Second grade 'estimated' multiplication

#391 · 04-17-2007, 03:11 PM

So I'm checking over my daughter's homework tonight. It's a math assignment called 'estimated' multiplication. It goes something like this:

62 X 6 = ?

You round the 62 to the nearest ten (60), then multiply it by the 6. So the "correct" answer is 360.

W.....T.....F??????

She knows how to multiply 62 X 6, but is being forced to use this..."fuzzy math"... multiplication. Can any educators please explain to me the logic behind this??? Why not just teach multiplication the proper way?

widebody911 · widebody911's Garage

Got me! Must be another liberal plot.

Bill Verburg · Bill Verburg's Garage

It's a good idea to know when a numeric result is in the ballpark or not.

People need to get a feel for all sorts of things about #s. That is an important one.

SlowToady · 04-17-2007, 03:17 PM

So that when they get into higher level math courses later on in life, they won't know what the **** is going on, because no one has the foresight to teach them properly.

And yet some people wonder why America isn't the hallmark of science and mathematics.

mattdavis11 · 04-17-2007, 03:21 PM

I do it all the time when I have to do it in my head. Seems easier sometimes to multiply 6x60 and add on the twelve to get 372.

If I was asked what 15x17 was, it's easier knowing that 15 squared is 225, I then add 30 to it to get my answer.

Maybe that's the approach they have in mind, only using your mind.

SlowToady · 04-17-2007, 03:29 PM

Quote:

Originally posted by mattdavis11
I do it all the time when I have to do it in my head. Seems easier sometimes to multiply 6x60 and add on the twelve to get 372.

If I was asked what 15x17 was, it's easier knowing that 15 squared is 225, I then add 30 to it to get my answer.

Maybe that's the approach they have in mind, only using your mind.

Agreed, and I use the same techniques rather often (like in the store today, adding up prices and figuring tax). It's very useful in every day situations.

That said...if schools are going to teach methods like that, it is my opinion that they need to wait until the children are of such an age that they already have a firm understanding of the basics of mathematics before they teach shortcuts. In my (very recent and still ongoing) experience, mathematics in American schools today consists of guessing, memorization, and the almighty Texas Instruments calculator.

At the High School I attended, only 2 years of Mathematics was required to graduate, but 4 years of Physical Education was required for graduation. (I went to school in one of the top ~15 richest counties in America.)

Seems like America is getting farther and farther away from the sciences and more towards....wait, what is it we're teaching kids today? Oh yea, entitlement...

Apologies for the rant.

stomachmonkey · 04-17-2007, 03:35 PM

Quote:

Originally posted by mattdavis11
I do it all the time when I have to do it in my head. Seems easier sometimes to multiply 6x60 and add on the twelve to get 372.

If I was asked what 15x17 was, it's easier knowing that 15 squared is 225, I then add 30 to it to get my answer.

Maybe that's the approach they have in mind, only using your mind.

Exactly. It's a better foundation for actually learning "formulas" vs the old multiplication drills that only taught you to memorize the answer.

For me it's not 15x17, it's 300-45. I "see" 15x20-3x15.

Ever watch people try to make change? You can tell the ones that have been taught to calulate vs memorize.

Flatbutt1 · 04-17-2007, 03:40 PM

Quote:

Originally posted by stomachmonkey
Exactly. It's a better foundation for actually learning "formulas" vs the old multiplication drills that only taught you to memorize the answer.

For me it's not 15x17, it's 300-45. I "see" 15x20-3x15.

Ever watch people try to make change? You can tell the ones that have been taught to calulate vs memorize.

OK one more variant as I've always done this. To me this factoring,nothing more, in this one I see 150+70+35

edit: although the correct solution to the original post is NOT 360

#391 · 04-17-2007, 03:53 PM

Quote:

Originally posted by Flatbutt1
edit: although the correct solution to the original post is NOT 360

I guess that's my point, that the teacher is not having the students complete the equation.

Maybe this is just the first step, and she will introduce the second step (adding the 2 x 6 = 12 to 360) tomorrow.

