Why sequential order is the problem
The default approach is to learn the 1 times table, then the 2s, then the 3s, and so on to 12. It has the appeal of being obviously systematic. It also groups together tables that have nothing in common and buries the genuinely difficult facts at the end, where children reach them exhausted and short of time.
A better order groups tables by the pattern that makes them learnable, and deals with the hard residue directly rather than hoping to arrive at it.
Start with the patterns children can see
The 10s first. Every answer ends in zero and the other digit is the number you multiplied. Children get this almost immediately and it gives them a table they know completely, which matters for confidence more than it does for arithmetic.
Then the 5s. Every answer ends in 5 or 0, alternating. Children who can count in fives already have most of it, and the link to clock faces makes it concrete.
Then the 2s, which is doubling — something most children can already do informally with objects long before they meet it written down.
These three cover a third of the multiplication grid and take comparatively little effort, because each carries a visible pattern rather than being a list.
Then the ones built from those
The 4s are double the 2s. A child who knows 6 × 2 = 12 can get 6 × 4 by doubling again. Teaching it as a relationship rather than a new list means they have a route to any fact they forget.
The 8s are double the 4s, by the same argument.
The 3s do not have a shortcut of that kind, but they are small enough numbers to be manageable and they come up constantly.
The 9s have two patterns worth showing: the digits of every answer sum to nine, and as the answers climb, the tens digit increases by one while the units digit decreases by one. There is also the finger method, which children enjoy and which works. It is a crutch rather than knowledge, but it is a crutch that gets them through the table while genuine recall builds.
Commutativity is the biggest single saving
If a child knows 7 × 8, they also know 8 × 7. This is obvious to any adult and it is very frequently never said out loud to the child.
Said explicitly, it changes the size of the task dramatically. The tables to twelve contain 144 facts. Once you know that order does not matter, there are 78 to learn. Take out the 1s, 2s, 5s and 10s that come nearly free, and what is left is around ten facts that need real work.
Ten facts is a job a child can see the end of. A hundred and forty-four is not. Telling a struggling child this one thing frequently changes their whole relationship with the topic, because the task stops looking infinite.
The facts that are actually hard
Strip out everything with a pattern and what remains is roughly: 6 × 7, 6 × 8, 7 × 8, 6 × 6, 7 × 7, 8 × 8, and the 12s. These sit in no useful pattern, which is exactly why they are hard.
They are also, in sequential teaching, the last things reached — so they get the least practice, at the point when everyone is most tired of tables. This is why so many adults who are otherwise fluent still hesitate on 7 × 8.
The remedy is unglamorous: attack them directly, early, in short sessions, before finishing the rest. A sheet of ten facts practised for four minutes a day is more effective than another pass through the 3s, and it targets the actual gap.
Recall and method are different sheets
Knowing 6 × 7 instantly and being able to calculate 34 × 6 on paper are separate abilities. A sheet that mixes them measures neither well, because a child slow on facts will be slow on the method for reasons that have nothing to do with the method.
Keep fact recall short and, if you like, timed — that is what timing is for, facts that are already understood. Keep written method untimed, with room to set the work out properly. A child can be strong at one and lost in the other, and only separate sheets will tell you which.
Little and often, and keep revisiting
Five minutes daily builds tables. Forty minutes on a Sunday does not, and the difference is large enough to be worth rearranging your week for.
Recall also decays quietly. A table that was secure in October is often shaky by February if it has not come up, and nobody notices because nobody is looking. Mixed revision sheets covering everything learned so far, every few weeks, are how you find out — and they take a minute to produce.