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This course examines the families of linear,
quadratic, power, polynomial, exponential, and trigonometric functions.
Emphasis is placed on studying functions as bridges between the
mathematics and the situations they model. Graphing calculator
skills are reinforced and expanded. Prerequisite: Math X468B (Topics in Algebra and Geometry)
SIERPINSKI TRIANGLE (ST)
As an introduction to functions, participants create several stages
of the Sierpinski triangle and record patterns. Participants
then use the patterns to generate recursive and explicit functions.
Participants also learn basic concepts for graphing functions
on the TI-73 graphing calculator.
KOCH SNOWFLAKE (SNOW)
Participants practice some basic function concepts by creating
several stages of the Koch snowflake on isometric dot paper. Participants
then use the graphing calculator to examine properties of the Koch
snowflake.
LINEAR AND NONLINEAR SYSTEMS (INEQ)
Participants learn ways to solve and graph linear inequalities.
Participants use graphing and algebraic techniques to solve linear
and nonlinear systems of equations. Finally, participants apply
their knowledge to analyze a real-world application problem.
BEHAVIOR
OF POLYNOMIALS 1: MORE QUADRATICS (BP1)
Participants review the parent graph activity from Quadratics
1 and determine what types of changes in the parent equation
result
in certain changes in the graph. Participants create a quadratic
graph by marking the height where a thrown object passes in front
of them. Participants then collect the data and use the TI-73 graphing
calculator to guess the quadratic equation that fits their data
the best. Finally, participants use the quadratic regression function
on their graphing calculator to determine the accuracy of their
guess.
BEHAVIOR OF POLYNOMIALS 2: CUBICS AND MORE (BP2)
Participants investigate polynomial functions of various degrees
through the painted cubes activity. Participants use the TI-73
graphing calculator to explore and generalize characteristics of
polynomial functions.
BEHAVIOR OF POLYNOMIALS 3: ROOTS AND CRITICAL
POINTS (BP3)
In this unit, participants will look at various types of factoring
techniques used in factoring higher order polynomials. Participants
will continue to use the ideas developed in previous units involving
algebra tiles and the generic rectangle, to develop a geometric
model for factoring. Participants will apply these factoring techniques
to find roots of higher order polynomials, in order to graph them.
Participants will summarize the behavior of different polynomial
families, and note the local maximums, minimums, domains, and ranges
of various polynomials.
EXPONENTIAL FUNCTIONS 1 (EXPO1)
In part 1, participants simulate an exponential decay model through
the M&Ms probability experiment and investigate the behavior
of the function on graphing calculator.
In part 2, participants plot various exponential functions on graph
paper to investigate various translations and transformations. INTRODUCTION
TO TRIGONOMETRIC FUNCTIONS (TRIG2)
Participants develop the radian system of angle measurement using
circular objects and string. They find the ratios of the sides
of special triangles, and they use these values to graph the
sine, cosine, and tangent functions.
EQUATIONS (EQNS)
This module includes a collection of typical algebra textbook
equations and inequalities and the common errors that students
make when
solving them. These problems provide skills practice for participants
as they analyze and discuss student errors. Participants also
examine alternative teaching and intervention strategies to
help students
avoid the common errors.
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