# Buonano G4 10-22-03

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Okay, I need somebody to take a look at the subtraction problem
on the board and I need somebody to tell me
what the subtraction problem actually is
Aishan!
124 minus 25
And how do I show that problem with base 10 pieces?
This represents what?
One hundred.
and then 2 sticks.
which represents?
Twenty.
You put 4 bits to represent 4
So thats 124 and its minus 25
So how do we shoe -25 with the base 10 pieces?
What does it mean when you are subtracting?
John!
Can you say that louder?
You are taking away.
So how do I take away 25 from this problem?
You need to take away 2 sticks and 5 bits
So how do I start this off?
And actually can you show that base 10 short hand?
I'll show the part where you have it represented and
you are done solving it with this one.
I have 125 and I am supposed to subtract how much?
So the picture tells
tells the same problem or should tell the same problem
or if it doesn't we know right away that you weren't paying attention
Okay. Looking up here. I have 124
and John tells me that I have to take away 25.
How am I going to do that?
You have to take away 2 tens and 5 bits
Aziz!
You would want to take away one stick and
keep ten bits.
Oh. Why would I want to do that?
Because there's not 5 bits
So you cant take away 5 from 4
So he tells that we dont have enough bits here to take away 5 bits
So the great thing is right next door here
we have a skinny
and it counts to how many bits? Ten.
So I trade that for how many?
Ten bits.
Or 10
Ones
Can you consider showing them the trade over there?
Who can tell me how I can show the same thing I have
just showed with the base 10?
Aisha.
So when you take this stick away I am going to circle it
Where do I have my arrow go?
The place to where the bits go
So the place to where the bits go.
And it turns into?
How many bits?
Ten bits. That sounds like a fair trade to me.
Ten for ten.
Ten bits for one skinny
which is equal to how much?
A skinny
And a skinny equals how much?
Ten bits.
Fair trade.
So we started to solve. You have traded one skinny for ten bits
ten ones. Now what am I going to do?
So you are saying we take away 10 skinnies?
Not from here. From the flag.
You trade it for ten skinnies
Ok. Marco says we have to trade the flag for ten skinnies
Why do you think he thinks that?
And I need you to tell me and I need you to speak up
because I am an old woman and I cant hear you.
Because you need to take away 2 skinnies
and you have only one such one
Oh ok. I need to take away 2 skinnies and I dont
have enough. So I am going to trade this for?
A flag for ten skinnies.
Wonder what that might look in the base 10 short hand.
I want to hear from somebody I haven't heard from yet
How do we show the same thing which Ms. Buonano showed with base 10 pieces
How do we tell the same story?
Jackie.
We have to cut down a flag
What do I take?
A flag away and put in ten skinnies
So I take a flag and put in skinnies my arrow?
One two three four five
Am I counting this skinny in it?
No.
Six seven eight nine ten.
Thats a fair trade.
All together now I have how many skinnies here?
Eleven.
Jen.
Eleven.
How many skinnies does Ms. Buonano have
with her base 10 pieces?
Eleven.
Ok.So same problem.
And do I have the same number up here as we started with?
Do I have the same number up here?
No.
How is it different?
Because you added ten bits
and you added ten skinnies.
I thought we said we were trading
Yes we have the same number because
Now you are saying yes?
Yes.
Because you still have the same even if
you trade some in
At first, you start off with 124
No. its different because now we have
130.
Now we have 130?
I mean 129.
Alright lets just make sure
Whoever thinks its the same number raise your hand
Whoever thinks its a different number raise your hand
We are going to talk about whats going on here
Count out loud
Ten twenty thirty forty fifty sixty seventy
eigthy ninety hundred one hundred ten
111 112 113 114
115 116 117 118 119
120 121 122 123 124
Its the same
Ok. So whats different about this number?
He just counted and saw it is the same
What is different about it?
And why are we all so cool?
Diana
Because when we take away a flag
we replace it with ten skinnies
and ten skinnies took away your flag
And you took away your skinny and you had ten bits
and you had four bits
in the beginning
you didnt get rid of them
We are looking at it in different ways but
it is the same number.
So any one want to add to her explanation?
Alia.
When you add the ten so that you are supposed to take away 5 bits
you are supposed to take away 5 bits
and then you are supposed to take away 2 tens
Ok. Alia is telling us how to get on with the problem
Now we need to subtract.
So will you tell now what do I need to do here?
You take away one two three four five bits
and then two tens
And thats your answer
And this is our answer. So what is it?
10 20 30 40 50 60 70 80 90
91 92 93 94 95 96 97 98 99
Ninety nine.
Ninety nine. Ok. Thank you!
Now do we have the same number or different number than we started with?
Its a different one.
So lets a look at the base 10 shorthand and
see how it is shown
So to get a different number
what operation did you just perform?
Subraction.
I like how you remembered in all of this trading
and moving and changing the number around
Making the same number different
We are going to do the operation subtraction
How do I show the same thing as Ms. Buonano showed?
How do I show the same pieces?
What do I do?
Take 5 from the bits
How do I show I am taking this away?
How is it different than I did with replacing?
I take aside or take out somehow.
So I show them out
What do I do next?
Take away 2 tens
Why do I take 2 skinnies away?
And I am taking away how much?
What number do 2 skinnies represent?
Twenty.
So altogether there are 20 how much?
Skinnies and bits?
There's twenty five.
And how many flags do I have left?
Zero.
How many skinnies do I have left?
You have nine.
Nine. Number 90 that the skinnies signify.
How do I show 90? How many skinnies?
1 2 3 4 5 6 7 8 9
an how many bits?
do I have left?
Nine.
1 2 3 4 5 6 7 8 9
And so our end numbers - difference
between a 124 and 25
is how much?
Ninety nine.
Ninety nine. Good.
Do you want to take a look at how this looks in the short cut method?
So you got to take 10 out and borrow 1 skinny
and add the 1 skinny to the ones
I add one skinny to the ones and
one skinny is how much when added?
Fourteen.
One skinny. So how much is it when it is moved over to the ones?
Fourteen.
Ten. Do I have anything left in the tens column?
How much?
One ten or one skinny
Ok. What do I do next?
Ok. 14 minus 5 equals 9.
and then what do I do?
Take away the 1 from the hundreds
and the one in the tens column represent one what?
Ten.
Eleven.
I crossed this one out and I put this one here
So when I move it represents one what?
One flag. So one flag is how much?
A hundred.
So we add to one, one hundred. Thats right.
Now I have
a eleven and eleven minus 2 equals 9
11 minus 2 equals 9. Thats true
We say 11 minus 2 meaning eleven what
eleven tens take away
2 tens
9 skinnies which is?
ninety
or ninety nine with the ones
Good. So a shortcut method tells the same problem
as our base 10 short hand which tells
the same problem as Ms. Buonano's
base 10 pieces.
This seems like everybody's fine.
I wonder if you are all ready to try on your own.
Raise your hand if you are ready to try.