Visual-spatial: How to memorize math facts?? - Mothering Forums
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#1 of 62 Old 01-20-2009, 07:46 PM - Thread Starter
 
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I'm not sure that my daughter actually is V-S or just visual, BUT she definitely is not auditory-sequential.
Any sugestion on HOW to memorize math facts for a V-S or visual student? Repetition doesn't work. The girl can figure out multiplication, but can't remember she just counted out 4+3 and will do it again if I give her the same problem.

Tammy
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#2 of 62 Old 01-20-2009, 09:38 PM
 
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Try Linda Silverman's website. She has some articles and downloadable books on how to teach v-s kids. I haven't read any of them but I really liked her book.
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#3 of 62 Old 01-20-2009, 10:42 PM
 
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Schoolhouse Rock has a great series of videos on multiplication that would be visual and auditory. You can find them on You Tube and there's a dvd.

If she's visual...

Have her count things by twos, threes, fours (pennies, pencils, anything!). Use nickels and pennies to count by fives, showing the equivalent in pennies so she can see it.

Play multiplication war where you use one multiplier per round and the first person to shout out the answer wins the card i.e. one card flipped up at a time which must be multiplied by 2 in order to 'win'--remove face cards. This is good for rote learning as you keep playing until she wins all the cards for each multiplier.)

Fill in a multiplication facts grid (1-10 on top and down the side, fill in with multiplication facts) and look for the relationships there. Mark the relationships with colored highlighters and let her post the grid on the wall or fridge.

Show her rows and columns and how multiplying counts them.

Have her visualize a problem in her mind and see if she can come up with the answer.

Give her a multiplication problem and have her form the answer with playdoh.

Play contig.
Lattice multiplication is great for larger multiplication problems.

I'm a professional tutor just in case you wondered!

V

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#4 of 62 Old 01-20-2009, 11:01 PM
 
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As a V-S learner myself, I found that generally, the best way to learn a lot of things was just to write them out clearly and neatly on a piece of paper, then look at the paper, then look away. Or to associate an image with the thing I was trying to remember.

But I never had anyone think of all the things the PP said, which all would have been good, too.

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#5 of 62 Old 01-20-2009, 11:05 PM
 
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Stop trying to make her memorize it. Though her way of doing it is slightly slower, in the long run it will lead to a deeper understanding of mathmatics.

Memorization is a crutch A/S people use, why try to force a child who is capable of grasping number theory use a crutch.

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#6 of 62 Old 01-20-2009, 11:13 PM
 
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Yeah! You tell her! V-S people unite!

I have to agree on this one, though. Trying to get a v-s person to memorize math facts is like... trying to get a a-s person to do a puzzle face-down. A pointless waste of energy. But, more power to you girl! We all have to have a hobby.

Besides, she's GIFTED, right? I still don't know my basic addition or multiplication facts but it never slowed my learning down. In my own head it seems like I take FOREVER to calculate anything, but I'm still ten times faster than anyone around me. If you're fast enough, it doesn't matter, KWIM?
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#7 of 62 Old 01-20-2009, 11:19 PM
 
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Sort of like my speech. Sometimes I'm grasping for the word I wish to use and feel like it takes a long time to find it, mentally. However, most people don't even notice because my speech (which is way too fast) is so much slower than my thoughts. I have plenty of ruminating time left.
Same with typing. I type lightning-fast but I still can't keep up with my thoughts so sometimes I'll wierd people out IRL. They'll see me typing something, come up and ask me a question, and I'll answer them, looking at them, while I continue to type. It's just that my fingers haven't caught up yet. Yeah, it's wierd.

My point being, if your processing time is fast enough, you can add all kinds of interim steps, recalculate, recalculate, and recalculate, and nobody will even notice. I never learned my math facts and NOBODY noticed.
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#8 of 62 Old 01-21-2009, 12:53 AM
 
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I asked my DH about this and he said, "Well, doesn't everybody compute the answers?" He was baffled to realize that there are people out there who actually have this stuff memorized. He finds it absolutely amazing. And he's an electrical engineer who does advanced math in his free time as a hobby. He said, "That's pretty cool. But sort of useless, isn't it? You're limited to the things that you know." I'd never thought of it that way before.

