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Algebra I: Goals and Course Outline

 

 

 

DEPARTMENT: Mathematics                                          DATE: 2006-2007

COURSE TITLE: Algebra I                                              COURSE NUMBER:  5120

o YEAR                                                                     QPA: 4.5

o SEMESTER                                                            CREDITS: 5

 

 

 

TEXTBOOK: (Title, Author, Publisher, Edition)

McDougal Littell Algebra I (Both print and electronic editions), Larson, Boswell, Kanold, & Stiff, McDougal Littell Inc., 2001

 

MATERIALS USED:  TI-84 Plus graphing calculators, IBM ThinkPad, supplementary

      materials supplied by McDougal Littell and other resources

 

GOALS:  

1.      To achieve mastery of the symbolic language of algebra as a foundation for all other mathematics courses.

2.      To provide a thorough college preparatory coverage of Algebra I.

3.      To prepare students for the Math portions of the SAT.

4.      To demonstrate the relevance of algebraic problem solving to the real world.

5.      To use graphing calculators and modern computer graphics to analyze, solve, visualize, and clarify mathematical concepts.

 

CONTENT OF COURSE:

 

FIRST SEMESTER

 

Unit 1: Introduction to Algebra

1.      Translating verbal phrases into algebraic

2.      Evaluating expressions using prescribed order of operations and absolute value

3.      Add, subtract, multiply, and divide signed numbers

4.      Creating models that represent real-life situations with concomitant unit analysis

5.      Introduction to functions

6.      Probability

 

Unit 2: Solving Linear Equations

1.      Solving equations at all levels of difficulty using inverse operations

2.      Single solution, infinite solutions, no solution equations

3.      Formulas and functions

4.      Rates, ratios, and percents

5.      Real-life application problems

 

Unit 3: Graphing Linear Equations and Functions

1.      Plotting points in a coordinate plane

2.      Graphing linear equations

3.      The slope of a line

4.      Direct variation

5.      Functions and relations

 

SECOND SEMESTER

 

Unit 4: Linear Equations and Linear Inequalities

1.      Writing linear equations given pertinent information about the graph of the function

2.      Forms of a linear equation

3.      Solving linear inequalities and compound inequalities

4.      Graphing linear inequalities in two variables

5.      Solving linear systems by graphing, substitution, or linear combination

 

Unit 5: Exponents and Exponential Functions

1.      Multiplication and division properties of exponents

2.      Zero and negative exponents

 

Unit 6: Polynomials

1.      Definition and standard form of a polynomial

2.      Classifying polynomials by degree and number of terms

3.      Addition, subtraction, and multiplication of polynomials

4.      Using the distributive property to factor polynomials

5.      Factoring the various types of trinomials

 

Unit 7: Applications of Factoring

1.      Using factoring to solve quadratic equations

2.      Using factoring to simplify rational expressions

3.      Using factoring to multiply, divide, add, and subtract rational expressions

 

Unit 8: Rational Equations and Functions

1.      Ratio and Proportion

2.      Percents

 

 

 

 

 

 

 

Algebra I Proficiencies

 

Core course proficiencies (present in all units)

 

Students will be able to…

 

  1. Communicate mathematical ideas correctly in oral and written form.
  2. Read for comprehension, demonstrating conceptual understanding.
  3. Make mathematical connections to other subjects and real-life situations.
  4. Confidently problem solve by thinking critically, logically, analytically, and ethically.
  5. Use technology to confirm and enhance analytical techniques presented.
  6. Acquire the mathematical skills and understanding needed to be successful in

their daily lives and future math courses.

 

Algebra I Unit Proficiencies:

 

Students will be able to…

 

Unit 1:  Introduction to Algebra

 

  1. Interpret and evaluate algebraic expressions using the correct order of operations.

2.      Translate verbal phrases into algebraic expressions/equations/inequalities.

  1. Interpret algebraic models designed to solve real-life application problems.
  2. Compare and order real numbers and demonstrate an understanding of absolute value using a number line.
  3. Easily assess the signage of a result when adding, subtracting, multiplying, and dividing signed numbers.
  4. Interpret and use tables and graphs of organized data.
  5. Identify when a relation is a function.
  6. Define a function’s domain and range and organize this data in table form.
  7. Determine the probability of an event as a tool for predicting the future occur-rence of this event.

 

Unit 2:  Linear Equations and Inequalities

 

  1. Select the correct inverse operations in proper sequence for solving linear equa-tions.
  2. Recognize when an equation has one solution, infinite solutions or no solution.
  3. Check the accuracy of a solution by substituting it in the original equation.
  4. Rewrite a formula to solve for any one of its variable components.
  5. Use formulas, rates, ratios and percents to solve real-life problems.
  6. Rewrite a two-variable equation in function form.

 

Unit 3: Graphing Linear Equations and Functions

 

  1. Graph linear equations and understand the significance of the slope and intercept points of these graphs.
  2. Write and use linear equations that use direct variation.
  3. Determine whether a relation is a function when given its graph by means of the vertical line test.
  4. Use technology to confirm and enhance analytical techniques presented.

 

Unit 4: Linear Equations and Linear Inequalities

 

  1. Write an equation of a line given slope and any point on the line, or, any two points on the line.
  2. Choose the most appropriate form of a linear equation given the problematic situation.
  3. Write and solve linear inequalities and apply these skills to solving real-life problems.
  4. Write and solve compound inequalities and apply these skills to solving real-life problems.
  5. Graph and interpret a linear inequality in two variables.
  6. Solve systems of linear equations both graphically and algebraically; choose the best method given the system.
  7. Recognize different types of situations that lend themselves to a systems approach.

 

Unit 5:  Exponents and Exponential Functions

 

  1. Use properties of exponents to multiply and divide exponential expressions.
  2. Use technology to simplify exponentiation.

 

Unit 6:  Polynomials

 

  1. Recognize different types of polynomials and write them in standard form.
  2. Classify each type of polynomial expressions by degree and number of terms.
  3. Simplify polynomial expressions depending on the operation.
  4. Choose the greatest common factor out of the polynomial.
  5. Recognize whether the polynomial is factored completely.

 

Unit 7: Applications of Factoring

 

  1. Use factoring and the zero product rule to solve quadratic equations.
  2. Use factoring to simplify rational expressions.

 

Unit 8: Rational Equations and Functions

 

1.      Solve the given proportion.

2.      Determine the appropriate equation form to solve the different types of percent problems.

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