Gifted Issues Discussion homepage Forums General Discussion multiplication table - advice please

Visualization, semantic encoding, memory castles, etc. are great for memorizing sequential primarily disconnected information. They are effective for that purpose. Ideally math isn't disconnected. Math works best integrated. Numerical patterns work extra math skills and their usefulness reoccur outside of just say solving timed times tables. Discovering that adding the digits of a number divisible by nine gives a number that is also divisible by nine has more uses than the image of a basketball star surfing on a pizza box.

One of the old MOEMs problems that my son was looking at was:
What is the remainder of 111,111 divided by 27.

If the go-to skill is memorized multiplication tables, the path to the answer may be slow grinding. With some of the patterns a kid may discover in exploring multiplication, this can be much quicker. And these skills continually to build and diversify with more multiplication problems.

With either path the end result is automaticity. On one of the paths there are also tons of other patterns, methods, and insights earned.

I suppose I can see how a mathematician would cringe at this method. My DD already understands the concept quite well and was pretty good at picking up on patterns to help her figure it out also. How many children learn multiplication tables by flash cards, songs or other rote memorization. I just knew that this was something that my DD would love because it is verbal, visual and silly and it would give her confidence and boost her automaticity with little effort. I don't really think that this or any of the other memorization methods comes at the cost of exploring patterns and developing additional math skills. Then again perhaps if she is trying to remember the answer to 9 x 7 for example, maybe she will fall back on trying to remember the story rather than working with the numbers. I don't know. I don't expect her to mind to go from question to story to answer much at this point. It just seemed to be one additional way to connect the numbers and she just seems to know them now without thinking about it. You have started me thinking though. My daughters school math is mind numbing repetition of the same nearly identical worksheets for the past 6 weeks. Clearly she is not exploring anything of use there. I was hoping that increasing fluency with math facts would help open up new options for her but perhaps I need to think of more than advancing her into more appropriate material. There is a lot of exploration she could do with a little encouragement.

Search for "Vi Hart" her videos can stir quite a lot of thinking.

I can't help but wonder if that was 111,111 divided by 37 instead.

I could've misremembered it; I'm good at that.

27 would be more interesting.
111111/3=37037 cong 2 mod 9
111111 cong 6 mod 27

Knowing MOEMs It would have been 37. Make you do all the work for nothing.

It all depend on where you are at in learning. If you are memorizing the Presidents or State or digits of Pi then a little song would be fine. If you are doing it for math facts you need to quickly see the patterns and properties. You can usually go far just using a simple table show them some patterns and let them discover some of their own.

So to OP.
My ds was probably around 5 when he got his multiplication facts down 0-10. Division tripped him up for a bit on recall. He loved doing worksheets.
He would make a big multiplication Table outline in sidewalk chalk on the drive way and fill it in before he knew what it actually was.

Thanks 22B for the explanation. If I were homeschooling I believe we would be handling our tables differently.

I haven't read all the posts so not sure this has been mentioned but DS, now 6, learned it through the Rock n' Learn multiplication CD's at 4 1/2. He loved the music and we played it in the car. He was obsessed with numbers and this was a way to satisfy his "number needs" :-)