Curriculum Alignment Form

	16. Recognize fundamental mathematical models (such as polynomial, exponential, and trigonometric functions) and apply basic translations, reflections, and dilations to their graphs.
	17. Develop and explain the concept of the slope of a curve and use that concept to discuss the information contained in graphs.
	18. Develop an understanding of the concept of continuity of a function.
	19. Understand and apply approximation techniques to situations involving initial portions of infinite decimals and measurement.
Standard 4.16: *All Students Will Demonstrate High Levels Of Mathematical Thought Through Experiences Which Extend Beyond Traditional Computation, Algebra, And Geometry*
	1. Study a core curriculum containing challenging ideas and tasks, rather than one limited to repetitive, low-level cognitive activities.
	2. Work at rich, open-ended problems which require them to use mathematics in meaningful ways, and which provide them with exciting and interesting mathematical experiences.
	3. Recognize mathematics as integral to the development of all cultures and civilizations, and in particular to that of our own society.
	4. Understand the important role that mathematics plays in their own success, regardless of career.
	5. Interact frequently with parents and other members of their communities, including men and women from a variety of cultural backgrounds, who use mathematics in their daily lives and occupations.
	6. Receive services that help them understand the mathematical skills and concepts necessary to assure success in the core curriculum.
	7. Receive equitable treatment without regard to gender, ethnicity, or predetermined expectations for success.
	8. Learn mathematics in classes which reflect the diversity of the school's total student population.
	9. Be provided with opportunities at all grade levels for further study of mathematics, especially including topics beyond traditional computation, algebra, and geometry.
	10. Be challenged to maximize their mathematical achievements at all grade levels.
	11. Experience a full program of meaningful mathematics so that they can pursue post- secondary education.

Standard 4.1: *All Students Will Develop The Ability To Pose And Solve Mathematical Problems In Mathematics, Other Disciplines, And Everyday Experiences*
	15. Use discovery-oriented, inquiry-based, and problem-centered approaches to investigate and understand the mathematical content appropriate to the high school grades.
	16. Recognize, formulate, and solve problems arising from mathematical situations, everyday experiences, applications to other disciplines, and career applications.
	17. Monitor their own progress toward problem solutions.
	18. Explore the validity and efficiency of various problem-posing and problem-solving strategies, and develop alternative strategies and generalizations as needed.
Standard 4.2: *All Students Will Communicate Mathematically Through Written, Oral, Symbolic, And Visual Forms Of Expression*
	9. Formulate questions, conjectures, and generalizations about data, information, and problem situations.
	10. Reflect on and clarify their thinking so as to present convincing arguments for their conclusions.
Standard 4.3: All Students Will Connect Mathematics To Other Learning By Understanding The Interrelationships Of Mathematical Ideas And The Roles That Mathematics And Mathematical Modeling Play In Other Disciplines And In Life
	12. Recognize how mathematics responds to the changing needs of society, through the study of the history of mathematics.
Standard 4.4: *All Students Will Develop Reasoning Ability And Will Become Self-Reliant, Independent Mathematical Thinkers*
	12. Make conjectures based on observation and information, and test mathematical conjectures, arguments, and proofs.
	13. Formulate counter-examples to disprove an argument.
Standard 4.5: All Students Will Regularly And Routinely Use Calculators, Computers, Manipulatives, And Other Mathematical Tools To Enhance Mathematical Thinking, Understanding, And Power
	8. Use calculators and computers effectively and efficiently in applying mathematical concepts and principles to various types of problems.
Standard 4.6: *All Students Will Develop Number Sense And An Ability To Represent Numbers In A Variety Of Forms And Use Numbers In Diverse Situations*
	20. Extend their understanding of the number system to include real numbers and an awareness of other number systems.
	21. Develop conjectures and informal proofs of properties of number systems and sets of numbers.
	22. Extend their intuitive grasp of number relationships, uses, and interpretations, and develop an ability to work with rational and irrational numbers.
	23. Explore a variety of infinite sequences and informally evaluate their limits.
Standard 4.7: *All Students Will Develop Spatial Sense And An Ability To Use Geometric Properties And Relationships To Solve Problems In Mathematics And In Everyday Life*
	20. Understand and apply properties involving angles, parallel lines, and perpendicular lines.
	21. Analyze properties of three-dimensional shapes by constructing models and by drawing and interpreting two-dimensional representations of them.
	22. Use transformations, coordinates, and vectors to solve problems in Euclidean geometry.
	23. Use basic trigonometric ratios to solve problems involving indirect measurement.
	24. Solve real-world and mathematical problems using geometric models.
	25. Use inductive and deductive reasoning to solve problems and to present reasonable explanations of and justifications for the solutions.
	26. Analyze patterns produced by processes of geometric change, and express them in terms of iteration, approximation, limits, self-similarity, and fractals.
	27. Explore applications of other geometries in real-world contexts.
Standard 4.8: *All Students Will Understand, Select, And Apply Various Methods Of Performing Numerical Operations*
	13. Extend their understanding and use of operations to real numbers and algebraic procedures.
	14. Develop, apply, and explain methods for solving problems involving factorials, exponents, and matrices.
Standard 4.9: *All Students Will Develop An Understanding Of And Will Use Measurement To Describe And Analyze Phenomena.*
	17. Use techniques of algebra, geometry, and trigonometry to measure quantities indirectly.
	18. Use measurement appropriately in other subject areas and career-based contexts.
	19. Choose appropriate techniques and tools to measure quantities in order to achieve specified degrees of precision, accuracy, and error (or tolerance) of measurements.
Standard 4.10: *All Students Will Use A Variety Of Estimation Strategies And Recognize Situations In Which Estimation Is Appropriate*
	11. Estimate probabilities and predict outcomes from real-world data.
	12. Recognize the limitations of estimation, assess the amount of error resulting from estimation, and determine whether the error is within acceptable tolerance limits.
Standard 4.11: *All Students Will Develop An Understanding Of Patterns, Relationships, And Functions And Will Use Them To Represent And Explain Real-World Phenomena*
	14. Analyze and describe how a change in an independent variable can produce a change in a dependent variable.
	15. Use polynomial, rational, trigonometric, and exponential functions to model real-world phenomena.
	16. Recognize that a variety of phenomena can be modeled by the same type of function.
	17. Analyze and explain the general properties and behavior of functions, and use appropriate graphing technologies to represent them.
	18. Analyze the effects of changes in parameters on the graphs of functions.
	19. Understand the role of functions as a unifying concept in mathematics.
Standard 4.12: All Students Will Develop An Understanding Of Statistics And Probability And Will Use Them To Describe Sets Of Data, Model Situations, And Support Appropriate Inferences And Arguments
	17. Estimate probabilities and predict outcomes from actual data.
	18. Understand sampling and recognize its role in statistical claims.
	19. Evaluate bias, accuracy, and reasonableness of data in real-world contexts.
	20. Understand and apply measures of dispersion and correlation.
	21. Design a statistical experiment to study a problem, conduct the experiment, and interpret and communicate the outcomes.
	22. Make predictions using curve fitting and numerical procedures to interpolate and extrapolate from known data.
	23. Use relative frequency and probability, as appropriate, to represent and solve problems involving uncertainty.
	24. Use simulations to estimate probabilities.
	25. Create and interpret discrete and continuous probability distributions, and understand their application to real-world situations.
	26. Describe the normal curve in general terms, and use its properties to answer questions about sets of data that are assumed to be normally distributed.
	27. Understand and use the law of large numbers (that experimental results tend to approach theoretical probabilities after a large number of trials).

