What is the relationship between fractions and rational numbers? Can you explain why the product of two fractions between 0 and 1 is less than either factor? How are rational numbers related to irrational numbers, which your students will study in later grades?
How much do you know… and how much do you need to know?
Helping your upper elementary school students develop a robust understanding of rational numbers requires that you understand this mathematics deeply. But what does that mean?
This book focuses on essential knowledge for teachers about rational numbers. It is organized around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to rational numbers, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students—and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students’ understanding of the topic.
Focus on the ideas that you need to understand thoroughly to teach confidently.
Product   Description  List Price  
Developing Essential Understanding of Number and Numeration for Teaching Mathematics in PreK2 
 Move beyond the mathematics you expect your students to learn.  $29.95 

Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics: Grades 68 
 Move beyond the mathematics you expect your students to learn.  $32.95 

Developing Essential Understanding of Multiplication and Division for Teaching Mathematics in Grades 35 
 Move beyond the mathematics you expect your students to learn.
"Unpacking" the ideas related to multiplication and division is a critical step in developing a deeper understanding. To those without specialized training, may of these ideas might appear to be easy to teach. But those who teach in grades 35 are aware of their subtleties and complexities.  $32.95 

Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in PreKGrade 2 
 Move beyond the mathematics you expect your students to learn.  $32.95 

Developing Essential Understanding of Algebraic Thinking for Teaching Mathematics in Grades 35 
 Like algebra at any level, early algebra is a way to explore, analyze, represent, and generalize mathematical ideas and relationships. This book shows that children can and do engage in generalizing about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential understandings for developing algebraic thinking in grades 3–5.  $32.95 

Developing Essential Understanding of Functions for Teaching Mathematics in Grades 912 
 Help your high school students develop a robust understanding of functions.  $35.95 

Developing Essential Understanding of Mathematical Reasoning for Teaching Mathematics in Grades PreK8 
 This book focuses on essential knowledge for teachers about mathematical reasoning. It is organized around one big idea, supported by multiple smaller, interconnected ideas—essential understandings.Taking you beyond a simple introduction to mathematical reasoning, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students—and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students' understanding of the topic.
 $32.95 

Developing Essential Understanding of Expressions, Equations, and Functions for Teaching Mathematics in Grades 68 
 This book focuses on essential knowledge for teachers about expressions, equations, and functions. It is organized around five big ideas, supported by multiple smaller, interconnected ideas—essential understandings.Taking you beyond a simple introduction to expressions, equations, and functions, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students—and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students' understanding of the topic.
 $36.95 

Focus in High School Mathematics: Reasoning and Sense Making in Geometry 
 One of a series of books that support NCTM’s Focus in High School Mathematics: Reasoning and Sense Making by providing additional guidance for making reasoning and sense making part of the mathematics experiences of all high school students every day.
 $29.95 

Focus in High School Mathematics: Reasoning and Sense Making in Algebra 
 This volume is one of a series of books that support NCTM’s Focus in High School Mathematics: Reasoning and Sense Making by providing additional guidance for making reasoning and sense making part of the mathematics experiences of all high school students every day.
 $27.95 
