Lompoc Unified School District
C o u r s e O u t l i n e
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: 1521Semester 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
1.0Students 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.
1.1Students use properties of numbers to demonstrate whether assertions are true or false.
2.0Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and using a fractional power.
3.0Students solve equations and inequalities involving absolute values.
4.0Students simplify expressions before solving linear equations and inequalities in one variable.
5.0Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.
6.0Students graph a linear equation and compute the x- and y- intercepts. They are also able to sketch the region defined by linear equality.
7.0Students 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.
8.0Students 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.
9.0Students 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.
10.0Students add, subtract, multiply, and divide monomials and polynomials; solve multi-step problems, including word problems, by using these techniques.
15.0Students 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
11.0Students 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.
12.0Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms.
13.0Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques.
14.0Students solve a quadratic equation by factoring or completing the square.
15.0Students apply algebraic techniques to solve rate problems, word problems, and percent mixture problems.
19.0Students know the quadratic formula and are familiar with its proof by completing the square.
20.0Students use the quadratic formula to find the roots of a second-degree polynomial and to solve equations.
21.0Students graph quadratic functions and know that their roots are the x-intercepts.
22.0Students 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.
23.0Students 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
- 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
- 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% = A
89 – 80% = B
79 – 70% = C
69 – 60% = D
59 & below= F