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1. The Devil's Arithmetic (Puffin
2. Arithmetic and Algebra Again:
3. Sideways Arithmetic From Wayside
4. More Sideways Arithmetic From
5. The Theology of Arithmetic
6. The Devil's Arithmetic
7. Arithmetic Refresher: Improve
8. Quick Arithmetic: A Self-Teaching
9. The Higher Arithmetic: An Introduction
10. Arithmetic and Algebra Again (Schaum's
11. Lessons for Introducing Multiplication,
12. Pre-Nursing Reviews in Arithmetic
13. Lessons for Addition and Subtraction:
14. Thinking Mathematically: Integrating
15. A Course in Arithmetic (Graduate
16. Ray's New Primary Arithmetic For
17. Introduction to Arithmetic for
18. How to Solve Word Problems inArithmetic
19. Arithmetic 1 Work-text Teacher
20. Arithmetic we need

1. The Devil's Arithmetic (Puffin Modern Classics)
by Jane Yolen
Paperback: 176 Pages (2004-04-12)
list price: US$6.99 -- used & new: US$2.44
(price subject to change: see help)
Asin: 0142401099
Average Customer Review: 4.5 out of 5 stars
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Editorial Review

Product Description
Hannah thinks tonight’s Passover Seder will be the same as always. Little does she know that this year she will be mysteriously transported into the past where only she knows the horrors that await. ... Read more

Customer Reviews (280)

5-0 out of 5 stars excellent
I read this to my 12 year old and it felt like about the right age, I don't think I would read it to a younger child.The first chapter was a disappointment and we would have stopped had this not been recommended by a favorite teacher.Starting with chapter 2 the story completely drew is in.It is well written, suspenseful, and sensitive. This book places the reader in the middle of the holocaust like no other book, in that way it is masterful.Despite the really difficult subject matter, we loved this book. Bravo!

4-0 out of 5 stars Excellent introduction to the Holocaust for young readers
Hannah is a young Jewish girl who is bored with the seemingly pointless traditions of her heritage and the ranting and raving of her Holocaust survivor relatives. During the Passover Seder, she is asked to open the door for Elijah the Prophet and finds herself transported to a small Polish village in the 1940's.

Now known as Chaya, she is overwhelmed by the change in setting and wonders if her memories of a modern world are real or just a forgotten dream. At a wedding ceremony, the entire village is rounded up by Nazis and Hannah remembers the terrible things that are about to happen to the Jewish villagers.

Despite her pleas and protests, history continues to unfold in the same way and the journey of the villagers and Hannah to a concentration camp is described in vivid detail. Hannah is forced to experience the harsh conditions and inhumane treatment that her older relatives had described to her a lifetime ago. At the novel's grim climax, Hannah finally understands the importance of sacrifice, and subsequently, of remembering the horrible events of the past.

Although the subject matter is heavy, this is a great book for introducing young readers to the Holocaust. It is accurate in its details, seemingly derived from Primo Levi's Survival in Auschwitz (AKA, Is This a Man?) and other sources. Yolen's narrative structure is very well-suited toward drawing in readers who might not be interested in the subject.

[Disclosure: This review also appears on FingerFlow.com, a site for review and discussion of creative works.]

5-0 out of 5 stars Sobering
This was one of those books I heard about when I was a kid in school.I never read it when I was in grade school, so I was interested when I found it recently.

Yolen does an amazing job of bringing such a horrific time to life in a way that's approachable to young people.Hannah's foray as Chaya is both sweet and sobering as she shows both compassion and the will to survive.

The Devil's Arithmetic is one of those amazing books that makes you stop and think.Well done, Ms. Yolen.

3-0 out of 5 stars from a teacher's perspective
I ordered this book from Scholastic for my classroom.After reading it, I realize that it is more suited for Jr. High or High School students than 4th graders.Although I think that younger studentsbenefit from learning about the Holocaust, I think books more like Number the Stars are more age appropriate for 9 and 10 year olds.being sent to a concentration camp.The story told has a magical element of time travel, that she had a hard time selling to me.However, the purpose and story is there.

