After reviewing algebra skills associated with exponents students explore exponential
functions using the graphing utilities of Algebra Xpressor. On the board I write
several functions I want the students to graph such as
Students observe the characteristics of the graphs with different values for the
base. If the base is greater than one, what is the shape of the curve? What common
point is on the graphs of the equations? What is the relationship when the bases
are reciprocals of each other? What is the effect of the negative with the exponent? What
is the effect of the negative in the base? What if a negative base is raised
to a power? Consider the effect of using parentheses in these problems. Predict
what y=1^x will be. A lively discussion closes the class. As an assignment the students graph
many exponential functions and create a table of values for some of the equations.
This one day introductory activity did not require any written summary, so the class
continues quickly to applications of exponential functions.
As an aside to the reader about my attempts to integrate technology appropriately
into the other classes that I'm currently teaching...In geometry the unit on lines
lends itself well to the Algebra Xpressor. To review the concepts about standard
form, slope-intercept form, students select their own linear equations in standard form. They
enter these equations, graph them, record slope, both y and x intercepts, and sketch
the graphs. Algebraically they manipulate the standard equations into slope-intercept form and repeat the exercise. It amazes me to hear comments, "Heh, its the same
line!" Glimmers of understanding make my day. The following day students enter
the homework problems to check the accuracy of their work. If any discrepancy between
their work and the computer graphs appears, they consult with me or a neighbor to clarify
the discrepancy. I hear all kinds of good math talk and I know students are improving
their understanding of linear equations.
Another aside to the reader concerns the use of the Merrill interactive software with
students who are repeating the first half of algebra in the spring semester. The
motivation level in this class is almost in the negative numbers. They come in and
start yawning. Enthusiasm picks up considerably when students go through the multimedia
manual on the computer. At the end of each lesson ( which is an interactive, computer
version of manipulative activities) a journal entry asks the student several questions. The students really like to see their name in print when the journal entries
are printed. I'm pleased with the upbeat attitude students exhibit on days when
we use the computers...That counts for something!
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