THINKING
SKILLS: INTEGRATING LIBRARY RESOURCES WITH
LEARNING OBJECTIVES
Keeley Library August 22, 2000 

Pre Calculus 
NUMBER 
OBJECTIVES 
Keeley Library Resources : Click on the Internet Links in the First Column on the Left.  

1H4
IH2

CONTENT:
Operating with Complex Numbers: Define
complex numbers and operate with them. Use Estimation to judge the reasonableness
of results of computations and of solutions to problems involving real
numbers.
PERFORMANCE: Problem Solving Students will work in groups on a real world application using complex numbers. Short answer. 
(to construct graphs etc See below).

2H7
2H5

CONTENT:
Exploring Exponential and Logarithmic Functions. Describe
and model phenomena using functions, including exponential, logarithmic,
trigonometric, polynomial, rational, step, absolute value, and square root.
Describe similarities and differences among the families of linear, quadratic,
and exponential functions using graphs, tables, formulas and verbal descriptions
Describe the graphical significance of parameters.
PERFORMANCE Tables and Short Answer Students will be asked to work alone using various exponential and logarithmic equations to model and project growth and decay predictions. Short answer 
(to construct graphs etc. See below)

2H8
2H3

CONTENT:
Solving Exponential , Logarithmic, and Trigonometric Equations by Computing
and Graphing Solve polynomial,
exponential, logarithmic trigonometric equations, and equations with
rational expressions by symbolic (quadratic) graphical and numerical methods.
Apply each method when appropriate. Use Algebra and graphical methods to
solve systems of linear equations and inequalities, and
describe relationships between different solution methods.
PERFORMANCE: Graph, Problem Solving: Students will work in groups to solve and graph trigonometric, logarithmic and exponential relationships and equations.. Short Answer 
(to construct graphs etc. See below)

2H10
2H5

CONTENT:
Exploring Quadratic Functions Classify
functions into families. Describe the effects of parameter changes on different
representations of polynomial, rational, logarithmic, exponential and trigonometric
functions. Describe similarities and differences among the families
of linear, quadratic, and exponential functions using graphs, tables, formulas
and verbal descriptions Describe the graphical significance of parameters.
PERFORMANCE: Graph and Explanation Students will be able to translate ,reflect, and geometrically transform graphs of linear, quadratic, exponential and trigonometric functions. Students apply the concepts of amplitude and phase shifts. Short answer. 
Collaborative Work

2H11
2M11

CONTENT:
Maximizing Profits and Minimizing costs Identify
maximum and minimum values of a function and use them in applications.
Explain and generalize how a change in one variable results in a change
in another variable in functional relationships...
PERFORMANCE: Problem Solving: Students will be able to find first and second derivatives of polynomial functions, then find the maximum and minimum points of inflection. In addition, students will find the zeros of the function and sketch a graph of the function. Openended response. 
(to construct graphs etc. See below)

2H12
2H1

CONTENT:
Composite Functions Perform
operations on functions, including compositions. Find inverses of functions.
Demonstrate facility in transforming polynomial expressions by rearranging
and collecting terms, factoring, and applying and applying the properties
of exponents in order to solve problems.
PERFORMANCE: Problem Solving Students working individually will be given two defined functions f(x)and g(x) and ge asked to find fog(x) and gof (x )for the two defined functions. Short answer. 
Writing Essays

2H13
3H6

CONTENT:
Examples of Period Functions in the Real World Model
real work phenomena involving growth, decay, and periodic processes. Apply
and interpret transformations on figures in the coordinate plane.
PERFORMANCE: Essay Students working alone will be asked to research real world phenomena to find examples in nature that can be modeled after a periodic function. Short essay 
Mathematics

2H14
3H8

CONTENT:
Finding the Sum of an Arithmetic Sequence
Identify arithmetic and geometric sequences and series and their properties.
Solve problems including the nth term recursively and explicitly.
Identify and describe geometric patterns of change using recursive notations.
PERFORMANCE: Problem Solving Students will be asked to find the sum of the first 937 odd integers. Short answer. 
Mathematics

2H15
3H8

CONTENT:
Using the Binomial Theorem: Define linear,
exponential and quadratic functions recursively, and to find closed form
expressions. Identify and describe geometric patterns of change using
recursive notations.
PERFORMANCE: Problem Solving Students working alone will use the Binomial Theorem in summation notation form to expand a binomial to some nth power. Fill in the blank 
Collaborative Work

3H9
3H5

CONTENT:
Navigation Derive and apply
trigonometric identities and the law of sines and cosines. Apply trigonometric
ratios in right triangles to solve problems.
PERFORMANCE: Problem Solving Students working in groups will solve navigation word problems using both the law of cosines and the law of sines to solve the problem. Short answer. 
Collaborative Work

4H6
4M10

CONTENT:
Determining the Period of a Pendulum Describe
the relationship between degree and radian measures ,and use radian measure
in the solution of problems. Use proportions to model and solve indirect
measurement problems .
PERFORMANCE: Diagram, Problem Solving: Students working in groups will solve real world problems involving the length and period of a pendulum which involves angular measures in radians. Short answer. 
Mathematics

4H7
4H6

CONTENT:
SportsBicycle Wheel Use dimensional
analysis for unit conversion and to confirm that expressions and equations
make sense. Describe the relationship between degree and radian measure.
PERFORMANCE: Problem Solving for miles/hour Students will be able to solve problems involving a rotating bicycle wheel changing revolutions per minute to miles/hour. Short answer. 
Note.The
following guide may also be useful for students who need to locate statistics
for projects. Statistics
We would also like to add links for online tutorials to cover items assumed to be already learned, and to help students who missed learning these concepts because of illness, etc. Microsoft has a number of tutorials. As we locate this information, we will place it as links in the file, Using Computers for Assignments. Constructive criticism and suggestions are welcomed. 
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Jane Constant, Reference Librarian
Keeley Library, B.M.C.Durfee High School
of Fall River
September, 1978 to June, 2001