4-0 out of 5 stars Read it before your child....
This is for parents of school age kids, since many elementary schools are using this book to start the discussions on the Holocaust. The last half of the book takes place in a concentration camp and the author goes into detail. This is a good book, a very good book, and every person on this planet should read and be reminded about the horrible events in history that took place in Europe during World War II; but there is an appropriate age to learn about certain details.

Please note that Publisher's Weekly (under editorial reviews) says it's for ages 12 and up. But under product details the reading level stated is ages 9-12 (I think "reading level" means they can read it and comprehend it; it does not mean the material is appropriate).

Some schools send home advanced warnings that this book will be used; and let the parents opt out. If that's your case, it would be wise to take a copy from your library, and make your own decision.
... Read more

2. Arithmetic and Algebra Again: Leaving Math Anxiety Behind Forever
by Britta Immergut, Jean Burr Smith
Paperback: 391 Pages (2005-01-18)
list price: US$16.95 -- used & new: US$9.58
(price subject to change: see help)
Asin: 0071435336
Average Customer Review: 5.0 out of 5 stars
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Editorial Review

Product Description

The bestselling guide updated and expanded for today's mathphobes

Written by two pioneers of the concept of math anxiety and how to overcome it, Arithmetic and Algebra Again has helped tens of thousands of people conquer their irrational fear of math.

This revised and expanded second edition of the perennial bestseller:

  • Features the latest techniques for breaking through common anxieties about numbers
  • Takes a real-world approach that lets mathphobes learn the math they need as they need it
  • Covers all key math areas--from whole numbers and fractions to basic algebra
  • Features a section on practical math for banking, mortgages, interest, and statistics and probability
  • Includes a new section on the graphing calculator, a chapter on the metric system, a section on word problems, and all updated exercises
... Read more

Customer Reviews (5)

5-0 out of 5 stars Great Book
This is a great book for any one that wants to re-learn math with out the fear; the author explains arithmetic and algebra in a very easy steps understandable for any one.

5-0 out of 5 stars exactly what I needed
I received the book in a timely fashion as well as in great condition. Thanks for being reliable!

5-0 out of 5 stars For us math challenged peeps!
I am back to school after how many years and was half panicking when I was told I would have not one but TWO math classes.This book is one of the texts.It is easy to follow and quite thorough.Out of the 6 books I need for these classes, so far I understand this one the best.

5-0 out of 5 stars Outstanding for people who struggle with math
I had to prepare for a test for certification in middle school math and was terrified. I hadn't studied algebra or statistics in over 20 years.I ordered several books online and got more at the public library, and this was the ONLY book written in a way that allowed for effective self teaching.The other reviewer said it best, the language they use to explain concepts is the key.I wanted a book that talked to me like I was 6 years old.It needed a bit more on geometry, other than that is was an excellent study guide.Great for Praxis preparation.

5-0 out of 5 stars What I've been looking for....
This is a very well-thought-out book. I've looked at many many math books, looking for one with good, clear explanations. This one is deceptive - at first glance it looks just like any other math book, but this is what I was looking for. For example, the explanation of why we invert and multiply when we divide fractions is clear and understandable - few other math books even bother to try to explain why or how this works, but this book does and does it well. Another wonderful thing about this book is that the authors are aware that words used in math can be confusing - they take the time to explain, for example, why we often use the word "of" when multiplying fractions (1/6 of 3/4) instead of saying "times" (1/6 times 3/4).

The explanations in this book are excellent (and that is what I was looking for) and they always show every step of a solution, so it is easy to follow along. They also use visual explanations, again making sure to show every step.

The focus in this book is on relating the math to practical life - this also really aids understanding.

There are lots of exercises to practice with - and answers are provided for all of them.

The best thing about this book is the "tone" of the authors. They write in an easy-to-understand, clear way. The book doesn't seem to have been written in "mathese" another language, but in normal English for normal people. It gives the feeling of being written by people who are caring and helpful and want the reader to understand - as opposed to most math textbooks that seem to be written more to impress other math educators than for real people who aren't used to math-style writing.

The book covers all the usual topics of arithmetic and goes up through elementary algebra.

