
Topic: Multiplication
Summary
Multiplication is a Mathematical operation of adding together multiple copies of the same thing.
Intro
For example, the multiplication of Whole Numbers can be illustrated with this example....
5 + 5 + 5 = 15
This example above has 5 multiplied 3 times. Or, said another way, this is: 3 times 5.
This is often written as the short hand....
3 × 5 = 15
That symbol that looks similar to an "x", is actually a different symbol. The "×" is called the "Multiplication Sign".
When you see the "×", it is read as "times". So "3 × 5" would be read as "three times five".
Some people don't use the multiplication sign  "×"  to denote multiplication. Some people write it like this instead, with a Middle Dot (which is also called a middot)....
3 · 5 = 15
And still some put the dot lower, and write....
3 . 5 = 15
In many Programming Languages, multiplication is done using the Asterisk. And although the notation below would likely not be seen in any of these computer programming languages, it is suggestive of it....
3 * 5 = 15
All these mean the same thing though. I tend to normally use the Multiplication Sign  "×"  if given the choice.
My History
Most of the credit for teaching me how to multiply goes to my mother. She started teaching me Mathematics before I could even talk. And once some of my Elementary Schools teachers saw how advanced my brother and I were in many many of our studies (including math), they asked my mother to volunteer at the school and teach. Which she did.
I also learned alot about teaching Math, including multiplication, from when I was a Math Tutor. I figured out that one of the biggest problems people have with math, in general, is not being able to multiply in their heads.
It was one of the things I checked for first, when a student had trouble in math. It's never too late to learn to multiply in your head. (But it's best to learn it as young as possible!)
Learning and Teaching HOWTO Multiply
Being able to multiply in you head is an important skill! And something you should teach your kids to do while they are still young!
(Start this education before they are able to talk.)
Even in this age, with electronic calculators and computers, it's still better to be able to multiply in your head. I can multiply numbers faster in my head, than the time it would take to enter them into an electronic calculator or a computer.
Make sure your kids learn how to multiply in their heads!!!
Do not let them become dependent on machines. (It is a weakness. And they could suffer because of it. And could be put at a disadvantage.)
Kids who are not able to multiply in their head often have alot of trouble learning new or more advanced Math topics, because they are still struggling with the multiplication part of it, and not able to get to the "real" problem.
Counting By Multiples
One skill that's useful in learning how to and being able to multiply is being able to count by multiples.
For example....
 being able to count by 1s
 being able to count by 2s
 being able to count by 3s
 being able to count by 4s
 being able to count by 5s
 being able to count by 6s
 being able to count by 7s
 being able to count by 8s
 being able to count by 9s
 being able to count by 10s
 being able to count by 11s
 being able to count by 12s
 being able to count by 13s
 being able to count by 14s
 ...
Counting By 1s
This is a very very basic skill, and is the same as justing being able to count. You should start teaching your kids this before they can talk.
Counting By 2s
Once you child can count by 1s  can count  then they know the numbers (up to whatever limit you taught them up to). The next step is to teach them to count by 2s.
Just help them memorize the sequence...
2, 4, 6, 8, 10, 12, 14, 16, 18, 20,...
... and make sure you associate this with numbers of physical objects. Like use blocks, legos, pieces of food, toys, coins, or whatever, and count the objects by twos with them. And get them to do the same!
Counting By 3s, 4s, 5s,...
After doing 2s, do the same for 3s, 4s, 5s, etc....
First make sure they know the sequence. And then associate this with counting objects.
Note, make sure you they don't forget what they have already learned. And keep on going over the old stuff too.
Multiplication Table
After they can count by 1s, 2s, 3s,... the next thing to do it to get them to memorize the Multiplication Table.
The memorization of this can be aided with some "tricks" and some Mnemonics.
You can also start them off with a smaller multiplication table first, and then expand it.
Here's one you can start with....

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
1 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
2 
2 
4 
6 
8 
10 
12 
14 
16 
18 
20 
3 
3 
6 
9 
12 
15 
18 
21 
24 
27 
30 
4 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
5 
5 
10 
15 
20 
25 
30 
35 
40 
45 
50 
6 
6 
12 
18 
24 
30 
36 
42 
48 
54 
60 
7 
7 
14 
21 
28 
35 
42 
49 
56 
63 
70 
8 
8 
16 
24 
32 
40 
48 
56 
64 
72 
80 
9 
9 
18 
27 
36 
45 
54 
63 
72 
81 
90 
10 
10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
And here's one you can do next....

