessing, D. (1984). Preteaching vocabulary and the comprehension of social studies materials by elementary school children. Social Education, 48(3), 195-196. Daly, E., & Martens, B. (1994). A comparison of three interventions for increasing oral reading performance: Application of the instructional hierarchy. Journal of Applied Behavior Analysis, 27,459-469. Eckert, T. L., Ardoin, S. P., Daisey, D. M., & Scarola, M. D. (2000). Empirically evaluating the effectiveness of reading interventions: The use of brief experimental analysis and single-case designs. Psychology in the Schools, 37, 463-474. Faulkner, H. J., & Levy, B. A. (1999). Fluent and nonfluent forms of transfer in reading: Words and their message. Psychonomic Bulletin and Review, 6, 111-116. Gickling, E. E., & Armstrong, D. L. (1978). Levels of instructional difficulty as related to on-task behavior, task completion, and comprehension. Journal of Learning Disabilities, 11,559-566. Hall, K. M., Sabey, B. L., & McClellan, M. (2005). Expository text comprehension: Helping primary-grade teachers use expository texts to full advantage. Reading Psychology, 26,211-234. Levy, B. A., Nicholls, A., & Kohen, D. (1993). Repeated readings: Process benefits for good and poor readers. Journal of Experimental Child Psychology, 56, 303-327. McComas, J. J., Wacker, D. P. & Cooper, L. J. (1996). Experimental analysis of academic performance in an academic setting. Journal of Behavioral Education, 6,191-201. Neill, K. (1979). Turn kids on with repeated reading. Teaching Exceptional Children, 12, 63-64. O’Shea, L. J., Sindelar, P. T., & O’Shea, D. J. (1985). The effects of repeated readings and attentional cues on reading fluency and comprehension. Journal of Reading Behavior, 17, 129-142. Pany, D., & McCoy, K. M. (1988). Effects of corrective feedback on word accuracy and reading comprehension of readers with learning disabilities. Journal of Learning Disabilities, 21, 546-550. Rasinski, T. V. (1990). Effects of repeated reading and listening-while-reading on reading fluency. Journal of Educational Research, 83, 147-150. Reitsma, P. (1988). Reading practice for beginners: Effects of guided reading, reading-while-listening, and independent reading with computer-based speech feedback. Reading Research Quarterly, 23, 219-235. Rose, T. L., & Beattie, J. R. (1986). Relative effects of teacher-directed and taped previewing on oral reading. Learning Disability Quarterly, 9, 193-199. Sanford, A. K., & Horner, R. H. (2013). Effects of matching instruction difficulty to students with escapemaintained problem behavior. Journal of Positive Behavior Interventions, 15, 79-89. Sindelar, P. T., Monda, L. E., & O’Shea, L. J. (1990). Effects of repeated readings on instructional- and masterylevel readers. Journal of Educational Research, 83, 220-226. Smith, D. D. (1979). The improvement of children’s oral reading through the use of teacher modeling. Journal of Learning Disabilities, 12 (3), 39-42. Stoddard, K., Valcante, G., Sindelar, P., O’Shea, L., & Algozzine, B. (1993). Increasing reading rate and comprehension: The effects of repeated readings, sentence segmentation, and intonation training. Reading Research and Instruction, 32, 53-65. Taylor, N. E., Wade, M. R., & Yekovich, F. R. (1985). The effects of text manipulation and multiple reading strategies on the reading performance of good and poor readers. Reading Research Quarterly, 20, 566-574. Turpie, J. J., & Paratore, J. R. (1995). Using repeated reading to promote success in a heterogeneously grouped first grade. In K. A. Hinchman, D.J. Leu, & C.K. Kinzer (Eds.), Perspectives on literacy research and practice: Forty-fourth yearbook of the National Reading Conference (pp. 255-263). Chicago: The National Reading Conference. VanWagenen, M. A., Williams, R. L., & McLaughlin, T. F. (1994). Use of assisted reading to improve reading rate, word accuracy, and comprehension with ESL Spanish-speaking students. Perceptual and Motor Skills, 79, 227-230. Weinstein, G., & Cooke, N. L. (1992). The effects of two repeated reading interventions on generalization of fluency. Learning Disability Quarterly, 15, 21–28. Wixson, K.K. (1986). Vocabulary instruction and children’s comprehension of basal stories. Reading Research Quarterly, 21(3), 317-329.

infodroid 9y ago

> ... using a less strict version... Nice to know there's a name for it. Using distributivity for creative simplification of a hard multiplication problem is a useful skill... It's a mental shortcut, like Russian Peasant Multiplication. But it isn't the same as, or just a "less strict" version of it. The latter is an algorithm, and relies on binary arithmetic and the "simple" operations of doubling, halving, and summation.

xster 9y ago

ya, surprised too. I always thought this is just how everyone informally does multiplications in their head.

knowThySelfx 9y ago

Divide and conquer, in a way :D

reacweb 9y ago

I do it quite differently, because I am good at operations, but I have a bad memory. 37 x 110 -> 4070 (mentally I visualize 3700+370 . This is not fully obvious because of the carry), then I try to remember this number so that I can add 185 (when I see 37x5, I see 18.5x10 without other intermediate step) to it and remember the result. The "normal" way is 30 x 115 -> 3450 (easy because I can see 3x15->45, so it is as if there was no carry), then 7 x 115 -> 805 (not obvious because of 2 carries), then I have forgotten the 3450, I recompute it while trying to remember 805. For me, the aim of all these tricks is to cope with a bad memory.

reacweb 9y ago
I also likes the table of 37, but this works better for smaller numbers. This gives: 37 x 115 -> 37 x 3 + (114 / 3) + 37. I know that 37x3=111. With some efforts, I can see that 114 / 3 -> 38. I am still memory free to perform the difficult 111x38 -> 3800+380+38 = 4180+38 = 4218 that I pain to remember to add 37. In this case, the table of 37 is not very effective.

underwoodley 9y ago

This is a pretty standard way of doing mental multiplication. The interesting thing about the method in the article is that it involves binary not base 10.