GeoLibrary - Websites Library Style: Algebra I Standards

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Standards of Learning--Algebra I Resources

There are links at the bottom of this page and every page on GeoLibrary to link to other GeoLibrary pages. The standards below outline the content for a one-year course in Algebra I. All students are expected to achieve the Algebra I standards. When planning for instruction, consideration should be given to the student's cognitive level and readiness for dealing with abstract concepts. Students should be helped to make connections and to build relationships between algebra and arithmetic, geometry, and probability and statistics. Connections also should be made to other subject areas through practical applications. This approach to teaching algebra should help students attach meaning to the abstract concepts of algebra.

These standards require students to use algebra as a tool for representing and solving a variety of practical problems. Tables and graphs will be used to interpret algebraic expressions, equations, and inequalities and to analyze functions. Matrices will be used to organize and manipulate data.

Calculators, computers, spreadsheets, and graphing utilities (graphing calculators or computer graphing simulators) should be used as tools to assist in problem solving. Graphing utilities enhance the understanding of functions; they provide a powerful tool for solving and verifying solutions to equations and inequalities.

Throughout the course, students should be encouraged to talk about mathematics, to use the language and symbols of mathematics to communicate, to discuss problems and problem solving, and to develop their confidence in mathematics.

Online Algebra
Algebra 1 -- richmond.edu SOL Sites

Amusement Parks and Virginia's Educational SOL's
Dave's Math Tables
Algebra I Lesson Index

A.1 The student will solve linear equations and inequalities in one variable, solve literal equations (formulas) for a given variable and apply these skills to solve practical problems. Graphing calculators will be used to confirm algebraic solutions.
Menu: EQUATIONS Outcome Based Lessons -- accompanies software program
Problem Solving

A.2 The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables. Students will choose an appropriate computational technique, such as mental mathematics, calculator, or paper and pencil.
Lesson2.01: Evaluating Variable Expressions
Algebra I: Integers and Operations

A.3 The student will justify steps used in simplifying expressions and solving equations and inequalities Justifications will include the use of concrete objects, pictorial representations, and the properties of real numbers.
Basic Identities -- Properties - commutative, associative, distributive,...

A.4 The student will use matrices to organize and manipulate data, including matrix addition, subtraction, and scalar multiplication. Data will arise from business, industrial, and consumer situations.
Chapter 2 Test (Systems of Linear Equations and Matrices)

A.5 The student will analyze a given set of data for the existence of a pattern, represent the pattern algebraically and graphically, if possible, and determine if the relation is a function.

A.6 The student will select, justify, and apply an appropriate technique to graph a linear function in two variables. Techniques will include slope-intercept, x- and y-intercepts, graphing by transformation, and the use of the graphing calculator.
Systems of Linear Equations
Graphing Linear Equations

A.7 The student will determine the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined. The graphing calculator will be used to investigate the effect of changes in the slope on the graph of the line.
Slope of a Line

A.8 The student will write an equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line.

A.9 The student will solve systems of two linear equations in two variables, both algebraically and graphically, and apply these techniques to solve practical problems. Graphing calculators will be used as both a primary tool of solution and to confirm an algebraic solution.
Some lessons to learn from graphing 2 equations in 2 unknowns
Review of Systens of Linear Equations and Gaussian Elimination

A.10 The student will apply the laws of exponents to perform operations on expressions with integral exponents, using scientific notation when appropriate.
Explorer: Laws of Exponents -- downloadable hyperstudio stack?

A.11 The student will add, subtract, and multiply polynomials and divide polynomials with monomial divisors, using concrete objects, pictorial representations, and algebraic manipulations.

A.12 The student will factor completely first- and second-degree binomials and trinomials in one or two variables. The graphing calculator will be used as both a primary tool for factoring and for confirming an algebraic factorization.

Webmath.com: Factoring a Polynomial

A.13 The student will estimate square roots to the nearest tenth and use a calculator to compute decimal approximations of radicals.

Webmath.com: Simplifying Expressions Involving Radicals
Synopses of Topics - Square Roots and Other Radicals

A.14 The student will solve quadratic equations in one variable both algebraically and graphically. Graphing calculators will be used both as a primary tool in solving problems and to verify algebraic solutions.
How do you solve Quadratic Equations?
Math Forum - Ask Dr. Math
Cybermath: Quadratic Equations -- requires a plug-in
Webmath.com: Solving Quadratic Equations
Chapater 7 Quadratic Equations -- Completing the square

A.15 The student will determine the domain and range of a relation given a graph or a set of ordered pairs and will identify the relations that are functions.

A.16 The student will, given a rule, find the values of a function for elements in its domain and locate the zeros of the function both algebraically and with a graphing calculator. The value of f(x) will be related to the ordinate on the graph.

Using ROOT to find Zeros of a Function -- TI-86

A.17 The student will, given a set of data points, write an equation for a line of best fit, using the median fit method, and use the equation to make predictions.
Investigating Line of Best Fit
How does the calculator determine the line of best fit?

A.18 The student will compare multiple one-variable data sets, using statistical techniques that include measures of central tendency, range, stem-and-leaf plots, and box-and-whisker graphs.
Math Forum - Ask Dr. Math

A.19 The student will analyze a relation to determine whether a direct or inverse variation exists and represent it algebraically and graphically, if possible.
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