How about teaching the kids to make change without having to use a calculator?

The cake is a lie

Damn! This is what passes for multiplication now?

I'd hate to see what they've done to plane wave solutions.

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Originally posted by MikeinNC:
The cake is a lie

My first thought as well.

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Originally posted by architect:
How about teaching the kids to make change without having to use a calculator?

This

quote:

Originally posted by maladat:
It’s absolutely a stupid way to actually do math on paper.

That’s not the point.

Most people that do much math in their heads do multiplication in a way that is conceptually the same as those area models, and they are trying to teach kids to do that kind of mental math.

No idea how effectively it actually teaches that skill, but the goal makes sense.

This plus Yellowjacket's response.

It's about learning to break down larger numbers into groups that are easier to operate on mentally.

I'm 43. Not a math person in any way and was never taught how to math like this, but this is exactly how I do math in my head.

It works for figuring out discounts, tips, dividing checks, etc.

It looks goofy if you see it represented visually like this or as a word problem with no explanation, but I bet many people here intuitively do this very thing.

And not to stray too far off of math, but this is related to how you unconsciously process words. Your mind chunks words into phrases and stores phrases in working memory instead of storing individual words in working memory. It is easier to remember or manipulate chunks or ideas than it is their constituent parts. Your brain has limited working memory, so parsing information is necessary to make up for limited working memory before you shift the information into short term memory.

quote:

Originally posted by maladat:
It’s absolutely a stupid way to actually do math on paper.

That’s not the point.

Most people that do much math in their heads do multiplication in a way that is conceptually the same as those area models, and they are trying to teach kids to do that kind of mental math.

No idea how effectively it actually teaches that skill, but the goal makes sense.

Right. It's about breaking numbers into sets not only to make it easier to do in your head, but also to get students thinking about number sets much earlier than rote memorization of time tables allows. I believe the theo7 is it will make Algebra, Geometry, and Calculus easier to understand.

Those pictures suck though. It's not obvious the two large rectangles represent 10 sets of 10 each or that the thin rectangles represent 1 set of ten each. I stared at them long enough, I thought I saw a schooner.

The way I've seen it done is there would be 4 large squares each with a 10x10 grid. 2 of the squares would be completely shaded in and the other 2 would have 7 rows in each shaded in. Each little square is 1, each row/column is 10, and each big square is 100, so it's 100+100+70+70=340.

Or, you can look at the 4 10x10 squares and subtract the unshaded squares to the get same result. 400-30-30=340. This is closer to what I would actually do if some one asked me what 17x20 was. I would do 20x20 and subtract 3 sets of 20 from that; 400-60=340.

I might also do 2x17 and slap a zero on it, but good luck explaining that to 4th graders.

That doesn't teach you math; it teaches you to be a mind reader and get into the head of the test writer. It makes you start to think like the test writer and to see the world the way the test writer sees it. This is indoctrination.

My answer isn't a canned response; it comes from looking at the test question and having the word "model" highlighted. It takes away from the concreteness of math on which everyone can objectively come to an agreement whether the result is right or wrong. A model is just a model and not the actual thing it is trying to model. And whether the model is accurate depends on what attributes are actually being modeled. One can make many interpretations about each of the model which can lead to an ambiguity in determining which is the correct model. Because the correct model is the one that the test writer has chose to be the correct model and not necessarily based on objective criteria.

Even w/ a technical degree, I don't understand the solution. I would fail 4th grade math I guess.

I really don't see what was wrong w/ teaching math the way has been for 1000 years? Or at least the last 100? Seems like we have invented quite a bit using the old methods. Been to the moon and back and such.

People learning the new math - can't seem to even keep basic functions in a stupid app to watch movies.

still don't get it..

the question is: " Which shows a model that represents the total number of cake trays?"

none of the diagrams, assuming the little lines are the trays, shows 340 trays and so my answer would be none of them.

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Originally posted by konata88:

I really don't see what was wrong w/ teaching math the way has been for 1000 years? Or at least the last 100? Seems like we have invented quite a bit using the old methods. Been to the moon and back and such.

Because there was likely one megalomaniac shithead in the federal government who thought he knew better than everyone else and forced it on all of us.

Hey! I’ve got an idea! Let’s teach math this way, and also to spell words by the way they sound! Then next year, we can start over!

quote:

Originally posted by konata88:
Even w/ a technical degree, I don't understand the solution. I would fail 4th grade math I guess.

I really don't see what was wrong w/ teaching math the way has been for 1000 years? Or at least the last 100? Seems like we have invented quite a bit using the old methods. Been to the moon and back and such.

People learning the new math - can't seem to even keep basic functions in a stupid app to watch movies.

