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Egyptians introduced the earliest fully developed base 10 numeration system around 5000 years ago. They could use large numbers and also fractions (unit fractions and Eye of Horus fractions) and their construction techniques included precision surveying. About 700 years later they were using abstract arithmetic methods - they had arrived at approximations for pi and square roots, they used written arithmetic tables, solved algebra problems and applied maths to problems involving weights and measures.
Ancient Egypt had two number systems. One was the Hieroglyph numeral system, using a decimal based tally system with separate symbols for 10, 100, 1000, etc. and hieratic unit fractions. The other Hieratic numeral system was very different. Written in a new ciphered one-number-to-one-symbol system it was a type of digital system, replacing each 'tally' (previously used to denote multiples of a unit) with a symbol, and was later adopted and adapted by the Romans.
Much of our information about Egyptian maths comes from The Rhind Mathematical Papyrus (RMP) was written in hieratic and contains examples of how the Egyptians did their mathematical calculations. Early scholars understood Egyptian fraction notation on the Rhind Mathematical Papyrus on a basic additive level, but are only now (in the 21st century) grasping a deeper understanding. The Egyptian Mathematical Leather Roll and the Akhmim Wooden Tablet have also been helpful.
The Ancient Egyptians multiplied by repeatedly doubling the number to be multiplied, and selecting which of the doublings to add together, rather like using a binary system (obviously this is an over-simplification). They also used mathematical short-cuts.
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Designed as an introduction to solid geometry, this is a story of a brother and sister and their dog who are accidentally shut into a pyramid during their scientist parents' search for an ancient pharaoh's mummy. Matt and Bibi use good observation skills to analyse the path to the mummy (it is delineated by 'faces') and then find their way through the pyramid by applying maths to further observations in order to unravel clues hidden in the hieroglyphics. Finding find the mummy and a map enables them to escape from a pharaoh's tomb.
A little far fetched and may require some skilled guidance by the teacher, but good fun, and well illustrated with colorful impressionist cartoons. Also suggests some good maths activities to help children learn about geometric solids. One reviewer was inspired by this book to make a game board and game cards as an engaging way to count faces, vertices, and edges with maths students.
C for Cubit has a story which begins "Suppose you live in ancient Egypt and you pick some papyrus on the banks of the Nile . . . ". and continues with the a drama demonstrating difficulties of trading your papyrus with Ahmmos (a papermaker you find in the marketplace in Alexandria) in the absence of 'standard units'. There's also a nice little hieroglyphic code to figure out, and a nice panel on measuring in 'hands' (with hand prints various paw prints illustrated too - a nice touch!)
C, we are told, also stands for catenary curve, chaos, chart, circle, circumference, coordinate, cube, cube root, curve and cylinder. These are covered briefly in a glossary which will absorb the kind of more advanced reader who really wants to know a little bit about catenary curves and chaos.
Ancient Egyptians return later in the book with Pharaoh's foot and some more amusing cartoons in Ancient Egyptian style.
Hypatia - a brilliant philosopher and mathematician - lived in fourth-century Alexandria in Egypt (when it was ruled by the Ancient Greeks). Her father was the last director of the Library of Alexandria and Hypatia herself tutored both pagan and Christian pupils in her own home, but rumors that Hypatia was involved in witchcraft led to her murder.
Sidebars and illustrations add interest, but the captions (printed in pink) may be hard to read. Varied information formats - a time line of her life and corresponding world events, capsules of facts, additional resource lists, glossary, source notes , bibliography, index - all combine to make this a useful reference.
Also in the 'Signature Lives' series is Alexander the Great : World Conqueror
'Of Numbers And Stars: The Story Of Hypatia' has a reading level of 9-12 years, but may be challenging, both in the phraseology (such as: 'In search of true wisdom, she read the pronouncements of the oracles . . . .') and in the notes - Hypatia's violent death is described, and ancient mathematics is discussed. Illustrations are stylized acrylic paintings incorporating decorative motifs reminiscent of ancient Greek and Egyptian art.
A story set in ancient Egypt conveys the history of mathematics through the eyes of a young genius
The story of Eratosthenes, the ancient Greek librarian who figured out how to calculate the circumference of the earth by a sophisticated process involving sun and shadows. He became tutor to the son of King Ptolemy III of Egypt, and eventually became the head of the magnificent library in Alexandria', Egypt.
This is an ususual book for which it would be hard to specify an age group - Kathryn Lasky is trying to convey formal mathematical concepts in a picture-book format, using fable, history and science. The paintings by Kevin hawkes are great; the story is told in simple words - but the mathematical concepts are perhaps too abstract for the younger end of the 4-8 age group. Children at the older end may be put off by the young looking picture boook style.
However, the book also conveys history, science and biography quite wonderfully. The authentic examples of the art, architecture, and social system of the period incorporated into Hawkes' paintings are combined with many humourous touches - very lively and appealing! The pictures support the textual explanation of the librarian's scientific / mathematical discovery admirably. A fine combination of history, science, and biography.
