Provides instructions for shortcuts of varying degrees of difficulty for doing arithmetical calculations and estimates, and for checking answers.

Games designed to reinforce and consolidate a variety of mathematical concepts with an emphasis on language.

Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.

The Cyrists are swiftly moving into position to begin the Culling, and Kate's options are dwindling. With each jump to the past or the future, Kate may trigger a new timeline shift. Worse, the loyalties of those around her--including the allegiances of Kiernan and the Fifth Column, the shadowy group working with Kate--are increasingly unclear. Kate will risk everything, including her life, to prevent the future her grandfather and the Cyrists have planned. But, when time runs out, it may take an even bigger sacrifice to protect the people she loves.