# Kell - G6 - 05-23-01

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Remember we had to take the 8 and half strips
and measures for each one. Do you have the answers for them?
Because that's what we need to graph
Theresa just asked if we plot the same, uh, variables
as on this picture here under the question
Yes, certainly. What do you have in the horizontal axis?
Days. And what do you have on the vertical axis?
Amount Collected. Ok.
This was the data that we collected
and... we see
if you see day two, when we took the fraction strips
and we measure out of 300, so far was 75 dollars
and then on the fourth day, they collected 100 dollars
and the sixth day, it was 180 dollars
and on the eightth day, it was 225
and on day 10, it was 250 dollars
So that was their progress
On the 26th, it says to show the sixth grade progress
So we have to show this and plot it on the graph
So, just that, on the horizontal axis, we have days, right
and on the vertical axis, we have amount collected
So, if you look, at uh,
If you look at the numbers 75, 100, 180
225, I think we should go by 50s (fifties)
on the vertical axis
for the Amount collected. Ok?
But, maybe we should skip spaces
because we might have too much and the data
would be stuck in, just one,
area. So maybe we should skip like, two spaces
Zero and then Fifty, One.. Two.. and go.. you know what I mean
I have this doubt
Every two days they make about fifty dollars
Because I took 250 divided by 10, I got 25 per day
So for two days, its fify
So we can just go in that pattern
So in the next two days, they should make
about 50 more dollars and that would be 300 on the twelfth day
So let me understand this. On the first and the second right
They were at 75 according to your graph
So they were above their, actually, no..
Ya.. They were above their goal
Above their goal. So are you saying every day or every two days?
Every two days they make about fifty dollars
About fifty dollars. Show me how you know it from your graph.
Ok. I took their final one. Ten days - 250
divided by 10 for ten days
and I got 25. But they measured it every two days and not every day.
So I multiplied by 2 to get 50.
So if your pattern is true, then on the second day they would have 50
But its not quite so right.
Ya they were above standard.
But you still believe there is a pattern here?
No, well, but, their goal was set for 300 dollars and
300 divided by 5 would be 60. But they are still above their goal
Ok. But what you are trying to do is to use
the pattern that every two days is 50 dollars
about 50 dollars. Correct?
Ok. So show me how it is 50 dollars every two days
Because the first day, you see, they went to about..
Everyday if they were that number, then I don't see how
It doesn't depend on how much..
how much they increase from the previous 2 days
Ok. Show me that they are increasing by fifties
Well, instead of 50, they got about 75
But they increased this one only by 25 dollars
So that balances it out.
Very good. Ok. Do you agree with his point? Ok. Fine. Then...
Ok, well, then they increase it by a lot and right here
By how many? What is a lot?
Well, they increase it here by 80 dollars, I would say
So I don't see that pattern. Do you?
No. Well, I mean. But then
They increased it by about.. I'd say
Two Hundred. 25 times 8. So they'd even out.
It would be 200. But they are just a little over.
So when you say even out, what are you talking about?
When we say even out something, what kind of average are we talking about?
Balance... Mean.
The mean. So, on an average, it would be still
50 even though there were variations. Is that what
are you trying to tell me?
Well, they made.. They increased it by 45 dollars right here
and then only 25 right here
So what would your answer be then?
So it balances out.. 50 dollars every two days.
So they should make 50 more.
to make 300 on day 12.
So, I predict in two days, they would make 300 dollars.
Ok. You guys agree with that?
Very Interesting. So now it would be interesting to check
if people who drew the best fit line. If their answer would be close to yours.
Does it have to be exactly the same?
No. But.
Does it have to be close?
Probably.
So ok. that would be one way to get the answer, right?
Other way to find out the exact amount
the company would make is to
They made 300 dollars if they make 50 dollars in two days
But then, if we use the
This graph, No..
This one. Then we can try to figure out
how much they make in day 12
by using, like in day 2 they had one-fourth
and on day 4 they had one-third
day 6.. three-fifth
day 8 they have three-fourth cash
and day 10, they had five-sixth
So, using fractions, by good prediction about the average that they use
Think about it and talk to your buddy
and we'll discuss it in the class.
It is an interesting thought and I want to clarify
Do you understand what I am saying?
and then we will discuss it in the class.
But would that make a reasonable answer though?
You tell me, is that reasonable?
Ya.. Well..
If you average it to about 50 dollars every two days
I think it is feasible to say, that they'll make 50 dollars
in the next two days, they would make about 50 dollars
Ok. Now. Rikan has a different strategy here.
He wants to look at these patterns, in terms of fractions.
So if your strategy was good and if his strategy
was good, then your answers should be what?
Close to theirs.
Well, you can also see what he does.
Actually I do agree with Kevin. But
In order to find out, like
how much they would make on day 12
the raising company.. More than 300 dollars
But right now we are assuming that its 300 on day 12.
