Algebra I Syllabus

Angel Website:  http://pcps.myelearning.org/frameIndex.htm
Angela Schmit's Website:  http://manila.esu4.org/angelaschmit/

Course Syllabus

Description of Course

Prerequisites

• Math 7 and/or Math 8 or Pre-Algebra

The Objectives of the Course

• Understand and realize the value of the symbolism of algebra language.
• Use the language of algebra as a natural way of expressing mathematical ideas.
• Help students become independent thinkerd using various learning strategies.
• Learn through "trial and error" and realize that real learning takes place through asking questions, trying guesses, starting down false paths, and trying new methods of approach to algebraic problems.
• Learn problem solving strategies that can help with algebra, as well as other academic courses.
• Appreciate the power of mathematics and see the connections mathematics has with other subject areas, as well as everyday and career applications.
• Improve students' thinking skills, use them more effectively, and acquire additional skills.

Texts

Explanation of Instruction

• Lecture and discussion every day.
• Quizzes every two or three lessons.
• Tests after every unit.
• Spelling/Writing assignments as needed.
• Angel Website--On-Line Learning
  

Visual Aids, Utilized Films, Film Strips, Etc.

• Marker board
• Calculators (Texas Instruments--TI 83, TI 85, and TI 92) provided by the school district
• Computer Software/Technology
• Supplementary Workbooks

Units and Contents

Chapter 1:  Introdution to Algebra

• Variables
  To simplify numerical expressions and evaluate algebraic expressions
  
• Grouping Symbols
  To simplify expressions with and without grouping symbols
  
• Equations
  To find solution sets of equations over a given domain
  
• Translating Words into Symbols
  To translate phrases into variable expressions
  
• Translating Sentences into Equations
  To translate word sentences into equations
  
• Translating Problems into Equations
  To translate simple word problems into equations
  
• A Problem Solving Plan
  To use the five-step plan to solve word problems over a given domain
  
• Number Lines
  To graph real numbers on a number line and to compare real numbers
  
• Opposites and Absolute Value
  To use opposites and absolute values
  

Chapter 2:  Working with Real Numbers

• Basic Assumptions
  To use number properties to simplify expressions
  
• Addition on a Number Line
  To add real numbers using a number line or properties about opposites
  
• Rules for Addition
  To add real numbers using rules for addition
  
• Subtracting Real Numbers
  To subtract real numbers and to simplify expressions involving differences
  
• The Distributive Property
  To use the distribution property to simplify expression
  
• Rules for Multiplication
  To multiply real numbers
  
• Problem Solving:  Consecutive Integers
  To write equations to represent relationships among integers
  
• The Reciprocal of a Real Number
  To simplify expressions involving reciprocals
  
• Dividing Real Numbers
  To divide real numbers and to simplify expressions involving quotients
  

Chapter 3:  Solving Equations and Problems

• Transforming Equations: Addition and Subtraction
  To solve equations using addition or subtraction
  
• Transforming Equations: Multiplication and Division
  To solve equations using multiplication or division
  
• Using Several Transformations
  To solve equations by using more than one transformation
  
• Using Equations to Solve Problems
  To use the five-step plan to solve word problems
  
• Equations with the Variable on Both Sides
  To solve equations with the variable on both sides
  
• Problem Solving: Using Charts
  To organize the facts of a problem in a chart
  
• Cost, Income, and Value Problems
  To solve problems involving cost, income, and value
  
• Proof in Algebra
  To prove statements in algebra
  

Chapter 4:  Polynomials

• Exponents
  To write and simplify expressions involving exponents
  
• Adding and Subtracting Polynomials
  To add and subtract polynomials
  
• Multiplying Monomials
  To multiply monomials
  
• Powers of Monomials
  To find powers of monomials
  
• Multiplying Polynomials by Monomials
  To multiply a polynomial by a monomial
  
• Multiplying Polynomials
  To multiply polynomials
  
• Transforming Formulas
  To transform a formula
  
• Rate-Time-Distance Problems
  To solve some word problems involving uniform motion
  
