GLEN RIDGE PUBLIC
SCHOOLS
Curriculum Guide
Course
Title: INTERMEDIATE
ALGEBRA
Subject: Mathematics
Grade: 9-10
Department/School: Mathematics/Glen
Ridge High School
Duration: Full
Year
Number of
Credits: 5
Prerequisite: Math 8
Grade “C” or higher
Elective
or Required: Required
Author: Sean Fitzpatrick
Date Submitted:
Summer 2007
Course Description
The purpose of this
course is twofold. First, it seeks to
strengthen the student’s understanding of the concepts studied in the Core
Algebra course by reviewing techniques for solving linear equations, factoring
polynomials, and solving word problems.
Second, it seeks to provide the student with a foundation in fundamental
Algebra II concepts that are typically expected of a student entering college.
GLEN RIDGE PUBLIC SCHOOLS
MATHEMATICS
Mathematics and Computer Science are an integral part of our lives. Students must be actively involved in their mathematics education with problem solving being an essential part of the curriculum. The mathematics and computer science curricula should emphasize thinking skills through a balance of computation, intuition, common sense, logic, analysis and technology. Students will be engaged and challenged in a student centered learning environment that is developmentally appropriate. Students will communicate mathematical ideas effectively by applying hands-on manipulatives, basic computational skills, mathematical models, and technology in order to solve practical problems.
The Mathematics Standards
consist of five statements, which describe what is essential to excellent
mathematics education, and present a view of mathematics teaching and learning
that integrates the processes of mathematical activity, the content of
mathematics, and the learning environment in the classroom. The following standards were adopted by the
New Jersey State Board of Education.
This course will cover the
following Core Curriculum Standards:
STANDARD 4.1
(NUMBER AND NUMERICAL OPERATIONS) ALL STUDENTS WILL DEVELOP NUMBER SENSE AND
WILL PERFORM STANDARD NUMERICAL OPERATIONS AND ESTIMATIONS ON ALL TYPES OF
NUMBERS IN A VARIETY OF WAYS.
Descriptive Statement: Numbers and arithmetic
operations are what most of the general public think about when they think of
mathematics; and, even though other areas like geometry, algebra, and data
analysis have become increasingly important in recent years, numbers and
operations remain at the heart of mathematical teaching and learning. Facility with numbers, the ability to choose
the appropriate types of numbers and the appropriate operations for a given
situation, and the ability to perform those operations as well as to estimate
their results, are all skills that are essential for modern day life.
Number Sense
Numerical Operations
Estimation
STANDARD 4.2
(GEOMETRY AND MEASUREMENT) ALL STUDENTS WILL DEVELOP SPATIAL SENSE AND THE
ABILITY TO USE GEOMETRIC PROPERTIES, RELATIONSHIPS, AND MEASUREMENT TO MODEL,
DESCRIBE AND ANALYZE PHENOMENA.
Descriptive Statement: Spatial sense
is an intuitive feel for shape and space.
Geometry and measurement both involve describing the shapes we see all
around us in art, nature and the things we make. Spatial sense, geometric modeling, and
measurement can help us to describe and interpret our physical environment and
to solve problems.
Geometric Properties Units
of Measurement
Transforming Shapes Measuring
Geometric Objects
Coordinate Geometry
STANDARD 4.3 (PATTERNS AND ALGEBRA) ALL STUDENTS WILL
REPRESENT AND ANALYZE RELATIONSHIPS AMONG VARIABLE QUANTITIES AND SOLVE
PROBLEMS INVOLVING PATTERNS, FUNCTIONS, AND ALGEBRAIC CONCEPTS AND PROCESSES.
Descriptive Statement: Algebra is a
symbolic language used to express mathematical relationships. Students need to understand how quantities
are related to one another, and how algebra can be used to concisely express
and analyze those relationships. Modern
technology provides tools for supplementing the traditional focus on algebraic
procedures, such as solving equations, with a more visual perspective, with
graphs of equations displayed on a screen.
Students can then focus on understanding the relationship between the
equation and the graph, and on what the graph represents in a real-life
situation.
Patterns
Functions and Relationships
Modeling
Procedures
STANDARD 4.4 (DATA ANALYSIS, PROBABILITY, AND DISCRETE
MATHEMATICS) ALL STUDENTS WILL DEVELOP AN UNDERSTANDING OF THE CONCEPTS AND
TECHNIQUES OF DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS, AND WILL
USE THEM TO MODEL SITUATIONS, SOLVE PROBLEMS AND ANALYZE AND DRAW APPROPRIATE
INFERENCES FROM DATA.
Descriptive Statement: Data analysis,
probability, and discrete mathematics are important interrelated areas of
applied mathematics. Each provides
students with powerful mathematical perspectives on everyday phenomena and with
important examples of how mathematics is used in the modern world. Two important areas of discrete mathematics
are addressed in this standard; a third area, iterations and recursion, is
addressed in Standard 4.3 (Patterns and Algebra).
Data Analysis (or Statistics)
Probability
Discrete Mathematics – Systematic Listing and Counting
Discrete Mathematics – Vertex-Edge Graphs and
Algorithms
STANDARD 4.5 (MATHEMATICAL PROCESSES) ALL STUDENTS
WILL USE MATHEMATICAL PROCESSES OF PROBLEM SOLVING, COMMUNICATION, CONNECTIONS,
REASONING, REPRESENTATIONS, AND TECHNOLOGY TO SOLVE PROBLEMS AND COMMUNICATE
MATHEMATICAL IDEAS.
Descriptive Statement: The
mathematical processes described here highlight ways of acquiring and using the
content knowledge and skills delineated in the first four mathematical
standards.
