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Topic: Number Sense and Computational Fluency
Replies: 92   Last Post: Jul 24, 2008 5:09 AM

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 Linda Dodge Posts: 2 Registered: 12/3/04
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.

Date Subject Author
11/23/98 wendy
2/3/99 concerned teacher
2/12/99 Nancy B.
3/4/99 Mary Brown
3/28/99 Missy Taft
3/28/99 Barbara
4/2/99 Missy Taft
4/3/99 Mary Brown
4/9/99 Cornelia Tierney
4/25/99 Mary Beth LaHaye
5/28/99 Rachelle Tome
5/28/99 Rachelle Tome
10/9/03 Patty
5/9/99 Mary Beth LaHaye
7/24/08 Pukar
4/14/99 Meghan Anderson
4/17/99 Cindy Stogsdill
5/21/08 Emma1
4/21/99 Janice Odom
4/25/99 Mary Beth LaHaye
10/27/99 Gary Woodford
10/31/99 Sam Morris
10/31/99 Wayne Watson
11/22/99 Rachelle Tome
11/29/99 Sam Morris
11/29/99 Wayne Watson
12/6/99 Joan Schaffer
12/8/99 Julie
12/11/99 Sam Morris
2/27/00 Missy Taft
3/3/00 Sam Morris
3/6/00 Missy Taft
3/12/00 Sam Morris
3/6/00 Joan Schaffer
3/12/00 Sam Morris
3/13/00 Wendy Gulley
3/13/00 Joan Schaffer
3/13/00 Wendy Gulley
3/9/01 mary jane giardi
3/10/01 Cynthia Garland-Dore
3/17/00 Gary Woodford
3/25/00 Sam Morris
3/30/00 Wendy Gulley
4/27/08 Megan
7/22/08 chitra
6/15/00 Melissa Mohan
11/12/00 judy Berkowitz
11/19/00 Sam Morris
11/19/00 Mike Swaine
11/27/00 Jacki Riffey
11/27/00 Sam Morris
10/22/03 Patty
10/24/03 Euthecia Hancewicz
11/27/00 Sam Morris
11/28/00 Susan Weiss
11/28/00 Wayne
11/29/00 Jacki Riffey
11/30/00 Susan Weiss
12/5/00 Sam Morris
12/7/00 Rachelle Tome
12/4/00 Mike Swaine
12/12/00 Wendy Gulley
2/8/01 Sharon Peck
2/14/01 Cynthia Garland-Dore
4/29/01 LA Pruske
4/29/01 Cynthia Garland-Dore
5/7/01 LA Pruske
5/8/01 Melissa Mohan
7/5/01 Linda Dodge
12/11/01 Maize Micek
12/11/01 Linda Dodge
7/5/02 Yolanda Farmer
7/5/02 Jacki Riffey
7/5/02 Debra
7/6/02 Wayne
7/11/02 Paul Hickman
7/17/02 Cynthia Garland-Dore
7/7/02 Peg Dillman
10/8/02 Rachel
10/18/02 Beth Perry
4/23/03 Hannah, interested student
4/23/03 Debra
7/28/03 Meggan Henerlau
7/28/03 Sarah Hogg
10/7/03 betsy
10/7/03 Bob Nagle
10/8/03 Nancy
10/9/03 betsy
10/19/03 fred
4/27/08 Megan
5/10/08 Hema
7/22/08 chitra
7/24/08 Pukar

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