lördag 19 februari 2011

Russian multiplication

Russian farmers are said to have used this method to multiply numbers between 6 and 10. The fingers are numbered from 6 to 10. Any couple can then be multiplied. 

Emily shows off her nice nails:)

To multiply 7 & 8 you put the fingers representing the numbers against each other. The fingers that touch and those below represent tens. In this case 50. The other fingers are multiplied and then added to the numbers we got on the lower fingers. Three times two is six and added to the tens you get 6 + 50 = 56 

Lucas and Rebecca examines whether the method works. It does! And it was fun!

37 kommentarer:

  1. in English: Are both hands labeled 6-10?

    SvaraRadera
  2. I don't get it. I'm not seeing how you get 50.

    SvaraRadera
  3. Place fingertip 7 on first hand against fingertip 8 on the other hand. The touching fingers and those below (pointer and thumb on first hand and middle, pointer and thumb on the other hand) each represent 10. 5 fingers equals 50. The fingers above (middle, ring and pinky on first hand and ring and pinky on the other) represent 3 x 2= 6. 50 + 6=56

    SvaraRadera
  4. This would take more time for my elementary student to figure out. Sorry but this is not helpful and your explanation is not very helpful.

    SvaraRadera
  5. Here's another example: 6x7...touch left thumb to right forefinger. You have 3 fingers total (two touching, one--the thumb--below). 3x10=30. Next, you have four fingers above your thumb on the left, and three above your forefinger on the right. that is 4x3=12. 30+12=42 (6x7=42).

    SvaraRadera
  6. I believe this is very helpful for those that like to think outside the box. I think The Egan 4's comment was rude. The explanation is fine. And the pictures help to show how to label the fingers. Thank you for showing us a new and different way to teach our students.

    SvaraRadera
  7. Fascinating! Thanks for sharing!

    SvaraRadera
  8. Very interesting! Thank you for sharing the information. We are homeschoolers and the rote memorization of multiplication tables is monotonous. This will be fun to try.

    PS your explanation was exquisite!

    SvaraRadera
  9. Quite interesting! Neat trick!

    I also liked seeing how all multiples of 9 (1-10) sum up to equal 9, a nice trick to double check your answer:

    9*2=18 (1+8=9)
    9*3=27 (2+7=9)
    9*4=36 (3+6=9)
    9*12=108 (1+0+8=9)
    9*27=243 (2+4+3=9)

    works all the way up!

    SvaraRadera
    Svar
    1. That is an awesome point! Thanks for bringing that to my attention. I am terrible at math (I am SOOO right brained) so any little tricks are a huge help to me.

      Radera
  10. Love this strategy...but can anyone explain why it works? That's where I'm stumped. :)

    SvaraRadera
    Svar
    1. Mrs. B asked why this works, and I was curious too, so I worked out the math. Here it is. First, I'm representing the two original numbers being multiplied together as x and y.

      A mathematical way of representing the number of fingers you're counting to get the number in the tens place is: (x-5)+(y-5). Since that number is going in the tens place, it will need to be multiplied by 10. This part of the equation will be:

      10((x-5)+(y-5))

      The number you'll be adding to the above expression can be represented by: (10-x)(10-y).

      Putting those two pieces together, along with the fact that the whole thing will need to equal xy, you have:

      xy = 10((x-5)+(y-5)) + (10-x)(10-y)

      Now here's the step-by-step process of showing that the two sides are equal:

      xy = 10((x-5)+(y-5)) + (10-x)(10-y)
      xy = 10(x-5+y-5) + (10-x)(10-y)
      xy = 10(x+y-10) + (10-x)(10-y)
      xy = 10x+10y-100 + (10-x)(10-y)
      xy = 10x+10y-100 + 100-10y-10x+xy
      xy = (10x-10x)+(10y-10y)+(-100+100)+xy
      xy = (0) + (0) + (0) +xy
      xy = xy

      Radera
  11. I've successfully taught this to fourth grade students for the past 5 years. There is a youtube video that is excruciatingly hard to watch because he goes so slow, but if you watch it a couple times it will be clear. http://www.youtube.com/watch?v=YL3PtlxYkZ4&feature=related

    I have my kids write the numbers on their fingers with marker, but the sticky notes are a great alternative.

    SvaraRadera
    Svar
    1. Oh my goodness, you weren't joking when you said that video was excruciating. This video - http://www.youtube.com/watch?v=twv-ynv_m9o - isn't quite as clear, but since he walks you through three examples, you should be able to understand the process by the end. More importantly, it isn't nearly as painful to watch.

      Radera
  12. Multiples of nine is super easy. Hold out both hands with your fingers splayed. Let's say you're multiplying 9x3. Bend the middle finger of your left hand. You have 2 fingers (pinky and ring) to the left of your bent finger, and 7 to the right. 9x3=27. 9x7. Bend the pointer finger on your right hand. You have 6 fingers to the right of your bent finger, and 3 to the left. 9x7=63.