• Area Problems
  To solve some problems involving area
  
• Problems Without Solutions
  To recongnize problems that do not have solutions
  

Chapter 5:  Factoring Polynomials

• Factoring Integers
  Factor integers and find the GCF of integers
  
• Dividing Monomials
  Simplify quotients of monomials and find the GCF of several monomials
  
• Monomial Factors of Polynomials
  Divide polynomials by monomials and find monomial factors of polynomials
  
• Multiplying Binomials Mentally
  Find the product of two binomials mentally
  
• Differences of Two Squares
  Simplify products of the form (a + b)(a - b) and factor differences of two squares
  
• Squares of Binomials
  Find squares of binomials and factor perfect square trinomials
  
• Factoring Pattern for ax^2 + bx + c, c positive
  Factor quadratice trinomials whose quadratic coefficient is 1 and whose constant term is positive
  
• Factoring Pattern for ax^2 + bx + c, c negative
  Factor quadratic trinomials whode quadratic coefficient is 1 and whose constant term is negative
  
• Factoring Pattern for ax^2 + bx + c
  Factor general quadratic trinomials with integral coefficients
  
• Factoring by Grouping
  Factor a polynomial by grouping terms
  
• Using Several Methods of Factoring
  Factor polynomials completely
  
• Solving Equations by Factoring
  Use factoring to in solving polynomial equations
  
• Using Factoring to Solve Problems
  Solve problems by writing and factoring quadratic equations
  

Chapter 6:  Fractions

• Simplifying Fractions
  To simplify algebraic fractions
  
• Multiplying Fractions
  To multiply algebraic functions
  
• Dividing Fractions
  To divide algebraic functions
  
• Least Common Denominators
  To express two or more fractions with their least common denominator
  
• Adding and Subtracting Fractions
  To add and subtact algebraic fractions
  
• Mixed Expressions
  To write mixed expressions as fractions in simplest form
  
• Polynomial Long Division
  To divide polynomials
  

Chapter 7:  Applying Fractions

• Ratios
  To solve problems involving ratios
  
• Proportions
  To solve problems involving proportions
  
• Equations with Fractional Coefficients
  To solve equations with fractional coefficients
  
• Fractional Equations
  To solve fractional equations
  
• Percents
  To work with percents and decimals
  
• Percent Problems
  To solve problems involving percents
  
• Mixture Problems
  To solve mixture problems
  
• Work Problems
  To solve work problems
  
• Negative Exponents
  To use negative exponents
  
• Scientific Notation
  To use scientific notation
  

Chapter 8:  Introduction to Functions

• Equations in Two Variables
  To solve equations in two variables over given domains of the variables
  
• Points, Lines, and Their Graphs
  To graph ordered pairs and linear equations in two variables
  
• Slope of a Line
  To find the slope of a line
  
• The Slope-Intercept Form of a Linear Equation
  To use the slope-intercept form of a linear equation
  
• Determining an Equation of a Line
  To find an equation of a line given the slope and one point on the line or given two points on the line
  
• Functions Defined by Tables and Graphs
  To understand what a function is and to define a function by using tables and graphs
  
• Functions Defined by Equations
  To define a function by using equations
  
• Linear and Quadratic Functions
  To graph linear and quadratic functions
  
• Direct Variation
  To use direct variation to solve problems
  
• Inverse Variation
  To use inverse variation to solve problems
  

Chapter 9:  Systems of Linear Equations

• The Graphing Method
  To use graphs to solve systems of linear equations
  
• The Substitution Method
  To use the substitution method to solve systems of linear equations
  
• Solving Problems with Two Variables
  To use systems of linear equations in two variables to solve problems
  
• The Addition-or-Subtraction Method
  To use addition or subtraction to solve systems of linear equations in two variables
  
