How do composing and decomposing numbers connect with the properties of addition? Focus on the ideas that you need to thoroughly understand in order to teach with confidence. The mathematical content of this book focuses on essential knowledge for teachers about numbers and number systems. It is organized around one big idea and supported by smaller, more specific, interconnected ideas (essential understandings). Gaining this understanding is essential because numbers and numeration are building blocks for other mathematical concepts and for thinking quantitatively about the real-world. Essential Understanding Series topics: Number and Numeration for Grades Pre-K 2 Addition and Subtraction for Grades Pre-K 2 Geometry for Grades Pre-K 2 Reasoning and Proof for Grades Pre-K 8 Multiplication and Division for Grades 3 5 Rational Numbers for Grades 3 5 Algebraic Ideas and Readiness for Grades 3 5 Geometric Shapes and Solids for Grades 3 5 Ratio, Proportion, and Proportionality for Grades 6 8 Expressions and Equations for Grades 6 8 Measurement for Grades 6 8 Data Analysis and Statistics for Grades 6 8 Function for Grades 9 12 Geometric Relationships for Grades 9 12 Reasoning and Proof for Grades 9 12 Statistics for Grades 9 12

Developing Essential Understanding of Number and Numeration for Teaching Mathematics in Pre-K–2

Science & Math

Barbara Dougherty

Alfinio Flores

Catherine Sophian

Rose Mary Zbiek

Everett,Louis

Mathematics

NCTM

How can you build on young children's interactions with the world to develop their geometric thinking? What can you say to a student who claims that a diamond isn't a square because it "stands on a point"? How can knowing what does not change when shapes are transformed help you extend your students' thinking about the area of geometric figures? How much do you know ...and how much do you need to know? Helping your students develop a robust understanding of geometry and measurement requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about geometry and measurement. It is organized around four big ideas, supported by multiple smaller, interconnected ideas-- essential understandings . Taking you beyond a simple introduction to geometry and measurement, 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. About the Series: Focus on the ideas that you need to understand thoroughly to teach confidently. Move beyond the mathematics you expect your students to learn. Students who fail to get a solid grounding in pivotal concepts struggle in subsequent work in mathematics and related disciplines. By bringing a deeper understanding to your teaching, you can help students who don't get it the first time by presenting the mathematics in multiple ways. The Essential Understanding Series addresses topics in school mathematics that are critical to the mathematical development of students but are often difficult to teach. Each book in the series gives an overview of the topic, highlights the differences between what teachers and students need to know, examines the big ideas and related essential understandings, reconsiders the ideas presented in light of connections with other mathematical ideas, and includes questions for readers' reflection.

Developing Essential Understanding of Geometry and Measurement for Teaching Mathematics in Pre-K–Grade 2

E.Paul Goldenberg

Douglas Clements

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. The big ideas relate to the fundamental properties of number and operations, the use of the equals sign to represent equivalence, variables as efficient tools for representing mathematical ideas, quantitative reasoning as a way to understand mathematical relationships, and functional thinking to generalize relationships between covarying quantities. The book examines challenges in teaching, learning, and assessment and is interspersed with questions for teachers reflection.

Developing Essential Understanding of Algebraic Thinking for Teaching Mathematics in Grades 3–5

Maria Blanton

Linda Levi

Terry Crites

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Books by Barbara Dougherty