School Administrative District #4
Unity of purpose
CORE CURRICULUM: SCOPE AND SEQUENCE
Department: Mathematics
CONTENT STANDARD: NUMBERS AND NUMBER SENSE
Students will understand and demonstrate a sense of what numbers mean and how they are used. Numbers are used to describe and interpret phenomena. Building a sense of number relationships is essential for developing the ability to deal with any set of numbers. Number sense involves understanding the meaning of numbers, relationships among numbers, relative number magnitudes, and the effects of operations on numbers. Skilled estimation is also an important component of number sense.
Performance Indicators: The learner will·
|
Grade 11 |
1. Review and extend prior learning
2. Explain what complex numbers (real and imaginary) mean and describe some of their many uses
CONTENT STANDARD: COMPUTATION
Students will understand and demonstrate computation skills. Computation involves understanding the fundamental operations of and relationships between and among addition, subtraction, multiplication, and division. Proficiency in computational skills requires that students learn to evaluate the reasonableness of an answer and to obtain accuracy in calculations with ever-increasing ease and confidence, with and without technological tools.
Performance Indicators: The learner will·
|
Grade 11 |
1. Review and extend prior learning
CONTENT STANDARD: MEASUREMENT
Students will understand and demonstrate measurement skills. Measurement is valuable as an integrating skill throughout the curriculum and in everyday life. The use of estimation is vital in determining the reasonableness of measurement. Measurement attributes (e.g., length, volume, time), U.S. customary and metric units, and tools enhance the ability to describe and understand the world.
Performance Indicators: The learner will·
|
Grade 11 |
1. Review and extend prior learning
2. Select and use the appropriate measurement tool to solve problems involving
á Temperature (Kelvin)
CONTENT STANDARD: PATTERNS, RELATIONS, AND FUNCTIONS
Students will understand that mathematics is the science of patterns, relationships, and functions. Relationships are central to mathematical understanding. A study of patterns often reveals regularity, indicating the presence of a mathematical relationship. Studying relationships allows students to make generalizations and predictions about phenomena and occurrences.
Performance Indicators: The learner will·
|
Grade 11 |
1. Review and extend prior learning
2. Understand the language of functions
á Inverse/one-one
á Function symbolism
á Composite
á Piecewise/multi-description
3. Manipulate with functions
á Evaluate
á Add
á Subtract
á Multiply
á Divide
á Graph
á Form reciprocals
á Find inverse
á Composition
4. Find the coordinates of end points of the terminal side of a right triangle
5. Find formula from graph
6. Identify and use trigonometric functions and their inverses
á Sine - cosecant
á Cosine - secant
á Tangent - cotangent
7. Determine the signs of the trigonometric functions in the four quadrants
8. Use laws of sine and cosine to solve oblique triangles
9. Identify the functions of negative angles
10. Explain phenomena using a variety of functions (e.g., linear, quadratic, exponential, trigonometric, etc.)
11. Identify and use the different types of functions and their descriptions
á Absolute value
á Exponential
á Logarithmic
á Trigonometric (inverse trigonometric)
á Greatest/least integer
á Step
12. Identify a variety of situations explained by the same type of function
13. Analyze and interpret graphical representations of functions
14. Calculate combinations and recognize properties of Pascal's triangle
CONTENT STANDARD: DISCRETE MATHEMATICS
Students will understand and apply concepts in discrete mathematics. Discrete mathematics studies discrete processes (e.g., all possible bus routes in a school district). This study includes the exploration of diagrams, networks, and flowcharts that students construct to model situations or use for planning, scheduling, and decision making. Three main concerns of discrete mathematics are existence (Is there a solution?), counting (How many solutions are there?), and efficiency (What is the best solution?).
Performance Indicators: The learner will·
|
Grade 11 |
1. Review and extend prior learning
CONTENT STANDARD: MATHEMATICAL REASONING
Students will understand and apply concepts of mathematical reasoning. Reasoning is fundamental to the knowing and doing of mathematics. To give more students access to mathematics as a powerful way of making sense of the world, it is essential that an emphasis on reasoning pervade all mathematics. Students need a great deal of time and many experiences to develop their ability to construct and evaluate valid arguments in problem settings and to evaluate the arguments of others.
Performance Indicators: The learner will·
|
Grade 11 |
1. Review and extend prior learning
2. Follow logical arguments
á Analyze situations where more than one logical conclusion can be drawn from data presented
CONTENT STANDARD: DATA ANALYSIS AND STATISTICS
Students will understand and apply concepts of data analysis. Individuals are faced with massive quantities of information which must be selected, sorted, and analyzed to reach conclusions. Sound decision making requires the ability to collect data effectively, organize data, discover patterns, summarize trends, make inferences, draw conclusions, and make predictions. The ethical use of statistics is a paramount concern in the Information Age.