Even though the intended market for this book is adults or college students who have already been through years of math, much of which they've forgotten, I recommend it also for homeschoolers. This inexpensive book can take the place of purchasing curriculum for years. It also can be used as a reference for finding good explanations and examples of specific topics - it has an excellent table of contents and index. ... Read more

3. Sideways Arithmetic From Wayside School
by Louis Sachar
Mass Market Paperback: 96 Pages (1994-09-01)
list price: US$5.99 -- used & new: US$0.99
(price subject to change: see help)
Asin: 0590457268
Average Customer Review: 4.0 out of 5 stars
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Editorial Review

Product Description
A collection of 50 hilarious stories, each filled with brainteasers, designed to painlessly teach math skills. ... Read more

Customer Reviews (18)

5-0 out of 5 stars Awesome book!
My fourth-grade daughter loved this book.She went through the problems very quickly.Some of them were pretty tricky and confusing in the beginning, but she had fun as she began to learn how to tackle them.We strongly recomend this book to all people who enjoy math, math puzzles and sudoku.

5-0 out of 5 stars Want you child to read...get these series
My granddaughter loves all of these author's books.She started reading them at school and ask me to purchase some for her own collection.She is 9 and now has 4 of his books.Get your child reading with this author's work.

5-0 out of 5 stars An excellent supplementary book for elementary school mathematics
The first 24 problems in this book are alphametics, which solidified my belief that alphametics are one of the best types of problems for teaching children the rules of algebra. The problems are fairly simple, some examples are



There are also five more difficult alphametics where the operation is multiplication.
The remaining problems are lengthy word problems that involve logic, while requiring some thought; all are within the grasp of the late elementary school student. Solutions to all 55 problems are included at the end. This is an excellent supplementary book for elementary school mathematics.

Published in Journal of Recreational Mathematics, reprinted with permission

5-0 out of 5 stars It's great
Although this book looks like a kid's book, it is really for teenagers and older.It is full of math puzzles, so if you have a bent for figuring out puzzles, don't let the cover and title put you off.It's not really arithmetic -- it's more logic puzzles.I loved this book, and so did my high school aged kids.

This is not a story book.It is a math book.It is too difficult for a young reader.Most adults or older teenagers would probably enjoy it but only if they love math.My 9 year old child said it gave her a headache.My child was given this book at school to read and expected to do the problems in it.Some of the problems required math skills she has not even been introduced too.It is simply too hard for young readers.
... Read more

4. More Sideways Arithmetic From Wayside School
by Louis Sachar
Mass Market Paperback: 112 Pages (1994-09-01)
list price: US$5.99 -- used & new: US$0.95
(price subject to change: see help)
Asin: 0590477625
Average Customer Review: 4.5 out of 5 stars
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Editorial Review

Product Description
A sequel to the original collection of brain twisters and math puzzles includes ""How much is PEPPERS + PIG LIPS?"" and ""If Jenny's shirt has sparkles on it, will Todd have egg in his hair?"" ... Read more

Customer Reviews (10)

5-0 out of 5 stars Great fun with math.
This was a favorite for me as a child. When I read it and did all of the math problems in it, it changed math from a dreaded school subject into something that was a lot of fun. This book made me love algebra and was filled with fun problem solving. It may not be for everyone, but it changed the way I thought as a child and was probably part of the reason I did so well in Algebra. Bottom line: your child may or may not love it, but if they do love it, it will make them smarter at math and instill a love of math in them.

5-0 out of 5 stars An excellent supplemental math text for late elementary school
In my life as a mathematics educator at the college level, I have used alphametics to teach the fundamentals of arithmetic and have touted the value of doing that at professional conferences. Therefore, I was gratified to see alphametics used in this book to teach algebra to students in late elementary school.
An alphametic is an algebra problem where a few words make up a phrase and each letter represents a digit. When the letters are replaced by the digits, the result is a correct arithmetic problem. For example the first problem in this book is


Where the solution is


The first 39 problems are alphametics and the rest are word problems where the solution is derived via logic. There is a section of hints to the problems and complete solutions are included. This is an excellent supplemental math text for students in late elementary school.