Standard 4.13: All Students Will Develop An Understanding Of Algebraic Concepts And Processes And Will Use Them To Represent And Analyze Relationships Among Variable Quantities And To Solve Problems
	14. Model and solve problems that involve varying quantities using variables, expressions, equations, inequalities, absolute values, vectors, and matrices.
	15. Use tables and graphs as tools to interpret expressions, equations, and inequalities.
	16. Develop, explain, use, and analyze procedures for operating on algebraic expressions and matrices.
	17. Solve equations and inequalities of varying degrees using graphing calculators and computers as well as appropriate paper-and-pencil techniques.
	18. Understand the logic and purposes of algebraic procedures.
	19. Interpret algebraic equations and inequalities geometrically, and describe geometric objects algebraically.
Standard 4.14: *All Students Will Apply The Concepts And Methods Of Discrete Mathematics To Model And Explore A Variety Of Practical Situations.*
	11. Understand the basic principles of iteration, recursion, and mathematical induction.
	12. Use basic principles to solve combinatorial and algorithmic problems
	13. Use discrete models to represent and solve problems.
	14. Analyze iterative processes with the aid of calculators and computers.
	15. Apply discrete methods to storing, processing, and communicating information.
	16. Apply discrete methods to problems of voting, apportionment, and allocations, and use fundamental strategies of optimization to solve problems
Standard 4.15: *All Students Will Develop An Understanding Of The Conceptual Building Blocks Of Calculus And Will Use Them To Model And Analyze Natural Phenomena*
	12. Develop and use models based on sequences and series
	13. Develop and apply procedures for finding the sum of finite arithmetic series and of finite and infinite geometric series.
	14. Develop an informal notion of limit.
	15. Use linear, quadratic, trigonometric, and exponential models to explain growth and change in the natural world.