Memorizing math facts

7 x 3 is a tough one for some reason. (Okay, the 7’s are tough for lots of good reasons.)
Just like spelling he cuold benefit from some good strategies — and unlike spelling, there are NO EXCEPTIIONS :-) :-) For example: first, does he know that 7 x 3 is the same as 3 x 7? That it doesn’t matter which way you multiply — just as it doesn’t matter which order you’re counting something? (Whether you count a rectangle of chiars by the rows or the columns, it’s still the same clump of chairs.)
and once he realizes that…
Does he know 3 x 5 or 5 x 3 automatically? Start from there and go up six…

What helped my son at that age was Singapore Math level 2 workbooks. You can look at samples at www.singaporemath.com. This made a huge difference in his test scores.

One strength of these workbooks is that they show that there are many ways of deriving a math fact. For example, if you forget what 3 x 7 is, you can always figure it out by adding 7 + 7 + 7. If you forget what 6 x 7 is, but you know what 6 x 6 is, you can figure it out by adding 36 + 7.

After he finished the Singapore workbooks (took him 3 or 4 months), he did 5 to 10 minutes a day of Quarter Mile Math (www.thequartermile.com) for awhile. There’s so much in that program, I still have him use it periodically — above and beyond just the math facts. QMM kept the math facts fresh and improved his speed.

Hope this helps!

Lil,

My son had trouble with sequencing. It was extremely bad before Interactive metronome but I saw a big jump with that.

We just started audiblox. One of the activities is to count the blocks to 30 forward and then back. He can do it but almost always muffs up at least once on the way back down.
This tells me that his sequencing of the basic numbers is not competely automatic.

Now he can skip count and do higher order things but I have learned to get down to the very very basics and make sure they are automatic so that everything else will become easer. If you don’t do this they will be able to function but the very basic things that are not automatic will always take brain power away from the higher level skills.

Victoria says this alot and she is so right. I really saw this with audiblox.

I am a fourth grade teacher and I can provide you with a method that I use to teach multiplication and division and the connection between them. I teach them as “fact families”. Many times addition and subtraction facts are taught this way.
Each family is composed of three numbers.
For example: 3, 7, & 21
I teach students that in multiplication the largest number is always the answer, so they then know that 3x7=21 or 7x3=21.
I tell them that if they flip it around, they can do division. 21 this time will be the first number, so 21/7=3 or 21/3=7.
I have found that this approach really helps some of my students understand the commutative property of multiplication. There are many good resources on the internet (internet flashcards and such) that would also be a good supplemental resources. Good Luck!!!

Lil, having your son skip count in the way you described is great but also make sure that he counts them backwards too…3,6,9,12,15,18,21,24,27,30,30,27,24,21…etc. I’ve found that the cementing of the facts comes in the skip counting back down the numbers.

I also always make sure, from the outset, the kids get the commutative property concept. I use a Montessori board that shows all the times tables and I have the kids cover up all the ones that have the same product. That of course eliminates half the facts. They like it when they see that for themselves. Then I show them the various tricks for the 9 tables. Natch. That one’s done. They’re starting to feel like these tables just might be do-able.

Most kids know their 2’s and 5’s. The 4’s are among the easier tables if you can get them to see that the answer is twice what the 2’s are. Most kids seem to get the 3’s with relatively little work.

Then I show them that, really, it’s the 6’s (but they’re double the 3’s), 7’s, and 8’s that are hard, and then of course only a handful of them (because the commutative property takes care of half of them too). Before you know it, they discover there aren’t all that many times tables to memorize and they feel up to the task.

Sometimes I think it’s the sheer volume that kids struggle with. If they can think of the facts as being do-able, they’re more motivated to get it done.

Lil,

My son is the same age with the same problem. This is what we’ve been doing. It has been quite a long process.

1. We started with skip counting 2 and 3’s to a metronome. We did it to 100. I had to start with a sheet of paper with the numbers on it in boxes. So it would be 2 4 6 8 10
12 14 16 18 20

and so on. When he could do this easily in time, I had him do the same thing without the sheet of paper. I would chime in with him if he missed one.

2. When he mastered 2’s, we did 3’s and 4’s using the same process.

This process helped get his sequencing down (he always understood the concept of multiplying).

3. We then did Victoria’s exercise of chanting the tables except we had him do it on the trampoline. My son’s motor system is very involved in his deficits and incoprorating motor activity makes a tremendous difference in his automating learning. At this point, my son would know that 7 x 3 was one of the 3 numbers but would guess the wrong one.

We did 2 X 0 = 0
2 x 1 = 2
2 x 2 = 4

We had tried this earlier but without the skip counting first, he just couldn’t do it.
4. Then we moved to paper for those facts that were mastered doing the chanting. I have sixty math facts written out for 0 - 6’s, one to a line with space in between. They are on three pages. They have the answer on them. I read the problem and he tells me the answer. I time it with a radio shack timer. Then he does the same thing with the sheets without the answer on them. Basically, he is seeing the problem at the same time as he is hearing it.

5. Once the two times are equal, I will move him to Quarter Math. His Neuronet therapist told me to do number 4 first because he is hearing and seeing the facts at the same time.

6. We are working on different facts at different levels. He is doing skip counting (now on a ball) for 7 and 8’s while doing number four above for 0-6’s.

7. It is working!!! I see a big difference in how hard his multiplication homework is for him. Also, he now knows when he doesn’t know—the beginning of wisdom is knowing when you don’t know.

8. We did do IM this past summer and I see a difference with math for him. He actually got an A last marking period while he was getting C’s last year and that was a gift. Unfort. it hasn’t made basic memorization easier, although I think acquiring the sequencing was enabled by IM.!