• Multiplication with the Addition-or-Subtraction Method
  To use multiplication with the addition-or-subtraction method to solve systems of linear equations
  
• Wind and Water Current Problems
  To use systems of equations to solve wind and water current problems
  
• Puzzle Problems
  To use systems of equations to solve digit, age, and fraction problems
  

Chapter 10:  Inequalities

• Order of Real Numbers
  To review the concept of order and to graph inequalities in one variable
  
• Solving Inequalities
  To transform inequalities in order to solve them
  
• Solving Problems Involving Inequalities
  To solve problems that involve inequalities
  
• Solving Combined Inequalities
  To find the solution sets of combined inequalities
  
• Absolute Value in Open Sentences
  To solve equations and inequalities involving absolute value
  
• Absolute Value of Products in Open Sentences
  To extend your skill in solving open sentences that involve absolute value
  
• Graphing Linear Inequalities
  To graph linear inequalities in two variables
  
• Systems of Linear Inequalities
  To graph the solution set o f a system of two linear inequalities in two variables
  

Chapter 11:  Rational and Irrational Numbers

• Properties of Rational Numbers
  To learn and apply some properties of rational numbers
  
• Decimal Forms of Rational Numbers
  To express rational numbers as decimals or fractions
  
• Rational Square Roots
  To find the square roots of numbers that have rational square roots
  
• Irrational Square Roots
  To simplify radicals and to find decimal approximations of irrational square roots
  
• Square Roots of Variable Expressions
  To find square roots of variable expressions and to use them to solve equations and problems
  
• The Pythagorean Theorem
  To use the Pythagorean theorem and its converse geometric problems
  
• Multiplying, Dividing, and Simplifying Radicals
  To simply products and quotients of radicals
  
• Adding and Subtracting Radicals
  To simply sums and differences of radicals
  
• Multiplication of Binomials Containing Radicals
  To multiply binomials containing square-root radicals and to rationalize binomial denominators that contain square-root radicals
  
• Simple Radical Equations
  To solve simple radical equations
  

Chapter 12:  Quadratic Functions

• Quadratic Equations with Perfect Squares
  To solve quadratic equations involving perfect squares
  
• Completing the Square
  To solve quadratic equations by completing the square
  
• The Quadratic Formula
  To learn the quadratic formula and use it to solve equations
  
• Graphs of Quadratic Equations; The Discriminant
  To use the discriminant to find the number of roots of the equation ax^2 + bx + c = 0 and the number of x-intercepts of the graph of the related equation y = ax^2 + bx + c
  
• Methods of Solution
  To choose the best method for solving a quadratic equation
  
• Solving Problems Involving Quadratic Equations
  To use quadratic equations to solve problems
  
• Direct and Inverse Variation Involving Squares
  To use quadratic direct variation and inverse variation as a square in problem solving
  
• Joint and Combined Variation
  To solve problems involving joint variation and combined variation
  

• Sample Spaces and Events
  To specify the sample space and events for a random experiment
  
• Probability
  To find the probability that an event will happen
  
• Frequency Distributions
  To recognize and analyze frequency distributions
  
• Presenting Statistical Data
  To construct stem-and-leaf plots and box-and-whisker plots
  

• Points, Lines, and Angles
  To represent points, lines, and angles and to measure angles
  
• Pairs of Angles
  To learn names and properties of special pairs of angles
  
• Triangles
  To learn some properties of triangles
• Similar Triangles
  To solve problems involving similar triangles
  

• Trigonometric Ratios
  To find the sine, cosine, and tangent of an acute angle
  
• Values of Trigonometric Ratios
  To find the values of trigonometric ratios for given angles, and measures of angles for given trigonometric ratios
  
• Problem Solving Using Trigonometry
  To use trigonometric ratios to solve problems
  

This Page was last update: Wednesday, January 20, 2010 at 7:58:21 PM
This page was originally posted: 5/31/2006; 5:36:47 PM.
Copyright 2010 Pawnee City Schools

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