Last night at dinner

[conuly]

The scene: Dinnertime
The backstory: Ana's learning her times tables

Me: Okaaaaaaaay... *drumroll* Ana! What is... SIX times SEVEN?
Ana: Wait. What? I didn't come here to learn! I came here to eat!
Me: Well, have I got a deal for you! Today's special! You can do both! TWO THINGS FOR THE PRICE OF ONE!
Ana: Seriously?

It worked out well enough, though. Ms. "I Came Here to Eat!" was able to get through her problems correctly, and she REALIZED something. IF it's something multiplied by ELEVEN, like... nine times eleven or five or something... it's going to ALWAYS be 99 or 55 or so on! WOW!

I acted suitably awed by this revelation, naturally :) Then I showed her the trick for two digit numbers and eleven, which isn't really a "trick" but meh. (Basically, since anything times eleven is OBVIOUSLY ten times one, you add a 0 onto your number and then add the original number, sans zero, to the new one.)

Comments

[diatryma.livejournal.com]

Huh. I learned a different, more convoluted trick: take the number (say 14) and split it: 1_4. The middle number is 1+4: 154.

I also spent a while bootstrapping a remarkably inefficient way to get squares when you know a neighboring square-- like seventeen squared when you only learned up to sixteen. I'm better at adding in my head than multiplying, I guess.

[conuly]

I also spent a while bootstrapping a remarkably inefficient way to get squares when you know a neighboring square-- like seventeen squared when you only learned up to sixteen. I'm better at adding in my head than multiplying, I guess.

Well, you can get squares by adding up consecutive odd numbers. (I mentioned this in a math class once and totally flabbergasted my teacher, who had NEVER realized that.)

Edit: Also, your trick is basically mine, but without the rationale clearly spelled out. I took the time to spell out the reasoning.

[diatryma.livejournal.com]

Mine is yours, ish, but the rationale means holding more complicated numbers in my head. I'd not heard of squares and odd numbers, though. Could you explain it?

[conuly]

I can explain it in numbers, and you can prove it by grouping buttons into a square.

1 x 1 = 1

2 x 2 = 4
1 + 3 = 4

3 x 3 = 9
4 + 5 = 9

4 x 4 = 16
9 + 7 = 16

5 x 5 = 25
16 + 9 = 25

And so on. 6 squared is 25 and 11, 7 squared is 36 and 13....

You can picture this as an actual square made of buttons or counters or coins or whatever you like. Each time you increase the square, you add one button for each on the upper edge, and one button for each on the left-hand edge, and one button in the corner where the two new edges meet.

[diatryma.livejournal.com]

That is clever, and not something I'd have noticed.