Back before handheld electronic calculators, we learned math first by long hand on paper. Write down numbers and do all the steps.

But then in high school we were taught how to use a slide rule. That exposed how math works. Even though the slide rule was a tool, it made math make sense. It made solving problems easier, and it also engaged the brain.

New math and now the method in this thread make solving a problem more difficult by making the process more complex. It also does nothing to teach how/why math works.

Are the cake trays shown in plan, profile or cross sectional view? This engineer can be a real asshat when I want to be. Teacher asks a dumb question, I can justify it any way I want. This is one of the minor reasons my wife got out of teaching. They were forced to do this crap.

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Originally posted by jcsabolt2:
Are the cake trays shown in plan, profile or cross sectional view?

It's not about cake trays. It could be beans in cups, or rounds in mags. It doesn't matter. It's just a multiplication problem.

It's just a graphical method for multiplying 20 X 17

I'm still sitting here eating paste trying to figure out why the answers options are F,G,H,I and not A,B,C,D.

I still don't understand why this question would need to be answered in this fashion. Seems overly complicated. Basically trying to guess what each set of boxes could represent.

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Originally posted by gpbst3:
I'm still sitting here eating paste trying to figure out why the answers options are F,G,H,I and not A,B,C,D.

I still don't understand why this question would need to be answered in this fashion. Seems overly complicated. Basically trying to guess what each set of boxes could represent.

There is no guessing involved.

It is a drawing of a rectangle with sides the lengths of the numbers being multiplied, so that the area of the rectangle is the answer to the multiplication problem.

The lines inside the rectangle are a way of graphically representing the numbers instead of writing the numbers down. Doing it this way makes splitting the problem into (multiple of 10) times something plus (leftover part less than 10) times something really obvious.

This is not something the kid would have to guess about, because the kid’s teacher will have been using this specific “area model” technique in class frequently as part of teaching kids to break down problems to make them easier to do in your head.

The drawing has nothing to do with the “word problem” part of the problem. Nothing in the drawing represents boxes or cake trays. The drawing represents 17 x 20.

This question is not checking “can you answer 17 x 20?” It is checking “do you understand the first part of how to break down multiplication problems into easier pieces the way we are learning to do in class?”

No, but I guessed the "right" answer.

Without prior education, one would not immediately know that the large boxes represented multiple trays, or how many. Perhaps the 4th graders had been given enough prior instruction to enable them to solve the problem that way, but it's not the way I'd solve 17x20. Since 20=2x10, I'd do 2x17=34 and multiply by 10 (add a zero).

flashguy

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Originally posted by maladat:
A big gap between lines is 10, a small gap is 1.

The bottom right diagram is 20 wide and 17 tall, the area is the answer.

It’s just a specific shorthand way of drawing the obvious geometric interpretation.

Bottom right.

Mission: Select model representing total number of trays.

Solution:

1. Unbox all trays. 17 boxes of 20 trays each is 340 trays.

2. Two large rectangles divides tray population in half (170 to each side). Check.

3. Each rectangle holds an equal number of trays; therefore, looks most like bottom right.

I suspect people think the narrow strips crossing a large rectangle is equal to a tray or box, when no such equivalence is presented.



It is all in the question being asked. If it’s not there, it’s a mistake or a trap or you cannot give positive whole number solutions.

quote:

Originally posted by flashguy:
No, but I guessed the "right" answer.

Without prior education, one would not immediately know that the large boxes represented multiple trays, or how many. Perhaps the 4th graders had been given enough prior instruction to enable them to solve the problem that way, but it's not the way I'd solve 17x20. Since 20=2x10, I'd do 2x17=34 and multiply by 10 (add a zero).

flashguy

Sure, multiples of 10 are a special case where it’s extra easy.

If it were, say, 23 x 17, most people doing it in their head would break it into pieces.

The point of the area model thing is that it makes how to break it up really obvious - pick easy to calculate pieces that cover the whole area and don’t overlap.

If you can do bigger pieces in your head, you might do 20 x 17 + 3 x 17.

Maybe 20 x 17 is easy for you but 3 x 17 is too hard so you split it again to 3 x 10 + 3 x 7.

Maybe you just split the whole thing up all the way: 20 x 10 + 20 x 7 + 3 x 10 + 3 x 7.

Setting aside the iconography that you aren’t familiar with, the area model concept lets kids literally just look at it and see the pieces they can split it into. It is supposed to develop the intuition and understanding about how to do that, rather than waiting for them to figure it out for themselves or making them memorize a specific algorithm that they’ll probably screw up for a while, that doesn’t let them skip easy parts, and that doesn’t work when the numbers get bigger.

If you do multiplication in your head, you are probably, at least sometimes, doing it exactly the way this approach is trying to teach.