My visiting niece expresses she wants to go to one of her favorite playgrounds, so we hop in the car and I take a new route so she won’t recognize the place since we’re approaching it differently. I want to see how long it takes before she catches on.
Turns out, I was the one that got the surprise.
I park the car, and we get out and start walking along a black path towards the playground.
“How looooooong to do have to walk?” she asks.
At my height, I can see it. “About a minute.”
“What if it’s two minutes?” she asks.
“What if it’s an hour?” I retort.
“What if it’s two hours?” she counters.
“What if it’s one hundred hours?” I escalate.
“What if it’s two hundred hours?” she throws back.
We’re almost to the playground, so I figure, just for fun I’ll give her a word problem that will bug her all week.
“So, how many days is 200 hours?”
She pauses, looks up at me. “Good question.” She puts her finger on her chin, and immediately answers “Eight days and eight hours?”
I do a double take. “Uh, that sounds about right.”
And at that point she sees the playground, screams “Come on!” and breaks into a full run.
I take a more leisurely pace to cover my thought process. “Let’s see 24 into 20, nope gotta do the whole thing, 24 into 200, wait, 10 is too much, 9? That still feels high. She said 8, let’s go with that, 8 times 24, ok, ok, 8 times 4, that’s 32, okay, carry the 3, 8 times what was it, yes, 2, ok, 14, no 16, dumb Walt, dumb, ok, 16 plus, what was it before, 24, no, 32, wait, carry the 3, 16 plus 3, that’s 19, what was in the last one’s column, 32, ok, 2, alright 192, then I need to what, subtract that from…”
At this point I’m concerned because this little girl just did lightning math in her head without preparation, and I don’t know if she’s going to be able to understand the concept of explaining the thought process that happens in one’s own head. Figuring out how she did this is going to bug me all week.
200/(24+1)= 8
8+((25-24)*8)
8+(1*8)=8 day & 8 hours
This is how I do it:
24+24 = 48
48+48=96 = 4 days, which is about half of 200.
so double it; 192 = 8 days.
200-192=8 hours
8 days 8 hours.
I like the way Brad (Above) did it.
But still, impressive for any kid to do, especially with a Playground on the horizon.
To put this in context, my niece is 8 years old and solved the problem in her head in about 2-3 seconds. What’s disconcerting about the whole thing is that I don’t think she’s been taught clever ways to alter problems to get equivalence. I think she really did the long division, which she admits is one of her favorite things about math, that fast.
Far be it from me to suggest that your niece is not indeed the smartest 8 year old on the planet, but is it possible that she had been asked that question before? I know as the father of a 7 year old son, that kids have a very good memory. Conner will pull out facts that he has heard before a lot quicker then I would.
It could very well be that she is a math prodigy. Perhaps she had worked out the problem in a previous park outing that you were not part of?
Actually, if she was just recalling the answer from a previously being asked this would give me great comfort, given the raw speed that she apparently did the calculation.
However, since the exchange leading up to it was verbal word play, it’s hard to think of how she’d have been asked the question before.
That’s it, I’m calling… I want to know how she did it.
Oh. My. Gosh.
Just got off the phone.
“Hi, do you remember how you did it? And, if so, can you tell me how you figured out, explaining what was going on in your head?”
“Sure! First I figured out there were four 25’s in 100. Since I had 200, I knew I was one short for each, that’s where I got the 8 hours from.”
“That’s amazing! Where did you learn to do that?”
“Well, the hard part was figuring out there were 24 hours in a day.”
Converting hours to days is a 3rd grade topic in public school (http://www.aaaknow.com/grade3.htm). But I wish they taught me her method back then.
Backwards, maybe?
She might automatically know that 24X10 is 240, and then it’s just a simple matter of subtracting 40 hours from 10 days.
Not that I could do this in 2-3 seconds, however.
Of course I’m late to this party, given that Walt’s blog isn’t in my rss feed or anything. But I read it last night and it bugged me. Not seeing the comments, and not giving it too much thought, I just went on with life. Then, in one of those almost-falling-asleep moments, I discovered my brain had been working on this in the background. I came up with the exact method that she used and was all excited to come post it here. It was so obvious and useful. Alas, months ago the mystery was solved.
The part of the story that intrigues me and escapes a lot of readers is not that a clever trick was used to solve the problem, but that she had never been taught such tricks in her schooling. Compound this with she did it all in her head and that she gave a speed answer (that was correct) — it was pretty shocking.
Admittedly, I’m dismissive of the explanation that what she did was 3rd grade math, primarily because other kids (and adults) I’ve asked haven’t been able to get the answer as fast as she did, if at all. As we all know from experience, knowing how to do math and knowing how to solve a problem (especially a word problem) are different skills.
Incidentally, her parents had her formally tested after the incident. She scored a perfect score in all five math categories, every other topic was “high mastery,” and her ‘worst’ score was nine points above national average. I wish I had been home schooled.