Multiplication/Help

Notice: Incomplete

Removing unnecessary detail

We're used to this multiplication table:

x	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

To reduce the mental strain, remove the 10-, 11- and 12-times tables and replace the 1-times tables with a rule of 'one times anything is itself'. If you must, here are some more rules for the 10-times tables and most of the 11-times tables.

10*x= Add a 0

11*x; x<10. Repeat the digit

Truth is, the 10-, 11- and 12-times tables aren't necessary for multiplication to work

Removing duplicates

x	2	3	4	5	6	7	8	9
2	4	6	8	10	12	14	16	18
3	6	9	12	15	18	21	24	27
4	8	12	16	20	24	28	32	36
5	10	15	20	25	30	35	40	45
6	12	18	24	30	36	42	48	54
7	14	21	28	35	42	49	56	63
8	16	24	32	40	48	56	64	72
9	18	27	36	45	54	63	72	81

This is the multiplication table that would now be taught. Notice the duplicates? They can be removed, and the child can be taught to flip the multiplication to solve it:

2	4
3	6	9
4	8	12	16
5	10	15	20	25
6	12	18	24	30	36
7	14	21	28	35	42	49
8	16	24	32	40	48	56	64
9	18	27	36	45	54	63	72	81
x	2	3	4	5	6	7	8	9

We get this multiplication table, with only 36 facts, a quarter of the original table!

Applying the distributive law

2	4
3	6	9
4	8	12	16
5	10		20
6		18		30
7		21			42	49
8		24		40
9		27				63		81
x	2	3	4	5	6	7	8	9

Changing the method

If your child still can't grasp the above multiplication table, just have them remember this list of 19 numbers:

0	0
1	0
2	1
3	2
4	4
5	6
6	9
7	12
8	16
9	20
10	25
11	30
12	36
13	42
14	49
15	56
16	64
17	72
18	81

To use this table, if you want to do 8*7, you take 8+7, which is 15 and 8-7, which is 1. 15 goes to 56 and 1 goes to 0. Therefore, 8*7=56-0=56.

This works because $\frac{(a+b{)}^2}{4}-\frac{(a-b{)}^2}{4}=ab$. The numbers in the list go to a quarter of its square. However, you may notice that the odd numbers map to a number that is off by 0.25. They can be omitted as they cancel each other out in the final subtraction for integers.

Explaining why it works should be saved until your child learns algebra. However, if your child asks why before then, here's a visual explanation: