One-Sixteenth

That happened to me in Sixth Grade with Michelle. I looked at the problem and even knew the answer, but the only way I could see to explain it was using algebra, and they weren't using that method yet. You wanna see someone with a Math degree go crazy? That's how.....

You have no idea how much better that makes me feel. Really. I'm going to edit to include the problem.

I remember this problem! It was a hard one for me, too. I have never liked word problems, but with using Singapore, I feel like I have a handle on them... and while oldest kid's speed and fact recall isn't terribly strong yet, his problem solving is terrific.

I'm more curious in the solution that doesn't involve algebra. Even we don't label it "algebra", I suspect that similar "tools" are used to solve it.

Oh, and S=L=32, right?

Actually, this one really doesn't require algebra. Finding the difference between how much each girl spent tells us that L has $7 more than S. Since we also know that L has twice as much as S, we know that she has $14 left and S has $7. So then you either add $14 to $18 or $7 to $25 and get the answer $32. So algebra isn't really needed, it just makes a prettier equation. :)

My problem? I saw the solution fairly quickly, but it took me five minutes to figure out why that solution would work. :P And I have no idea how to show that with Singapore's little bar diagrams.

I really want to brush up on my Algebra and Geometry before Jared gets there, but since I can't even find time for my Latin right now, I don't see it happening anytime soon.

It doesn't require algebra at all. But using algebra was the easiest way for me to solve it. I am *not* able to look at that problem and do what you did, KathyJo. Sad, but true. I'd like to blame it on the pathetic math education I had. We'll know the truth of that in a year or two.

I'll do a graphic of the bar diagram. Once I figured out the bar diagram I could see how ridiculously easy the problem is. However, though I can compute, I really have no idea how to approach problems like that. And it's all in the approach.

Okay, well here's a confession: I still don't get the damn bar diagrams. And since I don't get them, I can't really explain them to Jared, who also doesn't get them. 'Cause it seems like you have to really understand the problem to draw the diagram correctly, but if you understand the problem, why do you need the damn bar diagram? And, of course, soon Jared is going to be referring to them as "the damn bar diagrams."

Alright, I keep looking at your diagram, and I finally understand how to set it up from the problem. :) I'm even starting to see how they can be helpful. But I still think they're a bloody PITA.

The bar diagrams are amazing. I didn't get them at first, but I've worked very hard at it. And I've already learned a great deal about how to turn things around to look at them in different ways. They really are helpful. But yes, they are a bloody PITA. And a half.

I'm ordering the Challenging Word Problem supplement for him (us).

Heh. Your timing is perfect. Our entire Singapore lesson today consisted of word problems for which Singapore expected us to draw diagrams. FTR, my son is NOT happy with you right now, but he's blaming me. ;)

Do you remember earlier this year when I emailed about a Singapor word problem R had? It was the same thing for me. I quickly and easily figured it out in my head with algebra. But I knew this was NOT what they were looking for. Of course the bar diagram way also didn't come to me - as in, I didn't even think to work it out with the bars. Rachel was in level 3.

I am very worried about level 4 and what word problems they throw at her/us. I was NEVER good at word problems unless they were in algebra class. In fact I was in honors algebra because that kind of math came so easily to me. HA! They assume that if you can do algebra so easliy that geometry will be a breeze too...no so for my brain. I was dropped out of honors geometry and then flunked regular geom. Had to take it again :-/

Will you let me know what you think of the Word Supplement book? I've been contemplating that for R since last year when she showed us that word problems are NOT her forte either.

FTR, Mike's like KathyJo. He can see the answer without giving it much thought. When asked to explain it, his explanation was in algebraic terms. But that wasn't what he went thru in his head to figure it out.

You might have made a better cosmologist than you think! I have a Ph.D. in theoretical physics and hold several patents for computers and microwave satellite systems. I'm also now a homeschooling dad, and we too are using Singapore math (though we're not up to 5A yet).

All of the good engineers and theoretical physicists I know think in more or less the way you described getting the solution to the problem. When we face a tough technical problem, we start using pictures, sometimes in our minds, often on paper or a chalkboard.

I used to do consulting work with a colleague who lived in another town. We'd get on the phone and the conversation would be like: "Look, to really understand the math on all this, you need to sketch this thing out. Get a pencil and sheet of paper and start sketching a box divided into five parts..." etc.

I'm convinced that the major difference between good physicists and engineers versus "ordinary" people is that we technical types keep sketching, erasing, sketching agian, scratching our heads, etc. until we finally "see" what's going on. As Edison said, "genius" is 99 % perspiration. I've known several Nobel prize winners in physics and read about many more. Those guys were not really all that brilliant -- but they would keep gnawing on a problem like a dog gnawing on a bone until they finally figured it out. (Einstein claimed to have spent ten years -- from age 15 to 25 --figuring out special relativity, and then he spent another ten year -- and made some egregious mistakes on the way -- figuring out general relativity. Hard work pays off.)

Dave M. in Sacramento

Dave, no one, ever, taught me to sketch out problems. "Math" was numbers. But one of the best things about homeschooling is that I get to educate myself, as well.

My son resists both drawing out the diagrams, and even writing down his work in computation. He prefers to do it all in his head, and likes a nice, clean page with nothing but an answer. We're engaged in an ongoing battle with this right now, as I want him to write it down. All of it. I can see, from here, just how useful that will be in the future.

Thanks for giving me reinforcement that we're headed in the right direction!

And KathyJo - it's nice to be able to torture someone else's kid for a change ;-)

MamaLynx wrote:
>My son resists both drawing out the diagrams, and even writing down his work in computation. He prefers to do it all in his head, and likes a nice, clean page with nothing but an answer.

Well...in the advanced physics classes in college, I used to try to do the same thing. I went to Caltech, and, if you got exactly the right answer, you would get full credit even if you did not show your work. Of course, if you made the tiniest error, you could only get partial credit if you had not bothered to show any of your work.

I'm homeschooling twin seven-year-old girls: one of them is happy to follow exactly the procedure she was told to follow, but the other is determined to do everything in her head, preferably with a novel "trick" invented for that particular problem.

It's a difficult line to draw, isn't it? On the one hand, creatively inventing new problem-solving methods is good; on the other hand, some problems only open up when you (to quote one of my old teachers) just "plug and grind' to get the answer. Kids do need to know the "standard" way to get the answer.

If you find a magic solution, let us all know!

Dave M. in Sacramento

Thank you. We are currently in Singapore 5A and came to this exact problem. I couldn't figure it out, so I Googled it and it brought up your solution. Thank you. I figured out that "$7" was key, but couldn't figure out what to do with it. Thank you.

Homeschooling Mom in Chattanooga, Tennessee