5-0 out of 5 stars Kids and parents laugh
We read the Wayside School books together and the kids and parents all laugh.These stories are funny, silly, goofy, and enjoyable.We love them all.We only wish there were more as we have read them all.Recommended for those reluctant readers (and listeners) as well.

5-0 out of 5 stars Great for challenge seekers
This book is amazing. It entertains my kids with its funny and hard math questions. My son spent some time to solve them and we did some of them together. It is a nice book to read and it makes you think as well.

5-0 out of 5 stars Great Book for a Math/Logic Wiz
I had this book when I was in fifth grade, and I absolutely loved it.I was already a big fan of the Wayside books, and I also liked math so these books were the perfect combination for me.I even remember working through the entire book multiple times.I especially loved the early problems wtih the convertion of basic math equations with letters to numbers like BOYS + BOYS = GIRLS and stuff like that.Now I am a physics major in college so I guess I came out pretty well.This book (and the first as well) is highly recommended for any kid who likes the Wayside books and also enjoys math/logic puzzles.Who knows, maybe this kid will be working with Schrodinger's equation in several years. ... Read more

5. The Theology of Arithmetic
by Iambilichus
Paperback: 136 Pages (1988-11-01)
list price: US$17.00 -- used & new: US$11.00
(price subject to change: see help)
Asin: 0933999720
Average Customer Review: 4.5 out of 5 stars
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Editorial Review

Product Description
Attributed to Iamblichus (4th cent. AD), The Theology of Arithmetic is about the mystical, mathmatical and cosmological symbolism of the first ten numbers. Its is the longest work on number symbolism to survive from the ancient world, and Robin Waterfield's careful translation contains helpful footnotes, an extensive glossary, bibliography, and foreword by Keith Critchlow. Never before translated from ancient Greek, this important sourcework is indispensable for anyone intereted in Pythagorean though, Neoplatonism, or the symbolism of Numbers. ... Read more

Customer Reviews (6)

2-0 out of 5 stars Nonsense
For those who are interested in this for a better understanding of Neopythagoreanism and Neoplatonism. Fine.
But you won't find good philosophy in this little book you will find nonsense allegorical applications of Homeric texts and philosophers sayings, nonsense philosophy.

5-0 out of 5 stars The Missing Link Between Geometry, Neo-Pythagoreanism and Kabbalah
If you're one of the few people interested in the history of mathematics/science, Neo-Pythagoreanism, serious study of Kabbalah/mystic theology (not New Age nonsense), or cultural history of number, buy this now before it goes out of print.

Essentially, this is the only book I've seen which lays out the relationships between the Neo-Pythagorean Exoteric Theology and the Esoteric study of Number. This is quite obviously the basis for much of the Kabbalah (e.g. Sefer Yetzirah: The Book of Creation). In itself, that's extremely fascinating.

It's really baffling and amazing to see how a culture without numerals dealt with symbology and ratio. The translation is scholarly and without the new age slant I expected.

For a decidedly limited audience, but highly recommended for them.

A precaution - you should have already read some Euclid e.g. Euclid's Elements, or at least be familiar with him before attempting this. Ditto Plato and Plotinus, though only broad familiarity is needed with the latter two. A scholarly volume (Kaplan's good) on the Kabbalah (which is quite similar in some regards) would also be helpful, but not necessary. Even with these sources, it's an extremely difficult read. Even the translator, who is to be commended for his honesty, admits he didn't understand several portions.

5-0 out of 5 stars Its as good as they say..
This is a translation of Iamblichus lecture notes on the foundational symbolism of the numbers, Iamblichus was highly inspired by the work of Nichomachus and includes numerous pieces quoted from his lost work 'Theology of Arithmetic' (hence the title of this book).

The fact that this translation is of lecture notes means it is relatively concise and to the point, which I personally liked.As other reviewers have noted, the commentary by Robin Waterfield is both extensive and insightful, it definitely makes the material much easier to digest.Highly recommended.