I just hated to see her write 360 as the answer to 62 x 6, when she is quite capable of figuring out the correct answer. I understand your points about breaking the problem down into more workable chunks. I'll follow up on how the lesson progresses.

stomachmonkey · 04-17-2007, 03:56 PM

Quote:

Originally posted by SlowToady

That said...if schools are going to teach methods like that, it is my opinion that they need to wait until the children are of such an age that they already have a firm understanding of the basics of mathematics before they teach shortcuts. In my (very recent and still ongoing) experience, mathematics in American schools today consists of guessing, memorization, and the almighty Texas Instruments calculator.

I actually disagree. I don't see this method as a shortcut. It's a very logical approach. It's critical to start wiring their brains at a young age when you can still influence it.

I started teaching my daughter simple relational "math" exercises very early. She is seven now and is doing very well with complex calculations.

the · 05:09 PM

Yeah, I think it's just the first step of teaching the concept of grouping (probably not the right word) to get the correct answer. They are just multiplying the 10s first.

60 x 6 = 360.

Then later they'll do the 6 x 2 = 12, and 12 + 360 = 372, the correct answer.

Whether that's effective for a 2nd grader, I don't know, but I think at least there's a rational thought process going on by the teacher/school, not an attempt to teach "fuzzy math."

red-beard · red-beard's Garage

This is brought to you by the same people who "legislate" that pi=3

mattdavis11 · 04-17-2007, 04:34 PM

Not only grouping, but a method that can be used that will not discourage the kids who are intimidated by the task of tackling multiplication of larger numbers.
In second grade, IIRC, they started to time your calculations. The more you can do in your head the faster you will be.

many944s · 04-17-2007, 04:43 PM

Oh, now you have touched on a nerve....
The "estimated math" is almost as good as the new method of "invented spelling". If you haven't heard of it, the student writes the word the way they "think" it is spelled. And is NOT corrected. The teacher doesn't correct the student so they don't get "down on themselves" for not knowing the proper spelling like other students may. Just another facet to the "no child left behind" bulls**t.

I can't wait to see how they start teaching chemistry... The students wont be able to preform proper math, and wont be able to spell. It's only a matter of time before the high schools start going "BOOM" because some student was "inventing" their own methods!

masraum · 04-17-2007, 04:54 PM

On a vaguely related note...

Something that I think would be a GREAT idea for folks with younger kids would be to teach the kids to use an abacus. You think about numbers differently when using an abacus. I'm pretty good in math. It's always been one of my strengths. I think learning the abacus, especially at an early age, would help kids that have a hard time with math as well as helping kids that excel at math.

mattdavis11 · 05:57 PM

I see your point. However, I think this method is an approach that will increase the speed of those who already know how to multiply large numbers, and educate those who are falling back at the same time. No real fall backs, unless the teachers do not complete the aforementioned task by having the students add the 12 into the "correct" answer.

Last time I checked chemist didn't spell, they abbreviated. Maybe that was because they couldn't spell?

techweenie · techweenie's Garage

Quote:

Originally posted by the
Yeah, I think it's just the first step of teaching the concept of grouping (probably not the right word) to get the correct answer. They are just multiplying the 10s first.

62 x 6 = 360.

Then later they'll do the 6 x 2 = 12, and 12 + 360 = 372, the correct answer.

Whether that's effective for a 2nd grader, I don't know, but I think at least there's a rational thought process going on by the teacher/school, not an attempt to teach "fuzzy math."

I can't tell you how many times I've seen situations where it would have been useful if someone had taught this before. People who have no concept of the appropriate 'neighborhood' of an answer would come up with answers that were way off. Multiple decimal points off.

Teaching this was irrelevant before calculators and computers, but is probably pretty useful now. It would be in my world.

Jims5543 · 04-17-2007, 07:15 PM

You never look at a large number and estimate?

Look at this equation as a starter problem for a 7 year old.

62X6 =

or as I see it

6x6 = 36 or 60x6= 360

I think its a pretty good exercise.

Porsche-O-Phile · Porsche-O-Phile's Garage

Can he "estimate" his SAT scores when it comes time to apply for college? Seems appropriate given what he's being taught.

sammyg2 · 04-17-2007, 07:43 PM

BTDT, heped my daughter with her homework and tried to explain to her that what was in that book was not real math, it was a travesty. typical of liberal arts majors trying to polute what is supposed to be a pure science.
2 x 2 = 4, how does that make you feel? Asshats.

opps, I hope I didn't offend the overpaid underworked part time workers we call teachers, they might go on strike again.