Teach Multiplication Facts: One at a Time or All at Once?

As a teacher, I found the approach described Tools for the Times Tables, combined with Touchmath for those with retrival problems to work the best. You can find Tools for the Times tables at Sue Jones website http://www.resourceroom.net/Math/index.asp

Explaining the concept of multiplication clearly, as is done in Tools for the Times Tables, seemed to give my students something to hang their memorization of math facts on, so that they were much more successful at recall over the long term. The book clearly explains the communicative property of multiplication very early on, which does make knowing your facts seem less daunting to students.

I’ve also tried Times Tables the Fun Way, which worked really well for my students the year they were in my classroom, but did not carry over to the next year. Carry over is one of my major concerns whenever I use a new program…if they can’t take it out of my classroom, it ain’t worth much, IMHO.

I think this is one of the biggest mistakes out there. Even your whole-to-part learner isn’t going to get all of it at once. It’s best to learn one “whole part” (such as — anything times zero is zero, because no matter what it is you did, if you did it zero times, you haven’t done anything).
I apply the same principles that work with reading to math — learn it, learn it well, bring it to automaticity, and then keep reviewing it. Exactly where you start to work in a second thing to learn usually comes somehwere after “learn it well,” not somehwere before “learn it” as I was prone to do in my first teaching. Also, going beyond rote and incorporating the how & why is important all the way around. Kids shouldn’t learn just a rule (“anything times zero is zero, anything times one is itself”) — they should talk about why.
Making the connection between the symbols of the areithmetic and regular language and common sense is, IMHO, what separates the “Kids who are good at math” from teh “oh, I just can’t do math” crowd — but it’s not innate. We can teach it.
Thanks Karyn for the great feedback on Tools for the TImes Tables!

Teaching rote is usually a waste of time. Teach what it means using simple examples:

4
x 3
___

I show this and this say that four groups of three

4 groups is four plates
of three, three in each plate

count them

Until the student can show me a simple mult. problem w/o hesitation - it is not time to memorize meaningless facts.

aLSO, they should be able to make up their own examples — even if they’ve “memorized” to think of rows and columns of chairs, or parking lots, or doing the same thing 5 times (e.g. running 3 miles 5 times, spending 5 dollars 3 times).

This probably varies quite a bit, but I’m wondering what might be a reasonable amount of time to expect the average kid to learn their times tables? I realize the LD kid may take longer.

Thanks for all the good suggestions!

I’m thinking I may try a variety of multisensory type of exercises (in the hope that one may help him commit the facts to memory).

I’ll also try working further on the concept and using concrete examples.

Generally he understands math concepts pretty quickly. For example today he asked me how many milliseconds there are in a month. I told him I had no idea. He then said it wouldn’t be that difficult to figure out because all you’d need to know is how many milliseconds are in 24 hours and then figure out how many days are in the month. I asked him who told him this, or if his teacher had been talking about it in school. He told me that no one had told him this. He had just been thinking about it and wondered if his idea would work. I was kind of impressed that he thought of this on his own. I also let him know that I thought that he was very clever to figure this out (this is important because he doesn’t feel he’s very bright) It also seems like we spend so much time focusing on reading that it’s nice to know he does think about math concepts.

When your child understands that multiplication is better than adding up gigantic long columns - and he wants to handle “millisecond” problems - the calculator is ok. What a great way to teach increased place value.

Then you can show how it works in reverse - just for later.

A lot of math is in the language. By the time mine have hit fractions, they’re ready - the terms have been in their vocabulary for as long as they remember. For example, I teach a lot about fractions and figuring with fractions while we cook.

I have one Gifted/ADHD child who never had to learn his tables-they just made sense to him, in fact he skipped third grade math where they “teach” the facts. I have one gifted child who took a long time to memorize hers-in fact she started last year in May and just finally could get 100% on the timed test in school (3 minutes, 100 facts) this last week before vacation. My NLD child could not learn them after 3 years of trying nad would still use her fingers and get them wrong. We purchased Math Facts the Fun Way from City Creek Press. It is a system where they learn a picture/saying to go with each fact. Miracle-she learned them in days this way. She is a very verbal child and memorized the saying that went with the picture. It took much of the frustration out of it for her and enjoyed learning them.

