Before embarking upon any study of mathematics, it is important to warm up by practicing math concepts you’ve probably seen before. This practice will help refresh mathematical ideas that will be helpful aids to understanding the material presented in upcoming sections of the text. A good review will help make new math less challenging and will enable deeper thought about familiar ideas. As you work through this course you may even find that you have missed a particular concept altogether in your previous study. This is perfectly natural for a subject with such depth and breadth as mathematics. It is with these ideas in mind that review sections such as this one will appear at the beginning of each module in this course.

When working through this review section, at times you may find that only a light reading and practice is necessary to bring the ideas back to working memory. At other times, you may encounter an idea in a review section that feels completely new, in which case it will be beneficial to dive deeply into the given examples and practice problems. Either way, even if your instructor doesn’t specifically assign material from the review sections, it’s a good idea to make sure you are familiar with the vocabulary, concepts, and processes involved.

Our first review section is concerned with whole numbers and their characteristics. An understanding of how place value is used to make sense of quantities will help you as you read about historical counting systems. Humans have not always counted or perceived quantities in the way we do today. A careful study of our modern understanding of counting and place value will set the stage to discover how these ideas may have differed in the past.