Algebra I

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Welcome to the Algebra I course page. Below you will find the course outline and the section texts that will be used throughout the course. Algebra I is designed as a two-semseter rigorous course in Algebra, and will prepare you for your subsequent Geometry and Algebra II courses.

Algebra is a branch of Mathematics concerning the study of structure, relation and quantity. The name is derived from the treatise written by the Persian mathematician, astronomer, astrologer and geographer, Muhammad ibn Mūsā al-Khwārizmī titled Kitab al-Jabr wa-l-Muqabala (meaning "The Compendious Book on Calculation by Completion and Balancing"), which provided symbolic operations for the systematic solution of linear and quadratic equations.

Together with geometry, mathematical analysis, combinatorics, and number theory, algebra is one of the main branches of mathematics. Elementary algebra is often part of the curriculum in secondary education and provides an introduction to the basic ideas of algebra, including effects of addition and multiplication of numbers, the concept of variables, definition of polynomials, along with factorization and determining their roots.

Algebra is much broader than elementary algebra and can be generalized. In addition to working directly with numbers, algebra covers working with symbols, variables, and set elements. Addition and multiplication are viewed as general operations, and their precise definitions lead to structures such as groups, rings and fields.

The course syllabus for Algebra I can be viewed and downloaded here: Algebra I Course Syllabus

Contents 1 Course Outline 1.1 Number Operations & Concepts 1.2 Expressions & Variables 1.3 Equations & Inequalities 1.4 Linear Equations 1.5 Systems of Equations 1.6 Exponential Functions 1.7 Polynomials 1.8 Quadratic Equations 1.9 Probability & Statistics 1.10 Projects 1.11 Online Activities 1.12 References

Course Outline

Number Operations & Concepts

This unit should be covered in the first three to four weeks of class. It is a review of past concepts as well as an introduction to more complex operations with numbers, especially those used most frequently in the applications of Algebra I.

1. Addition & Subtraction of Integers
2. Multiplication & Division of Integers
3. Rational Numbers
4. Square Roots & Exponents
5. Sets & Domains
6. Simple Inequalities

Expressions & Variables

This unit should be covered in the following three to four weeks of class. It is a review of past concepts as well as an introduction to more complex uses of variables. The understanding of these concepts is essential to the further understanding of the Algebra I course.

1. Order of Operations
2. Combining Like Terms
3. Simplifying Expressions
4. Formulas
5. Properties of Algebra

Equations & Inequalities

This unit should be covered in four to five weeks of the class. It is an introduction to the algebraic process and its applications. The topics covered in this unit are of utmost importance to the rest of the Algebra I course.

1. Solving One-Step Equations
2. Solving Two-Step Equations
3. Solving Multi-Step Equations
4. Equations with Variables on Both Sides
5. Solving Inequalities
6. Functions

Linear Equations

This unit should be covered in three to four weeks of class. The topics covered in this unit prepare the students to apply mathematics to real-world situations. Mathematical Modeling is an important field of mathematics and it's applications to the sciences. Students must master these concepts in order to be successful in the rest of this course as well as in following courses.

1. The Coordinate Plane
2. Equations With Two Variables
3. Equations of the Line
4. Slopes of Lines
5. Graphing Linear Inequalities
6. Parallel & Perpendicular Lines

Systems of Equations

This unit should be covered in three to four weeks of class. The equation to each linear equation has an infinite number of solutions, but when two lines intersect, their intersection is limited to specific (one or more) solutions. These solutions are important in that they can tell us information on ideal situations.

1. Solving Systems by Graphing
2. Solving Systems by Substitution
3. Solving Systems by Elimination
4. Systems of Linear Inequalities

Exponential Functions

1. Zero and Negative Exponents
2. Scientific Notation
3. Properties of Exponents
4. Exponential Functions
5. Growth & Decay

Polynomials

1. Adding & Subtracting Polynomials
2. Multiplying & Dividing Polynomials
3. Factoring Polynomials
4. Factoring by Grouping
5. Factoring Special Cases

Quadratic Equations

1. Quadratic Graphs
2. Quadratic Functions
3. Solving Quadratic Equations
4. The Quadratic Formula
5. The Discriminant

Probability & Statistics

1. The Counting Principle & Permutations
2. Solving One-Step Equations & Inequalities
3. Data Analysis
4. Mean, Median, & Mode
5. Theoretical & Experimental Probability
6. Compound Probability

Projects

1. Baloons & Linear Regression - Inflating baloons and fitting a linear, quadratic, or exponential line to the data.
2. Polling Peers - Using SurveyMonkey to develop a survey to give to student peers and evaluate the data.
3. Finding π with Pizza - Students will measure actual circumference and diameter of pizzas and determine best buys.
4. Stock Market Mark-It - Students will select a company they have an interest in and evaluate it over time.
5. M&M's and Probability - Students will evaluate a pack of M&M's for colors content, and determine probabilities based on their data.
6. Candy Box - Students will receive a box of candy and use it to find surface area and volume.
7. Bottle Rocketry - Students will construct a bottle rocket out of common household items and a soda pop bottle and evaluate it's flight.
8. Deer Herd Size Study - The students will study deer herd populations via TI Calculators or Excel spreadsheets.

Online Activities

1. Arithmetic Four
2. Crossword Puzzle 1
3. Crossword Puzzle 2
4. Memory Game
5. Road Trip 1
6. Road Trip 2
7. Road Trip 3
8. Road Trip 4
9. Deep Sea Diving
10. Mummy Chase
11. Pemdas Four
12. Planet Blaster
13. Equation Buster - Click here for more levels

References

1. http://en.wikibooks.org/wiki/Algebra