I know. And 7x can be done from taking 3x off the 10x, and 8x can likewise save an addition by taking 2x off the 10x I intentionally left the 5s and 7s blank because they are 3-addition operations and also require you to mentally hold on to the very first number. Instead of the overhead of juggling an extra value and doing an extra step, I find it easier to switch around the multiplication terms and handle them using a different rule. The remaining cases of 5x5, 5x7, 7x7 are small enough to effortlessly memorize. Especially since 5x can be done with counting by 5 (which is just normal counting but with 0 and 5 appended to everything). 6 ends up being the only thing in the 10x10 table that requires 3 additions to reach. All the others can be done with just 2 additions/subtractions. For 8 you get a choice between 3 additions or 2 subtractions but with temporarily juggling one extra number.
If you add division by two into the list of primitives, 5 and 6 become accessible within 2 steps and so the system can reach the whole 10s table within a cost of 2 (times 10 is considered a zero cost step). That makes the cost one step worse than traditional memorization but you end up being faster overall because you only need to focus on being fast at the three primitives.
Recognizing the general principle that you can change A into BC or (B+C) where B and C are both easier to multiply with than A is far more useful than memorizing the table. The best part is except for the (optional) division by two, all the primitive operations are things you already learned how to do at that stage. You can short circuit a tedious, long and wasteful part of the early math curriculum AND walk away with genuine understanding of why the rules are and how to figure things out for yourself. While everyone else struggles to multiply by 17, you can be the smarty who doubled 4 times and added once. Or put zero at the end, doubled, and subtracted 3x. Or put zero at the end, subtracted 1x, doubled it, subtracted 1x. With a bit of thought, you can extend the entire multiplication table to 20x20 such that very few rarely does anything cost more than 3 steps.
If you add division by two into the list of primitives, 5 and 6 become accessible within 2 steps and so the system can reach the whole 10s table within a cost of 2 (times 10 is considered a zero cost step). That makes the cost one step worse than traditional memorization but you end up being faster overall because you only need to focus on being fast at the three primitives.
Recognizing the general principle that you can change A into BC or (B+C) where B and C are both easier to multiply with than A is far more useful than memorizing the table. The best part is except for the (optional) division by two, all the primitive operations are things you already learned how to do at that stage. You can short circuit a tedious, long and wasteful part of the early math curriculum AND walk away with genuine understanding of why the rules are and how to figure things out for yourself. While everyone else struggles to multiply by 17, you can be the smarty who doubled 4 times and added once. Or put zero at the end, doubled, and subtracted 3x. Or put zero at the end, subtracted 1x, doubled it, subtracted 1x. With a bit of thought, you can extend the entire multiplication table to 20x20 such that very few rarely does anything cost more than 3 steps.