Performance Indicators: The learner will·
|
Grade 11 |
1. Review and extend prior learning
CONTENT STANDARD: PROBABILITY
Students will understand and apply concepts of probability. Probability is the study of uncertainty. Informed consumers of information understand the basic principles of probability. People need to understand the uncertainties and limitations involved when drawing conclusions from data.
Performance Indicators: The learner will·
|
Grade 11 |
1. Review and extend prior learning
2. Apply concepts involving probability to real-life problems involving
á Binomial distribution
á Binomial experiments
á Binomial Probability Theorem
CONTENT STANDARD: ALGEBRA CONCEPTS
Students will understand and apply algebraic concepts. Algebra and analytic thinking are fundamental tools for working in and thinking about mathematics. These tools provide ways to generalize and predict problem solutions when not all information is known. Taught within the context of mathematical and practical applications, the concept of functions is a unifying theme for algebraic concepts.
Performance Indicators: The learner will·
|
Grade 11 |
1. Review and extend prior learning
2. Distinguish and compute between the various sets of complex numbers, including
á Imaginary numbers
3. Expand binomials, using the Binomial Theorem
4. Understand and manipulate polynomials
á Divide polynomials with monomial and binomial divisors
á Expand polynomials by using the Binomial Theorem
5. Understand and apply the Remainder Theorem
á Synthetic division
á Rational Root Theorem
á Factor Theorem
6. Manipulate radicals by
á Translating to fractional exponential form
á Simplifying by adding, subtracting, multiplying, and dividing radicals
á Converting radicals to decimals
7. Solve word problems, involving
á Work
á Coin
á Mixture
á Abstract rate problems
á Ideal Gas Law
á Direct, inverse, and linear variation
á Joint and combined variation
8. Solve linear and non-linear systems of equations and inequalities by using
á Multiplication/addition method, i.e., elimination method
á Cramer's Rule
á Matrices/determinants
9. Solve and graph inequalities
á Compound inequalities
á Absolute value
á Non-linear inequalities
á Linear programming
10. Complete the square in order to
á Solve quadratic equations
á Develop the Quadratic Formula
á Write the standard form of conic sections
11. Write and graph linear equations by
á Using parallel and perpendicular lines
á Finding the equation of a perpendicular to a line
12. Solve second-, third-, and fourth-degree equations, using
á Factor Theorem
á Rational Root Theorem
á Graphs
á Quadratic Formula
13. Demonstrate an initial understanding of how to manipulate matrices by
á Adding
á Subtracting
á Multiplying
á Finding the inverse
á Finding the determinant
14. Demonstrate an initial understanding of the kinds of conic sections
á Circle
á Parabola
á Hyperbola
á Ellipse
15. Manipulate conic sections by
á Graphing the conics
á Writing equations of conics
á Finding the asymptotes of hyperbolas
á Finding the foci of an ellipse
á Translating the axis
16. Use vectors
17. Use an x-y coordinate plane to
á Convert rectangular coordinates to polar coordinates and vice versa
18. Use conjunctions and disjunctions
19. Demonstrate an initial understanding of exponential equations in order to
á Graph exponential equations
á Solve exponential equations
á Translate to log form
á Solve problems involving exponentials
20. Demonstrate an initial understanding of the laws of logarithms in order to
á Graph the log of a function
á Solve log equations
á Convert to and from different bases
á Solve anti-logs
á Translate to exponential form
á Solve problems involving logarithms
21. Demonstrate an initial understanding of the kinds of progressions
á Arithmetic
á Explicit
á Recursive
á Geometric
á Explicit
á Recursive
22. Demonstrate an initial understanding of how to manipulate progressions by
á Finding the arithmetic and geometric means
á Finding the nth term of arithmetic and geometric progressions
23. Demonstrate an initial understanding of the kinds of series
á Arithmetic
á Geometric
24. Demonstrate an initial understanding of how to manipulate series by
á Finding the nth term of arithmetic and geometric series
á Finding the sum of arithmetic and geometric series
á Finding the sum of infinite geometric series
á Solving problems involving series
CONTENT STANDARD: GEOMETRY
Students will understand and apply concepts from geometry. Geometry is the study of the spatial world and its symmetries. The ideas of geometry are used to describe, interpret, represent, and change the spatial world in which people live. The understanding and development of spatial and visual skills strengthens problem-solving abilities.
Performance Indicators: The learner will·
|
Grade 11 |
1. Review and extend prior learning
2. Solve locus problems
á Set of points equidistant from
á A given point (circle)
á Two points (line)
á A point and a line (parabola)
á Set of points such that
á The sum of the distance from two fixed points is constant (ellipse)
á The difference of the distances from two fixed points is constant (hyperbola)
3. Apply matrices to geometric transformations with respect to
á Size change
á Scale change
4. Demonstrate an initial understanding of how to apply matrices to geometric transformations with respect to
á Reflections
á Rotations
á Translations
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Developed 07/17/97 Revised 07/08/98 |
curr-math-scope-11.doc |