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to be a good secretary when...
These tips for "showing your work" come from Teacher-2-Teacher
contributors, Mrs. Zisow and Mrs. Meltzer.
How To Be A Good Secretary When Doing Long Division
1. Put the correct number of dashes in the quotient.
2. Record how many blocks you have placed on each divisor.
3. Record how many blocks you have used.
4. Record how many blocks you have left.
5. Record how many blocks you will now be working with.
6. Repeat steps 2-6 until you have either no more blocks, or until you
have a remainder.
7. Record your remainder.
How To Do Long Division with Base Ten Blocks
Long division is taught by connecting the process as closely as possible
to real life events of banking. Although the analogy is not precisely
accurate, it is a place for children to begin from something they know
(banking) to the actual process of long division itself. Before beginning
the actual process of long division, the terms of dividend, divisors and
quotients are presented.
A. Dividend - We begin the discussion of dividend
with banking. How do banks work? The concept of banks is discussed as
being the place where our money is placed for "safe keeping"
without the bank actually keeping our money in a self contained box. Instead,
money given to the bank is invested in safe investments which are insured
by the government (FDIC). The amount of money the bank makes by investing
our money is returned to us by means of interest-a form of dividends,
i.e. how much the bank gives us. This concept is expanded into who gets
a percentage or part of the money the bank earns by using our money for
investments. The people who get the dividends (in the form of interest)
are the divisors. Naturally, it would be unfair to give one divisor more
of the interest than the other divisor so the interest or dividends must
be divided equally among each divisor to keep all of the divisors happy.
The actual amount each divisor gets once the dividends are divided equally
is then called the quotient.
B. We now concretely show each of these terms, i.e. the dividend,
the divisors and the quotient.
C. The dividend, (the amount the bank is going to give the divisors)
is placed in the "Bank" which in our case is a Base Tens Block
Placemat-the plain large piece of paper with the hundreds, tens, and ones
blocks at the top of it. So, if the first problem is 3) 154 . I would
have the children put 154 into their bank since this is the dividend the
bank must distribute.
D. I then explain that the 3 in the problem tells us how many people
or divisors, the bank must divide the dividend among equally. To represent
the three divisors, I give the children 3 pieces of colored paper about
5 by 7 inches.
E. Our job is now to figure out how much each divisor will get
so that the dividend is divided fairly and equally among each divisor.
The Process of Long Division
A. The first rule of long division is that we must begin with the
largest unit in the bank. (This is contradictory to previous learning
of addition and subtraction where we always begin with the Ones blocks.)
B. Children take the 1-Hundreds block (flat) into their hand and
are asked to divide it equally among our three divisors. Naturally, they
can clearly see that this cannot be done. Discussion ensues as to what
can we do. Children quickly come up with the idea (from previous work
with Base Ten blocks), that they can trade the Hundreds block for 10-Tens
C. At this point, I show the children on the board that because
I am unable to use the one hundreds block, I am going to put a dash on
top of the 5 in the problem indicating that that is where my first "answer"
is going to be placed" shortly. I also instruct them to put dashes
on top of any digits after that first digit to correspond to the remaining
number of digits in the dividend. In the below example then, I'd put a
dash above the 5 and a dash above the 4 indicating that my answer will
eventually have two digits in it.
D. The children are then instructed to go ahead
and make the exchange of the 1-One hundred block for the 10-Tens blocks.
They put these new blocks into their bank and I point out that now, instead
of having 5-Ten blocks in the bank, they actually have 15 - the exact
amount my dash is showing on the board.
E. I now ask them to take the 15-Ten blocks and divide them equally
among the divisors. Children literally pick up the 15 blocks and place
them equally on each of the colored placemats (divisors). I then ask them
how many blocks they were able to put onto each placemat and they can
easily count and discover there are five on each one. I show the children
how to record how many they've put onto the placemat right above the first
dash. So we now have:
F. I now ask the children to tell me how many of
the Tens blocks they've used up? They answer 15 and I show them how to
record this on the board. (5 x 3; 5 tens x 3 divisors)
G. I then ask how many tens blocks are left in
their bank and they respond zero. I show them how to record this.
H. I remind the children that we began with the
largest block because that's what we always must do in long division,
then we went on to the next largest block, i.e. the Tens, and now what
we will need to go onto- the Ones.
I. I ask the children how many ones they have in the bank, they
tell me they have 4-Ones in the bank and I show them on the board how
I will now show that.
J. I ask the children to pick up those 4-Ones and
distribute them equally among their divisors. They proceed to put 1-One
on each placemat and invariably question what to do with the leftover.
Before discussing the leftover . . . . .
K. I ask the children how many Ones they gave to each divisor.
They tell me 1 and I show them on the board how to record this.
L. I now ask them how many they've used up and
they respond, they've used up 3. Again I show them how to record this.
M. I again ask how many are now left over. They
respond 1. I ask if we can distribute this one evenly among each of the
divisors, they answer no and I tell them we call this "1" a
remainder since it is leftover and we can't use it. I show them how to
show that they have it leftover by putting a capital R next to the rest
of the quotient.
N. I now ask the children how much each divisor
received. They tell me 51 R1 and I tell the children that the amount each
divisor receives is called the quotient.
Practice and Reinforcement
A. We will be practicing long division throughout the week. As the
children progress, more and more difficult problems will be given. Eventually,
(but not this week, of course!), your child will be able to divide one
and two digit divisors into four and five digit dividends.
B. Here's where you come in!
C. Each of your children are being sent home Base Ten blocks along
with a Bank Placemat and divisor sheets.
When doing homework, please insist that your children use these manipulatives
at least through the first week of practice. After that, we'll leave it
up to your child if he or she needs them. Please check your child's math
homework to reinforce the process of long division. If the answer is wrong,
please do not correct it. Instead, ask your child to show you step by
step with the blocks, Placemat and divisors, how they got that answer.
In this way, homework will become a positive reinforcement of what is
being taught in school. If your child still does not get the correct answer
even with the blocks, just initial the problem so I know it has been attempted
again with the blocks, and I will make sure that particular problem is
done in class.