The “drill and kill” system does not work for all children. I would really suggest checking out the web site for City Creek and see if this is something that might work for your child.

There really is a *whole lot* of variation — but from your story, he understands multiplication, though it’s possible if he’s LD that he understands it only in that way (so he’d understand how many ounces in a ton… but wouldn’t understand that if you bought 12 shirts at 7.00 apiece you should multiply to get the answer).
That would be highly unusual.
He sounds very ready to learn these things — whenever you can, solidify those connections between language and math.
HOw does he do with rote memory? It may be all he needs to do is to visualize rows and columns with stars or cars in ‘em.
But… I would still start with the zeroes, and make sure real mastery happens before adding more. Let’s face it, if he took an entire school year to *really* learn them to mastery, he’d be so far ahead of the scads and scads of kids who “learn” them so much more quickly and flounder with them all the way through to college.

Confused by some of these posts. Elsewhere math teachers seem to say that drill is necessary. And yet here experts are saying it’s not. My son gets concepts easily but then just like anyone else needs to reach automaticity. How do you get there wo just memorizing 7x8=56 and why not in tables since that seems easier than having to memorize 7x8, 6x3, 4x9 …. all the facts out of sequence? I don’t think someone totally dependent on a calculater for adding and multiplication is going to be able to do collge physics. I’m probably just not getting what you’re saying so someone please clarify for me??

Re: the 12 shirts at $7.00 bucks a piece, my gifted/LD daughter just doesn’t get it. She will add a column of 12, 7 x. Drives me nuts. She has a “meltdown” though, if I try to show her the “easy” way. She always gets the right answer…. Teacher thinks it’s great that she uses “visual strategies” (sometimes she will actually draw the shirts.) ny suggestions, or should I just let her be? Se knows most of her facts by memory, though a little slow. Good thing we have extended time on those state assessments.

I am firmly on the side of doing both. First understand, and then drill to automaticity and review to overlearn. And yes, I’m a math major. And yes, in Grade 4 my mother drilled 5x8 with me a few hundred times, and now I have good number sense; my daughter’s school thought they knew better and told her not to do her hoework with me, and she never did get multiplication down as well as she should and it caused her delays and nuisances right through university math. But first understand!
Patterns are good. Patterns are what math is all about. Learning tables makes much more sense than memorizing facts at random. And do the visual with the table.

Balance, balance.

Drill without comprehension has limited use. Comprehension without quick automatic retrieval of the facts has limited use.

I watch students who don’t know the tables and how much it slows them down and interrupts the thought process. It’s similar to the way having to decode every word even if you’re accurate does rotten things to comprehension for an otherwise capable learner, and has that same nasty long-term cumulative effect.

I must have missed a message or two — hadn’t gotten a “No-drill” message at all.

Well, meltdowns sort of preclude learning. Does she do it the long way around even on really short ones? It maybe easier for her to “see” the pattern with easier facts. But it could also be that she cognitively needs to “see” that 12 x 7 grid in her mind, and that trying to shortcut to the completely abstract 12 x 7 = 84 fact leaves her with nothing comprehensible to hang onto.

I think I’d encourage her to start with that process and sneak in shortcuts so that she’s visualizing it but cutting back on the slower calculation process… just brainstorming here so this might not work… but if she could practice the facts by drawing the rows & columns and seeing how fast she could uncover a row and say “7 x 1 is 7,” then slide the index card down to reveal the second row and say “7 x 2 is 14”… the goal being to get to where she’s just thinking ” 7, 14, 21, 28” and then, perhaps, even going straight to “7 x 5 is 35… 6 is 42” to get to the bigger ones (or “7 . 10 is 70 so 7 x 9 is 63” and peeling off 7).

