rounding and approximation

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rounding and approximation

by karen

Nov 17, 2015

I found difficulty in explaining the answer of this question to the pupil write the smallest and largest numbers that will give the following: 8460000 when rounded to the nearest ten thousand would please help

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Terri Go to dr math and search for rounding

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On 11/17/15, karen wrote:

> I found difficulty in explaining the answer of this > question to the pupil > write the smallest and largest numbers that will give the > following: > 8460000 when rounded to the nearest ten thousand > would please help

Nov 17, 2015

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Yikes On 11/17/15, karen wrote: > I found difficulty in explaining the answer of this > question to the pupil > write the smallest and largest numbers that will give the > following: > 8460000 when rounded to the nearest ten thousand > would please help

what a useless exercise. First of all it is horribly worded. I was a math m...See MoreOn 11/17/15, karen wrote: > I found difficulty in explaining the answer of this > question to the pupil > write the smallest and largest numbers that will give the > following: > 8460000 when rounded to the nearest ten thousand > would please help

what a useless exercise. First of all it is horribly worded. I was a math major in college and have worked in a math field in business for 20 years and taught math for 15 years and I had to read it twice to see what they were after.

Secondly, it is mathematically incoherent, as there is no greatest number that rounds to that nor is there a smallest number that rounds to that There is a largest and smallest WHOLE number that rounds to that, but without making that restriction, which the problem doesn't, it is a problem without an answer. Except, you are going to frustrate the dickens out of the brightest kids who assume that if you ask for an answer there is one, but who are smart enough to see this problem does not have an answer.

Try a simpler version - what is the biggest number that, rounded to the nearest 10, yields 100. well, 105 rounds to 110, so that is too big. 104.9 would work - but 104.9 is bigger and still rounds to 100. But 104.99 is even bigger and still rounds to 100. In fact, any number you can give me that rounds to 100 can be made bigger, while still rounding to 100 - just add another decimal place and put a 9 in it.

It is like asking "what is the biggest number that is less than 5". There is no answer.

Now lets say that you add the restriction and ask for the largest and smallest WHOLE numbers (proper wording is why it is important that math amateurs not make up test). Then you have a problem that at least has an answer questions, but is still of very questionable mathematical or pedagogical value.

So if a kid says there isn't any answer and can come up with any kind of semblance of an explanation indicating that they knows why I would be giving them full credit, an attaboy/girl, and marking them as someone to watch and expect great thing from. Unfortunately, in most classrooms I think they get marked wrong because it isn't the answer in the book. Which is why we need teachers, not just books and computers.

BUT - only if the teachers really know what they are doing. Which isn't always the case in math.

Nov 17, 2015

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