Lompoc Unified School District
Course Outline
Mathematics Department
Algebra 1
Information
Date: November 7, 2011
Alternate title: Algebra 1 STAR, Algebra 1 CASH, Basic Algebra 1,
Fundamental Algebra 1
If applicable, previous title: None
NCLB Core Course: Yes
UC/CSU approved: Yes
Name of CST test, if applicable: Algebra 1
Subject area: Mathematics
Department: Mathematics
Grade level: 9-12
Course length: One year
Credits per semester: 5 credits per semester (10 credits for the year)
Weighted or non-weighted: Non-weighted
Elective or required course: Required course
Prerequisites: None
CBEDS code: 2403
Zangle course number: Semester 1: 1521 Semester 2: 1522
COURSE DESCRIPTION
Algebra 1 content involves understanding, writing, solving, and graphing
linear and quadratic equations—including systems of two linear equations
and inequalities with two unknowns. Quadratic equations are solved by
factoring, by completing the square, by using graphs, or by applying the
quadratic formula. Students will become proficient with operations on
monomial and polynomial expressions. Students are introduced to rational
expressions and use their factoring skills to simplify and compute expressions.
INSTRUCTIONAL MATERIALS
TEXTBOOK: Algebra I California Edition: c. 2008 Holt, Rinehart, Winston
Mathematics Department, Algebra 1 Course Outline, page two
ESSENTIAL STANDARDS or CONCEPTS
FALL SEMESTER ESSENTIAL STANDARDS AND BENCHMARKS
1.0
Students identify and use the arithmetic properties of integers and rational,
irrational, and real numbers, including closure properties for the four basic
arithmetic operations where applicable.
1.1
Students use properties of numbers to demonstrate whether
assertions are true or false.
2.0
Students understand and use such operations as taking the opposite, finding the
reciprocal, taking a root, and using a fractional power.
3.0
Students solve equations and inequalities involving absolute values.
4.0
Students simplify expressions before solving linear equations and inequalities in
one variable.
5.0
Students solve multi-step problems, including word problems, involving linear
equations and linear inequalities in one variable and provide justification for each
step.
6.0
Students graph a linear equation and compute the x- and y- intercepts. They are
also able to sketch the region defined by linear equality.
7.0
Students verify that a point lies on a line, given an equation of the line.
Students are able to derive linear equations using the point-slope formula.
8.0
Students understand the concepts of parallel lines and perpendicular lines and how
those slopes are related. Students are able to find the equation of a line
perpendicular to a given line that passes through a given point.
9.0
Students solve a system of two linear equations in two variables algebraically
and are able to interpret the answer graphically. Students are able to solve a system
of two linear inequalities in two variables and to sketch the solution sets.
10.0
Students add, subtract, multiply, and divide monomials and polynomials; solve
multi-step problems, including word problems, by using these techniques.
15.0
Students apply algebraic techniques to solve rate problems, word problems, and
percent mixture problems.
Mathematics Department, Algebra 1 Course Outline, page three
SPRING SEMESTER ESSENTIAL STANDARDS AND BENCHMARKS
11.0
Students apply basic factoring techniques to second-degree and simple third-degree
polynomials. This includes finding a common factor for all terms in a polynomial,
recognizing the difference of two squares, and recognizing perfect squares of
binomials.
12.0
Students simplify fractions with polynomials in the numerator and denominator by
factoring both and reducing them to the lowest terms.
13.0
Students add, subtract, multiply, and divide rational expressions and functions.
Students solve both computationally and conceptually challenging problems by
using these techniques.
14.0
Students solve a quadratic equation by factoring or completing the square.
15.0
Students apply algebraic techniques to solve rate problems, word problems, and
percent mixture problems.
19.0
Students know the quadratic formula and are familiar with its proof by
completing the square.
20.0
Students use the quadratic formula to find the roots of a second-degree
polynomial and to solve equations.
21.0
Students graph quadratic functions and know that their roots are the xintercepts.
22.0
Students use the quadratic formula or factoring techniques or both to determine
whether the graph of a quadratic function will intersect the
x-axis in zero, one, or two points.
23.0
Students apply quadratic equations to physical problems, such as the motion of an
object under the force of gravity.
Mathematics Department, Algebra 1 Course Outline, page four
COURSE OUTLINE
FALL SEMESTER
A.
Tools for Algebra
 Properties of real numbers
 Rules of exponents
 Roots and irrational numbers
 Simplifying expressions
 Multi-step equations
 Solving with variables on both sides of the equation
 One-step and multi-step inequalities
 Solving absolute value equations and inequalities
B.
Concepts of Linear Equations, Inequalities, and Graphing
 Solving linear equations
 Graphing linear equations
 Slope, slope-intercept form, and point-slope form of the line
 x-intercepts and y-intercepts
 Applications of linear equations
 Graphing linear inequalities
C.
Systems of Linear Equations
 Solving linear systems by graphing
 Solving linear systems by substitution
 Solving linear systems by elimination
 Applications of systems of equations
 Solving systems of linear inequalities
D.
Exponents and Basic Operations with Polynomials
 Properties of exponents
 Zero and negative exponents
 Fractional exponents
 Addition and subtraction of polynomials
 Multiplying polynomials
Mathematics Department, Algebra 1 Course Outline, page five
SPRING SEMESTER
E.
Factoring Polynomials
 Using GCF (greatest common factor)
 Factoring x2 + bx + c and ax2 + bx + c
 Factoring special products
 Completing the square
F.
Quadratic Equations and Functions
 Solving quadratic equations by factoring
 Solving quadratics by using square roots
 Graphing quadratics
 Quadratic formula and discriminant
G.
Rational Expressions
 Simplifying rational expressions
 Multiplying and dividing rational expressions
 Adding and subtracting rational expressions
 Solving rational equations
 Applications of rational equations
H.
Radical Expressions
 Simplifying radicals
 Add and subtract radicals
 Multiply and divide radicals
INSTRUCTIONAL METHODS
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Lecture, modeling, and demonstrations
Graphic organizers and note-taking
Use of manipulatives (overhead and individual)
Use of individual white boards
Guided and independent practice
Discussion (whole class/small group)
Collaborative learning groups
Technology including visual, audio, data processing
Math journals, toolkits, vocabulary building
Warm-ups or bell work, daily math review (CAHSEE practice)
Mathematics Department, Algebra 1 Course Outline, page six
ASSESSMENTS and EVALUATIONS
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Tests, benchmark assessments, and semester final exams
Quizzes
Group or partner assignments and projects
Observation and informal assessment
Self-evaluation and participation
Classwork and homework
GRADING POLICY
Reports of student progress are provided every six weeks, with final grades
provided at the end of the semester. Final grades will be determined by
classroom assessments of student proficiency levels based upon individual
student achievement of the course content standards included within this
course outline. Final grades reflect only academic factors and do not include
non-academic factors. Non- academic factors such as attendance and
behavior may impact a student's ability to master concepts and skills.
NOTE: Refer to alternative school handbooks and planning guides for
information about when final grades and credit are assigned.
All final grades will follow Lompoc Unified School District Board Policy,
including adhering to the approved grading scale below.
100 – 90%
89 – 80%
79 – 70%
69 – 60%
59 & below
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