Numbers And Numerals

Searchable electronic version of print product with fully hyperlinked cross-references.

The bestselling workbook and grammar guide, revised and updated! Hailed as one of the best books around for teaching grammar, The Blue Book of Grammar and Punctuation includes easy-to-understand rules, abundant examples, dozens of reproducible quizzes, and pre- and post-tests to help teach grammar to middle and high schoolers, college students, ESL students, homeschoolers, and more. This concise, entertaining workbook makes learning English grammar and usage simple and fun. This updated 12th edition reflects the latest updates to English usage and grammar, and includes answers to all reproducible quizzes to facilitate self-assessment and learning. Clear and concise, with easy-to-follow explanations, offering "just the facts" on English grammar, punctuation, and usage Fully updated to reflect the latest rules, along with even more quizzes and pre- and post-tests to help teach grammar Ideal for students from seventh grade through adulthood in the US and abroad For anyone who wants to understand the major rules and subtle guidelines of English grammar and usage, The Blue Book of Grammar and Punctuation offers comprehensive, straightforward instruction.

THE HISTORY OF NUMBERS FROM THE CLAY TABLETS OF SUMEREA TO MODERN DAY MATHEMATICS.

This book displays large images of numerals used in all of the world's major numbering systems from antiquity to the present. Numbers 1 to 20 are displayed in almost all of these numbering systems, and the tens, hundreds, thousands and beyond are displayed where place value systems with zero are not used. These images are greatly enlarged so that those newly encountering them can appreciate and remember them more easily. Numbers are very important in almost every branch of learning. They are the basic essentials of trade and commerce as well as architecture, building and construction. Then there are the fields of mathematics and astronomy as well as almost every other branch of learning. The book begins with the numbering systems of the ancient Inca and Maya and then progresses to the numerals etched on oracle bones in China 3,400 years ago. The Chinese use of zero and negative numbers in rod numerals is also covered. Following this are the Babylonian cuneiform numbers and Egyptian hieroglyphic and hieratic numbers. Then the first European numbering system from Minoan Crete is followed by Phoenician, Attic and Etruscan numerals. Roman numerals and Ionian Greek alphabetic numerals are presented with an explanation of how they had their origin in the Phoenician alphabet. Then we move on to the partly Greek-derived numerals used by the Ethiopians who speak the Semitic Amharic language. The alphabetic Hebrew numerals of Greek inspiration are followed by the Arabic abjad numerals which assign numbers to the letters of the Arabic alphabet. Armenian and Georgian numbers are also displayed and then the Kharosthi numerals of Afghanistan and India. Emphasis is then placed on the Brahmi numerals of 4th century BC India which gave rise to all of the numbering systems of modern India and Southeast Asia as well as Tibet and Mongolia and even Europe. The Indian development of the concept of zero and a place value system is also covered in detail. Dozens of images are shown of numbers in the Devanagari, Gujarati, Punjabi, Bengali, Odiya, Telugu, Kannada, Tamil and Malayalam scripts. Then the stylistic but obsolete Sinhala numerals of Sri Lanka are followed by the Javanese, Burmese, Khmer, Thai and Lao numerals. Finally the Eastern Arabic numerals used in modern Arabic speaking countries appear with Persian variants. Next are the medieval European variants of Western Arabic numbers, including those from the Codex Vigilanus of the year 976 and numerals from 11th century France. The numerals of Bernelinus, a pupil of Pope Sylvester II, are followed by the 12th century numerals of Gerlandus of Besancon and the 13th century numerals of the English scholar Roger Bacon.

Classic study discusses number sequence and number language, then explores written numerals and computations in a wide range of cultures. 282 illustrations. "Superior narrative ability." — Library Journal.

Insights from the history of numerical notation suggest that how humans write numbers is an active choice involving cognitive and social factors. Over the past 5,000 years, more than 100 methods of numerical notation--distinct ways of writing numbers--have been developed and used by specific communities. Most of these are barely known today; where they are known, they are often derided as cognitively cumbersome and outdated. In Reckonings, Stephen Chrisomalis considers how humans past and present use numerals, reinterpreting historical and archaeological representations of numerical notation and exploring the implications of why we write numbers with figures rather than words.

In this groundbreaking and highly practical book,Number Sense Routines: Building Numerical Literacy Every Day in Grades K-3, author Jessica Shumway proposes that all children have innate number sense which can be developed through daily exercise. Shumway createda series of math routines designed to help young students strengthen and build their facility with numbers. These quick 5, 10, or 15 minute exercises are easy to implement as an add-on to any elementary math curriculum. Understanding Number Sense: Students with strong number sense understand numbers, how to subitize, relationships among numbers, and number systems. They make reasonable estimates, compute fluently, use reasoning strategies, and use visual models to solve problems. Number Sense Routines supports the early learner by instilling the importance of daily warm-ups and explains how they benefit developing math minds for long-term learning. Real Classroom Examples: Shumway compiled her classroom observations from around the country. She includes conversations among students who practice number sense routines to illustrate them in action, how children's number sense develops with daily use, and math strategies students learn as they develop their numerical literacy through self-paced practice. Assessment Strategies: Number Sense Routines demonstrates the importance of listening to your students and knowing what to look for. Teachers will gain a deeper understanding of the underlying math skills and strategies students learn as they develop numerical literacy. Shumway writes, As you read, you will step into various classrooms and listen in on students' conversations, which I hope will give you insight into the power of number sense routines and the impact they have on students' number sense development. My hope is that going into the classroom, into students' conversations, and into their thought processes, you will come away with new ideas and tools to use in your own classroom.