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Geneva CUSD 304
Content-Area Curriculum Frameworks
Grades 6-12
Mathematics
Mission Statement
The study of mathematics can be an exciting and interesting challenge.
Yet, the major reason to become proficient in this discipline revolves
around the use of mathematics as a tool to solve problems from the
areas of science, business, engineering, economics, and all other areas
which involve data collection and analysis. The mathematics program
is designed to establish connections between the key concepts of math
and the applications.
Theoretical structure of mathematics - Students will demonstrate an
understanding of the theoretical foundations of mathematics.
• Thought processes (intuition, deduction, induction)
• Logical arguments (two column, narrative, flow chart
proofs)
• Structure of axiomatic systems (Euclidian geometry, real
and complex number systems)
• Fundamental concepts (functions, sets, limits, infinity,
infinitesimals, statistics, probability)
Problem solving - Students will formulate problem solving strategies.
• Establishment of relationships (numerical, geometric,
pictorial, graphic, symbolic)
• Recognition, collection, and analysis of pertinent data
• Development and evaluation of methods and algorithms
• Validation of results (estimation, approximation,
reasonableness)
Mechanics of mathematics - Students will symbolically manipulate
mathematical expressions and statements.
• Performance of operations and computational processes
(arithmetic, algebraic, graphic)
• Illustration of solution processes for equations and
inequalities
• Calculation using electronic devices (scientific and
graphing)
Appropriate use of emerging technology - Students will use
technology to improve and extend their understanding of mathematics.
• Calculators at appropriate levels (scientific and graphing)
• Computer software (graphic, spread sheets, data bases,
Trigonometry and Trigonometry Honors Frameworks.doc
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•
symbolic manipulators, simulations)
Information management systems (compact disk,
telecommunication, internet, video disk)
All students will experience an evolving curriculum designed to be a
rich tapestry of traditional mathematics skills intertwined with problem
solving, graphical analysis, measurement, probability, and statistics.
The use of manipulatives, calculators (scientific and graphing),
computers, writing assignments, and cooperative learning activities
will all be designed to achieve this mission.
Course Sequence
(Grades 6-12)
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6th Grade Mathematics
7th Grade Mathematics
Pre- Algebra
Integrated Mathematics I, II
Algebra I (4 semesters) A and B
Algebra I
Geometry /Concepts and Applications
Geometry (Regular & Honors)
Algebra II (Regular & Honors)
Algebra II 1/3-3/3
Pre-Calculus (Regular & Honors)
Trigonometry (Regular & Honors)
Calculus
AP Calculus
AP Statistics
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Course Framework
Course Title
Trigonometry
Grade Level
10, 11, 12
Semesters
1
Prerequisite
Pre-Calculus or Pre-Calculus Honors
Course Description
This second semester course completes the traditional
curriculum designed to prepare students for the mathematics of
science, engineering, and architecture-related careers. The
course concentrates on circular and right triangle trigonometry,
polar coordinates, complex number expansions, theory of limits,
a high dependence on technology, and an overall preparation for
traditional scientific calculus. Emphasis is placed on scientific
applications throughout the course. Trigonometry provides the
prerequisite for Calculus and AP Calculus.
Larson Hostetler, Edwards, Pre-Calculus with Limits, Houghton
Mifflin. 2001
ISBN 0-618-05291-7
District-approved Materials
and/or Resources
(H) Signifies material covered only in the honors course
Course Title
Trigonometry Honors
Grade Level
10, 11, 12
Semesters
1
Prerequisite
Pre-Calculus Honors or
Pre-Calculus and Department Approval
Course Description
This course in the honors sequence covers all of the topics of
regular Trigonometry. Trigonometry Honors is recommended
for highly motivated students planning to pursue math-related
areas. This course is a prerequisite for AP Calculus and
Calculus.
Larson Hostetler, Edwards, Pre-Calculus with Limits,
Houghton Mifflin. 2001
ISBN 0-618-05291-7
District-approved Materials
and/or Resources
Trigonometry and Trigonometry Honors Frameworks.doc
August 2008
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Unit Frameworks
Resources that will support
instruction
Unit of Study:
major topics
Circular Trigonometric Functions
Illinois Learning
Standards,
Benchmarks,
7.A.4b Apply formulas in a wide variety of theoretical and practical realworld measurement applications involving perimeter, area, volume, angle,
time, temperature, mass, speed, distance, density and monetary values.
