Do you want to know a secret?
I never learned my multiplication table. This is actually true.
Somehow I made it through three semesters of calculus and analytic geometry at this questionably situated school without being able to tell you what 7x7 is. I mean, yes, given a few seconds, I have the ability to figure it out, but if you jump out at me from behind the doorway and say "QUICK -- WHAT IS SEVEN TIMES SEVEN?" you will be met with a blank stare.
Benny get borrowing and carrying now, and can tell time and make change, and all that other stuff, so the next thing is... multiplication table. I was actually approaching this with a little trepidation, given my own incapacity on this subject, but yesterday morning I decided to get on with it. Now I see I didn't need to worry. He is doing just fine.
I started off by drawing a grid with four squares. I put an X in the top left square, and a 1 in the other squares. Then I drew a grid with nine squares. An X in the top left square, one and two across the top, one and two down the side, and I filled in everything but the four, and gave it to him. He didn't totally know what it was, but eventually he guessed that a four belonged in that hole, and I told him that was right.
Then I drew a grid with sixteen squares, and had him fill them all in. Which he did. And we ended up with this:
This morning, I gave him the grid with 64 squares and he filled it all in again. I've also written out some problems for him to do, like 3x5=___ and also like 3x___=15 and he's doing just fine with those too. It's... pretty miraculous. At no time did I ever explain how filling in the table is like counting by 3s or 5s or whatever, and I didn't tell him how to follow the columns and rows to find answers, and I didn't really explain anything at any time. He figured it all out, because as it builds on itself, it really makes sense. And if you are allowed to see it as a whole thing, I guess, that becomes clear to you pretty fast.
He hasn't memorized his multiplication table yet, and we're only up to the 7s, really. But it's day 2 of our effort to tackle this new skill, and I'd say it's going swimmingly. Once again, I stand amazed at how very little time it actually takes to teach a child, when you are giving them one-on-one attention, and presenting the material in a way specifically tailored to the child's own learning style. I expect to be up to the 12s by the end of the week, and let me tell you: We are doing all of this BEFORE NINE AM. Before the little sister even wakes up.
Which means that when the sister wakes up, there is lots of time for more important stuff like this:
Another happy homeschool day!