Departmental Course Outline for Algebra 1
Courses: 221 Algebra 1The following outline describes the Algebra 1 curriculum of the Lexington schools, which may be studied in middle school and/or high school. At Lexington High School, Algebra 1 (221) covers this complete outline, while Algebra 1B (222) covers the remainder of these topics for students who have already learned some of the material in 8th grade.
Note: This working document describes our coverage
plans, but may be revised somewhat during the year.
We hope you will find it useful as an overview of the course
and as an approximation of what topics will be covered.
Minimum Topic Coverage
- Connections to algebra
- Problem solving using models
- Tables and graphs
- Introduction to functions
- Calculations in the real number system
- The distributive property
- Division and fractions: basic manipulation and simplification
- Solving linear equations
- Solving equations using addition and subtraction
- Solving equations using multiplication and division
- Solving multistep equations
- Solving equations with variables on both sides
- Linear equations and problem solving
- Solving decimal equations
- Formulas and functions
- Rates, ratios and percents
- Graphing linear equations and functions
- Coordinates and scatter plots
- Graphing linear equations
- Quick graphs using intercepts
- The slope of a line
- Direct variation
- Quick graphs using slope-intercept form
- Solving linear equations using graphs
- Functions and relations
- Writing linear equations
- Writing linear equations in slope-intercept form
- Writing linear equations given the slope and a point
- Writing linear equations given two points
- Fitting a line to data
- Point-slope form of a linear equation
- The standard form of a linear equation (ax+by=c)
- Predicting with linear models
- Solving and graphing linear inequalities
- Solving one-step linear inequalities
- Solving multi-step linear inequalities
- Solving compound inequalities
- Solving absolute-value equations and inequalities
- (Optional) Graphing linear inequalities in two variables
- Systems of linear equations and inequalities
- Solving linear systems by graphing
- Solving linear systems by substitution
- Solving linear systems by linear combinations
- Applications of linear systems
- Special types of linear systems
- Exponents and exponential functions
- Multiplication properties of integer exponents
- Zero and negative integer exponents
- Division properties of integer exponents
- Scientific notation
- Exponential growth and decay functions
- Quadratic equations and functions
- Square roots and their basic properties
- Solve quadratic equations using square root
- Graphs of quadratic functions
- Solve quadratic equations by graphing
- Solve quadratic equations by factoring ax^2+bx+c=0
- Applications to real situations
- Polynomials and factoring
- Adding and subtracting polynomials
- Multiplying polynomials
- Solving polynomial equations in factored form
- Factoring x^2+bx+c and ax^2+bx+c
- Factoring out a common factor
- (Optional) Rational equations and functions
- ("") Simplifying rational expressions
- ("") Multiplying and dividing rational expressions
- ("") Adding and subtracting rational expressions
Calculator Skills
- Enter algebraic expressions (using parentheses, negative key, carat key)
- Graph functions and set appropriate graph window
- Analyze functions (values, tables, x and y intercepts)
- Analyze data (scatterplots, linear regression)
- Use of exact answers in subsequent calculations (for accuracy)
Textbook Usage
Algebra 1 by Larson, Boswell, et al.
(McDougall Littell, 2001). The course generally covers the contents
of Chapters 1.5-1.7, 2.6, 2.7, 3, 4, 5, 6.1-6.4, 7.1-7.5, 8, 9.1-9.4, 10.1, 10.2, 10.4-10.6, and 10.8.
The material in Chapters 1.1-1.4, 2.1-2.3, and 2.5 is considered prerequisite,
and not expected to be taught except remedially as needed.