Eepster: THANK YOU! :

I couldn't stop thinking about what you just posted. OMG, you are so right! My whole life I've felt like an idiot because I can't memorize math facts. But, who cares? Who cares if I see 6+3 and know immediately that the answer is 9 or if I know that the answer is nine because I can count in 3s (3, 6, 9) and recognize the pattern. Either way, I immediately know the answer. Who cares if I see 8+9 and think 17 or if I know the answer because I know that 9 plus a number is always 10 plus one less than the number? Either way, I immediately know the answer. Who cares if I memorize 12x12 or if I know the answer is 144 because of the symmetry of the equation? Either way, I immediately know the answer.

Besides, what do math-facts people do once they get past the ones they know? It's so much easier to break the problems down in your head and use patterns. Or, at least it's easier for me.

: I'm free!
Schools have coached us to think that the math facts are correct math and that the patterns in math are just tricks we use to calculate the things we don't know. That's completely backwards. Number theory is not a crutch.

On the other hand, once she's spent some more time working on math she'll probably have the simplest parts memorized. I don't have to compute 4+5 or 18/3, for example. It's just that if I can't remember it I can compute it rather quickly.

And now I finally understand how I can not know my math facts but still be great at advanced math and statistics: I'm good at pattern-recognition.
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#9 of 62 Old 01-21-2009, 01:47 AM
 
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very interesting discussion
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#10 of 62 Old 01-21-2009, 01:56 AM
 
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Originally Posted by VanessaS View Post
Besides, what do math-facts people do once they get past the ones they know? It's so much easier to break the problems down in your head and use patterns. Or, at least it's easier for me.
And this is why most Americans are mathmatically funtionally illitterate.

While I never memorized the times tables in grade school, I do understand algebra (and yes I have actually used it in adult life.) On the other hand if I want to do arithmatic fast, I can always use a calculator.

Memorizing math facts is just a way of teaching to the test.

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#11 of 62 Old 01-21-2009, 02:05 AM
 
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Really interesting discussion.

I'm struggling to find ways to help my DD, who someone recently told me they feel is a V/S learner.

He who can no longer pause to wonder and stand rapt in awe is as good as dead; his eyes are closed.  ~Albert Einstein
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#12 of 62 Old 01-21-2009, 04:49 AM
 
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I'm just nodding my head to all of this.

My dd1 is my most v/s, and just don't even try the memorization route.

Like a previous poster mentioned, if we counted with objects, she got it. We would line up her favorite colors of crayons, and count that way. Then, it clicked.

Also, I learned one day, randomly, that if I set up flash cards in order, where she could see the pattern, like 2+2=4, 2+3=5, 2+4+6, it clicked right away. But she had to see all the cards for each number, the big picture.

I can also only agree with those who said they didn't learn basic addition or subtraction perfectly, but could do algebra, geometry, etc.

They tested dd1 in first grade, thinking she was slow. I'll never forget the call I got saying somehow, despite not knowing basic math, she was doing algebra and geometry.

I'm still trying to understand it all, as I'm SO a/s, but it's completely fascinating to me.
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#13 of 62 Old 01-21-2009, 09:31 AM
 
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Originally Posted by eepster View Post
Stop trying to make her memorize it. Though her way of doing it is slightly slower, in the long run it will lead to a deeper understanding of mathmatics.

Memorization is a crutch A/S people use, why try to force a child who is capable of grasping number theory use a crutch.
Hear, hear! My husband, who is a computer programmer with a freaky knack for math, has never learned his math facts. I have learned all of mine and I just do not understand math at all.

Anyway, after a period of time, some "facts" naturally stick. I guess if you figure them so many times, you eventually memorize them by accident. For my own kids, simple single-digit addition/subtraction facts were helped by board games with dice.

