Learning Outcomes
By the end of this section, you will be able to:

 Identify the whole numbers and counting numbers from a list of numbers
 Identify the place value of a digit in a number
 Write a whole number given as digits or in words
 Round a whole number to a specific place value
 Use symbols and words to represent addition, subtraction, multiplication, and division
 Identify and use the identity properties of addition and multiplication
 Identify and use the commutative properties of addition and multiplication
 Identify and use the multiplication property of zero
 Use the long division algorithm
 Perform applications using addition, subtraction, multiplication, and division
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.
Recall for success
Look for red boxes like this one throughout the text. They’ll show up just in time to give helpful reminders of the math you’ll need, right where you’ll need it.