Problem Solving Reasoning
Communication Representations
Connections Technology
Course Description
UNIT
I: TOOLS OF ALGEBRA
Objectives:
Students
will be able to:
1. Graph and
order real numbers. (4.1.A.1)
2. Identify and use properties of real numbers. (4.1.B.1)
- Simplify numerical
expressions by using the order of operations. (4.1.B.1)
- Use the commutative,
associative, and distributive properties to simplify numerical and
variable expressions. (4.1.B.1)
- Apply the distributive
property to numerical and variable expressions. (4.1.B.1)
- Compare real numbers
(4.1.A.2) and find square roots. (4.1.B.1)
3. Simplify and
evaluate algebraic expressions. (4.1.B.1)
4. Solve
linear equations using several transformations. (4.1.B.1)
5. Solve
problems by writing equations. (4.3.C.1)
6. Solve and
graph inequalities. (4.3.D.2)
7. Solve and
write compound inequalities. (4.3.D.2)
8. Solve
absolute value equations and inequalities. (4.3.C.1)
9. Find
experimental and theoretical probabilities. (4.4.B.3)
Duration of time: 20
days
UNIT
II: FUNCTIONS, EQUATIONS, AND GRAPHS
Objectives:
Students
will be able to:
1. Graph
relations and identify functions. (4.3.B.1)
2. Graph
linear equations. (4.3.B.2)
3. Write
equations of a line when: (4.3.B.2)
- Slope and y-intercept
are given.
- Slope and point are
known.
- At least two points are
known.
4. Write
linear equations and make predictions using real-world data. (4.3.C.1)
5. Graph absolute value functions, linear inequalities, and absolute value inequalities. (4.3.C.1)
Duration
of time: 20 days
UNIT
III: LINEAR SYSTEMS
Objectives:
Students
will be able to:
1. Solve
systems of linear equations by:
- Graphing. (4.3.B.2)
- Elimination. (4.3.D.2)
- Substitution
Method. (4.3.D.2)
2.
Solve
systems of linear inequalities in two variables. (4.3.D.2)
3.
Graph
points and equations in three dimensions. (4.3.D.2)
4.
Solve
systems in three variables by elimination and substitution. (4.3.D.2)
Duration of time:
25 days
UNIT
IV: MATRICES
Objectives:
Students
will be able to:
1. Identify
and classify matrices and their elements.
(4.1.B.3)
2. Organize
data into matrices. (4.1.B.3)
3. Add and
subtract matrices. (4.1.B.3)
4. Solve
basic matrix equations. (4.1.B.3)
5. Multiple a
matrix by a scalar. (4.1.B.3)
6. Multiply
two matrices. (4.1.B.3)
7. Evaluate
determinants of 2 by 2 and 3 by 3 matrices. (4.1.B.3)
8. Solve a
system of equations using Cramer’s Rule. (4.1.B.3)
Duration
of time: 25 days
UNIT
V: QUADRATIC EQUATIONS AND FUNCTIONS
Objectives:
Students
will be able to:
1. Identify
quadratic functions and graphs. (4.3.B.2)
2. Model data
with quadratic functions. (4.3.B.2)
3. Graph
quadratic functions. (4.3.B.2)
4. Find
maximum and minimum values of quadratic functions. (4.3.B.2)
5. Use the
vertex form of a quadratic function. (4.3.C.1)
6. Find
common and binomial factors of quadratic expressions. (4.3.D.2)
7. Solve quadratic
equations by factoring, finding square roots, completing the square, and by using
the Quadratic formula. (4.3.D.2)
8. Determine types of solutions by using the discriminate. (4.3.B.2)
Duration
of time: 30 days
UNIT
VI: POLYNOMIALS AND POLYNOMIAL FUNCTIONS
Objectives:
Students
will be able to:
1. Classify
polynomials by terms and degree. (4.3.D.1)
2.
Multiply polynomials. (4.3.D.1)
·
Polynomials by a monomial.
·
Two binomials.
·
Binomial by a trinomial.
3. Solve
equations in factored form. (4.3.D.1)
4. Factor
polynomials by: (4.3.D.2)
·
Factoring out the GCF.
·
Factoring by grouping.
·
Difference of squares.
·
Quadratic trinomial (splitting the middle
term).
5. Solve
equations and word problems by factoring. (4.3.D.2)
6. Divide
polynomials using long division. (4.3.D.1)
Duration
of time: 20 days
Additional Topics if Time Permits
UNIT VII: RADICAL FUNCTIONS AND RATIONAL EXPONENTS
Objectives:
Students
will be able to:
1. Simplify,
multiply, and divide radical expressions. (4.3.D.1)
2. Add and
subtract radical expressions. (4.3.D.1)
3.
Multiply and divide binomial radical expressions. (4.3.D.1)
4.
Simplify expressions with rational exponents. (4.3.D.1)
UNIT VIII: EXPONENTIAL FUNCTIONS
Objectives:
Students
will be able to:
1. Model
exponential growth. (4.3.C.1)
2. Model
exponential decay. (4.3.C.1)
UNIT
IX: RATIONAL EQUATIONS AND FUNCTIONS
Objectives:
Students
will be able to:
1.
Simplify algebraic fractions by factoring numerator and/or denominator. (4.3.D.1)
2. Add,
subtract, multiply, and divide rational expressions. (4.3.D.1)
3. Solve
rational equations. (4.3.D.2)
Lists of texts,
resources and/or literature:
Textbook:
·
Bellman, Bragg, Handlin; Algebra 2; Pearson Education, Inc., publishing as Pearson Prentice
Hall,