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
1 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
2 
2 
4 
6 
8 
10 
12 
14 
16 
18 
20 
22 
24 
3 
3 
6 
9 
12 
15 
18 
21 
24 
27 
30 
33 
36 
4 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
5 
5 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 
60 
6 
6 
12 
18 
24 
30 
36 
42 
48 
54 
60 
66 
72 
7 
7 
14 
21 
28 
35 
42 
49 
56 
63 
70 
77 
84 
8 
8 
16 
24 
32 
40 
48 
56 
64 
72 
80 
88 
96 
9 
9 
18 
27 
36 
45 
54 
63 
72 
81 
90 
99 
108 
10 
10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
110 
120 
11 
11 
22 
33 
44 
55 
66 
77 
88 
99 
110 
121 
132 
12 
12 
24 
36 
48 
60 
72 
84 
96 
108 
120 
132 
144 
And this one after that....

0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
1 
0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
2 
0 
2 
4 
6 
8 
10 
12 
14 
16 
18 
20 
22 
24 
26 
28 
3 
0 
3 
6 
9 
12 
15 
18 
21 
24 
27 
30 
33 
36 
39 
42 
4 
0 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
44 
48 
52 
56 
5 
0 
5 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 
60 
65 
70 
6 
0 
6 
12 
18 
24 
30 
36 
42 
48 
54 
60 
66 
72 
78 
84 
7 
0 
7 
14 
21 
28 
35 
42 
49 
56 
63 
70 
77 
84 
91 
98 
8 
0 
8 
16 
24 
32 
40 
48 
56 
64 
72 
80 
88 
96 
104 
112 
9 
0 
9 
18 
27 
36 
45 
54 
63 
72 
81 
90 
99 
108 
117 
126 
10 
0 
10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
110 
120 
130 
140 
11 
0 
11 
22 
33 
44 
55 
66 
77 
88 
99 
110 
121 
132 
143 
154 
12 
0 
12 
24 
36 
48 
60 
72 
84 
96 
108 
120 
132 
144 
156 
168 
13 
0 
13 
26 
39 
52 
65 
78 
91 
104 
117 
130 
143 
156 
169 
182 
14 
0 
14 
28 
42 
56 
70 
84 
98 
112 
126 
140 
154 
168 
182 
196 
Note, thes multiplication tables shown above are meant to be illustrative of what needs to be learned and memorized. You and your kids should be able to multiply any and all these values, in your head, without lookig at this.
Error Detection Tricks
TODO
Error Detection For Multiplying By 3
TODO
The answer to anything multiplied by 3 should end in a: 3, 6, or 9.
TODO
Error Detection For Multiplying By 5
TODO
The answer to anything multiplied by 5 should end in a: 0 or a 5.
TODO
Error Detection For Multiplying By 10
TODO
The answer to anything multiplied by 10 should end in a: 0.
TODO
Mutlplication Tricks
TODO
Mutlply MultiDigit Numbers
For multiplying multidigit numbers that you don't have memorized, there are Algorithms you can use to perform the multiplication.
TODO
Things To Know
TODO
 do you have this sequence memorized: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20,...
 do you have this sequence memorized: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30,...
 do you have this sequence memorized: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40,...
 do you have this sequence memorized: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50,...
 do you have this sequence memorized: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60,...
 do you have this sequence memorized: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70,...
 do you have this sequence memorized: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80,...
 do you have this sequence memorized: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90,...
 do you have this sequence memorized: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100,...
 do you have this sequence memorized: 11, 22, 33, 44, 55, 66, 77, 88, 99, 121,...
 do you have this sequence memorized: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120,...
 do you know the "trick" for multiplying 0 with anything else?
 do you know the "trick" for multiplying 1 with anything else?
 do you know the "trick" for multiplying 2 with anything else?
 do you know the "trick" for multiplying 5 with anything else?
 do you know the "trick" for multiplying 10 with anything else?
 do you know the "trick" for multiplying numbers that end in 0's?
 do you know the "trick" for multiplying anything that end in a 5 with itself? (ex: 15 × 15 or 25 × 25 or 35 × 35 or ... or 1125 × 1125 or ...)
TODO
See Also
 Mirza Charles Iliya Krempeaux