If you like this, I also recommend Nichomachus 'Manual of Harmonics' which discusses similar themes

5-0 out of 5 stars The Holy Grail
The most valuable book I ever found on Pythagorean number philosophy, highly recommended, good luck at ever finding it in print!!!!

5-0 out of 5 stars You cannot IMAGINE how excellent this book is. I'm stunned
When I bought this book, I presumed I was buying a remotely dry and dull book of late Neoplatonic praddle on numbers. However it turns out this book is a copy of a copy of a copy by Iambblichus all the way back to Pythagoras himself (although this isn't proven).

The content of this book is an ABSOLUTE MUST TOOL in the comprehension of Plato, and , my favorite, Plotinus, the logical and numerical philosophical Emanation model (of Plato and Neoplatonists) as expressed in this book is mind blowing. I myself find that 99.9% of the many 1000s of books I've bought get a quick glance and are ditched on the shelf SOON afterwards. I've read the "Theology of Arithmetic" now more than 8 times!

I forward, and rightly so, that this book is in fact an INDESPENSIBLE tool to grasping the logical and numerical ontological expression-model of Pythagoras and Plato/Plotinus in their philosophy of Emanation and necessity in their illuminating the werks (eklampsis/emanation) of the One, the Divine. What's better, is the pithiness of this book is astounding, with main content around 120 pages, its incredibly condensed and packed with revelations and connections leading to insights into Plato's ontology "by" numbers that I never could have made without THIS book.

As per Plotinus in 5.1.1 and his "mystery" world TOLMA as the primordial cause of the "souls descent", I found the answer of this 1500 year-old philosophical-contention mystery SOLVED by means of this very book, "Theology of Arithmetic"


My copy of this book is so underlined and highlighted, I'm buying another copy of it.
... Read more

6. The Devil's Arithmetic
by Jane Yolen
Mass Market Paperback: 170 Pages (2000)
-- used & new: US$4.74
(price subject to change: see help)
Asin: 0590965786
Average Customer Review: 5.0 out of 5 stars
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Customer Reviews (2)

5-0 out of 5 stars The Devil's Arithmetic
I absolutely love this book. It is very sad, though, because you have to relive the Holocaust with the characters. Both the granddad and aunt survived the Holocaust with the loss of almost their whole family. The girl Hannah - which in Hebrew is Chaya - is invited to enjoy the festivities of Passover where Hannah's family also relived the horrid things that happened in the concentration camps/death camps. After Hannah opens the door to let the prophet Elijah in, she is in an alternate world! This is a great book because it has things that have most certainly happened, but the author adds a little twist to the book. This makes The Devil's Arithmetic very intriguing and gives a lot of suspense. I like it because it makes you think twice about what people have gone through. To conclude my review, I would like to say that this is a very good book, and I recommend it to anyone!

5-0 out of 5 stars A very moving account of the realities of the Second World War in Eastern Europe
It continues to astound me that there are people who deny The Holocaust. In some sense I can understand it because it is so difficult to believe that such a thing could have been done as a part of official state policy. Nevertheless, the documentation is so overwhelming that the people who deny it look like pathetic fools.
This story describes the events in one of the camps, but from a unique perspective. Hannah is a young girl living in New Rochelle, New York in modern times. She is with her family and they are going to a Passover service at the home of her elderly relatives that survived the camps. Hannah is a bit rebellious, growing tired of the rituals and wishing she were elsewhere.
Everything changes when Hannah opens the door as a symbolic gesture to let the Prophet Elijah into their home to take part in the ceremony. Suddenly, she is now Chaya, a Jewish girl in Eastern Europe during the Second World War. Shortly after she arrives, the Jews in their shtetl are rounded up, packed into railroad cars and shipped off to a death camp. Her life then becomes a daily challenge to survive.
Like all the others in the camp Chaya is now being slowly worked and starved to death, looking over at the smoke rising from the crematoriums and knowing what it means. Her "time" at the camp ends when she is with four friends and a guard comes over and says he must select three of them to be killed. After all, he has a daily quota that must be filled.
Suddenly, she is Hannah once more and she looks at her Aunt Eva and she can explain the meaning of the tattoo on Eva's arm. Furthermore, she recognizes her Aunt Eva and Grandpa Will as people she knew in the camp. This realization changes her outlook on her Jewish heritage as she now has firsthand knowledge of what took place.
This book is very moving and descriptive of those terrible times. The perspective is always that of a young girl, although she grows up very fast once she arrives at the camps. It should be required reading for all middle school children. While some may object to the depictions of brutality, the history of the human race is not pretty, and the best way to avoid the ugliness is to understand the consequences.
... Read more