But seriously, if I say "9 times 7", I will get a visual of the 9s table in my head and then pull out the right answer (which is also very vs, I think, although I stink at math). My husband, OTOH, will tell himself, "10 times 7 is 70 so taking away one of the 7s is 63." It really works for him.
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#14 of 62 Old 01-21-2009, 09:39 AM
 
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I'm replying one more time because I had another idea. I mentioned that board games with dice really worked for my kids. I'm not sure how old your daughter is (don't know which one you are asking about)...but board games have been great for my kids. We unschool and they are generally very resistant to instruction. But even if they were in school, I think that board games would greatly help them with math because they can "see it" rather than just manipulating numbers on paper.

For multi-digit addition, it helps to understand place value. When I tried to do mental multiplication, I would actually draw the numbers in my head and mentally move them, crossing certain numbers out, carrying, mentally writing stuff below the line, etc. My husband, OTOH, just breaks numbers down into 10s and stuff and then he can do almost anything. Understanding place value helps one do the latter.

We have a board game that we really love, if your child does not understand place value yet. It's called, "Dino Math Tracks". In the easy version of the game, you roll multiple dice at once, arrange them to make a number up to 4 digits and then move your 4 dinosaurs down various paths according to the place value. So, the yellow dinosaur moves down the ones path, the orange dinosaur moves down the 10s path, the purple one moves down the 100s path and the blue one moves down the 1000s path; the number of spaces they move depends on what 4 digit number you made. Yesterday, after playing it, I was showing my kids how they can add something like 31 and 23, by pulling out the 10s and 1s and just adding up the 10s, then the 1s and then the total 10s and 1s together. This is how my husband does math. And as I've said, after figuring the same ones over a period of time, the higher frequency ones just stuck with him. I envy his math abilities.
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#15 of 62 Old 01-21-2009, 11:26 AM
 
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And as I've said, after figuring the same ones over a period of time, the higher frequency ones just stuck with him.
This is true. Dice and board games work, too.

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Memorizing math facts is just a way of teaching to the test.
Actually, I think it's about lowering processing time. This didn't work for me. It's not that I never TRIED to memorize the math facts, just that when it became time to use them I'd draw a blank. If I sat there long enough and thought hard enough I could probably bring up the answer or at least make a good guess. But, for me at least, it's easier and faster to remember the pattern or do a calculation.

What I never understood is why the other students in the class (most of whom had the answers memorized) were still slower than I to answer the questions, and got more of the questions wrong. We used to do speed drills in elementary school and I usually won. How can that be if most everyone else is using simple recall?

Sort of like remembering dates in history. I'm a complete dunce at that. But I always aced the essay questions because I really UNDERSTAND history.

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When I tried to do mental multiplication, I would actually draw the numbers in my head and mentally move them, crossing certain numbers out, carrying, mentally writing stuff below the line, etc.
That is so fascinating to me. I can't do that at all because the numbers swim around in my head and I lose track of what step I'm on. I have to write everything down.

Teaching place value is really important for v-s students. I also break things down and regroup in my head, so does my DH. Strangely enough, the numbers don't swim when I do that. Only when I try to calculate conventionally.

And don't even get me started on my personal nightmare: long division. The whole show-your-work thing drove me bonkers. I'd usually answer the questions and then go back and write down the work. Which drove my teachers crazy as sometimes the work would be all wrong but the answer correct. I used to do this in Algebra2, too. We were supposed to simplify the problem and then draw a graph to display the answer. I'd simplify and graph but leave out the "plotting step". I didn't need to do it as I already knew what the graph would look like. This became useful during testing time when we'd have multiple-choice answers (display a graph and then ask what line is displayed).

Anyway, in this century recall of memorized facts isn't actually that useful. Internet, anyone? Besides, once you get to binary and hexadecimal math the whole math-facts thing breaks down entirely. Quick: What is 1010+1101? Answer: 10111 Easy as pie! Can we say: assembly programming?
In fact, I don't think I REALLY understood place value until I learned binary math.
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#16 of 62 Old 01-21-2009, 11:49 AM
 
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Originally Posted by VanessaS View Post
I asked my DH about this and he said, "Well, doesn't everybody compute the answers?" He was baffled to realize that there are people out there who actually have this stuff memorized. He finds it absolutely amazing. And he's an electrical engineer who does advanced math in his free time as a hobby. He said, "That's pretty cool. But sort of useless, isn't it? You're limited to the things that you know." I'd never thought of it that way before.