National Standards
Assessment
Frameworks, or
other standards that
will be taught in this
unit
7.B.4 Estimate and measure the magnitude and directions of physical
quantities (e.g., velocity, force, slope) using rulers, protractors and other
scientific instruments including timers, calculators and computers.
7.B.5 Estimate perimeter, area, volume, and capacity of irregular shapes,
regions and solids and explain the reasoning supporting the estimate.
7.C.4c Convert within and between measurement systems and monetary
systems using technology where appropriate.
8.A.5 Solve mathematical problems involving recursive patterns and use
models that employ such relationships.
8.A.4b Represent mathematical patterns and describe their properties using
variables and mathematical symbols.
8.B.4a Represent algebraic concepts with physical materials, words,
diagrams, tables, graphs, equations and inequalities and use appropriate
technology.
8.B.5 Use functions including exponential, polynomial, rational, parametric,
logarithmic, and trigonometric to describe numerical relationships.
8.C.5 Use polynomial, exponential, logarithmic and trigonometric functions
to model situations.
Objectives
o Conceptual
o Factual
o Procedural
9.D.5 Analyze and solve problems involving periodic patterns (e.g., sound
waves, tide variations) using circular functions and communicate results orally
and in writing.
(H) Signifies material covered only in the honors course
1. Describe angles
2. Use radian and degree measure
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3. Use angles to model and solve real-life problems
4. Identify a unit circle and its relationship to real numbers
5. Evaluate trigonometric functions using the unit circle
6. Use the domain and period to evaluate sine and cosine functions
7. Use a calculator to evaluate trigonometric functions
8. Evaluate trigonometric functions of acute angles
9. Use the fundamental trigonometric identities
10. Use a calculator to evaluate trigonometric functions
11. Use trigonometric functions to model and solve real-life problems
12. Evaluate trigonometric functions of any angle
13. Find the angle of inclination of a given line. (H)
14. Find the slope of a line given the angle of inclination. (H)
15. Use reference angles to evaluate trigonometric functions
16. Evaluate trigonometric functions of real numbers
17. Use amplitude and period to sketch the graphs of sine and cosine functions
18. Sketch translations of graphs of sine and cosine functions
19. Use sine and cosine functions to model real-life data
20. Sketch the graphs of tangent and cotangent functions
21. Sketch the graphs of secant and cosecant functions
22. Sketch the graphs of damped trigonometric functions (H)
23. Identify the domain and range of inverse trigonometric functions
24. Evaluate inverse trigonometric functions
25. Evaluate composition of trigonometric functions
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26. Solve real-life problems involving right triangles
27. Solve real-life problems involving directional bearings
28. Solve real-life problems involving harmonic motions
29. Solve non-routine real-life problems using trigonometric functions
30. Generalize concepts and skills throughout unit to solve non-routine rote
and application problems (H)
Assessments
Honors will devote significant time to the theoretical development of
concepts.
Performance tasks, chapter quizzes,
Other Evidence:
chapter tests, and semester exams will
be given. They will include multiple
Homework
choice and /or free response problems.
Board/Class Work
Other learning activities that may
include:
• Cooperative Learning
Activities
• Technology Based
Discovery Activities
Trigonometry and Trigonometry Honors Frameworks.doc
August 2008
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Unit Frameworks
Resources that will support
instruction
Unit of Study:
Equations and Identities
Illinois Learning
Standards,
Benchmarks,
7.A.4b Apply formulas in a wide variety of theoretical and practical realworld measurement applications involving perimeter, area, volume, angle,
time, temperature, mass, speed, distance, density and monetary values.
National Standards
Assessment
Frameworks, or
other standards that
will be taught in this
unit
8.A.5 Solve mathematical problems involving recursive patterns and use
models that employ such relationships.
8.B.5 Use functions including exponential, polynomial, rational,
parametric, logarithmic, and trigonometric to describe numerical
relationships.
8.C.5 Use polynomial, exponential, logarithmic and trigonometric
functions to model situations.