7. Arithmetic Refresher: Improve your working knowledge of arithmetic
by A. A. Klaf
Paperback: 438 Pages (1964)
list price: US$12.95 -- used & new: US$4.81
(price subject to change: see help)
Asin: 0486212416
Average Customer Review: 5.0 out of 5 stars
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Editorial Review

Product Description
most-asked questions deal with tax problems, interest and discount, time-payment, etc. 809 problems, answers. "...more than just a refresher...contains a great number of items that are not just reminders but entirely new ideas..."—Bookmarks.
... Read more

Customer Reviews (2)

5-0 out of 5 stars a math classic
This is a very interesting paperback book from Dover on arithmetic. It has fractions, division, square roots, the usual math stuff. But it also has world problems, like mixtures and percents that can still be applied in today's world. Dr. Klaf has written several other books that are equally interesting.

5-0 out of 5 stars Memory jogging review
Have you ever blanked out when someone asked you a simple arithmetic question?Yeah, you know what I'm talking about.

This book is aimed at adults who have forgotten much of the basic arithmetic taught in school.It starts with the basics: addition, subtraction, multiplication and division, and then ranges over a variety of topics (business and financial calculations, percentages, charts, angle measurements, logarithms, mixtures and solutions, averages, etc.).

It contains over 800 problems, easy-to-follow questions and answers in a question and answer style.

If you are returning to school, or have school aged children (and need to help with homework) this book can help to jog your memory. ... Read more

8. Quick Arithmetic: A Self-Teaching Guide (Wiley Self-Teaching Guides)
by Robert A. Carman, Marilyn J. Carman
Paperback: 288 Pages (2001-04-02)
list price: US$19.95 -- used & new: US$14.68
(price subject to change: see help)
Asin: 0471384941
Average Customer Review: 3.5 out of 5 stars
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Editorial Review

Product Description
Master math at your own pace!

Does working with numbers often frustrate you? Do you need to brush up on your basic math skills? Do you feel math stands between you and your career goals, or a better grade at school?

Quick Arithmetic, Third Editionis the quickest and easiest way to teach yourself the basic math skills you need to advance on the job or in school. Using cartoons and a clear writing style, this practical guide provides a fresh start for learning or reviewing how to work with whole numbers, fractions, decimals, and percentages. The book’s proven self-teaching approach allows you to work at your own pace and learn only the material you need. Previews and objectives at the beginning of each section help you determine your particular needs, while self-tests, practice problems, and a final exam let you measure your progress and reinforce what you’ve learned.

For anyone who has ever felt intimidated by a page of numbers, Quick Arithmetic, Third Edition has the answers! ... Read more

Customer Reviews (4)

1-0 out of 5 stars One of the worst math books ever
I purchased this book two years ago and I expected it to be great but it's really not that great of a book. When you do the problems it has the answers right under the problems.

5-0 out of 5 stars Good basic math review
I had a pretty good wake up call when I failed the math portion of a TABE test.I picked this book up to brush up on my math and it has helped greatly.Excellent book.

5-0 out of 5 stars A great math refresher course
I found myself floundering while trying to help with Algebra ll homework. It's a great reference for all the little things you've forgotten or maybe never known. Well organized and easy to navigate.