Eepster: THANK YOU! :

I couldn't stop thinking about what you just posted. OMG, you are so right! My whole life I've felt like an idiot because I can't memorize math facts. But, who cares? Who cares if I see 6+3 and know immediately that the answer is 9 or if I know that the answer is nine because I can count in 3s (3, 6, 9) and recognize the pattern. Either way, I immediately know the answer. Who cares if I see 8+9 and think 17 or if I know the answer because I know that 9 plus a number is always 10 plus one less than the number? Either way, I immediately know the answer. Who cares if I memorize 12x12 or if I know the answer is 144 because of the symmetry of the equation? Either way, I immediately know the answer.

Besides, what do math-facts people do once they get past the ones they know? It's so much easier to break the problems down in your head and use patterns. Or, at least it's easier for me.

: I'm free!
Schools have coached us to think that the math facts are correct math and that the patterns in math are just tricks we use to calculate the things we don't know. That's completely backwards. Number theory is not a crutch.

On the other hand, once she's spent some more time working on math she'll probably have the simplest parts memorized. I don't have to compute 4+5 or 18/3, for example. It's just that if I can't remember it I can compute it rather quickly.

And now I finally understand how I can not know my math facts but still be great at advanced math and statistics: I'm good at pattern-recognition.
The very interesting thing for me is that I am teaching number theory to my dd1 and I didn't even know it.

They didn't teach number theory in school when I was in school, and relied heavily on rote memorization. To this day I have trouble remembering my addition facts and times tables from 6-9.

Yet, when dd and I were talking about the math, I show her the patterns (like 3, 6, 9...)etc. Also, because they've learned early on how to add doubles, I'd been telling her to find the numbers she doesn't know by going to the nearest double and either adding or subtracting 1.

It's been eye-opening to think of things this way. I have heard that you understand things much better when you have to teach someone else.

Oh, yeah, dh too, does all the math tricks in his head superfast, so even though he didn't memorize his math facts, he can figure it out in barely a blink of an eye.

Mama of 3 girls: 7.5 , 6 , and 4.5
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#17 of 62 Old 01-21-2009, 12:49 PM
 
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OMG this is the best thread EVER!!

We are pretty unschooly type folk, so rote memorization just doesn't happen much around here

BUT...DD would fail miseralbly if that were the expectation. So, she counts everything on her fingers etc.

And...um....I do the same

I took calculus and trig in the 9th grade...and I can't do 'basic' math without thinking it through.

I think there's something to be said about that indicating a more in depth way of approaching math itself.

Awesome thread, can't wait to read more!

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#18 of 62 Old 01-21-2009, 01:25 PM
 
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I can also only agree with those who said they didn't learn basic addition or subtraction perfectly, but could do algebra, geometry, etc.
This was me, too. I couldn't give an automatic answer to 8 + 5 without thinking about it, like I knew 7 + 5 was 12, so it was one more than that until I was out of high school. But I took all the advanced math and science classes in high school without having a problem. Besides, the fun stuff for me was taking a higher level problem and figuring out the formula to solve it. Conceptually, I do get *most* math, I'm just challenged with the actual computation because it doesn't come easily to me. That's when I have to think. I got a lot of problems wrong because I didn't do the simple math right, but I had it laid out correctly with the right assumptions. Thank goodness for partial credit!

Today, I still do math *forward.* For a simple example, instead of 13 - 5 = x, I figure out what I need to add to 5 to get 13. Same with division.

I think if I had been taught some of the "10" tricks, like mentioned above in other pp's post, I would have had a much better time with math. Heck, I might have even thought I was good at math! Other than advanced statistics in college, I didn't go beyond calculus.

