COURSE TITLE: Accelerated Algebra I Honors
COURSE DESCRIPTION: Honors Algebra I covers new and traditional algebra concepts and skills through multi-concept problem-solving. Developing critical thinking skills and the ability to communicate mathematics is stressed. It is designed for the student who has a high aptitude in mathematics and who is highly motivated but has had no in-depth exposure to Algebra I in junior high school. This is a college preparatory course.
Prerequisite: High performance on the Entrance Test and the Algebra Placement Test, Junior High teacher and Math Department Chairperson recommendation.
COURSE REQUIREMENTS/REQUIRED MATERIALS:
A. Textbook
B. Loose - leaf paper.
C. Pencils (with erasers!).
D. Scientific calculator.
E. One spiral notebook to be used only for math.
F. One pocket and clip folder to be used only for math.
COURSE OBJECTIVES/STUDENT OUTCOMES:
1) Students will become familiar with the Real Number System.
Upon completing this goal the student will be able to:
• evaluate algebraic and numerical expressions using the rules for
order of operations
• identify the subsets of real numbers and relationships among them
• add, subtract, multiply and divide using real numbers
2) Students will learn the methods for solving equations and
inequalities in one variable.
Upon completing this goal the student will be able to:
• solve a linear equation in one variable
• solve equations that involve absolute value and graph their
solution sets
• solve quadratic equations by factoring
• solve fractional equations
• solve radical equations
• solve inequalities and graph their solution sets
• solve and graph inequalities that involve absolute value
• solve word problems that involve equations and inequalities in
one variable
3) Students will acquire an understanding of the nature of polynomials.
Upon completing this goal the student will be able to:
• add, subtract, multiply and divide polynomials
• simplify expressions with positive and negative exponents
• express numbers in scientific notation
• find the products and quotients of numbers expressed in
scientific notation
• identify the degree of a polynomial
• arrange the terms of a polynomial in ascending and descending order
• factor monomials into prime factors
• factor binomials and trinomials either by extracting common factors
or by using FOIL
• use grouping techniques to factor polynomials with four or more terms
4) Students will gain an understanding of the techniques for working
with rational expressions.
Upon completing this goal, the student will be able to:
• simplify rational expressions
• multiply and divide rational expressions
• add and subtract rational expressions
5) Students will discern the differences and similarities among
functions and relations.
Upon completing this goal,the student will be able to:
• show relations as sets of ordered pairs, mappings, tables,
graphs and equations
• identify the domain and range of a relation
• determine whether a given relation is a function
• calculate functional values for a given function
• write an equation to represent a relation, given a chart of values
6) Students will experience graphing linear equations and inequalities
with two variables.
Upon completing this goal, the student will be able to:
• graph linear equations
-by making a table and plotting points
-by using x- and y-intercepts
-by using the slope and y-intercept
• find the slope of a line
-when given two points
-when given the equation of a linear relation
• write a linear equation in standard and slope-intercept form given
-the coordinates of two points on the line
-the slope and the y-intercept
-the coordinates of a point on the line and the slope of the line
• determine whether two lines are parallel or perpendicular
• find the coordinates of the midpoint of a line segment
• graph lines using the graphing calculator
• graph linear inequalities
7) Students will develop the methods for solving systems of equations
and inequalities.
Upon completing this goal, the student will be able to:
• solve a system of linear equations
-by graphing by hand and using a graphing calculator
-by the substitution method
-by the elimination method
• determine whether a system of equations has one solution,
no solution or infinitely many solutions algebraically and graphically
• solve a system of inequalities by graphing
• use a system of two linear equations in two variables to solve
word problems
8) Students will gain an understanding of the properties of radicals.
Upon completing this goal, the student will be able to:
• simplify square roots
• find approximate value for square roots
• simplify radical expressions
• use the Pythagorean Theorem
• distinguish rational and irrational numbers
• add, subtract, multiply and divide radical expressions
• solve radical equations
• use the distance formula
COURSE OUTLINE:
I. Connections to Algebra
A. Numbers and number operations
B. Variables in Algebra
C. Exponents and powers
D. Order of operations
E. Equations and inequalities
F. Verbal models and algebraic models
G. Problem solving plan
H. Exploring date: tables and graphs
II. Rules of Algebra
A. The real number line
B. Addition of real numbers
C. Subtraction of real numbers
D. Exploring data: matrices
E. Multiplication of real numbers
F. The distributive property
G. Division of real numbers
H. Exploring date: rates and ratios
III. Solving Linear Equations
A. Solving equations using one transformation
B. Solving equations using two or more transformations
D. Linear equations and problem solving
E. Solving equations that involve decimals
F. Literal equations and formulas
G. Exploring data: scatterplots
IV. Graphing Linear Equations
A. Graphing linear equations in one variable
B. Graphing linear equations in two variables
C. Quick graphs using intercepts
D. The slope of a line
E. Quick graphs using slope-intercept form
F. Solutions and x-intercepts
G. Graphs of absolute value equations
H. Solving absolute value equations
V. Writing Linear Equations
A. Equations of lines using slope-intercept form
B. Equations of lines given the slope and a point
C. Equations of lines given two points
D. Fitting a line to data
E. Standard form of a linear equation
F. Point-slope form of the equation of a line
G. Problem solving using linear models
VI. Solving and graphing linear inequalities
A. Solving inequalities in one variable
B. Problem solving using inequalities
C. Compound inequalities
D. Absolute value and inequalities
E. Graphing linear inequalities in two variables
F. Exploring data: time lines, picture graphs and circle graphs
VII. Solving Systems of Linear Equations
A. Solving linear systems by graphing
B. Solving linear systems by substitution
C. Solving linear systems by linear combinations
D. Problem solving using linear systems
E. Special types of linear systems
F. Solving systems of linear inequalities
VIII. Powers and Exponents
A. Multiplication properties of exponents
B. Negative and zero exponents
C. Division properties of exponents
D. Scientific notation
E. Exploring data: exponential growth and decay
IX. Quadratic Equations
A. Square roots and the Pythagorean Theorem
B. Solving quadratic equations by finding square roots
C. Graphs of quadratic equations
D. The quadratic formula
E. Problem solving using the discriminate
F. Graphing quadratic inequalities
X. Polynomials and Factoring
A. Adding and subtracting polynomials
B. Multiplying polynomials
C. Factoring
D. Solving quadratic equations by factoring
E. Solving quadratic equations by completing the square
XI. Using proportions and rational equations
A. Problem solving using ratios and proportions
B. Problem solving using percents
C. Direct and inverse variation
D. Exploring data: probability
E. Simplifying rational expressions
F. Multiplying and dividing rational expressions
G. Dividing polynomials
H. Solving rational equations
XII. Functions
A. Functions and relations
B. Linear functions
C. Quadratic functions
D. Rational functions
XIII. Radical and Connections to Geometry
A. The distance formula
B. Simplifying radicals
C. Operations with radicals
D. Solving radical equations
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