Numeration and Place Value

From: Anonymous
Date: Tue, 1 Nov 1994 18:55:10 -0800
Subject: numeration and place value

Gee, Dr. Math, what a relief to have someone to talk to about this.

I have taught elementary math for quite some time (and maybe not all that
well), but in the last 5 or 10 years, I have found an increase in the
difficulty the kids have with place value and numeration and rounding. 
Some examples:

100,000 + 90,000 + 700 + 3 = 

Many students will not understand that there are no 1000's or tens.

Or, in the number 128,594,

What is the value of the 8 (8000), or the 22,000 or 4 (4 ones or 4)?

Round 9487 to the nearest 

10 - 90
100 - 500
1000 - 9000

Those are some examples.  I tested the grade 4's and 5's separately, and
they bombed on questions like those I have cited about.

Is there some strategy, exercise, drill or whatever to get these concepts
across to kids, some manipulatives that could be used?  Any help would be
appreciated.

Thanks, Doc.

Cliff Boldt, Grade 4/5 Regular Classroom Teacher
Brooksbank Elementary School  
North Vancouver, British Columbia   Canada  V7L 2N2           

Date: Tue, 1 Nov 1994 22:26:17 -0500 (EST)
From: Dr. Ethan
Subject: Re: Numeration and place value

Dear Cliff,

I recall that when I was a wee lad we had the little blocks.  There
were little cubes that stood for ones,

                    *  
bars that stood for tens,

                    **********  
and big squares made of a hundred little squares:

                    * * * * * * * * * *
                    * * * * * * * * * *
                    * * * * * * * * * *
                    * * * * * * * * * *
                    * * * * * * * * * *
                    * * * * * * * * * *
                    * * * * * * * * * *
                    * * * * * * * * * *
                    * * * * * * * * * *
                    * * * * * * * * * *

Then there was a big cube that had a thousand little squares. 
So two big cubes, two big squares, 4 bars, and 7 little cubes 
was 2247. This made it easy to see the different place values 
(what is in the thousands place? count the big cubes) - rounding 
to the nearest blank can now be visual: two to round to the 
nearest thousand; stack up the big squares - do they almost make 
a big cube? then you round up, etc.
                
Hope that helps you.  Any more questions just send them over.

Ethan - Doctor in Training

Date: Tue, 1 Nov 1994 22:44:35 -0500
From: Anonymous
Subject: Re: Numeration and place value

Hi Cliff, here are the first things I thought of:

1) In the same vein as Ethan's response: Most of the schools down here use
a program called _The Mind's Eye_, which is the follow-up to the younger
elementary _Math Their Way_.

In this and other programs there is a strategy analogous to what
is done with cuisinaire rods for basic arithmetic.  A set of manipulatives
is used, composed of basic elements.  Units, which are one-by-one cubes.
Strips, which are ten of these in a row.  Mats, which are one hundred of
the units laid out in a ten-by-ten fashion.  Then one can make compounds
such as StripMats, which are ten mats in a row.  MatMats, ten mats by ten
mats.  And so on.  These work well.  You don't need the special sets.
Heavy cardboard is good enough to simulate these materials.

2) Another good entry for us is the metric system, which we have to
learn consciously down here and which nicely models the base ten 
system.

3) Do you have access to the Internet/Usenet newsgroups such as 
k12.ed.math?  There are many teachers there who would also have good ideas.

There is also an excellent mailing list for math teachers named NCTM-L.  
For information on newsgroups and discussion lists see the Math Forum's page

  http://mathforum.org/kb/   

Good luck!

-- steve