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Day 6 Clip 1, January 31, 2007
Ms. Coombs then introduces a chart in which
she records all of the little changes that
the students determined the previous day.
For example, how much did her distance from
home change in 7.1 minutes versus in seven
minutes. The conversation then changes to
determining where Ms. Coombs was when she
started her watch or at zero minutes. In
this process, she is continually re-visiting
constant rate of change.
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Day 6 Clip 2, January 31, 2007
Later, Ms. Coombs continues with having
students reason about how the two variables
in a linear function change with respect to
each other. In particular, she relates a
change in x to a change in y.
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Day 6 Clip 3, January 31, 2007
Later, Ms. Coombs continues with having
students reason about how the two variables
in a linear function change with respect to
each other. In particular, she relates a
change in x to a change in y.
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Day 6 - Clip 1
January 31, 2007
Prior to this clip the students had been working
to develop a general linear function for a given
rate of change passing through a given point.
Today, Ms. Coombs works with the students to
reinforce their model for the function using a
graph.
The development makes the following points:
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Start with the point (j,k) and constant
rate of change, h.
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Remember that if I move in the x
direction some amount, say ½. Then y
would change by 1/2(h).
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But we need to find the initial value
(what we commonly call b). So, if x were
to change by (-j), returning me to the
y-axis, then y would change by
(-j)h. Since I was given a y value
of k, the value for y on the y-axis
would be k+(-j)h.
We now know that the value of y when x=0 is
(-j)h+k. Changes in y from that initial
value will be depend on changes in x.
Specifically, y will change by h times as much
as a change in x. This leads to
y=hx+(-j)h+k
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-Day 1
-Day 2
-Day 3
-Day 4
-Day 5
-Day 6
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