Hi Regina,
You wrote:
RF> Right now things are confusing anyway.  Jeremy is having a tuff time
  > understanding borrowing.  Plus we are going to be moving next month and
Many students have a problem with this concept. The problem is really
compounded if they haven't had a thorough grounding in "place-value". I
find this is not properly taught in most classrooms that I go into.
The biggest problem lies in the fact that this concept - place value -
is one of the hardest for children to grasp and if done abstractly
almost impossible for any but the brightest.
If you have any knowledge of the Mathematics Their Way program and book
written by Mary Barratta-Lorton you will know some of the ways to go
about this.
Children have to understand the meaning of ones and tens and that
everything has a "place". They do this much easier if they work with
concrete materials (manipulatives).
Barrata-Lorton does this by teaching the kids that when you get a
certain number of things it changes into something else. She doesn't
start in base tens but in smaller bases of four or five and then works
up. I did this with a grade one class when I was teaching them about
money.
Here are some things that I did...of course works best with a group of
children, in this case the more the merrier.
In this case we started off with a game. Our magic number was five and
we invented a new name for five. We counted round the circle until the
fifth person who said the new name and sat down. We then started from
one and kept going until there was only one student left.
Next we played another game. Still using our new name for five, I made
two areas in the classroom with the divider being a skipping rope. One
side was for the ones and the other for the fives (can't remember what
the new name was). We counted and as we counted the children jumped into
the ones area. When we got to five we had a problem, because five didn't
belong in the one section and five ones didn't belong in the five
section. I asked the children what we could do to show that they
belonged together as one unit of five. They decided to join hands, they
then jumped over the rope into the next section. We kept counting until
we had several groups of fives and ones. We then reversed the order by
taking away one. When we had exhausted the separated children on the one
side we again had a problem. When asked how we could solve it the
children came up with the idea of letting go hands and jumping back to
the other side so we could take one away.
The next step was to work with manipulatives. Here you can use cubes
that will snap together or beans. Make a two sided mat - piece of paper
divided into two sections of different colours. Put the ones on the
right side and the other (fives or tens or whatever) on the left. Then
you  start adding beans to the right side. When you get to five (or
whatever) you have to change sides. With the cubes you can snap them
together and put them on the other side. With the beans you can gather
them up and place them in a bathroom size Dixie cup or medicine
container (those little clear plastic ones) or something similar.
Keep practising adding to make units and ones and then subtracting.
Once the children have a grounding in this the concept of borrowing or
trading is easier for them to understand. If they have to take five away
and there is only three in the ones column they will know to borrow from
the other column - which has to be broken down into ones first.
I hope you understand what I'm trying to tell you here as it's hard to
do without showing you or without diagrams.
Hope this helps. If you have any questions write back or email me at (if
you have access to email- not netmail)
Ruth_LeBlanc@sbe.scarborough.on.ca
                Good luck,
                        -Ruth
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