But I still like your strategy. Let's check it out.
You know, see fraction-wise how much this increases.
Thats not a bad idea and let's see if it matches.
Well, I discovered this.
Day 10, they make five-sixth of their whole
and then it took them ten days to make five-sixths
So it should take them twelve days to make six-sixth or one whole
Ok. Do you see his logic?
Ya ya. But then they might be more.
See on the first day, they had 75 dollars
I mean this probably looks like its going to be more
I mean it can be. But the question is
estimate. So this is a good estimate right?
But if it goes in that pattern, by day 12, it should make about 300 dollars
Do you understand what he is saying?
Do you agree with Rikan?
Rikan looks at it from the perspective of fractions, right?
And Kevin is looking at patterns in
quantities - increasing per two days.
Does that make sense?
Do you understand this?
Ok. Now that you verbalize it very nicely
I would like to see the writing. Ok?
Just as clearly, for everybody.
So decide what you are gonna write.
Remember the rule - You cant add anything afterwards.
When you present, you must read what you wrote.
Should we test this out?
Is this equal or do you wanna
or not?
Ya. I think so.
Because it might be like a bit different
like on the first day they had 75 dollars
Ya. They were off a lot. Only one time actually they were
So like I'm saying, if they go in the pattern
of day, by day 12, they would reach about 300 dollars
Ya. That's what I was saying.
I agree too.
Ok, we, um..
if we, ok find on day 8, it goes up to
six. So six twelfth.
So that's a half of it.
Ya. A half more.
Day 6
Well, this is the last one we'll need
What's next?
They made about twenty five dollars a day.
This is not accurate. So we are gonna have to use the twelfths.
Its better. Ya. It equals seven-twelfths.
Seven-twelfths out of all of them.
We found out that, on day 4
they made one-tenth more than day 2
and day 6, they made four-tenth than day 4
and on day 10, they made half more than day 6
What do you mean half?
Like six-twelfth
So here the difference was four - tenth, right?
Don't you think it would make sense if you use
twelfths all across or tenths all across?
But then they are not equal and the same
Ok. What was the first fraction?
One - Fourth
Ok. What was the second fraction?
How much more or the whole?
No. The whole thing.
One - Third.
Ok. Can you bring them to a common denominator?
Students : Yes. Teacher: Ok. What would that be?
Twelve.
Ok. What is, one-fourth how many twelfths?
Or look at your fractions.
One-fourths is how many? Students : Three.
And how many,... One - Third is how many? Students : Four
So the difference is one-twelfths. Agree?
So between the second day, was it the second day..
the second day and the fourth day, you have one-twelfths of a difference, right?
So let's just record it and see if there is any pattern here.
So we have one-twelfths here. Student : Day 6.
Teacher : What was the fraction? Student: It's going to be about six-twelfths.
About six-twelfths right. So you went from, how many,
four-twelfths?
Day 4 - How many twelfths we have? Student : Four
Four-twelfths changes to six-twelfths. So increase by
how many twelfths? Student : Two
And then on day 8, they had
about nine-twelfths.
Ok. Nine-twelfths. So they had increased by how many?
Six over here, so three.
Three. So you had two-twelfths, then you had
First you had one-twelfths, then you had two-twelfths and then you had
Miss Kell, they had seven
Lets see. Ok.
So the first day, lets see, you had three-twelfths
The second day, you had four.
The difference is one, right?
Next day, you had how many? Student: Seven.
Wait a second. Why did you seven? One, two, three four, five, six, seven. Ya. Ok
Ok. So the first difference was one.
The next one was three.
Ok. What's the difference for the next thing?
We have nine over here. Teacher : So the difference is two.
Ok, and then.
From nine to ten. One.
So it goes one, two, three, one.
Ok. So what's the average?
About how many twelfths does it decrease?
If you were to average this - find the mean
So one, two, three and one. What's the mean?
One-twelfth?
Between one, three. Write numbers - one, three, two and one.
Just write. Forget it. Just write one, three
Don't write in fractions. One, three, two and one.
What's the mean here?
Equalize them. Student : Seven?
The mean. Not the total. The mean
How do you figure out the mean?
Add them and then divide by the number.
Ok. So what did you get?
About 2. Try to even them out. About 2 right?
So your average is two-twelfths or one-what?
sixths. Teacher : One-sixths, between the, every two days.
So if you take.
What was the total for the tenth day?
One-tenth.
All right. What was the amount?
250 dollars.
Ok. One-twelfths of 300 is what?
Do you see what I am trying to do now?
Ok. Then you go with it. I am not going to do it for you.
25.
25 more? Ok. So
Day twelve would be 275.
So, they would make 300 on what day?
14. So your answer to this would be 14.
And your answer to this was day 12.