Texas Instruments CBL 2, Руководство по началу работы

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38 G
ETTING
S
TARTED WITH THE
CBL 2™ S
YSTEM
© 2000, 2003 T
EXAS
I
NSTRUMENTS
I
NCORPORATED
Teacher Section
Theory
Science and Mathematics:
When batteries are lined up in series, the total voltage is the sum of the voltage of
each battery. Notice that the total voltage is calculated by the repeated addition of,
say, 1.4 volts. After gathering their data, students should use inductive reasoning to
notice that the sequence of voltage can be generalized to 1.4X where X is the
number of batteries. This gives a simple linear model of the relationship of voltage
versus number of batteries.
If the batteries are approximately 1.4 volts, the linear equation should be
approximately Y=1.4X + 0 where Y is the total voltage of the series and X is the
number of batteries. The slope, or rate of change of the total voltage, is 1.4 volts
per battery. The Y-intercept is at (0,0), no batteries, no volts. Have students write
the equation using variable names that fit the problem.
Students should compare their formula developed using their reasoning and
number sense with the Linear Regression Line, Line of Best Fit (Curve Fit), calculated
using the calculator. Point out that, for this simple problem, they were able to
develop the model using their own reasoning skills.
Discuss with the students that they could have used (B,V) instead of variables (X,Y)
to describe the model. The letters B and V may have more meaning in the physical
problem. Notice that there would be confusion if they use B also for the Y-intercept
in this case. Discuss this. Also, ask students how the linear equation used in the
activity, Y=AX+B compares to the use of y=mx+b in their math classes. Point out
that A=slope=m.
Note: If the batteries are brand new, the voltage measurement might be greater than 1.4
volts.
Answers
1.
Answers will vary.
2.
Sample graph: