MATHEMATICS CURRICULUM

MATH CURRICULUM STANDARDS

· Uses a variety of strategies in the problem solving process.

· Understands and applies properties of the concepts of numbers.

· Uses various procedures while performing the process of computation.

· Understands and applies properties of the concepts of measurement.

· Understands and applies properties of the concepts of geometry.

· Understands and applies concepts of statistics and data analysis.

· Understands and applies concepts of probability.

· Understands and applies properties of functions and algebra.

· Understands and applies the use of technology.

GENERAL MATH

Subject: General Mathematics

Grade: 9

Length of Course: First and Second Semester

Prerequisite: None

CURRICULUM BENCHMARKS:

To round decimals
To add whole numbers
To subtract whole numbers
To multiply whole numbers
To divide whole numbers
To use the order of operations on whole number operations
To find the prime factorization of whole numbers
To find the GCF of whole numbers
To reduce fractions to simplest form
To add fractions
To subtract fractions
To multiply fractions
To divide fractions
To convert between mixed numbers and improper fractions
To add mixed numbers
To subtract mixed numbers
To multiply mixed numbers
To divide mixed numbers
To evaluate formulas involving fractions
To write the name of a decimal
To recognize place values
To write a number in decimal form from written form
To round decimals
To add decimals
To subtract decimals
To multiply decimals
To divide decimals
To round decimals
To evaluate formulas involving decimals
To write percents as decimals and fractions
To write decimals as percents
To write fractions as percents
To perform operations involving percents
To add signed numbers
To subtract signed numbers
To multiply signed numbers
To divide signed numbers
To use the order of operations on signed number operations
To evaluate formulas involving signed numbers
To translate verbal statements to mathematical statements using variables
To solve one step equations
To solve multi-step equations
To write and reduce ratios
To set up and solve proportions
To understand rules of exponents
To evaluate exponents using calculator
To simplify scientific notation
To evaluate square roots

COURSE DESCRIPTION:

In general mathematics, there will be review of the four basic operations (addition, subtraction, multiplication and division) involving whole numbers, integers, decimals and fractions. Relations between decimals, fractions, and percents will be introduced. The metric system is discussed and related to everyday use. Problem solving of various degrees of difficulty is used as a strategy to develop individuals for adult life. Algebra 1 concepts are introduced.

WHAT STUDENTS ARE EXPECTED TO DO:

1) Complete homework on time with acceptable quality.

2) Take notes over examples.

3) Participate in classroom examples and discussion.

4) Maintain a successful average on tests and quizzes.

EVALUATION:

The students will be evaluated on successful completion of daily assignments, quizzes and tests.

CONSUMER MATH

Subject: Consumer Mathematics

Grade: 11, 12

Length of Course: First and Second Semester

Prerequisite: Successful Completion of One Year of High School Math – Not intended for students who have taken advanced math courses beyond Algebra I.

CURRICULUM BENCHMARKS:

· Uses a variety of strategies to understand new mathematical content and to develop more efficient solution methods of problem extensions.

· Understands connections between equivalent representations and corresponding procedures of the same problem situation.

· Uses number theory concepts to solve problems.

· Understands rational expressions.

· Solves problems involving rate as a measure.

· Selects and uses an appropriate direct or indirect method of measurement in a given situation.

· Understands properties of and relationships among figures.

· Understands measures of central tendency and their applications to specific situations.

· Understands basic concepts of probability.

· Knows that an expression is a mathematical statement using numbers and symbols to represent relationships and real world situations.

· Understands basic operations on algebraic expressions.

· Uses calculators in problems solving

COURSE DESCRIPTION:

This course reviews general mathematics skills and applies them to problems the student may experience. Through the course, fractions, decimals, and percents will be stressed and how they relate to different real life problem solving situations.

WHAT STUDENTS ARE EXPECTED TO DO:

1) Successfully complete all daily assignments on time.

2) To maintain a successful average on tests and quizzes.

3) To participate in classroom discussions and examples.

4) Be prepared for class and take notes over examples.

Evaluation

Students will be evaluated on completion of daily assignments, quizzes and tests.

FUNCTIONAL ALGEBRA

Subject: Functional Algebra

Grade: 9, 10

Length of Course: First and Second Semester

Prerequisite: Pass General Math with an average grade of “C” or better or recommendation based on 8^th grade math scores and results of Algebra placement test.

CURRICULUM BENCHMARKS:

1. To write variable expressions

2. To use the order of operations to simply an expression

3. To evaluate variable expressions

4. To graph integers on a number line and find their absolute values

5. To add and subtract integers

6. To multiply and divide integers

7. To graph ordered pairs in the coordinate plane

8. To simplify variable expressions

9. To solve one step equations involving integers and decimals

10. To solve and graph one step inequalities

11. To round numbers using place values, front end estimation, and clustering

12. To calculate the mean, median, and mode of a set of data

13. To evaluate formulas

14. To simplify expressions involving exponents

15. To find the prime factorization of a number

16. To reduce fractions

17. To use properties of powers to simplify expressions

18. To add and subtract fractions

19. To multiply and divide fractions

20. To convert between customary units of measurement

21. To solve equations involving fractions

22. To find powers of products and quotients

23. To write ratios and unit rates

24. To set up and solve proportions

25. To use proportions to find missing parts of similar figures or scale drawings

26. To calculate the probability of an event

27. To calculate the odds of an event

28. To convert between fractions, decimals and percents

29. To solve equations involving percents

30. To solve multi- step equations involving real numbers

31. To solve equations with variables on both sides

32. To solve multi-step inequalities

33. To calculate simple and compound interest using formulas

34. To determine if a relation is a function

35. To graph linear equations

36. To calculate slope between two points

37. To find the slope and y-intercept of a line

38. To find the area of a parallelogram

39. To find the area of a triangle, trapezoid and circle

40. To find the surface area 3-dimensional figures

41. To find the volume of 3-dimensional figures

COURSE DESCRIPTION:

This course will begin with basic concepts of Algebra I, but at a slower pace. Students will learn different methods of solving multiple step equations and will learn to simplify expressions involving multiple variables and powers.

WHAT STUDENTS ARE EXPECTED TO DO:

1. Complete all homework on time.

2. Be prepared for class and take notes over examples.

3. Maintain a successful average on tests and quizzes.

EVALUATION:

Students will be evaluated on completion of daily assignments, quizzes, and tests.

ALGEBRA I

Subject: Algebra 1

Grade: 8,9,10,11,12

Length of Course: First and Second Semester

Prerequisite: Successful completion of General Math or Functional Algebra. Eighth graders must achieve a passing score on the Algebra placement test and have teacher recommendation.

CURRICULUM BENCHMARKS:

· Uses a variety of strategies to understand new math content and to develop more efficient solution methods or problem extensions.

· Constructs algorithms for multi-step and non-routine problems.

· Constructs logical verifications or counter examples to test conjectures and to justify algorithms and solutions to problems.

· Uses form math language and notation to represent ideas, to demonstrate relationships within and among numerical systems, and to formulate generalizations.

· Understands connections between equivalent representations and corresponding procedures of the same problem situation or math concept.

· Understands the properties of the real number system and its subsystems.

· Simplifies rations expressions.

· Simplifies radical expressions containing positive rational numbers.

· Uses a variety of operations on expressions containing real numbers.

· Solves problems involving rate as a measure.

· Selects and uses an appropriate indirect method of measurement in a given situation.

· Solves real-world problems involving three-dimensional measures.

· Understands that objects and relations in geometry correspond directly to objects and relations in algebra.

· Understands appropriate terminology and notation used to define functions and the properties of functions.

· Uses calculators to examine and understand linear functions.

COURSE DESCRIPTION:

Students will write and solve equations and inequalities, graph on a number line, and in sequence. They will review the basic operations and properties, learn basic problem solving techniques, apply the basic operations to polynomials, and learn to factor polynomials.

WHAT THE STUDENT IS EXPECTED TO DO:

1) To complete assignments on a daily basis as assigned.

2) To actively participate in classroom discussions.

3) To successfully complete all tests and quizzes.

EVALUATION:

Evaluation will be made on the student’s classroom participation and successful completion of daily assignments, quizzes and unit test.

ALGEBRA II

Subject: Algebra II

Grade: 9‑12

Length of Course: First and Second Semester

Prerequisite: Pass Algebra I with an Average Grade of "C" or Better for Both Semesters.

CURRICULUM BENCHMARKS:

To solve basic equations.
To solve and graph basic inequalities.
To calculate experimental probability.
To calculate theoretical probability.
To identify functions.
To find the domain and range of a function.
To graph linear functions.
To write linear equations.
To solve problems involving direct variation.
To graph absolute value functions.
To solve and graph two variable inequalities.
To solve systems of equations.
To solve and graph systems of inequalities.
To find max/min values to solve linear programming.
To add/subtract matrices.
To multiply a matrix by a scalar.
To multiply a matrix by a matrix
To find the inverse of a 2x2 matrix.
To graph quadratic functions.
To find the max/min (vertex) of a quadratic function.
To factor polynomials using greatest common factor.
To factor trinomials.
To factor special expressions.
To solve a quadratic equation using factoring.
To solve a quadratic equation using completing the square.
To solve a quadratic equation using the quadratic formula.
To classify a polynomial expression be degree and term.
To divide polynomials using long division.
To divide polynomials using synthetic division.
To factor sum/difference of cubes.
To calculate permutations and combinations.
To use Pascal’s Triangle to expand a binomial.
To simplify radical expressions.
To convert between radical expressions and rational exponents.
To solve radical equations
To find composite function values.
To convert between log notation and exponential notation.
To simplify and expand logs
To solve exponential equations using logs.
To solve problems involving inverse variation.
To simplify rational expressions.
To solve rational equations.
To know the difference between irrational and rational numbers.
To simplify complex fractions.
To solve rational equations.

COURSE DESCRIPTION: Algebra II reviews concepts covered in Algebra I. The course begins with a thorough discussion of the properties of real numbers. Solving equations and inequalities is the primary focus of this course. To do this, students will learn various techniques for simplifying expressions, factoring polynomials, and graphing. Concepts like functions, relations and imaginary numbers will also be introduced. These algebraic skills will be applied through story problems.

WHAT STUDENTS ARE EXPECTED TO DO:

1) Complete homework on time with acceptable quality.

2) Be prepared for class and take notes over examples.

3) Participate in classroom examples and discussion.

4) Pass tests and quizzes.

Evaluation

Students will be evaluated on successful completion of daily assignments, quizzes and tests.

GEOMETRY

Subject: Geometry

Grade: 10, 11, 12

Length of Course: First and Second Semester

Prerequisite: Completion of Algebra 1 with "C" Average Strongly Urged, Along with Teacher Approval.

CURRICULUM BENCHMARKS:

· Uses a variety of strategies to understand new math content and to develop more efficient solution methods or problem extensions.

· Constructs algorithms for multi-step and non-routine problems.

· Understands the concept of a mathematical proof.

· Constructs logical verifications or counter examples to test conjectures and to justify algorithms and solutions to problems.

· Uses formal math language and notation to represent ideas, to demonstrate relationships within and among representation systems and to formulate generalizations.

· Understands the difference between a statement that is verified by mathematical proof and one that is verified empirically using examples or data.

· Understands the components of mathematical modeling.

· Selects and uses an appropriate indirect method of measurement in a given situation.

· Solves real-world problems involving three-dimensional measures.

· Understands that object and relations in geometry correspond directly to objects and relations in algebra.

· Uses the Pythagorean theorem and its converse and properties of right triangles to solve mathematical and real-world problems.

· Uses geometric constructions to complete simple proofs, to model, and to solve mathematical and real world problems.

· Understands the basic concepts of right triangle trigonometry.

· Uses trigonometric ration methods to solve mathematical and real world problems.

· Uses inductive and deductive reasoning to make observations about and to verify properties of and relationships among figures.

· Uses properties of and relationships among figures to solve mathematical and real-world problems.

· Understands the concept of a function as the correspondences between the elements of two sets.

· Uses calculators to solve problems involving area, volume and right triangle trigonometry.

· Uses graphing calculators to recognize symmetric functions.

COURSE DESCRIPTION:

The course deals with the proofs of theorems and properties of plane and solid figures and the relationships of their parts. Proofs are used in arriving at logical conclusions or to express ideas more precisely; practical applications are not stressed, but are included along with computation, measurement, construction, and the general analysis of problems.

EVALUATION:

The student’s evaluation will be made on the consistent completion of daily assignments, classroom participation, and a successful average on tests and quizzes.

MATH ANALYSIS CONCEPTS

Subject: Math Analysis Concepts

Grade: 11, 12

Length of Course: First and Second Semester

Prerequisite: Algebra II and Geometry with “C” Average Strongly Urged along with Teacher Approval.

CURRICULUM BENCHMARKS:

· Uses a variety of strategies to understand new math content and to develop more efficient solution methods or problem extensions.

· Constructs algorithms for multi-step and non-routine problems.

· Constructs logical verifications or counter examples to test conjectures and to justify algorithms and solutions to problems.

· Uses formal math language and notation to represent ideas, to demonstrate relationships within and among representation systems and to formulate generalizations.

· Understands connections between equivalent representations and corresponding procedures of the same problem situations or mathematical concept.

· Understands the components of mathematical modeling.

· Understands the properties of the real number system and its subsystems.

· Uses discrete structures to represent and to solve problems.

· Uses a variety of operations on expressions containing real numbers.

· Understands basic applications of and operations on matrices.

· Uses synthetic methods to solve problems involving symmetry and transformation of figures.

· Understands the basic concepts of right triangle trigonometry.

· Uses trigonometric ration methods to solve mathematical and real world problems.

· Understands the basic properties and uses of polar coordinates.

· Understands appropriate terminology and notation used to define functions and the properties of functions.

· Uses expressions, equations, inequalities and matrices to represent situations that involve variable quantities and translates among these representations.

· Understands characteristics and uses of basic trigonometric functions.

· Understands properties of graphs and the relationship between a graph and its corresponding expression.

· Understands basic concepts of polynomial equations.

· Understands the concept of a function as the correspondences between the elements of two sets.

· Uses a variety of models to represent functions, patterns and relationships.

· Understands the general properties and characteristics of many types of functions.

· Understands the effects of parameter changes on functions and their graphs.

· Understands the basic concept of inverse function and the corresponding graph.

· Uses a variety of methods to solve systems of equations and inequalities.

· Uses a variety of methods to solve complex equations.

· Uses graphing calculators to examine and understand many types of functions.

· Uses graphing calculators to solve problems involving matrices.

COURSE DESCRIPTION:

This course deals with the geometric coordinate system, conic system,

and how they relate. Circular and triangular trigonometric functions and

their origins will be studied.

WHAT THE STUDENTS IS EXPECTED TO DO:

1) Keep a notebook of class notes and assignments.

2) Successfully complete all tests and quizzes.

ADVANCED PLACEMENT CALCULUS

Grade: 11, 12

Length of Course: First and Second Semester Prerequisite: Algebra I, Algebra 2, Geometry, and Math Analysis with an average of “C” or better.

CURRICULUM BENCHMARKS:

· Constructs logical verifications or counter examples to test conjectures and to justify algorithms and solutions to problems.

· Uses formal math language and notation to represent ideas, to demonstrate relationships within and among representation systems and to formulate generalizations.

· Understands the components of mathematical modeling.

· Understands the properties of the real number system and its subsystems.

· Uses a variety of operations on expressions containing real numbers.

· Solves problems involving rate as a measure.

· Selects and uses an appropriate indirect method of measurement in a given situation.

· Solves real-world problems involving three-dimensional measures.

· Uses synthetic methods to solve problems involving symmetry and transformation of figures.

· Understands the basic concepts of right triangle trigonometry.

· Uses trigonometric identities.

· Understands appropriate terminology and notation used to define functions and the properties of functions.

· Understands properties of graphs and the relationship between a graph and its corresponding expression.

· Understands the concept of a function as the correspondences between the elements of two sets.

· Understands the general properties and characteristics of may types of functions.

· Uses a variety of methods to solve complex equations.

· Differentiates and integrates a variety of functions.

· Uses derivatives of functions to solve problems.

· Uses graphing calculators to examine and understand many types of functions.

COURSE DESCRIPTION

This class is designed to prepare the students for their first year of college calculus. Concepts in this course will also be applied to other mathematical disciplines like physics and economics.

WHAT THE STUDENTS IS EXPECTED TO DO:

1) Take notes on lectures and example problems.

2) Complete daily assignments neatly and on time.

3) Actively participate in class.

4) Maintain a successful average on tests and quizzes.

EVALUATION: The students will be evaluated on successful completion of daily assignments, quizzes and tests.