April 23, 2008

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Algebra 1A, of the National Repository of Online Courses.

Unit 1 of 4.

Basic algebra principles

Lesson 1: Real numbers & algebraic expressions Lesson 2: Simplifying expressions Lesson 3: Solving equations Lesson 4: More on solving equations

- Mathematics > General
- Mathematics > Algebra

- Grade 9
- Grade 10
- Grade 11
- Grade 12

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Algebra 1A, of the National Repository of Online Courses.

Unit 1 of 4.

Basic algebra principles

Lesson 1: Real numbers & algebraic expressions Lesson 2: Simplifying expressions Lesson 3: Solving equations Lesson 4: More on solving equations

This curriculum emphasizes a multi-representational approach to algebra, with concepts, results, and problems being expressed graphically, analytically, and verbally. It develops algebraic fluency by providing students with the skills needed to solve equations and perform important manipulations with numbers, variables, equations, and inequalities. In addition, the course develops proficiency with operations involving monomial and polynomial expressions. The main unifying themes of the course include understanding, writing, solving, and graphing linear equations, systems of linear equations and inequalities, quadratic equations, and rational equations. Upon completion of this course you will:

- Perform operations with real numbers
- Simplify and evaluate algebraic expressions
- Use equations to solve word problems
- Graph and solve problems involving inequalities and absolute value
- Graph and solve linear equations
- Solve systems of equations
- Solve many types of real-world problems
- Factor polynomial equations
- Understand relations and functions
- Solve quadratic equations
- Work with radical expressions and rational equations

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Lesson 1 Objectives

- Learn about the real number system and number lines
- Use number operations and properties
- Create, simplify, and evaluate expressions, equations, and formulas
- Learn about the real number system
- Learn about number lines
- Use number operations
- Use number properties
- Learn about real numbers: irrational, rational, integer, whole, and natural
- Learn about number lines and opposites
- Use a Venn diagram of the number system
- Understand what is a variable
- Understand what is an expression
- Create expressions from word descriptions
- Understand what is an equation
- Create equations from work descriptions
- Use number operations: addition, subtraction, multiplication, and division
- Learn about the order of operations
- Learn about closure and density properties
- Evaluate number expressions with multiple operations
- Use number identities: additive and multiplicative
- Use reciprocals: additive and multiplicative inverses
- Use the multiplicative property of zero
- Use reflexive property of equality
- Use symmetric property of equality
- Use transitive property of equality
- Use substitution property of equality

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Lesson 2 Objectives

- Work with basic expressions
- Use number properties to simplify expressions
- Use the associative property
- Use the commutative property
- Use the distributive property
- Evaluate number expressions using these properties
- Simplify basic expressions
- Simplify expressions using the distributive property
- Simplify expressions using the associative and commutative properties

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Lesson 3 Objectives

- Solve equations using properties of equality
- Solve equations with one variable using the addition property of equality
- Understand equivalent equations
- Solve single-step equations using the subtraction property of equality
- Solve single-step equations using the multiplication property of equality
- Solve single-step equations using the division property of equality
- Create and solve single-step word problems using equality properties

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Lesson 4 Objectives

- Solve equations with multiple steps
- Solve formulas with multiple variables
- Create a multi-step equation
- Solve a multi-step equation by working "backwards" through it
- Solve a word problem using multiple steps
- Create an equation with the same variable on both sides
- Solve an equation with the same variable on both sides
- Understanding formulas are equations with two or more different variables that are related
- Solving formulas for a specific variable using previously learned techniques

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