9.D.5 Analyze and solve problems involving periodic patterns (e.g., sound
waves, tide variations) using circular functions and communicate results
orally and in writing.
Objectives
o Conceptual
o Factual
o Procedural
(H) Signifies material covered only in the honors course
1. Recognize and write the fundamental trigonometric identities
2. Use fundamental trigonometric identities to evaluate trigonometric
functions, simplify trigonometric expressions, and rewrite trigonometric
expressions.
3. Verify trigonometric identities
4. Use standard algebraic techniques to solve trigonometric equations
5. Solve trigonometric equations of quadratic type
6. Solve trigonometric equations involving multiple angles
7. Use inverse trigonometric functions to solve trigonometric equations
8. Use sum and difference formulas to verify identities and solve
trigonometric equations
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9. Use sum and difference formulas to evaluate trigonometric functions
10. Use trigonometric equations to model and solve real-life problems
11. Use multiple-angle formulas to rewrite and evaluate trigonometric
formulas
12. Use power-reducing formulas to rewrite and evaluate trigonometric
functions
13. Use half-angle formulas to rewrite and evaluate trigonometric functions
14. Use product-sum formulas to rewrite and evaluate trigonometric
functions
15. Generalize concepts and skills throughout unit to solve non-routine rote
and application problems (H)
Assessments
Honors will devote significant time to the theoretical development of
concepts.
Performance tasks, chapter quizzes,
Other Evidence:
chapter tests, and semester exams
will be given. They will include
Homework
multiple choice and /or free response
problems.
Board/Class Work
Other learning activities that may
include:
• Cooperative Learning
Activities
• Technology Based
Discovery Activities
Trigonometry and Trigonometry Honors Frameworks.doc
August 2008
Page 8 of 14
Unit Frameworks
Resources that will support instruction
Unit of Study:
Triangles, Vectors and Additional
Topics
Illinois Learning
Standards,
Benchmarks,
7.B.4 Estimate and measure the magnitude and directions of physical quantities
(e.g., velocity, force, slope) using rulers, protractors and other scientific
instruments including timers, calculators and computers.
National Standards
Assessment
Frameworks, or
other standards that
will be taught in this
unit
8.C.4b Apply algebraic properties and procedures with matrices, vectors,
functions and sequences using data found in business, industry and consumer
situations.
8.B.5 Use functions including exponential, polynomial, rational, parametric,
logarithmic, and trigonometric to describe numerical relationships.
8.C.5 Use polynomial, exponential, logarithmic and trigonometric functions to
model situations.
9.A.5 Use geometric figures and their properties to solve problems in the arts, the
physical and life sciences and the building trades, with and without the use of
technology.
9.B.4 Recognize and apply relationships within and among geometric figures.
9.B.5 Construct and use two- and three-dimensional models of objects that have
practical applications (e.g., blueprints, topographical maps, scale models).
9.C.5b Apply physical models, graphs, coordinate systems, networks and vectors
to develop solutions in applied contexts (e.g., bus routing, areas of irregular
shapes, describing forces and other physical quantities).
9.D.4 Analyze and solve problems involving triangles (e.g., distances which
cannot be measured directly) using trigonometric ratios.
Objectives
o Conceptual
o Factual
o Procedural
(H) Signifies material covered only in the honors course
1. Use Law of Sines to solve oblique triangles (AAS, ASA, or SSA)
2. Find areas of oblique triangles
3. Use Law of Sines to model and solve real-life problems
4. Use the Law of Cosines to solve oblique triangles (SSS or SAS)
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5. Use Law of cosines to model and solve real-life problems
6. Use Heron’s Area Formula to find areas of triangles
7. Represent vectors as directed line segments
8. Write the component form of vectors
9. Perform basic vector operations and represent vectors graphically
10. Write vectors as linear combinations of unit vectors
11. Find the direction angles of vectors
12. Use vectors to model and solve real-life problems
13. Find the dot product of two vectors and use properties of the dot product
14. Find angles between vectors
15. Determine whether two vectors are orthogonal
16. Write vectors as sums of two vector components
17. Use vectors to find the work done be a force
18. Find absolute values of complex numbers
19. Write trigonometric forms of complex numbers
20. Multiply and divide complex numbers written in trigonometric form
21. Use DeMoivre’s Theorem to find powers of complex numbers
22. Find nth roots of complex numbers
23. Generalize concepts and skills throughout unit to solve non-routine rote and
application problems (H)
Honors will devote significant time to the theoretical development of
concepts.