3-0 out of 5 stars A bad start
This book looks decent on the whole, but it gets off to an annoyingly bad start.The way it is structured is that your ability to answer or not answer questions guides you to different sections within the book.The first chapter starts off with a preview quiz, to get you started on your path.Yet the very first question on the quiz has the wrong answer.So when you check your results and think you got it wrong - try it again.The answer given is off by 20.This would be unbelievable in a self teaching guide if I didn't have it right in front of me.I can understand a mistake here and there, but the very first question??!!And, of course, no way to contact the authors to see if they have released accurate answers or let them know.Now the entire book is suspect.There is also some confusion shortly after as the authors draw a clear distinction between a digit as a representation of an idea, then give a question using characters (which are the same, representations of sounds) but ignore the difference between the idea and the glyph.My favorite part so far: "The number three is the idea that describes any collection of three objects."What an incredible waste of ink.
I know this sounds harsh, and I am very disappointed in a few things I ran into right up front, but overall it does indeed look to be a good book.Better than the others I looked at, and it seems well organized and well written (if poorly edited).I do suggest that if you get an answer wrong and think maybe you had it right, you should check yourself with a calculator, the book may be wrong.So I do recommend it, but you have to beware the beginning! ... Read more

9. The Higher Arithmetic: An Introduction to the Theory of Numbers
by H. Davenport
Paperback: 248 Pages (2008-11-17)
list price: US$49.99 -- used & new: US$25.99
(price subject to change: see help)
Asin: 0521722365
Average Customer Review: 4.0 out of 5 stars
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Editorial Review

Product Description
Now into its Eighth edition, The Higher Arithmetic introduces the classic concepts and theorems of number theory in a way that does not require the reader to have an in-depth knowledge of the theory of numbers The theory of numbers is considered to be the purest branch of pure mathematics and is also one of the most highly active and engaging areas of mathematics today. Since earlier editions, additional material written by J. H. Davenport has been added, on topics such as Wiles' proof of Fermat's Last Theorem, computers & number theory, and primality testing. Written to be accessible to the general reader, this classic book is also ideal for undergraduate courses on number theory, and covers all the necessary material clearly and succinctly. ... Read more

Customer Reviews (5)

3-0 out of 5 stars some basic material explained
The title leads one to higher expectations than the text
actually delivers?
The book has some basic topics in number theory,
but isn't so new or so well written as one might expect.
That the book has gone past seven printing seems to show that it has been a popular seller?
As for me I don't find myself desperate to buy it.

3-0 out of 5 stars Disappointing
I've purchased this book based on the rave reviews it's received on Amazon.com, both on this page and elsewhere. I've been greatly disappointed.

This is the eighth edition, and, as such, is low on error count, so if all you're looking for in a math textbook is that it be error-free, this may be the book for you.

If you are looking for a little more than that: say, an interesting, well-motivated and pedagogically sound lecture, you'd be better off looking for it elsewhere, for instance in Jones & Jones' superb "Elementary Number Theory".

"The Higher Arithmetic"'s style of writing is unstructured prose (as opposed to the Definition-Theorem-Proof structure), supposedly rendering the text less rigid and more "friendly", when, in fact, it accomplishes the exact opposite effect: You're never sure where a proof begins and where it ends. This compounds unnecessary intellectual and psychological strains on top of those already naturally present whenever one learns new material.

The unstructured-ness also makes this book quite useless as a work of reference.

The proofs aren't particularly elegant or insightful (in fact, they are quite difficult to follow in some cases, for no good reason).

There's very little in terms of historical background and in terms of interesting applications and recreations.

Finally, the book is uncannily devoid of that geeky sense of humor that embellishes the best of math textbooks (e.g. "in this sense, at least, the prime 2 is very odd!", Jones & Jones, 1998, p. 106).

This book can best be recommended to those who have already studied number theory, and would like a refresher of the main topics an introductory course is likely to include.

This review is based on my impressions of the first three chapters (which constitute roughly one third of the book in terms of number of pages). I simply couldn't bear reading any further. I can't preclude the possibility that it gets better down the road.

5-0 out of 5 stars Dated due to lack of material on modern encryption, still suitable for learning number theory
The higher arithmetic is more commonly known as number theory and is one of the most enjoyable and complex areas of mathematics. Simultaneously simple and hard, the problems are generally easy to understand yet can be horrendously difficult to solve. Furthermore, the initial areas of number theory are easy to comprehend; in general it only takes a basic knowledge of algebra to manage the main points.
In this book, Davenport takes you through the basics of number theory, starting with prime factorization and going through some simple Diophantine equations. The chapter titles are:

*) Factorization and the primes
*) Congruences
*) Quadratic residues
*) Continued fractions
*) Sums of squares
*) Quadratic forms
*) Some Diophantine equations

This book is a solid introduction to number theory and can be understood by the advanced high school student. The primary drawback for the modern reader is that there is no coverage of the use of number theory in modern encryption techniques.

