Keep him playing with these cards until he can give the correct answer to any question and give the correct table as a whole. After the tables have been learned you can make many tests of speed and competitive games with several children of the same age or school grade.
The Difficult Tables
There are certain tables which seem harder for some than the others, yet there is often a difference as to which are considered most troublesome. The 2's, 3's, 5's, 10's, and 11's are easy for all of us. The 9's are as easily learned with the aid which follows. This leaves the 4's, 6's, 7's, 8's and 12's, remaining to work on. The combinations that are new in these tables are the following; all other combinations are known from the other tables:
| 4 × 4 = 16 | 6 × 6 = 36 | 7 × 7 = 49* | 8 × 8 = 64* |
| 4 × 6 = 24 | 6 × 7 = 42* | 7 × 8 = 56 | 8 × 12 = 96 |
| 4 × 7 = 28* | 6 × 8 = 48 | 7 × 12 = 84 | 12 × 11 = 132 |
| 4 × 8 = 32 | 6 × 12 = 72 | 12 × 12 = 144 | |
| 4 × 12 = 48 |
The first help in mastering these few necessary combinations is visualization. If you will print them in large figures and the answer in red, each table on a sheet or page by itself so that they can be handled and studied, they will form visual impressions that can be recalled with ease by almost any one. This is especially true of children at the ages when they will be learning these tables.
Repetition seems the most valuable aid, but to be most advantageously applied it should be a combination of visual and auditory repetition. Let the child look at the tables in the large form in which you have made them, while he repeats them.
Use addition and subtraction. In learning the tables there are always some which make a stronger impression and which the child will "never forget." Use these as starting points or bases of operation. For example, 4×5=20, all will recognize this at once. 4×4=16, just four less than twenty, and the subtraction will quickly give the correct answer. Also 4×6=24, or 4 more than the known point of 20. To take advantage of this it will only be necessary at first to learn 4×7=28 in order to master the entire table of 4's. The 4×4, and 4×6, would be figured from 4×5=20, and the 4×8 from the 4×7, and the 4×12, from the known 4×11=44. With these known bases to work from it is only necessary to fix the one starred combination in each table in mind indelibly at the beginning, the others will be easily figured from the known bases and will become fixtures from use.
The Table of 9's
There is a peculiar combination of figures in this table of 9's, which, if once noticed and perceived, will make this one of the easiest of the tables.
| 9 × 2 = 18 (1 + 8 = 9) | 9 × 8 = 72 (7 + 2 = 9) |
| 9 × 3 = 27 (2 + 7 = 9) | 9 × 9 = 81 (8 + 1 = 9) |
| 9 × 4 = 36 (3 + 6 = 9) | 9 × 10 = 90 (9 + 0 = 9) |
| 9 × 5 = 45 (4 + 5 = 9) | 9 × 11 = 99 (2 9's) |
| 9 × 6 = 54 (5 + 4 = 9) | 9 × 12 = 108 (1 + 0 + 8 = 9) |
| 9 × 7 = 63 (6 + 3 = 9) |