Algebra 1: An Open Course Coming Summer 2010

Goal: To offer a multi-modal approach to Algebra I that incorporates cutting edge online learning methods and technologies and is delivered to the world as an Open Educational Resource. Curriculum. Offering a scope and sequence of a two-semester Algebra 1 course that is traditionally a student’s first exposure to Algebra in middle or high school, this course will be correlated to national common core standards and to standards across the 50 states.

Approach. Designed to be a flexible, learner-centered experience, this project takes into account learning theory, research in mathematics education, and new research in technology, media and learning. The design process is informed by a rigorous study of current and proposed curriculum standards and products, including textbooks, software, web applications and tools. The evolving design concepts were further refined by an advisory panel of math experts, educational membership organizations, practitioners, and a series of focus groups around the country with administrators, instructors, and students. We will continue to collaborate with a full range of stakeholders throughout the development process.

Flexible Design. The learning experience integrates a broad range of approaches designed to open the door to mathematics concepts, procedures, mathematical reasoning and critical thinking for teachers and learners. The Learning Object architecture allows institutions and instructors to adapt the content to different programs and learners' needs.

Components. The portfolio of learning objects includes dynamic audio and video presentations, active and collaborative learning activities, problem sets, self-tests with feedback, and formative and summative assessment. Students work through activities in the sequence that leverages their own successful learning strategies while building their 21st century skills. Components include:

• Warm-ups: a series of problems to assess prior knowledge and recommend review.

• Presentations: the new media equivalent of a session with a teacher explaining the topic.

• Text: a textbook-style explanation that reinforces the concepts being taught.

• Worked Examples: narrated step-by-step presentations of a problem being solved.

• Problems: questions designed in adaptive sets, giving students practice and feedback.

• Review: self-test mastery before moving to the next lesson.

• Projects: promote collaboration in the project-based learning tradition to solve real-world problems.

• Study Group Simulations: put students in a virtual study group to help fellow students solve problems.

• Simple Games: give learners a chance to practice what they have learned in a no-fault environment.

• Assessment: formative and summative assessment designed to guide a learner's progress.

Distribution. Course content will be distributed to educational institutions through the National Repository of Online Courses (NROC), MITE’s highly respected library of learning objects and courses, and will be accessible to individual learners and teachers free of charge online at Hippocampus (www.hippocampus.org ).

A project of the Monterey Institute for Technology and Education (MITE) with support from The William and Flora Hewlett Foundation. NROC is an Open Educational Resource, part of a movement fueled by the belief that everyone is entitled to an education, regardless of their financial or social circumstances.

Algebra 1: An Open Course (Semester 1) UNIT 1: THE LANGUAGE OF ALGEBRA Lesson 1: Algebraic Expressions

Variables and Expressions Evaluating Expressions

Lesson 2: Properties of Numbers Associative and Commutative Properties The Distributive Property Properties of Equality, Identity and Inverse

UNIT 2: SOLVE LINEAR EQUATIONS Lesson 3: Writing and Solving Equations

Solving Equations (+, - , *, /) Solving Multi-Step Equations Writing Expressions and Equations Solving for a Specific Variable

Lesson 4: Absolute Value Equations Absolute Value Solving Absolute Value Equations

UNIT 3: FUNCTIONS AND PATTERNS Lesson 5: Working with Patterns

Inductive Patterns Representing Patterns

Lesson 6: Graphing Functions and Relations Representing Functions and Relations Domain and Range Proportional Functions (Direct Variation) Linear Functions Non-linear Functions

UNIT 4: ANALYZE AND GRAPH LINEAR EQUATIONS, FUNCTIONS AND RELATIONS Lesson 7: Graphing Linear Equations

Rate of Change and Slope Intercepts of Linear Equations Graphing Equations in Slope Intercept Form Point Slope Form and Standard Form of Linear Equations

Lesson 8: Parallel and Perpendicular Lines Parallel Lines Perpendicular Lines

UNIT 5: ANALYZE, SOLVE, AND GRAPH LINEAR INEQUALITIES Lesson 9: Writing, Solving and Graphing Inequalities

in One Variable Solving and Graphing Inequalities in One Variable Solving and Graphing Absolute Value Inequalities Writing and Using Inequalities

Lesson 10: Solving and Graphing Linear Inequalities in Two Variables

Solving and Graphing Linear Inequalities in Two Variables

UNIT 6: SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES Lesson 11: Solving Systems of Linear Equations

Solving Systems by Graphing Solving Systems by Substitution Solving Systems by Elimination

Lesson 12: Applying Systems of Equations Rate Problems Mixture Problems

Lesson 13: Graphing Systems of Inequalities Graphing Systems of Inequalities

Algebra 1: An Open Course (Semester 2) UNIT 7: RADICAL EXPRESSIONS Lesson 14: Exponents

Scientific Notation Simplifying Expressions with Exponents Fractional Exponents

Lesson 15: Radical Expressions and Equations Simplifying Radical Expressions Solving Radical Equations Applying Radical Equations

Lesson 16: The Pythagorean Theorem Applications of the Pythagorean Theorem

UNIT 8: POLYNOMIALS Lesson 17: Operations on Monomials

Multiplying and Dividing Monomials Lesson 18: Operations on Polynomials

Polynomials Adding and Subtracting Polynomials Multiplying Polynomials Special Products of Polynomials

UNIT 9: FACTORING Lesson 19: Factoring Monomials and Polynomials

Factoring and the Distributive Property Factoring Trinomials by Grouping 1 Factoring Trinomials by Grouping 2

Lesson 20: Factoring Special Products of Polynomials Factoring Special Products Solving Quadratic Equations by Factoring

UNIT 10: QUADRATIC FUNCTIONS Lesson 21: Quadratic Functions

Graphing Quadratic Functions Solving Quadratic Equations by Completing the Square Proving the Quadratic Formula Solving Quadratic Equations Using the Quadratic Formula The Discriminant

Lesson 22: Applying Quadratic Functions Applications of Quadratic Functions Systems of Non-Linear Equations

UNIT 11: RATIONAL EXPRESSIONS AND EQUATIONS Lesson 23: Rational Expressions

Simplifying Rational Expressions Multiplying and Dividing Rational Expressions Adding and Subtracting Rational Expressions

Lesson 24: Rational Equations Solving Rational Equations Applying Rational Equations

UNIT 12: EXTENSIONS AND APPLICATIONS Lesson 25: Logical Reasoning and Number Sets

Logic and Properties of Numbers Inductive and Deductive Reasoning Logic and Counterexamples Always, Sometimes and Never True Number Sets

Lesson 26: Probability Events and Outcomes (Counting) Permutations and Combinations Probability of Independent Events Probability of Compound Events