Problem Solving in Algebra I, Part I

Course Description

Description

CTY's Problem Solving and Enrichment Math courses sharpen investigative skills, broaden mathematical understanding of concepts, and enhance reasoning skills. Designed around performance objectives that reflect national and state mathematical standards, these courses demonstrate how mathematical issues arise out of real-life situations. Concepts are assessed through challenging quizzes and module tests. With the guidance of their instructors, students typically select enrichment or supplementary math courses of the appropriate level in between their accelerated courses to ensure a solid foundation and mastery of math concepts at each level.

In Problem Solving in Algebra I, Part I, students focus on the symbols and rules of algebra and how they are used to represent relationships. Topics include concepts typically covered in first semester algebra, such as:

• translating words into mathematical expressions
• solving equations using multiple operations
• applications of linear equations and systems
• solving systems of linear equations and inequalities
• examining perpendicular and parallel lines
• solving absolute value equations

Students master skills and concepts through practice problems, interactions within every lesson, and workout questions.

Materials Needed

There are no required materials for this course.

List of Topics

Module 1: The Language of Algebra

Variables, Expressions, and Equations

• Translating Words into Expressions
• Applying Properties of Real Numbers
• Evaluating and Simplifying Expressions

Linear Equations in One Variable

• Applying Inverse Operations
• Transforming Equations using Multiple Operations
• Solving Absolute Value Equations

Module 2: Linear Functions & Equations

The Rectangular Coordinate Plane

• Graphing Ordered Pairs
• Defining Slope
• Finding x- and y-Intercepts

Introduction to Functions

• Exploring the Slope-Intercept Equation of a Line
• Exploring the Point-Slope Equation of a Line
• Relations and Functions

Module 3: Systems of Linear Equations

Graphic Solutions of Linear Systems

• Finding the Point of Intersection
• Graphing Parallel & Perpendicular Lines

Algebraic Solutions of Linear Systems

• Using Substitution to Eliminate a Variable
• Using Addition or Subtraction to Eliminate a Variable

Module 4: Linear Inequalities

Inequalities in One Variable

• Applying Inverse Operations
• Graphing Solutions on a Number Line
• Solving Absolute Value Inequalities

Inequalities in Two Variables

• Graphing Solutions on a Rectangular Coordinate Plane
• Solving Systems by Graphing

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System Requirements

CTYOnline courses require a properly-maintained computer with Internet access and a recent-version web browser (such as Firefox, Safari, or Internet Explorer) with the Adobe Flash plugin. Students are expected to be familiar with standard computer operations (e.g. login, cut & paste, email attachments, etc).

This course requires high-speed Internet access (such as Cable or DSL) for online lesson videos. Your browser will need to allow javascript, login cookies, and popup windows from ctyjhu.org, bluejay.cty.jhu.edu, and any other course web sites.

This course uses an online mathematical whiteboard for individual or group discussions with the instructor. The whiteboard web site requires cookies, popup windows, and the Java Runtime Environment. (Note: iOS & Android devices cannot run Java applets.)