    SvaraRadera
    Svar
    1. THAT made sense to me! I am a homeschooler and teaching the tables to my daughter was quite excruciating indeed since her brain works much like mine, poor girl! ;) THANK YOU for explaining this in a way that makes sense to this gal! I've read ALL the responses along with the original article, and you helped me understand the concept in a way my mind can use it :) No offense to anyone else, my brain tries hard to understand your explanations too, it just has to be made visual for me :) Thanks again!

      Radera
  13. This is a neat trick, but the blog post explains the very poorly. I had to read the comments to understand.

    SvaraRadera
  14. Brenda, thanks for explaining. I finally get it. The blog post was a little confusing.

    SvaraRadera
  15. I think there's a language barrier. The post introduces the method intriguingly, and I think the Egan 4's comment was unnecessarily harsh, but I will search for more information about this method elsewhere.

    SvaraRadera
  16. I'm going to have to Google it too. I don't get it. To be fair, I tend to struggle with math anyway...

    SvaraRadera
    Svar
    1. I love your blog! I will try your Math trick with my 4th graders tomorrow. I will definitely be back to visit your blog. I would love to be able to write to your class from my class in California; we could set something up. =)

      Fabulous Finch Facts

      Radera
  17. I had to do it four or five times before I really "got it" but it was incredibly easy after that. Same for my 11 year old daughter.

    SvaraRadera
  18. I think a picture of the fingers touching would help the explanation. I am pretty good at math and it took me reading over and over and trying it several times to figure it out. I do get it, but a picture of the fingers touching would be a great help. Left finger touches right finger of the numbers you are multiplying. The fingers touching plus the fingers including thumbs are the 10s. Then the fingers above touching )towards pinkies are multiplied. Great idea!!!

    SvaraRadera
  19. This is great! My daughters struggle with the higher numbers. We got it, thank you for sharing, I will use this in the classroom too. Multiple strategies :-)

    SvaraRadera
  20. This is how my remedial math teacher taught us to do the higher numbers! I had forgotten how to do it!! Thanks!!

    SvaraRadera
  21. Wow. Once I got the hang of it, I found it fascinating. I can't wait to share this.

    SvaraRadera
  22. Better video than the previous given above. (from my point of view. At least quicker!)
    http://www.youtube.com/watch?v=twv-ynv_m9o
    Lili

    SvaraRadera
  23. Thanks! I have added this trick to my own page and linked back to you for giving me the idea. Have a great day.

    SvaraRadera
  24. Ooops meant to put the link : http://mfindingmyhappyplace.blogspot.com/2013/06/multiplication-fun.html

    SvaraRadera
  25. I've always been good at higher level math, but I still have to stop and think about my multiplication facts from 6-8. No more! This trick is so helpful! I wish I'd learned this years ago. I agree that the directions were confusing; I think many of us misunderstood and thought that instead of counting the number of fingers above and below the fingers that were touching, we were supposed to be combining the values written on those fingers. Once I read Brenda's example I understood that the only time the values written on the fingers mattered was when you were figuring out which fingers should be touching. However, given that this is a post written in English on a Swedish website, I think we should all be more forgiving of a slight miscommunication.

    SvaraRadera
  26. Den här kommentaren har tagits bort av skribenten.

    SvaraRadera
  27. OMG why didn't someone teach me this in elementary school!! I'm 50 and just now learning this?! I had to go to another website to figure this out only because you didn't mention putting the numbers 6-10 on both hands - that is why I was confused at first. But thank you!

    SvaraRadera
  28. explanation better on you tube
    http://www.youtube.com/watch?v=YL3PtlxYkZ4

    SvaraRadera
  29. Oh, my goodness...Thanks for all your comments on this blogpost. I completely forgot I hade this blog. A few years ago I went to the states and met some american colleagues. After that visit I decided to translate my swedish blog into "english". I had a lot of post and not a lot of time so I had google translate to do the job in a few seconds... and I know that gives you a lot of confusions but I mostly made the english version for the pictures and maybe some guidens in the text. Sorry about that!
    Im glad you all found me and my blog. I never did continue with doing translations but maybe by just looking on pictures you will get some more tip on my swedish blog. www.klassrumskul.blogspot.com
    You´re welcome to have a look.
    Im just starting to work again after being home with my third son.
    Thanks again for your comments and hope you have a lot of fun in your classroom. :-)

    SvaraRadera
  30. I think I get it. I'm going to practice some more but thanks.
    Touch the fingers together. The fingers that touch: count the number of fingers and multiply by 10 to get your 10's digit.
    Example: for 7x7 touch the index fingers. This gives you 4 fingers (index & thumbs) to multiply by 10. Then, the other figers (middle, ring, pinky), you mutilply by each other. 3 fingers on each hand.
    (4x10) +(3x3)=49
    I wish I had known this in school myself, but I can certainly use it with my students.

    SvaraRadera