One method I learned from a fellow tutor for the 3 times table got my student very intrigued.
This method uses a 3 by 3 grid. Since the number 3 is written from the top left down to the bottom left, we will start with the number 1 on the bottom left of the grid. Moving up in the first column, the numbers 2 and 3 are placed in the second and first slot of the grid respectively. the next column is filled in the same way with the numbers 4, 5, and 6, moving upwards from the bottom slot to the top one. The last column is again filled in the same way with the numbers 7, 8, and 9. You should get something like this:
3| 6| 9
2| 5| 8
1| 4| 7
Next, the number 0 is added in front of the numbers on the first row, the number 1 is added in front of the numbers on the 2nd row, and finally the number 3 is added in front of the numbers on the 3rd row. The final result should look like this:
03|06|09
12|15|18
21|24|27
If you go across the rows, you will get your 3 times table. :)