A story drama version of the picture book "The Librarian Who Measured The Earth" is featured in this book of 'story dramas'.
This story drama demonstrates exactly how a question drives research, and how research sources can be found all over the place. Suggestions for maths follow up activities (and costumes) are provided.
Beautifully illustrated maths activities with a strong cultural and historical perspective for a middle school age group. Topics range worldwide, with plenty about Ancient Egyptian Maths - from the Pyramids to the Rhind Payprus, and African number systems - from Ancient Egypt to Kenyan finger counting. The book clearly demonstrates and how diverse cultures have helped mathematics to develop, from our earliest counting systems to modern developments in chaos theory.
'AGNESI TO ZENO' provides practical ways to enrich any curriculum with historical perspectives, introducing concepts, events and influential mathematicians. Each 'unit' contains a single page introduction to a mathematician or concept, plus questions/projects for students.
(Paperback: 328 pages)
This classic heavyweight (800 pages) best-seller 'introduces mathematics history to math and math education majors'. Suggested essay topics and problem studies challenge students. 'Cultural Connections' sections explaining the time and culture in which mathematics developed and evolved, and portraits of mathematicians and material on women in mathematics give this book a fascinating personal feel.
The section on 'Babylonian and Egyptian Mathematics' you can find out about the Egyptian Sundial, the Egyptian plumb line and sight rod - and the 'A curious problem in the Rhind Papyrus' . . . The problem studies include 'the Seqt of a Pyramid', 'Egyptian Algebra' and Egyptian Geometry' (amongst others).
A brief introduction to the history of ancient Egypt sets the scene for examining the mathematical ideas of ancient Egypt - their number system, the ways they tackled arithmetic (including fractions), their calendar and their system for measuring land areas and weights. Complete with teacher's notes and reproducible masters.
Wider ranging and fascinating for 9-12s: " ... Papyrus is our most important source of information about Egyptian math"
Long ago, the earliest human civilizations discovered the strange and fascinating quality of particular numbers and wove them into their superstitions and religions - and the deeper we delve into numbers, the more surprises and enigmas we discover.
A beautifully presented and illustrated book.
A creative look at the role mathematics has played since prehistoric times and Ancient Egypt to the Guggenheim in Bilbao and hyperspace! This is maths presented in a fun-to-read, nonthreatening manner - and in many of its guises - in medicine, in art, in the patterns of nature . . . and its central role in the development of computers.
From 700 BCE to CE 1300, thousands of scholars from many different civilizations introduced mathematical ideas that established the foundations of arithmetic, number theory, algebra, geometry, and trigonometry, as well as the related sciences of astronomy and physics. "The Birth of Mathematics" covers maths from Babylonia, Egypt, and China - and also profiles 10 mathematical innovators from Greece, India, Arabia, and medieval Italy.
A comprehensive work on Egyptian mathematics - but as Gillings is not an Egyptologist there's no discussion of problems translating the texts.
This book explains the level of learning and advance of knowledge in maths and astronomy from discoveries made by mathemeticians in ancient Bablyon, ancient Sumer and ancient Egypt. Its range is interesting - for instance, it shows why astronomy did not evolve from astrology and shows how personality can affect the direction of mathematical investigation.
"Count Your Way Through the Arab World" introduces an arab country and culture through counting throught Arabic numerals from one to ten. Each double-page spread shows the number, the character or word for it, the pronunciation, and a full-color illustration, with a few facts about various aspects of life there. The kinds of topics featured are chosen arbitrarily for the way they fit into this number-related format - the number five is illustrated by the importance of Muslims praying five times a day. Sometimes it works, sometimes it's a bit strained. It might inspire your class to create their own version.
All over the world children play some form of a three-in-a-row game for two players - this fascinating book starts by tells the story of archaeologists in Egypt a hundred years ago who found the roof of a newly uncovered temple was covered with carved games-boards for mathematical games which are still played today - all around the world!
Maths, history, art and world cultures are combined in more than 70 math games, puzzles and projects from all over the world to help children hone their maths skills: use geometry to design games boards, logical thinking to devise strategies for playing and probability to analyse likely outcomes.
Other books by Claudia Zaslavsky include
"Multicultural Math", "Africa Counts" and "Fear of Math"
In the hands of Simon Singh, particle physicist turned science writer (and author of 'Fermat's Last Theorem') this subject becomes a fascinating journey into medieval treason trials, pre-historic lost cultures and modern day espionage.
Also available in hardcover, published by Thames & Hudson
To the casual observer the 3000 years-worth of wall paintings and reliefs in ancient Egyptian tombs and temples seem to have just one artistic style, showing one set of customs and beliefs. But in the groundbreaking 'Proportion And Style In Ancient Egyptian Art', Robins shows how innovative Egyptian art was - and how the artistic style of the scenes varied from century to century. She presents her original research into the grid systems and proportions used by the ancient artists to establish lifelike proportions for standing, sitting and kneeling human figures, tracing the system from its Old Kingdom origins through its development in the Middle Kingdom into its use in the Late and Ptolemaic periods. In particular, she considers how artists used the grid to differentiate between men and women, and conducts the first full analysis of how the grid system influenced composition as a whole.
