How to teach the 6x tables
in less than 20 minutes and only 3 steps
To do this exercise you will need a whiteboard, marker and duster or piece of paper and some pens. So long as you can work together on one surface, anything goes.
By the time your child is needing to commit their six times tables to memory, they will already be familiar with quite a few multiplication facts. Here is the order they are taught in schools:
As you can see, then, there is already plenty to work with when they get to their 6x tables.
Oh, and, it's a good idea for you to run through the table beforehand... just to be sure you know the answers!!
Step 1: Figure out "the easies"
The first step is to figure out the easy ones. This means they can answer any "6 x ?" almost instantly.
On your surface, write out the following, onebyone, and check them off:

6 x 1 = (answer = 6)

6 x 2 = (answer = 12)

6 x 10 = (answer = 60)

6 x 5 = (answer = 30)
From here, ask your child if there are any others they know really well. You may find 11x has already been conquered, but 3x, 4x, and 9x may be relatively new.
Don't forget to check 6 x 0, and 6 x 1. Some children get confused here.
Remind them that x ("times") is the same as "lots of", so 6 lots of nothing is nothing
and 6 lots of 1 is 6".
When you've got "the easies" figured out, write them down (with answers) on your surface and move on to Step 2.
Step 2: Identify strategies
Step 2 is about deriving strategies (that your child finds logical) to remember the rest of the table.
There are different ways to approach this, but here I'll show you what worked for 9yearold Ella.
We started with doubles from her 2x "easy":

6 x 2 = 12

6 x 4 = 24 ("2 doubled is 4, and 12 doubled is 24")

6 x 8 = 48 (4 doubled is 8, and 24 doubled is 48  you might need to pause while they process this)
Then I showed her this:

6 x 2 = 12 (she knew that)

6 x 4 = 24 (getting there)

6 x 6 = 36 (no idea)

6 x 8 = 48 (getting there)
The trick is to emphasize the coloured numbers and point out the pattern. Then point out the pattern before the coloured numbers in the answers (1, 2, 3, 4).
At this point we drilled these a couple of times in random order with her "easies" thrown in occasionally.
Together, work out sensible ways to remember "the difficults". Here's what we did:

6 x 3 = 12 + 6 = 18 (i.e., used 6 x 2)

6 x 12 = 66 + 6 = 72 (i.e., used 6 x 11)

6 x 7 = 48  6 = 42 (i.e., used 6 x 8)

6 x 9 = 60  6 = 54 (i.e., used 6 x 10)
Step 3: Revise and practice
Hopefully, your child will be eager to continue at this point, because they can feel how close they are to conquering this daunting task.
Now, it's time to quickly revise the new strategies (in clumps that make sense) and reel off all the sixes in a semirandom order. I did the "coloured" set first in random order, then "the easies" in random order, and then "the difficults" in random order.
If your child gets any wrong, remind them of the strategy they need to work it out correctly.
The next bit is vital. If you're at the 20minute mark. Stop. Let your child sleep on their new learning. Then, in the morning, see if they'll give it a go. If I know brains (and I do), they will have retained almost all the strategies you set in place the day before.
Good luck!