Grade 7-10
Credit: 1
Prerequisite: Middle School Mathematics

This course extends students’ knowledge and understanding of the real number system and its properties through the study of variables, expressions, equations, inequalities, and analysis of data derived from real-world phenomena. Emphasis is placed on making connections in algebra to arithmetic, geometry, and statistics.

Calculator and computer technologies should be used as tools wherever appropriate. Use of a graphing calculator is considered essential to provide a graphical and numerical approach to topics in addition to a symbolic approach.

Indicators marked with an asterisk * relate directly to the Virginia Standards of Learning for Algebra 1. All Virginia Standards of Learning for Algebra 1 are included in this course.

Benchmarks and indicators are organized by the following strands:

I. Mechanics of Algebra

II. Equations and Inequalities

III. Data Analysis

IV. Algebraic Geometry

Benchmark
Students develop proficiency in using properties of real numbers to simplify and evaluate numerical and algebraic expressions.

1. Use appropriate computational techniques to evaluate and simplify algebraic and numerical expressions to include absolute value expressions. These techniques include mental mathematics, a calculator or a computer, and paper and pencil.*
2. Simplify expressions: justify the process using concrete materials, pictorial representations, or properties of real numbers.*
3. Represent quantitative situations algebraically.*
4. Apply the laws of exponents to perform operations on expressions with integral exponents, using scientific notation where appropriate.*
5. Add, subtract, and multiply polynomials and divide polynomials with monomial divisors, using concrete objects, pictorial representations, and algebraic manipulations.*
6. Factor completely first- and second-degree binomials and trinomials in one or two variables.*
7. Simplify numerical radicals using decimal approximations and the product property.*
8. Perform matrix operations of addition, subtraction, and scalar multiplication.*

Students use a variety of methods to solve first-degree equations and inequalities and quadratic equations and apply these techniques to solve practical problems.

1. Solve first-degree equations and inequalities in one variable algebraically and graphically and apply these techniques to solve practical problems.*
2. Solve literal equations (formulas) for a given variable and apply these skills to solve practical problems.*
3. Justify steps in the solution of equations and inequalities in one variable using concrete objects, pictorial representations, and properties of real numbers.*
4. Solve systems of two linear equations in two variables algebraically and apply these techniques to solve practical problems.*
5. Solve quadratic equations in one variable algebraically, graphically, and numerically.*
6. Determine whether a given solution satisfies an equation, an inequality, or a system.

Benchmark
Students gather, organize, and analyze data algebraically, numerically, and graphically using models and simulations of real-world phenomena.

1. Organize and manipulate data from real-world phenomena using matrices.*
2. Analyze data for the existence of a pattern; represent the pattern algebraically and graphically, if possible.*
3. Write an equation for a line of best fit from a given set of data points using the median fit method and use the graph to make predictions.*
4. Compare multiple one-variable data sets using statistical techniques that include measures of central tendency, range, stem-and-leaf plots, and box-and-whisker plots.*

Benchmark
Students use multiple representations to analyze, solve, and compare linear equations and inequalities, quadratic equations, and their graphs.

1. Determine the domain and range of a relation given a set of ordered pairs or a graph and identify those relations that are functions.*
2. Find the values of a function, given a rule or a graph, for elements in its domain and locate the zeros of the function algebraically, numerically, and graphically.*
3. Graph a linear equation using a variety of techniques: table of values, slope-intercept, x- and y-intercepts, point-slope, graphing by transformation, and the use of graphing calculators and computers.*
4. Determine the slope of a line given an equation of the line, the graph of the line, or two points on the line.*
5. Write an equation of a line given the graph of the line, two points on the line, or the slope and a point on the line.*
6. Solve quadratic equations in two variables algebraically, numerically, and graphically.
7. Solve systems of two linear equations or inequalities or a linear equation and a quadratic equation graphically.*
8. Determine if a linear system represents intersecting, parallel, or coincident lines.
9. Graph linear inequalities using two variables.
10. Analyze a relation to determine whether a direct or inverse variation exists and represent it algebraically and graphically.*

*Indicators marked with an asterisk relate directly to the Virginia State SOLs.

All students will take the Virginia Standards of Learning Test for Algebra 1.

Last update: September 100, 1998