Introducing Place Value to Children

Date: 10/01/2007 at 19:06:45
From: Auria
Subject: teaching my son place value notations

I'm wondering how to teach my son about place value.  How can I show
him that units are up to 9 then when it comes to 10 is tens and so on?
I really get confused myself how to explain it to him.

1,2,3,4,5,6,7,8,9 are ones  10,11,12,13,14,15,16, up to 99 is tens and 
so on

Date: 10/01/2007 at 22:58:20
From: Doctor Peterson
Subject: Re: teaching my son place value notations

Hi, Auria.

I introduced place value to my children with several different models.

One was beans, cups, and trays: I would put 10 beans in each cup, and
10 cups on a tray, while counting beans.  Thus up to 9 would just go
on the table, individually; when there were 10 they would fill a cup,
and then I'd keep putting more on the table until there were another
10.  Eventually I might have 1 tray of 10 cups (100 beans), and 3
additional cups (30), and 7 single beans, for a total of 137.  The
hundreds place represents the number of trays (1), the tens place the
number of cups (3), and the ones place the number of single beans (7).
This makes it clear that any numeral represents a number we can count,
and any number of beans can be expressed this way.  You can also do
addition and subtraction with this system, and see how the digits 
work.

Another model was play money, which is a little more abstract so it
should be used after the beans are fully understood.  A $10 bill
represents a stack of 10 $1's; a $100 bill can be exchanged for a
stack of 10 $10's, or 100 $1's.  By always having no more than 9 of
any one kind of bill, we represent a number's places, and can do
addition and subtraction as with the beans.  Our number 137 would be
one 100, three 10's, and seven 1's.  To add $84 to that, I would add 4
more $1's, but since I have 11 now and that's too many, I change 10 of
them for a $10 and keep only 1 $1 in the pile.  Now I have 3, plus 8,
plus the new 1 $10's, for a total of 12 $10's; again I change 10 of
those for a $100, leaving me with a total of 2 $100's, 2 $10's, and 1 $1.

Another thing that was of interest was a mechanical counter, either
one that works like an old odometer (if you can find anything like
that any more), or the plastic counters they used to have where you
could click any digit to add one.  I don't know if anything like this
can still be found easily!

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 10/02/2007 at 22:32:30
From: Auria
Subject: Thank you (teaching my son place value notations)

Thank you so much for responding to my question.  It will help me 
explain to my son in a much better and easier way.  Auria.