That is not how I approach things.
For the how of my approach (copied from another thread, excuse the crummy formatting if this comes out looking wonky.)
...We automated the 5 and 10 fact families for addition and subtraction and the others we learned through repeated use---but we'd been taught to think of and visualize the relationships at all times from the beginning. I think mama specifically designed/chose to teach us this way so that we could do it that way--but I highly doubt that it was a happy accident or anything. All of my siblings and I did it this way and mama taught her tutoring students who struggled to think of numbers this way too, but it wasn't always successful for older kids who had been 'imprinted upon' by the local school.
If we were looking at, say 3 + 4, we usually did something like this:
1) use commutative property to put the larger number first: 4 + 3 = ___?
2) This is obviously smaller than 10
3) How is this related to 5? 4+ 1 is 5, so 4 + 3 is bigger than 5 *light bulb moment*
4) How much bigger than 5 is it well...we can disassociate 3!
5) 4 + 3 = (4 + 1) + 2 = 5 + 2 = 7!
I know that seems long and drawn out, but we got it down pat and could do it quickly. We learned math from about 3-6....
In K, I put a huge emphasis on number bonds within 10. "Making 10s" is is one of my main K-level goals.
We probably have similar approaches, but different time tables. In our family math begins at 2-3 yos, so that by the time we start K, the main goal is interpreting and solving story problems and building fluency with the number bonds/math facts using the strategy that I outlined above. We do a lot of applied math in our daily life with the child.
We spend the years prior to 1st grade playing, learning and exercising various math skills such as counting by place value, counting on/back, skip counting fwd & bwd, the units in the base-10 system, how/when to compose and decompose units, patterns, even/odd numbers, interpreting basic word problems and finding math scenarios in their day-to-day life. This type of exposure doesn't stop when the child starts grade K/1. It continues in the background--always going bigger and broader than whatever is happening in "math class"
After that, I switch almost all of the mental math focus onto manipulating numbers, not memorizing them. I would much rather them practice and learn how to figure out that 9 + 6 = 15, rather than just memorizing it as so. Strengthening the mental pathway that "sees" one move from the 6 to the 9 to make them into a 5 and a 10, that is a multi-tasker skill that will serve them well when dealing with all sorts of numbers.
Again, I think that we have similar approaches but different time tables.
I am a happy camper if my first graders can mentally add two or three 2/3/4 digit numbers...even if they haven't committed 7 + 5 to rote memory quite yet. In my experience, once I could instantly see that 7+5 = 12 (1ten-2/twelve), instead of having to think through 7+5= (5 + 5) + 2, the easier it was for me to add/subtract multiple 2-4 digit numbers in my head.
When we move on to multiplication, like Monica_in_Switzerland, I put very little emphasis on drilling the facts. Eventually, they will figure out that knowing the multiplication table is faster than having to calculate each answer every time. Until then, however, there is a lot of value in them "seeing" 7 * 8 as 7 * (10-2) = 70 - 14 = 56. That is the distributive property, and really, truly understanding how that works is worth a lot more to me than being able to simply spit back that 7 * 8 = 56.
Yep, we also use the distributive property and do our written calculations (once we get to that point) L-R. But we find it easier/smoother if the kids are learning their multiplication table. We always teach and acknowledge the properties of the real number system from early on though, so we don't have 100+ multiplication facts to memorize. Instead we have 36 and we do encourage/require them to memorize them and give them systematic exercises towards that end, with the goal of them having used and practiced them enough that by the end of
Because of the kids understanding of the concept of multiplication and the distributive property *0, *1, *10, *11 and *12 are never studied/practiced. We only do the tables 2-9. But since we do a lot of doubling/halving, tripling/thirding, quadrupling and quartering during our Pre-1st grade number play and all the skip counting that they have done/do regularly means that the student is familiar with the multiplication sequence already. So memorizing them is pretty easy.
To me, mental math is almost all about making numbers dance for you. Can a kiddo mentally figure out 38 * 4? Can they figure it out another way to confirm their first answer? Just for fun, how many different paths can they find to the answer? Are some faster? Are some slower? Which methods would be most helpful if the problem was 39 * 4? What about 38 * 5? Etc.
I think thats a great way to summarize it.