Trigonometry and Trigonometry Honors Frameworks.doc
August 2008
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Assessments
Performance tasks, chapter quizzes,
chapter tests, and semester exams will
be given. They will include multiple
choice and /or free response problems.
Other Evidence:
Homework
Board/Class Work
Other learning activities that may
include:
• Cooperative Learning Activities
• Technology Based Discovery
Activities
Trigonometry and Trigonometry Honors Frameworks.doc
August 2008
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Unit Frameworks
Resources that will support
instruction
Unit of Study:
major topics
Conics
Illinois Learning
Standards, Benchmarks,
7.C.4c Convert within and between measurement systems and monetary
systems using technology where appropriate.
National Standards
Assessment
Frameworks, or other
standards that will be
taught in this unit
8.A.5 Solve mathematical problems involving recursive patterns and use
models that employ such relationships.
8.A.4b Represent mathematical patterns and describe their properties
using variables and mathematical symbols.
8.B.4a Represent algebraic concepts with physical materials, words,
diagrams, tables, graphs, equations and inequalities and use appropriate
technology.
8.B.5 Use functions including exponential, polynomial, rational,
parametric, logarithmic, and trigonometric to describe numerical
relationships.
8.C.4a Analyze and report the effects of changing coefficients, exponents
and other parameters on functions and their graphs.
8.C.5 Use polynomial, exponential, logarithmic and trigonometric
functions to model situations.
Objectives
o Conceptual
o Factual
o Procedural
9.D.5 Analyze and solve problems involving periodic patterns (e.g.,
sound waves, tide variations) using circular functions and communicate
results orally and in writing.
(H) Signifies material covered only in the honors course
1. Recognize a conic as the intersection of a plane and a double-napped
cone.
2. Write equations of parabolas in standard form
3. Graph parabolas and identify vertex, focus, axis of symmetry, and
directrix
4. Use the reflective property of parabolas to solve real-life problems
5. Write equations of ellipses in standard form
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6. Graph ellipses and identify vertices, co-vertices, foci, minor axis, and
major axis
7. Use properties of ellipses to model and solve real-life problems
8. Find eccentricities of ellipses
9. Write equations of hyperbolas in standard form
10. Graph hyperbolas and identify vertices, asymptotes, transverse axis,
and foci.
11. Find asymptotes of hyperbolas
12. Use properties of hyperbolas to solve real-life problems
13. Classify conics from their general equations
14. Rotate the coordinate axes to eliminate the xy-term in equations of
conics (H)
15. Use the discriminant to classify conics (H)
16. Solve systems of quadratic equations
17. Evaluate sets of parametric equations for given values of the
parameter
18. Graph curves that are represented by sets of parametric equations
19. Rewrite sets of parametric equations as single rectangular equations
20. Find sets of parametric equations for graphs
21. Use parametric equations to solve real-life problems
22. Plot points in polar coordinate system
23. Convert points from rectangular to polar form and vice versa
24. Convert equations from rectangular to polar form and vice versa
25. Graph polar equations by point plotting
26. Use symmetry, zeros, and maximum r-values as graphing aids
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27. Recognize special polar graphs
28. Define conics in terms of eccentricities (H)
29. Write equations of conics in polar form (H)
30. Verify the rational of conics in polar form. (H)
30. Use equations of conics in polar form to model real-life problems
31. Generalize concepts and skills throughout unit to solve non-routine
rote and application problems (H)
Assessments
Honors will devote significant time to the theoretical development of
concepts.
Performance tasks, chapter quizzes, Other Evidence:
chapter tests, and semester exams
will be given. They will include
Homework
multiple choice and /or free
response problems.
Board/Class Work
Other learning activities that may
include:
• Cooperative Learning
Activities
• Technology Based
Discovery Activities
Trigonometry and Trigonometry Honors Frameworks.doc
August 2008
Page 14 of 14