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 12

1.        Review and extend prior learning

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 12

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 12

1.        Review and extend prior learning

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 12

NOTE: The following performance indicators apply to only those students taking Functions, Statistics, and Trigonometry (FST).

1.        Review and extend prior learning

2.        Understand the language of functions

á         Even/odd

3.        Identify and use the different types of functions and their descriptions

á         Rational

á         Hyperbolic

á         Recursively defined

á         Symmetrical

á         Circular

4.        Find the values of functions of angles, using tables and a calculator

á         Positive angles

á         Negative angles

á         Angles greater than 360o

5.        Develop the concept of trigonometric ratio for very large and very small angles

6.        Solve trigonometric equations, using

á         Factoring

á         Radicals

7.        Find remaining trigonometric functions of an angle when given one function

8.        Compute trigonometric functions by

á         Adding

á         Multiplying

9.        Graph circular functions in degree and radian measure

á         Sinusoides y = sin x, y = cos x

á         Change in amplitude

á         Change in period

á         Change in center line

á         Change in frequency

á         Phase shifts

á         Tangent, cotangent, secant, and cosecant

10.    Prove identities

á         Reciprocal

á         Pythagorean

á         Quotient

á         Double angle

á         Sum/difference

á         Half angles

á         Product identities

á         Tangent identities

11.    Apply circular functions to real-world problems

12.    Apply techniques to fit functions (model) to collected data and make predictions from the function of best fit

á         Log-log or semi-log transformation

á         Equation of the tangent to a curve

13.    Locate zeros of functions

á         Rational zeros

á         Decimal approximations

á         Irrational zeros

14.    Apply functions

á         Find the slope of a function at a particular point

á         Find the maximum/minimum values of a function at a particular point

15.    Evaluate functions, using Euler's notation

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 12

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 12

1.        Review and extend prior learning

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 12

NOTE: The following performance indicators apply to only those students taking Functions, Statistics, and Trigonometry (FST).

1.        Review and extend prior learning

2.        Demonstrate an understanding of

á         Correlation

á         Standard deviation/dispersion of data

á         Variance

á         Inferential statistics

á         Descriptive statistics

á         Outliers

á         Quartiles

á         Data

á         One variable

á         Two variables

á         Clusters and gaps

á         Interquartile range

á         Randomness

á         Median-fit line

3.        Demonstrate an understanding of the idea of random sampling and recognize his/her role in statistical claims and designs for data collection

4.        Revise studies to improve their validity in terms of better sampling, better controls, or better data-analysis techniques

5.        Collect, organize, display, and interpret data in a variety of graphical forms

á         Histogram

á         Normal distributions

á         Student's T and chi square

6.        Use summation notation to represent a sum, variance, or standard deviation

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 12

NOTE: The following performance indicators apply to only those students taking Functions, Statistics, and Trigonometry (FST).

1.        Review and extend prior learning

2.        Find the number of permutations of objects where conditions are attached to the arrangement

3.        Find the number of distinguishable permutations when some of the objects in an arrangement are alike

4.        Find the possible number of permutations of objects in a circle

5.        Find the number of combinations of n things taken r at a time

6.        Find the probability of a

á         Compound event, using

á         The Fundamental Counting Principle

á         Permutations

á         Combinations

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 12

NOTE: The following performance indicators apply to only those students taking Functions, Statistics, and Trigonometry (FST).

1.        Review and extend prior learning

2.        Recognize the kinds of series

á         Infinite

á         Convergent

3.        Understand and manipulate polynomials

á         Divide polynomials with trinomial divisors

4.        Manipulate matrices by

á         Adding

á         Subtracting

á         Multiplying

á         Finding the inverse

á         Finding the determinant

5.        Recognize kinds of conic sections

á         Circle

á         Parabola

á         Hyperbola

á         Ellipse

6.        Understand exponential equations in order to

á         Graph exponential equations

á         Solve exponential equations

á         Translate to log form

á         Solve problems involving exponentials

7.        Understand and apply 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

8.        Recognize the kinds of progressions

á         Arithmetic

á         Explicit

á         Recursive

á         Geometric

á         Explicit

á         Recursive

9.        Manipulate progressions by

á         Finding the arithmetic and geometric means

á         Finding the nth term of arithmetic and geometric progressions

10.    Recognize the kinds of series

á         Arithmetic

á         Geometric

11.    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 12

NOTE: The following performance indicators apply to only those students taking Functions, Statistics, and Trigonometry (FST).

1.      Review and extend prior learning

2.      Apply matrices to geometric transformations with respect to

á         Reflections

á         Rotations

á         Translations

Developed 07/17/97

Revised 07/08/98

curr-math-scope-12.doc