Just cause that kid has trouble reading and dealing with the ordinary stuff does not mean he is not bright. Have just read other posts where you said that other parents nad teachers have put him down because of his reading disability-but that is a first-class brain. Don’t let him ever think otherwise. That’s the kind of brain that will solve the problem everyone is in despair over and save the day.

My son can easily understand that the 12 shirts at $7 needs to be multiplied (although his biggest problem is reading these word problems, particularly the names!).

His problem seems to be with rote memorization although he didn’t have tremendous difficulty with addition and subtraction facts.

Yet, he did have a very difficult time learning to recognize the “teens.” For example, for the looongest time he’d think 15 was 51 and he still reverses numbers sometimes. But for some reason the teens were the most difficult. Just verbally memorizing to say “teen” following the number. It’s funny, but when I try to see it from his angle, I can sort of see how the teens don’t make logical sense (for example, it almost seems more logical to have “tenty” for the teens followed by twenty, thirty). I think for some of these kids with reversal difficulties it’s only more confusing that 17 starts with saying seven first in the word seventeen.

This is the key difficulty for my son with soo many things.

How to make everything automatic? Just like with reading which I drill over and over and over with my son (and the repetition does seem to help make slow steady progress).

Perhaps for math it’s similar. First, make sure a child understands the concept very well and can describe it. Review at various times.

Like Ken mentioned in the post above, teach the vocabulary (a good friend of mine who tutors math has told me this is very important). Maybe even make math vocabularly flashcards and practice them.

Then just drill, drill and drill until automaticity is reached.

Now, if I could just get this child to know what time of the day it is. He still sometimes asks if it’s morning, afternoon or evening in the middle of the day!!!!

Thanks PJK, I think it’s important we recognize and applaud our children’s strengths. Everyone needs to be able to look at themselves and feel good about something inside.

I have some symnpathy there because I recognize now I must have had some sort of math ld. I had the time probs and though I could memorize other things instantly the times tables were difficult until my grandmother broke them down for me and showed me the patterns within. I’m not using flashcards precisely becasue I couldn’t find any that were in sequence. I think they would work once the tables are memorized to improve speed and automaticity as weve done with some sight words ala the Seeing Stars Kit. Since my son is 7 I’m really concentrating on addition and multiplication this year even tho he understands the concepts of multiplication well -but beleive me not as well as yours. Touch math really helped with that too. We’re printed the addition and subtraction tables and are drilling those. When he can add and subtract smooth as glass then we’ll go on to multiplication. What helped with the teens for my son is counting by tens then ones. When he could count by tens, hundreds, thousands, with manipulatives then the teens fell into place. I’m learning more nad more that what the school system sees as a natural progression is not natural to my son. For time we learned about the solar system-the sun, 24 hours in a day,minutes in an hour, seconds in a minute, got a watch that marked minutes off on the outer dial with 15, 30 45, 60 minutes highlighted and now he can tell the time… but it wasn’t just here learn this. He HAD to know why so the system made sense to him. I think he learns by systems so he can predict the outcome logically. Wo any logic he has trouble memorizing.
Sorry this got so long.

(Did anybody else think of the parody to that — Kingston Trio — and hollering “Auutomaaaation!!”?? There’s an Orton-Gillingham parody waiting to be written…)

The nicer thing about math is that you don’t have exceptions — and it’s often a *lot* easier to make it visual.

For the time of day issue I’d try to teach a strategy for associating things… so that if he’s already done a and b (breakfast? played out side?) , or it’s been light… whatever he would remember… then it’s somewher earound midday. If the cat has already come howling for that midafternoon snack, it’s after 3:00…

Heck, my otherwise gifted daughter at age twenty can’t read a regular analog clock — has depended on digital watches since she was six; don’t know what she’ll do now they’re really out of style, think she buys them in the kids’ department.
I have great difficulty with time and elapsed time, and was in my thirties or forties before I got much of a handle on it; got through high school by watching when other people did things.
You don’t have to be wonderful at every single skill; learn the basics and learn how to cope around the details.