There are also nifty little "tricks" that once learned can make the memorization easier:
ie: multiplied by one will be the original number; by two will always be an even number, by three, the sum of the digits will be divisible by 3; by 4 will be every "other" even number; by five will end in "0" or "5"; by nine, the sum of the digits will equal 9 (9x9=81; 8+1=9) (9x11=99; 9+9=18; 1+8=9); tens will always end in zero - there are "tricks" for them all. I wish I could include them all here, but a search of the web should prove fruitful. I hope you find this helpful! :)

Oh my! I am new to this and had NO IDEA that so many had responded! Thank you all so much! There are so many great ideas, but it seems that memorization is the way to go. That's great! It makes me feel better that so many, with so much experience have come to the same conclusion. THANK YOU!

Speaking of tricks there is one that I find helpful in checking my arithmetic. It's caslled "casting out 9's" and it seems to be becoming lost.

What it is is that in any arithmetic operation you can replace any number by what you get by adding the digits of the number, and the result should be the same. For example 746 x 397 = 296,162. To check this we "cast out 9's" as above, thus
746 -> 7+4+6=17 -> 1+7=8
397 -> 3+9+7=19 -> 1+9=10 -> 1+0=1
296,162 -> 2+9+6+1+6+2=26 -> 2+6=8
and 8 x 1 = 8, so the multiplication is probably correct.

Note this is not foolproof. For example if I got an answer of 24 where the correct answer is 51 this procedure would not catch the error.

This procedure works for any integer arithmetic operation. This is because 10 to any power is 1 reduced modulo 9. So for example 296,162 = 2x10^5 + 9x10^4 + 6X10^3 + 1X10^2 + 6x10^1 + 2X10^0, which reduced modulo 9 is 2 + 9+ 6 + 1 + 6 + 2.

I realise this is an old question and so I apologise for reviving it, however as I found it through a Google search I'm sure others will too.

I would like to quickly reiterate the importance of children learning their multiplication tables. When I was young, I didn't. I found them to be menial, agonisingly boring and difficult. Although lacking the needed support at school, at home I found great support from a parent involved in the education industry. Still, I managed to slip by without learning them properly.

Today I'm in my early twenties completing a University degree that encompasses both logic (my love) and mathematics (my bane). I have been forced to extent my degree through sub-par mathematical performance, however I will still graduate near the top of my peers.

Multiplication tables are vitally important. Like suggested previously, I too can 'work things out' by other means but doing so takes excess time, imposes undue stress in both obvious and surprising areas of life and reduces confidence.

In truth, I have found myself quite fascinated by University level math and have a suspicion that my performance in them would have been starkly different had I taken the time to learn the basics at a young age.

Now I'm off to revise my tables!

I'm with you, Oranges!

What worked with both my children is something I did at school and that was chanting them to a tune 2x2= 4 3x2=6 etc etc, I used to get them chanting in the car on the way to school anywhere and everywhere. Worked for mine maths is their strength and where kids are concerned anything is worth a bash.