Double, then double
4 × 7: seven doubled is fourteen, fourteen doubled is twenty-eight. Two easy steps instead of one fact to remember. It works for every number in the table and it keeps working long after the table ends, which the chanting does not.
Why to teach the method and not only the answers
A child who has learned the method can do 4 × 13 the same afternoon. A child who has learned the ten answers cannot, and will not be able to until somebody teaches them again. The method is worth more than the table it came from.
Where it usually breaks
The second double is the problem, not the first. Doubling 6 to 12 is fine; doubling 12 to 24 crosses a ten and that is where a child slows down or guesses. If 4 × 6, 4 × 7 and 4 × 8 are the three that keep coming back wrong, the table is not the difficulty — doubling past ten is.