Publisher's Synopsis
The CCSS-M demand a higher standard for students at all levels, most particularly primary students. Research shows teachers will need to upgrade their skills to succeed with the new standards. This book supports all teachers at the primary and middle school levels who want a deeper knowledge of arithmetic in all its aspects. How the CCSS-M implements what is known about the importance of curriculum design is explained so that teachers will have a better sense of what was wrong with previous curricula and what is intended by the new standards. The book develops the integers from counting and the real numbers from geometry and shows how these two approaches are compatible. The Arabic system of notation and how it supports the standard computations of arithmetic is explained. The explanations reflect the historical development of mathematics by providing additional explanatory material as each additional level of abstraction is applied. This concludes with decimal computations. All the important rules of arithmetic necessary for success at algebra are presented. It is shown how these rules are sourced in the Commutative, Associative and Distributive Laws which in turn are derived from counting. Special emphasis is given to topics related to fractions.