Robins also reviews the revolutionary Amarna canon of proportions - which she herself discovered - from the time when the heretic king Akhenaten was making major changes. The canon of proportions did vary over the thousands of years of Egyptian civilisation, but her analysis of figures from different eras, does demonstrate that even though different systems were used in different eras, "classic proportions" can actually be demonstrated.
Line drawings of paintings and reliefs with superimposed grids (some derived from actual traces surviving on monuments, others calculated using ancient Egyptian methods) illustrate the book throughout.
A comprehensive, technical approach - covers everything from how architectural drawings and models were used to the 'foundation rituals' that show how intertwined religion was with ordinary life.
Deals with the ancient Egyptian view of 'proportion' before going on to study the geometry of the pyramids.
Children learn maths through experience and play with six interactive activities supporting Key Stages 1-2. Sophisticated tracking software adjusts the pace of learning and targets weak areas - the games can be customised to cover specific curriculum topics.
One activity uses mathematical symbols to solve the Pharoah's pyramid riddles - and for every activity comprehensive, well designed 'Help' pop-ups give step-by-step maths help tailored to each problem.
Friendly and clear explanations, and manages to be mathematically correct without feeling "mathematical". There's a good section about Ancient Egyptian mathematics.
The new edition of the established guide to primary maths for ages 5-11 also includes a fantastic bonus CD with useful check-ups from Derek Haylock's Numeracy for Teaching, as well as a full glossary of the mathematical terms used in the new edition of Mathematics Explained for Primary Teachers.
Real misconceptions about all the main maths topics that can mislead children - with strategies for avoiding them in the classroom (and at home). Because this book is also easy to read it's really useful for lesson planning - on the basis that 'prevention is better than cure' - but will also help teachers to help children clear away earlier stumbling blocks.
If you aim to become a reflective teacher of mathematics go straight to the "reader's review" on Amazon (click the link and scroll down) for a in depth review by someone who found the book "really useful when it comes to actually teaching mathematics in the class room, which when it comes down to it is what the PGCE course is all about!"
Helps you develop your analysis and self-evaluation skills, the knowledge of what you are trying to achieve and why; study examples of how experienced teachers deliver successful lessons; plan lessons, make good use of resources and assess pupils' progress effectively. Videos of teachers actually using these skills are useful (on on the companion website - which also links to extra planning and resource materials).
M-level PGCE research is also provided for - with examples of the research evidence needed in Masters level academic work.
The book and CD provide 200 teaching activities and 40 practical games - with clear instructions - to keep individuals, pairs or small groups of pupils entertained. Designed to help 7-14s with significant and specific difficulties in mathematics get to grips with:
The CD-rom accompanying the book contains printable and photocopiable resources.
A real-life history context in which to apply the teaching and learning of mathematics and history in a cross-curricular approach. Topics include numbers and the number system, calculations, problem solving, handling data and measures, shape and space. Differentiated photocopiable activities are presented at three ability levels. Includes teacher's notes and a vocabulary bank of mathematical language.
Is it an e-book? Is it useful for the mainstream - or too off-beat?
We seldom realize that in the past five hundred years while the human race has created lot of new technology, it has discovered very little new mathematical or scientific knowledge. It is quite likely that a key cause of this "decline" in high-intellect is the poor state of current early mathematics education in almost all cultures of the world. 'How Kids Learn Math: New Discoveries and Ancient Wisdom' presents and analyzes current research dealing with the emerging qualitative approach to math education in early learners, that is, in preschool children and in children who are 2-3 years into school. It also shows how the qualitative approach resonates with ancient wisdom about math learning, a wisdom that we can see not only in the aesthetically pleasing art, music and architecture but also in the breakthrough discoveries of knowledge accomplished by past civilizations around the globe.
Strategic problem solving set in historical contexts of Ancient Mesopotamia, Ancient Egypt, Ancient Greece, Ancient Rome, The Ancient Maya and the Mound Builders. The author has nearly three decades of classroom experience in the fields of maths and social studies.
A scholarly sourcebook written by experts in their fields for a general readership of maths teachers or maths graduates. Each mathematical culture is introduced by an expert, with explanations of why each selection has been included - Annette Imhausen has contributed the section about Egypt.
Mesopotamian mathematics is known from many Babylonian cuneiform texts but Egyptian mathematics is known from only a small number of papyrus texts. These extensive studies takes a new direction, explaining the author's methods for analysing all kinds of Egyptian mathematical texts, hieratic, demotic, or Greek-Egyptian.
Many new insights into the nature of Egyptian mathematics result from comparisons of many of individual Egyptian mathematical exercises with Babylonian parallels, and show that Egyptian and Babylonian mathematics display greater similarities than may have been expected.
Usefully detailed diagrams and figures, with an index.
Topics covered include: enumerative geometry, optical solitons, non-smooth dynamical systems, finite groups and mathematics education.