But I don't see numbers or equations. My basic math process is very auditory, I think - I talk out problems in my head. I know what the goal is, pull together the appropriate pieces, and through trial and error know what a reasonable answer is and why. And when I need an exact answer, I bring out the calculator. I go to a different place in my brain when I do things like geometry. Can you be A/S for one type of math and V/S for another?

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#19 of 62 Old 01-21-2009, 01:57 PM
 
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Originally Posted by quaz View Post
I'm not sure that my daughter actually is V-S or just visual, BUT she definitely is not auditory-sequential.
Any sugestion on HOW to memorize math facts for a V-S or visual student? Repetition doesn't work. The girl can figure out multiplication, but can't remember she just counted out 4+3 and will do it again if I give her the same problem.

Tammy
This looks interesting:
http://www.visualmathlearning.com/

I'm going to look through it, but ultimately something like this would be good. I still count on my fingers and have to write down addition like 258 + 29 or 29+47. I love algebra and geometry, though.

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#20 of 62 Old 01-21-2009, 02:00 PM
 
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As a V-S learner myself, I found that generally, the best way to learn a lot of things was just to write them out clearly and neatly on a piece of paper, then look at the paper, then look away. Or to associate an image with the thing I was trying to remember.

But I never had anyone think of all the things the PP said, which all would have been good, too.
this is what I did all through college! Even now, it is how I "memorize" something. It helps me to write it out over and over, I've memorized several poems as an adult this way. It helps to read it right before bedtime.

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#21 of 62 Old 01-21-2009, 02:41 PM
 
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Stop trying to make her memorize it. Though her way of doing it is slightly slower, in the long run it will lead to a deeper understanding of mathmatics.
I was thinking the same thing and tend to agree. Isn't understanding always better than memorizing? However, I do the see a benefit in being able to do both in the sense that complex math problems could be computed more quickly. I wonder if the OP's dd is being subjected to those "timed tests" that I recall from grade school? I also agree with what pp's said about "seeing" what the problem looks like and having this eventually become ingrained in one's memory. Flashcards and charts can be helpful for this. When I think of 9 times 7 equaling 63, I still see "9 x 7 = 63."
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#22 of 62 Old 01-21-2009, 02:49 PM
 
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Stop trying to make her memorize it. Though her way of doing it is slightly slower, in the long run it will lead to a deeper understanding of mathmatics.
I was thinking the same thing and tend to agree. Isn't understanding always better than memorizing? However, I do the see a benefit in being able to do both in the sense that complex math problems could be computed more quickly. I wonder if the OP's dd is being subjected to those "timed tests" that I recall from grade school? I also agree with what pp's said about "seeing" what the problem looks like and having this eventually become ingrained in one's memory. Flashcards and charts can be helpful for this. When I think of 9times 7 equalling 63, I still see "9 x 7 = 63."
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#23 of 62 Old 01-21-2009, 08:22 PM
 
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I was thinking the same thing and tend to agree. Isn't understanding always better than memorizing? However, I do the see a benefit in being able to do both in the sense that complex math problems could be computed more quickly. I wonder if the OP's dd is being subjected to those "timed tests" that I recall from grade school?
I think the bottom line is that someone isn't going to learn something until they have to or want to. Learning for a timed school test, in my opinion, is in the have to camp. And learning can be plain old memorization or it can be full understanding.

If someone can figure out a way to get by without having to memorize something because they don't need it, they just might.
There is a difference between arithmetic and mathematics. You definitely don't have to be great at arithmetic in order to be great at mathematics.

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#24 of 62 Old 01-22-2009, 11:12 AM
 
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So, she counts everything on her fingers etc.
And...um....I do the same
Me too! I felt a bit silly at times in college but then I discovered it works well with toes, too. Even if I don't actually count out individual digits, just moving my toes seems to work. Tapping a pencil on a table works, as well. Or rocking back and forth. I was always getting into trouble for fidgeting but I couldn't THINK without moving. Don't they call that kinesthetic learning, or something? I still fidget terribly and drive everyone crazy with it. I can't sit still when I hear music, either.

