Teaching elementary mathematics is complicated: teachers must not only understand the concepts, procedures, and application of seemingly "basic" mathematics, they must also understand mathematical misconceptions and apparently correct answers as well as the "logic" behind these answers.

Unfortunately, teachers are often trained to think about mathematics as basic procedures with correct or incorrect answers. Misconceptions and incomplete mathematical thinking often go undetected, as teachers are rarely trained to consider why or how an answer was generated. They often respond to incorrect answers by re-teaching the correct processes, and the underlying problem persists.

Sometimes even students' correct answers do not indicate accurate reasoning. Unrecognized misconceptions then become permanent ways of thinking; each new layer of mathematics knowledge builds upon on flawed foundations. This book addresses that problem head on. By covering the essential content or "big ideas" of 3-5 mathematics, it turns elementary teachers into experts in diagnosis, intervention, and evaluation (Hattie 2010), and delivers the tasks and tools to use in the classroom day-to-day.

As a result of using these books, teachers will be able to:

• Select and employ up to 180 rich tasks for instruction or assessment;
• Consider what counts as mathematical understanding;
• Anticipate and plan for student misconceptions;
• Make instructional decisions based on specific misconceptions or incomplete understandings;
• Learn how to adapt tasks for differentiation, different grade levels;
• Avoid certain hazards such as teacher misconceptions when giving correct answers, or misinterpreting student drawings, writing, or equations;
• Use the book in a professional learning community, communicate with parents, and support parent conferences.

Tackling math's "big ideas" for grades 3-5 such as addition and subtraction, multiplication and division, fractions, and decimals, the book is organized into 45 Big Ideas by mathematical domain and grad band, each offering a rich task that walks teachers through the analysis of several student-work examples to identify:

• What is happening with this student's thinking?
• What do we want to ask this student?
• What doesn't this student understand about the mathematics?
• What might we do next for this student?

Each section then offers three additional tasks and guiding information to use in the classroom for a total of 180 rich tasks teachers can implement immediately.

Tasks are aligned to Common Core and other state and international standards.