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NationalTutoringObservatory
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MathEd-PII

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volunteer
Can we rule out one more option now?
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volunteer
very good!
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volunteer
Any other problems you'd like to go over?
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volunteer
Or further questions on this one?
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student
yes I have more
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volunteer
okay!
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volunteer
For part a, the scenario tells us that the pool starts half full of water and ends half full of water
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volunteer
What does this tell us about the amount of water in the pool at the beginning and end of the stretch of time we are looking at?
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volunteer
Should the amount of water be the same or different at the beginning and end?
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student
decrease
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volunteer
If the pool is half full at the beginning and half full at the end, is the amount of water in the pool at the beginning the same as the amount of water in the pool at the end?
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student
no
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volunteer
Why do you say that?
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student
oh wait I mean yes
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volunteer
Yeah! Then, what options can we eliminate, knowing that the start and end amount should be the same?
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student
the third option
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student
second option
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volunteer
So we want to see the amount of water at time 0 be the same as the amount of water at the furthest x value
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volunteer
Which options have that quality?
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student
last option
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volunteer
To me, the last option looks like at time 0, there's a lot of water and at the furthest time, there's a lot less water
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volunteer
We want to see that y value at the beginning and end of the x range be the same
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volunteer
In other words, if we drew a line between the beginning and end points, we should have a constant line
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student
first option
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volunteer
The first option doesn't fit that description unfortunately. The first point is the point of the line on the y axis, at time 0. The last point is the end of the graph line drawn. Does that make sense?
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student
yes
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volunteer
So we want to look for options where the y values of those two points are the same
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volunteer
That means the amount of water in the pool started and ended at the same value because y is amount of water in the pool
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volunteer
And the y values of those two points being the same means they are at the same level on the y axis :)
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volunteer
If this way of looking at the problem isn't clear, there's another way we can approach this one? Would you like to try a different approach?
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student
yes
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volunteer
So a month ago, the pool was half full. Then, three weeks ago, the pool was filled.
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volunteer
So did the amount of water in the pool increase or decrease?
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student
increase
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volunteer
Very good!
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volunteer
Do any of the options show an increase in water level near the beginning of the month?
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volunteer
We would see the line on the graph go up then because the amount of water is increasing.
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volunteer
Do any of the graphs have an up line near the start?
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student
yes
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volunteer
Which ones/one?
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student
the first, second, and last options
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volunteer
Where do you see upward heading lines on those graphs?
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volunteer
Could you circle those areas?
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volunteer
Those lines represent that as time increases, amount of water decreases.
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volunteer
We want to find a line that represents as time increases, water amount increases
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volunteer
This is because the pool was filled near the beginning of the month
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volunteer
Which option has an line that represents amount of water increasing as time increases?
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volunteer
So as the x value, time, gets bigger, the line goes farther away from 0 on the y axis :)
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volunteer
Do you understand the question? :)
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student
yes
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volunteer
awesome :)
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volunteer
How are you feeling about this problem, Emily? I haven't heard from you in a bit.
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[ { "pii_type": "PERSON", "surrogate": "Emily", "start": 40, "end": 45 } ]
volunteer
:)
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student
ok
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volunteer
Okay! Let me know if you have any questions
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student
can we work on something else
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volunteer
Of course!
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volunteer
What else would you like to work on?
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volunteer
Do you have an idea where to start calculating f(-5)?
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student
no
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volunteer
So we're given the function definition for f(x)
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volunteer
the parameter x can take on the value of any real number
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volunteer
When we see f(-5), -5 is in the place of x. So we know this is the value of f(x) when x = -5
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volunteer
Any questions so far?
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student
no
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volunteer
Awesome
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volunteer
So the definition of function f gives us two case: 4 if x is not -2 and 2 if x is -2
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volunteer
in this case, f(-5), x is -5. Which case are we in then? x is -2 or x is not -2?
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student
-2
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volunteer
x equals -5. Can x equal -5 and -2 at the same time?
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student
no
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volunteer
Then x must not equal -2
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volunteer
Since x equals -5
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volunteer
Thus, we are in the case if x does not equal -2
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volunteer
The text I circled in green says, if x does not equal -2, f(x) equals 4
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volunteer
Can you use this to evaluate f(-5)?
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student
-20
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volunteer
Close! But that's not correct
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volunteer
f(x) can only be two values: 4 or 2
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volunteer
f(x) is 4 if x does not equal -2
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volunteer
f(x) is 2 if x equals -2
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volunteer
Since for f(-5), x equals -5, we know x does not equal -2
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volunteer
Since x does not equal -2, is f(-5) 4 or 2?
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student
4
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volunteer
yes!
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volunteer
What do you think for f(-2)?
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student
2
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volunteer
yes!
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volunteer
How about f(4)?
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student
-5
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volunteer
Why do you say that?
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student
from the first part
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volunteer
The first part of what?
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volunteer
Remember, f(x) is defined above to only be 4 or 2
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volunteer
so -5 is not correct
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volunteer
f(x) is 4 when x does not equal -2 and 2 when x equals -2
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volunteer
When calculating f(4), x equals 4
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volunteer
Since x equals 4, does x equal -2 or not equal -2?
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student
not
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volunteer
exactly!
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