9. Haven’t tried having him do skip counting backwards as Joan suggests but could incorporate

10. I keep telling myself that he will need multiplication forever!
Beth

Audiblox is big on doing things back and forward. It makes sense especially for my son because he can say the numbers but it is not always clear he understands what he is saying. Doing it forward and backwards they have to really understand what they are doing, not just regurgitating the numbers. My son is a master at regurgitating things only to have it become apparent later that it didn’t stick because he was just going through the motions.

Joan,
Saxon’s approach is interesting here. In the third grade series, there is a lot of work (oral and written) at the very begining about the number of days in one week, then after a while two weeks, followed by three weeks and so on. In the meantime, multiplication by ones is introduced and then twos (as I recall). By that time, the children have gotten up to how many days in nine weeks. Then the sevens multiplication facts are introduced—which, if all the work on weeks has been done, are easy. Then they do fours, followed by eights, and finally threes, sixes, and nines. (Somewhere along the line multiplication by 10 is introduced, but I don’t quite remember when.) The approach to addition is also interesting. The 1+ facts first, followed by doubles, then to the rest of them only after the doubles are learned.

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Yes, I really like that approach, mariedc. It makes great sense to approach those pesky 7’s in that fashion. There’s lots about Saxon math that I like, esp. for my struggling clients. Unfortunately few of them have had such exposure when they come to me privately.

Joan,

After reading your post, I had my son do skip counting backwards. He can do it, but not quite as fluently as forward. Do you work for the same fluidity, or is the fact of doing it enough?

Beth

We work on the same fluidity. It IS hard going backwards but that extra time practicing it that way seems to be what nails the facts.

Thanks for answering. I was actually surprised at how well he did. I visualize the numbers when I do it and I know that isn’t one of his strengths. We’ll add it to the routine and keep at it.

Beth

I have a son who is an LD 4th grader who has been taught addition, subtraction, multiplication and division with Touch Math. We ran into a road block with multiplication. He just could not skip count to get the 6,7, and 8s. I am a LD teacher who serves 3rd and 4th grades. Last year I taught my 3rd graders their math facts using a program called “Times Tables the Fun Way”. When I saw that my son was not mastering his facts I decided to teach him the program. I am delighted with how my students from last year have their facts down pat in 4th grade now. They are inclusioned this year and are basically keeping up with their peers because they aren’t playing catch up with their math facts. Also my son now knows his facts. Again my third graders are starting with this program and I hope to see the rewards next year!

I have to tell you that I used Math Facts the Fun way last year with my then third grader. He learned the little jiggles and managed to Ace his tests pretty much through. I was thrilled. However, he could not learn division—he just did not have the sense of what math facts went together. So I knew we had to find another appraoch. The multiplication also never automated into long term memory.

So, we’ve been back at it this year. He is getting it this time.

Try skip counting using a piece of paper with the numbers written on it first. My son couldn’t even do skip counting with 3’s without a visual guide at first.

Beth

My son also had problems with addition and subtraction. We introduced him to touchmath. They also have the program for multiplication, division, and fractions.

It is a great program that uses dots on the numbers so if your child is visual then they can multiply using the dots.

Your school resource person should have access to the program and should be purchased by the school district since he has an IEP. Check out the website at touchmath.com

Families are good — I always tell kids that they get four facts for the price of one, and they appreciate cutting the work load in four.

Be very careful about teaching half the truth as the whole truth. You tell the kids that the biggest number is “always” the answer in a multiplication. Well, as long as you’re doing positive whole numbers above 1 it is. When you do the one times, and then the fractions, and the decimals, and then the negative numbers, that statement is absolutely *false*.
I have taught, and now tutor, every grade level, so I see fallacies from earlier grades coming up and causing serious problems in higher grades. If a child at an impressionable age learns that multiplication *always* makes larger, and division *always* makes smaller, then he gets in trouble in the middle grades when all those other topics are introduced. It is far better to use the word “usually” instead of “always”, or to mention frequently “As long as we are using counting numbers …”
Don’t think that this is a small issue. Ask any of the parents here whose kids have hit high school and are trying to teach negative numbers how much resistance they have to overcome about the idea that you can subtract bigger from smaller (but Miss Smith told us that you can never do that!), or those trying to teach fractions how much resistance they have to the idea of dividing a smaller number by a larger (But Miss Smith said that’s *impossible*, you *always* divide the big number by the little one!) Kids waste months pointlessly, and some stall there for years or for life.

Hi ~ this is so far down this post I don’t know if anyone will see it :), but just wanted to throw in my two cents. I completely agree with what was written earlier about the Saxon program. I’ve had a number of LD kids learn their multiplication facts that way. We follow their daily calendar activities (at the 3rd gr. level) closely, and they do learn the number of days in 1 week, 2 weeks, etc., all the way up to 10 weeks. Meanwhile, they’re reviewing addition and subtraction facts learned (hopefully!) in the grade 2 program, as well as multiplying by 0, 1, and 10. We skip count every day: 2’s, 5’s, 10’s, 7’s, 4’s, 25’s (so far, they eventually move to 3’s, 6’s, 8’s, 9’s as well). After reviwing the days in 1-10 weeks for 2-3 months, they introduce multiplying by 7’s, the first “real” facts they’ve done. All my LD and NI kids have picked up multiplying by 7 within half an hour of that first lesson, and is sticks!!!! A few weeks later they teach the 2’s, then go from there. I’m teaching my older kids that the 4’s are the 2’s doubled, and the 6’s are the 3’s doubled. If you’re consisten and diligent to follow the lesson plan, you will see that they are learning them.