Welcome to a new experience in learning mathematics The approach of Foundations of Mathematics maintains a single focus, that of student-centered success. What does student-centered success mean? Up until now, as a student of mathematics, you have developed a certain body of knowledge and may or may not have developed a set of successful learning strategies. This course aims to build upon your capacity as a learner and raise your success level by incorporating techniques that will help you become a more efficient and effective learner.

This course is divided into six modules of math topics, supported by pre-activity reading and preparation, relevant activities, and practice tests.

The topics are:

• Module 1 – Whole Numbers

• Module 2 – Decimal Numbers

• Module 3 – Fractions

• Module 4 – Ratios and Proportions

• Module 5 – Percents

• Module 6 – Signed Numbers, Exponents, and Order of Operations

Book Features

This book is especially designed for you as an entering college student to assist you in your success in learning mathematics. Each chapter section provides the following featured components:

Pre-Activity Preparation, comprised of:

• An Introduction with brief real world examples

• Learning Objectives

• Terminology, with lists of new and previously used terms

• A list of Mathematical Properties and Principles particularly relevant to the section

• Building Mathematical Language, setting forth mathematical notation, language, and concepts as a basis for further exploration of the topic

• Methodologies and Techniques, providing the step-by-step processes to solve specific types of problems. By following the steps in a methodology or technique, you will be assured accuracy of your solution. As you read a step and study the included example, you must ask, “Can I do this myself?” To help you test your understanding, another column allows you to work through the methodology step-by-step.

• Models of problem-solving, with Special Cases and Shortcuts featured

• A table titled Addressing Common Errors, showing examples of errors commonly made in problem solving. Most importantly, resolutions and corrections are provided.

• A Preparation Inventory, a list of concepts that you should have gained from reading the section. The Inventory provides a check-off list to ensure your readiness to go on to the Activity.

Activity, comprised of:

• Performance Criteria, the expectations you will need to meet in order to succeed on each module test

• Critical Thinking Questions, a series of inquiries that challenge you to confirm and deepen your understanding of the terminology, properties, principles, methodologies, techniques, and applications of the mathematical concepts you have learned

• Tips for Success, special insights about learning and the tips that will strengthen your performance when applying the math concepts you have learned

• A set of exercises in which to Demonstrate Your Understanding of the section and how to apply its methodologies and techniques by solving problems and validating your answers

• Examples of incorrect student-written solutions, providing an opportunity to Identify and Correct the Errors. By analyzing these errors, you will be better able to identify and correct your own errors.