Textbook Lessons

Component Content

1. Students will express advanced mathematical ideas and relationships orally and in writing.
A. Students will apply the concepts of group and field.
B. Students will work with a conjunction and a disjunction.
C. Students will prove by direct, indirect, math induction, and truth tables.

2. Students will possess a working knowledge of trigonometry and be able to manipulate trigonometric identities.
A. Students will apply the definitions of trigonometric functions based on unit circle.
B. Students will graph using the six trigonometric functions and variables.
C. Students will find amplitude, period, and phase.
D. Students will apply the results of combining functions.
E. Students will apply common identities.
F. Students will establish new identification based on other identification.
G. Students will solve trigonometric equations.

3. Students will be able to apply trigonometry to find solutions.
A. Students will apply the polar coordinate system.
B. Students will apply complex numbers and limits.

4. Students will understand vectors and matrices.
A. Students will know what a vector and a matrix is.
B. Students will apply operations of vectors and matrices.
C. Students will show a proof with vectors and matrices.
D. Students will solve systems using matrices.

5. Students will understand sequences and series.
A. Students will know the difference between arithmetic and geometric sequences and series.
B. Students will know what a sequence and a series is.
C. Students will know the difference between finite and infinite.

6. Students will understand the basics of analytic geometry.
A. Students will know the four different conic sections.
B. Students will identify the equations of the conic sections.
C. Students will graph the conic sections by using the major components of each.

7. Students will be able to use logarithms and exponential functions.
A. Students will apply real number exponents.
B. Students will apply logarithmic functions and exponential functions.
C. Students will apply relationship between a logarithmic and exponential function.
D. Students will apply laws and properties of logarithmic and exponential functions.
E. Students will solve logarithmic and exponential equations.

8. Students will understand limits.
A. Students will know what a limit is.
B. Students will find the limit of a function.
C. Students will apply limits to the other areas of mathematics.





Logic

Component Content

1. Students will be able to recognize and use logical terms and symbols:
A. Students will recognize and understand propositions, premises, and conclusions.
B. Students will recognize symbolic logic and be skilled in the algebra of propositions.
C. Students will understand and use IF...THEN, AND, OR, and NOT terminology.

2. Students will be able to interpret and determine truth values:
A. Students will understand true and false terminology.
B. Students will understand and produce truth tables.

3. Students will be able to recognize and manipulate conditional statements and their variations:
A. Students will understand hypothesis/antecedent and conclusion/consequence clauses.
B. Students will understand converse, inverse, and contrapositive variations and use them to manipulate logical statements.

4. Students will be able to understand and perform deductive reasoning:
A. Students will perform deductive reasoning in mathematical systems.
B. Students will understand indirect deduction and the phenomena of paradoxes.

5. Students will be able to understand and perform inductive reasoning:
A. Students will perform inductive reasoning in mathematical systems.
B. Students will understand incomplete and complete inductive reasoning.

Calculator/Computer Laboratories

Component Content

1. Students will be able to design and conduct meaningful experiments:
A. Students will produce meaningful data.
B. Students will choose appropriate tools and methods to accurately and precisely measure experimental phenomena.
C. Students will effectively record and organize data.

2. Students will be able to effectively interpret data:
A. Students will select appropriate technology to record, display and analyze data (graphing calculator, spreadsheet, mathematical software).
B. Students will present data in a usable form (lists, tables, charts).
C. Students will display data in appropriate numerical or graphical format.
D. Students will analyze data using appropriate pencil and paper or electronic methods.
E. Students will develop mathematical models for experimental phenomena.
F. Students will use models to predict behavior of experimental phenomena.
G. Students will test models through experimentation.

3. Students will be able to develop and use mathematical models:
A. Students will select appropriate technology to build relationship models (Geometer's Sketchpad , Stella ).
B. Students will effectively use software to model relationships.
C. Students will develop and manipulate models to demonstrate mathematical truths and investigate mathematical relationships.