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Re: whole number computational fluency articulated to decimal computation
Posted:
Dec 11, 2001 5:39 PM
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In today's world I would not be the least bit opposed to having a
student find the answers to 3.45 x 2.8 or 0.453/2.6 using a
calculator. However, let's assume that the student MUST be able to
demonstrate paper-and-pencil computation for the 3.45 x 2.8 problem.
Why can't the student use whole numbers 345 x 28 to find the answer to
the number crunching and then locate the decimal point using the
lesson learned in CMP's Bits & Pieces II, lessons 6.3 and 6.4? Or
using methods learned in Investigations, the student could draw a
rectangle and write 300 + 40 + 5 along the top and 20 + 8 along the
left side and then proceed divide the large rectangle into 6 smaller
areas to find the answers to 20 x 300, 20 x 40, 20 x 5, 8 x 300, 8 x
40, and 8 x 5 and add up those 6 answers and then locate the decimal
point a la lesson 6.3. This method will still work in algebra when
they have to multiply binomials and trinomials. OR maybe it is now
time to introduce the standard algorithm. I don't think that
Investigations is OPPOSED to learning the standard algorithms; they
just want the students to understand why those algorithms work before
they blindly use them.
The division question is far more interesting. I know that Bits
II has a new 7th investigation on dividing fractions. I am not sure
if it includes dividing decimals as well. This question is asking how
many 2.6's will go into 0.453 and I guess the answer is "not many." I
know that I personally would reach for my calculator on this. I
suppose that if I HAD to use paper and pencil, I might try guess and
check. 0.1 x 2.6 would be 0.26, too small. 0.2 x 2.6 would be 0.52,
too big. Since 0.453 is considerably closer to 0.52 than 0.26, I
would guess an answer of about .17 or .18. But since the answer on my
calculator is 0.1742308, I don't think that guess and check would be
very efficient for much more than estimating! But then, I don't think
the long division algorithm would be very efficient in this case
either and I certainly wouldn't want to take the time in today's
packed math curriculum to spend the necessary time to make sure my
students could do 0.453/2.6 by hand. If I think of where in the world
outside of school a student would have to find the answer to
0.453/2.6, I imagine it would be in a highly technical field that
would require precision and I am sure that student's boss would
encourage the use of a calculator and discourage the use of finding
the answer by hand.
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