Because Southern California is on fire, and my work was in an evacuated area, I was able to stay home an extra three days this week. Since all activities (church, soccer) were also canceled, and we couldn’t really go anywhere (our neighborhood seemed like almost the only area of the city that wasn’t in danger this time, but still it was too smoky to let the kids run around outside), we spent the whole time cooped up indoors. And when Daddy’s home, school necessarily takes a turn for the mathematical!
For #1, who is the only one really doing homeschool, I decided it was time to start working on multiplication tables. He had sufficiently mastered the art of 4-digit addition/subtraction, carrying/borrowing that he usually makes only a couple of mistakes per daily worksheet of 20. (By the way, if anybody else out there is homeschooling, and wants addition/subtraction problems, just let me know, and I can hook you up with an infinite supply from a Perl script I wrote to randomly generate them, laid out in plain text so that they can easily be opened in WordPad and printed 20 per page.)
So we started on the tables. Fortunately, he already understood conceptually what multiplication is (repeated addition). Also, he is very good at addition in his head, so he can count “by” any number up to the product he needs, if he can’t just remember it right out. So I busted out the set of (Fisher Price) multiplication flash cards that have been waiting around. They’re two-sided, easy problems vs. hard problems. The easy ones are all 0x, 1x, 2x, and the first three 3x, which he basically didn’t even need to learn.
So then we switched to the backside. As we went through, I gave him as many rules as I could:
- times 10 is just slap a zero on the back
- count by fives when multiplying by 5, evens will always get you a ten, odds in between
- 9 times n is (n-1) in the tens digit, and the ones digit is whatever it takes to add up to nine
- times 2 means double it
- times 4 means double it and double again
- times 8 means double three times
So that left only x3 (which is easy enough to add), x6, and x7 without a shortcut — and those products could usually use whatever shortcut rule was available from the other number.
So as we worked through the flashcards, the method became this: any card that he answered right off (within a second or two, without having to mentally calculate) went into a done pile. Others went to the back of the stack to be flashed again. Quickly the done pile grew full of products with easy rules (10x, 9x) and ones he has well-memorized (and I try to point out how much bigger that done pile is). Then begins the cycling through the redos. After about three days of practice (probably actually a total of about three hours of drilling), his solid foundation of mental addition has gotten him about a dozen products away from a full multiplication table.
So that’s #1, but the other boys showed some numerical aptitude while I was home as well. #2 was jealous to “do school” like his big brother, so he spent a long time in my lap with his pre-school workbook, and did a great job counting objects, writing his answers (digits 1-6), even filling in squares of a bar graph. He’s had a lot of practice counting (especially lately with “Sorry!”), and is completely reliable up to the teens.
And #3 is getting in on the fun too! Not even 2 years old yet, and he has heard his brothers count so much that he can parrot them in one long counting-word which runs all the way to fifteen (skipping ten) before cycling into random teens. He likes to “play” whatever the rest of us are playing, by grabbing a game piece, tapping it on the board, and saying “one t’free four five six seven eight nine leven twelve firteen fourteen fit-teen twelve sixteen leven…”