# Algebra I

SKMA 097## Course Description

Prerequisite: MATH LEVEL 3. Includes natural number, integers, first-degree equations and inequalities, special products, factoring, rational expressions and equations, graphs, and linear systems, exponents, and quadratic equations. May receive credit in only one of the following: MTH 107 or MTH 097 or SKMA 097 or SKMA 102. Does not earn credit toward graduation. (45-0)

## Outcomes and Objectives

### Students will develop their skills in number patterns, relationships, and computation.

#### Objectives:

- Compute (add, subtract, multiply and divide) with signed numbers without the use of a calculator.
- Simplify numerical expressions with multiple operations and grouping symbols using the order of operations.
- Simplify rates and ratios.
- Compute the opposite, reciprocal, and absolute value of a given real number.
- Estimate the value of a numerical expression.
- Identify an approximate answer to an application problem prior to working it out.
- Identify the appropriate unit of an answer to a word problem.

### Students will develop their skills in the computation and recognition of algebraic expressions.

#### Objectives:

- Add, subtract, and multiply polynomial expressions.
- Simplify algebraic expressions with multiple operations and grouping symbols using the order of operations.
- Simplify algebraic expressions using the rules of exponents.
- Simplify algebraic expressions using the distributive property.
- Compare and contrast terms and factors.
- Simplify rational expressions.
- Factor polynomials by taking out a common factor.
- Factor trinomials.
- Factor binomials of the form x2 - y2
- Identify an algebraic expression that cannot be factored.
- Compute the opposite and reciprocal of a given algebraic expression.
- Identify and give examples of like and unlike terms.
- Identify and give examples of linear, quadratic, rational, and radical expressions.
- Compare and contrast expressions and equations.

### Student can solve a variety of equations, inequalities, and systems of equations.

#### Objectives:

- Solve a variety of linear, quadratic (using the factoring method and the quadratic formula), radical, and rational equations.
- Verify the solution of an equation.
- Recognize situations in which an equation has no solution or has multiple solutions.
- Solve a variety of linear inequalities.
- Verify the solution of a linear inequality.
- Recognize situations in which a linear inequality has no solution or multiple solutions.
- Use interval notation, relational symbols <, >, <, >) dimensional graph, or a verbal description to describe a set of numbers.
- Solve a variety of systems of linear equations.
- Verify the solution of a system of linear equations.
- Recognize situations in which a system of linear equations has no solution or multiple solutions.

### Student can recognize and understand concepts related to linear functions.

#### Objectives:

- Solve linear equations algebraically, graphically, and numerically.
- Solve systems of linear equations algebraically, graphically, and numerically.
- Compute the slope of a line in a variety of contexts.
- Identify the slope of a line as positive, negative, zero, or undefined.
- Interpret the slope of a line in context as a rate of change.
- Compute the y-intercept of a line in a variety of contexts.
- Interpret the y-intercept of a line in context as an initial amount.
- Compute the equation of a line in form in a variety of contexts.

### Students will develop their skills in the construction and interpretation of Cartesian graphs.

#### Objectives:

- Construct the graph of a line if given the equation of the line.
- Identify an appropriate scale for both axes when constructing a graph.
- Approximate one coordinate of a point on a graph is given the other.
- Identify graphs as linear or non-linear.

### Students will develop their problem-solving skills.

#### Objectives:

- Set up an equation or expression if given a word phrase.
- Describe in words the meaning of an expression or equation.
- Solve a variety of real world problems using the tools of algebra and mathematical modeling.

### Students will communicate effectively about mathematics.

#### Objectives:

- Use mathematics terminology effectively in writing and speaking.