Pawnee City Schools
Angela Schmit

 












Algebra I Syllabus













 
 

Algebra I Syllabus

algebra I book: sdf

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

Course Syllabus

Instructor:  Angela Schmit
Pawnee City High School
Phone:  (402) 852-2988
email:  aschmit@esu6.org
Planning Hour:  4th period



Description of Course

This course introduces problem solving early and integrates it thoughout the academic year.  Applications of algebra are presented using interesting and varied word problems.  Students will develop and use various reasoning skills and apply them to real-world problems.  Students will use algebra as a means of expressing their mathematical ideas and concepts.

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

Title:  Algebra:  Structure and Method, Book 1
Author:  Brown, Dolciani, Sorgenfrey, and Cole
Publisher:  McDougall Littell
Date:  2000

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
Looking Ahead

Probability
  • 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

Geometry
  • 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

Trigonometry
  • 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

This site is using the Adult Contemporary (red) theme.

Create your own Manila site in minutes. Everyone's doing it!