Algebra I Honors: Goals and Course Outline

 

 

 

DEPARTMENT: Mathematics                                         DATE: 2009-2010

COURSE TITLE: Algebra I Honors                                COURSE NUMBER:  5130

o YEAR                                                                    QPA: 5.0

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 challenging honors level approach preparatory for future honors level courses.

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. Review of fraction operations.

  2.  Translating verbal phrases into algebraic

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

  4.  Add, subtract, multiply and divide signed numbers

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

  6.  Introduction to functions

  7. 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. Solving rational equations

  4. Formulas and functions

  5. Rates, ratios, and percents

  6.  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. Predicting with linear models

  4.  Solving linear inequalities and compound inequalities

  5. Graphing linear inequalities in two variables

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

  7. Real-life application problems

 

Unit 5: Exponents and Exponential Functions

  1. Multiplication and division properties of exponents

  2. Zero and negative exponents

  3. Graphing exponential functions

 

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 trinomials

  6. Factoring difference of two squares pattern

 

Unit 7: Applications of Factoring

  1. Using factoring to solve quadratic equations

  2. Using factoring to simplify rational expressions

  3. Using factoring to multiply and divide rational expressions

  4. Adding and subtracting rational expressions with like denominators

 

Unit 8: Rational Equations and Functions

  1. Ratio and proportion

  2. Solving percent problems

 

 

Algebra I Honors 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.  Add, subtract, multiply, and divide rational numbers.
  2. Interpret and evaluate algebraic expressions using the correct order of operations.
  3. Translate verbal phrases into algebraic expressions/equations/inequalities.
  1. Create an algebraic model to problem solve in real-life situations.
  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 and as a mapping.
  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. Use the “LCD” move to solve rational equations.
  3. Recognize when an equation has one solution, infinite solutions or no solution.
  4. Check the accuracy of a solution by substituting it in the original equation.
  5. Rewrite a formula to solve for any one of its variable components.
  6. Use formulas, rates, ratios and percents to solve real-life problems.
  7. 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. Use a linear model to make real-life predictions.
  3. Interpret and use a scatter plot to make predictions about real-life situations.
  4. Write and use linear equations that use direct variation.
  5. Demonstrate a more in-depth understanding of the definition of a function intro-duced in Unit 1.
  6. Use the vertical line test to graphically distinguish a function from a relation.
  7. 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, solve and graph linear inequalities and apply these skills to solving real-life problems.
  4. Write, solve and graph 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 real-life problematic 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 expedite exponentiation.
  3. Recognize the graph of an exponential function.

 

Unit 6:  Polynomials

  1. Recognize when polynomials are to be added, subtracted, or multiplied.
  2. Correctly add, subtract and multiply polynomials.
  3. Execute the complete factorization of quadratic expressions.
  4. Use technology to confirm the accuracy of factorization.

 

Unit 7: Applications of Factoring

  1. Solve quadratic equations by means of factoring and the zero product rule.
  2. Confirm the accuracy of solution(s) by means of the graphing calculator.
  3. Recognize the graph of a quadratic function.
  4. Simplify rational expressions by means of factoring.
  5. Multiply and divide rational expressions and present final result in simplest form.
  6. Add rational expressions with like denominators and present final result in sim-plest form.

 

Unit 8: Rational Equations and Functions

  1. Recognize a proportion and successfully apply the cross product property to solve it

  2.  Recognize problematic situations that lend themselves to a proportion approach.

  3. Write a proportion to model a real life situation and execute its solution.

  4. Check solution(s) and determine if solution really does satisfy original equation or is extraneous.

  5. Write equations to solve all types of percent problems.

 

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