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Learning for a timed school test, in my opinion, is in the have to camp.
That was me. But, like I said, I just learned to compute faster, so I still didn't have to memorize anything. I think that's what most v-s people do. Memorize the easiest ones and compute the rest. The teachers just THINK we're memorizing everything. But then, they never ask, do they?
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#25 of 62 Old 01-22-2009, 11:45 AM
 
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I was thinking the same thing and tend to agree. Isn't understanding always better than memorizing? However, I do the see a benefit in being able to do both in the sense that complex math problems could be computed more quickly. I wonder if the OP's dd is being subjected to those "timed tests" that I recall from grade school? I also agree with what pp's said about "seeing" what the problem looks like and having this eventually become ingrained in one's memory. Flashcards and charts can be helpful for this. When I think of 9times 7 equalling 63, I still see "9 x 7 = 63."
For some reason, I can't see certain ones anymore. The 6-9 group is giving me problems.

On the other hand, dd1 made a great discovery yesterday.

She noticed that adding and multiplying odd numbers, they switch back and forth from even to odd. I can't quite remember how she said it, but it was cool that she noticed.

Dh was telling me about the method taught in the movie Stand and Deliver for multiplying 9s, using your hands. Hold up both hands facing away from you. For 9x7, fold down your index finger on the right hand. The result - the fingers on the left side add up to 6, the fingers on the right hand add up to 3.

Try it, it works for all of them. 9x2 = 18 (bend down your your ring finger down on your left hand, there is 1 on the left of it, 8 on the right).

9x9 = 81 is a little hard, because it's hard (for me anyway), to fold down the ring finger on my right hand, unless I'm placing my hands face down on a table.

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#26 of 62 Old 01-22-2009, 12:24 PM
 
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Tried it. That is too cool!
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#27 of 62 Old 01-22-2009, 12:27 PM
 
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Originally Posted by VanessaS View Post
Tried it. That is too cool!
Thought you might like it.

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#28 of 62 Old 01-22-2009, 12:29 PM
 
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That's a lot easier to remember than the 9x tables.
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#29 of 62 Old 01-22-2009, 12:29 PM
 
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Whenever I multiply a number by nine I take one less than the number for the first digit and the second digit is just nine minus the first digit. Yes, I have to do all of that every time I multiply a number by 9. Still, it is much better than when I try to multiply by 7 or 8, which always stumps me.

I do like the little hand trick. It's basically the same principle.
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#30 of 62 Old 01-22-2009, 04:35 PM
 
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Okay, now I see the number trick employed by one of the posters' husbands.

Dd wanted to work on multiplication last night, and she chose 9's. As we are working them out together, I realized the multiply by 10 and subtract by that number trick for 9s:

For instance 9x9 becomes

(10x9)-9 =
(90)-9 = 81

9X8 becomes

(10x8)-8 =
(80) - 8 = 72

9x7 becomes

(10x7)-7 =
(70) - 7 = 63

9x6 becomes

(10x6)-6 =
(60) - 6 = 54

and so on...

I only saw this pattern (and quite accidentally) when I laid it out for dd the other night. Literally, in all my 38 years, I had no algorithms of calculating 9s, other than pure memorization. In school, I didn't play with numbers and such. Life was too stressful at home to play number games (divorced and remarried mom = lots of issues). I hid in books instead.

Consequently, I kept on thinking, well I must be stupid or a dyscalculic, when if fact, I don't think that's the case. It's a case of not having examined and played with the relationships of numbers like that.

The reason I like doing the 9's this way, is because for me, I can see it better than any other way. Oddly enough, I can subtract 1-9 from 10 and it's multiples better than I can subtract the same numbers from 9. I don't know why that is.

And while I might employ the two-handed trick in the privacy of my own home and teach it to the kids, I want a way to figure it out when I'm out in public and being watched.

At any rate, it's pure fun to see now how many different ways to come up with calculating numbers.

And, it's funny how writing them down you can see things that you might not otherwise by thinking of them (dh can do that quite easily, he doesn't need pencil and paper).

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