Problem Solving in Pre-Algebra

The Problem Solving in Pre-Algebra course prepares students for the more formal study of mathematics in high school. Students continue their study of numbers and their operations by exploring ratios, proportions, and irrational numbers. They also begin a study of the fundamental skills and concepts found in algebra, geometry, statistics, and probability. In each workout that follows a tutorial, students apply what they have learned to solve sets of questions at varying levels of difficulty.

Scope and Sequence for Problem Solving in Pre-Algebra

Module 1: Essentials of Algebra

Algebra Fundamentals

• Introducing Variables
• Identifying Components of Algebraic Expressions
• Replacing Variables in a Formula

Evaluating an Algebraic Expression

• Representing the Dimensions and Area of a Rectangle
• Combining Like Terms
• Evaluating Expressions Using Substitution

Simple Equations

• Using Variables to Express Relationships
• Simplifying Algebraic Expressions
• Solving Simple Equations

Variables on Both Sides of the Equation

• Writing Equations
• Simplifying Both Sides of an Equation
• Checking the Solution to an Equation

Solving Literal Equations

• Identifying the Variables in a Given Formula
• Rewriting a Formula in Terms of a Different Variable
• Substituting Values and Solving an Equation

Module 2: Fundamentals of Geometry

Geometry Fundamentals

• Naming and Measuring Angles
• Defining Complementary and Supplementary Angles
• Recognizing Congruent Angles

Triangles

• Classifying Triangles by Sides
• Exploring the Area of a Triangle
• Classifying Triangles by Angles

Volume and Surface Area

• Calculating Volume of a Right Triangular Prism
• Calculating Surface Area of a Right Triangular Prism
• Calculating Volume and Surface Area of a Right Cylinder

Module 3: Radicals and Exponents

Introduction to Radicals & Pythagorean Theorem

• Exploring the Pythagorean Theorem
• Investigating Squares and Square Roots
• Defining Irrational Numbers

Introduction to Scientific Notation

• Writing Numbers Using Scientific Notation
• Comparing Numbers in Scientific Notation
• Writing Numbers Between 0 and 1 in Scientific Notation

Module 4: Ratio and Proportion

Ratio

• Defining Ratio
• Expressing Ratios as Equivalent Fractions and Decimals
• Forming Ratios Between Unlike Quantities

Proportion

• Defining a Proportion
• Solving for a Variable in a Proportion
• Applying the Means/Extremes Property

Direct and Inverse Variation

• Exploring and Solving Direct Variation Problems
• Exploring Inverse Variation
• Solving Inverse Variation Problems

Similar Polygons

• Defining Similarity
• Identifying Equivalent Ratios
• Setting Up and Solving Proportions in Similar Polygons

Module 5: Statistics

Interpreting and Constructing Graphs

• Exploring Line Graphs
• Exploring Bar Graphs
• Interpreting Pie Charts

The Mean, Median, and Mode

• Defining the Mean and Median
• Defining the Mode
• Calculating the Mean, Median, and Mode

Frequency Distribution and Histograms

• Creating and Interpreting a Frequency Table
• Defining a Histogram
• Exploring Cumulative Frequency Graphs

Module 6: Probability

Simple Probability

• Defining and Expressing Probability
• Calculating Probabilities on a Color Wheel
• Determining Probability of Complementary Events

Probability of Combined Events

• Calculating the Probability of Independent Events
• Determining the Sample Space of an Experiment
• Calculating the Probability of Dependent Events

Course Management and Assessment

Students are evaluated by a series of Unit Quizzes, Module Tests and a comprehensive Final Exam. Our CTY Distance Education Quiz Corner tests and tracks students progress. Tutors monitor the progress of each student by reviewing and responding to work and maintaining communication via email, phone and the online whiteboard. When necessary, tutors may also refer students to the Distance Math Web site for additional on-line resources.

Homework

Students in the Problem Solving Series of courses receive Print Activities with their course materials. Print Activities provide reinforcement and help to promote concept retention for each module of the software. Students are not required to complete the activities, but we highly recommend that they do. Students are able to check their work using the answer key provided.

Unit Quizzes and Module Tests

Student progress is evaluated through the CTY Distance Education Quiz Corner. Unit Quizzes are to be completed after each Unit. Your score on the Unit Quizzes is automatically emailed to your tutor. The tutor responds via e-mail with help on difficult concepts or trouble areas. Module Tests are another important assessment tool. Students log onto Quiz Corner to print the Module Test, then complete the test and fax or mail the completed test to the tutor. Tutors provide feedback, as necessary.

Final Exam

All students are required to take a paper and pencil Final Exam. As a student nears the completion of a course, the tutor will send the final exam via e-mail (pdf), fax, or the student can download the final from the course website. Students should plan ahead for review and make use of the tutor for feedback and review suggestions. Students often require more tutorial support during the time when they are studying for the final than at any other point in the course. We strongly encourage students to utilize and stay in contact with their tutor during final exam preparation. Each test is given a percentage score, and students will receive an e-mail containing their score.

Grading Policy

With a passing grade (B or better) course completion documents are mailed. These include a copy of the scope and sequence for the course, an assessment of the students work by the tutor, and a course completion certificate.

If a student scores below an 85% on Final Form A then the student will have the oppurtunity to take Form B of the Final Exam. The highest grade, regardless of the percent scored, that a student can achieve when taking Form B of the Final Exam is a B for the course

If a student scores below an 85% on the Final Form B, a statement of participation, rather than Final Course Completion documents, will be issued upon request.

last updates 24 Oct 2002