4-0 out of 5 stars Good book, but if you have the money, there are better
Well, this is definitely a very good introduction to number theory.The author provides clear, readable proofs of all the most basic theorems on topics such as congruences, sums of squares, etc.He explains things quite well.However, despite costing almost 2.5 times as much, I would recommend Hardy and Wright's book An Introduction to the Theory of Numbers more highly than Davenport's book.Seriously, although it may seem good that Davenport doesn't require a knowledge of calculus as a prerequisite for his book (which Hardy DOES require), one probably shouldn't learn number theory until one has a good backrground on topics ranging from improper integrals to infinite series.Because Davenport does not require calculus as a prerequisite, he neglects HUGE aspects of what could actually be considered BASIC number theory: namely, the basic analytic aspects (such as Tchebycheff's results on the Prime Number Theorem) and the additive theory (i.e. partitions and such, as well as the basics of the generalized theory surrounding Waring's problem for high powers of integers).So, my recommendation is, wait until you know integral calculus and the theory of infinite series BEFORE buying a book on number theory, and then buy Hardy and Wright's book rather than this one.

5-0 out of 5 stars This is a MUST BUY if you want to learn Number Theory!
This book is an AMAZING introduction to the Theory of Numbers. It assumes no previous exposure to the subject, or any technical mathematical knowledge for that matter. Its prose is lucid and the style appealing.Davenport chose NOT to write a lemma-theorem-proof kind of book, and theresult is a marvelous, eminently readable introduction to the subject. Itswonderful to read a book where good prose is used to appropiatelysubstitute a massive collection of uninviting symbols. I've also beenreading other books on Number Theory, such as Hardy & Wright, but noneare as clear as this one.

I found the chapter on quadratic residues(which includes the reciprocity law) to be especially well written. Thesection on computers and number theory is excelent as well. A concise andcoherent discussion of crytography and the RSA system is included here.The organization of the book's chapters is fantastic. Each chapter buildsup on results proven in the previous ones, showing well the connectionsbetween the different aspects of Number Theory. The exercises of the bookrange from simple to challenging, but are all accesible to someone willingto put effort into them.

This would be an excelent source for learningnumber theory for mathematical competition purposes, such as the ASHME,AIME, USAMO, and even for the International Mathematical Olympiad. The bookcontains much more than what is needed for these competitions, but theolympiad/contest reader will benefit greatly from a study of Davenport'swork.

The book can certainly be used for an undergraduate course inNumber Theory, though it might need supplementary materials, to cover asemester's worth of work. I know the book has been used in the past inprevious editions as the main text for Math 124: Number Theory at HarvardUniversity.

I would also recommend this book to anyone interested inacquanting themselves with Number Theory.

Awesome!There is simply noother word that describes The Higher Arithmetic. ... Read more

10. Arithmetic and Algebra Again (Schaum's Paperbacks)
by Brita Immergut, Jean Burr Smith
Paperback: 379 Pages (1993-12-01)
list price: US$15.95 -- used & new: US$9.94
(price subject to change: see help)
Asin: 0070317208
Average Customer Review: 5.0 out of 5 stars
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Product Description
With this easy-to-use guide you can banish your fear of mathematics and algebra forever!

This anxiety-calming guide helps you excel in math­­even if you thought you were a hopeless case. Arithmetic and Algebra ... Again offers you real help and real hope. Written by teachers who have years of experience teaching the math-anxious, it gives you specific, one-step-at-a-time support in overcoming your anxiety, learning about numbers, and solving problems. Before you know it, you'll be looking forward to algebra exams! ... Read more

Customer Reviews (4)

5-0 out of 5 stars I'm Not Math Illiterate!
After years of thinking that I just couldn't do math, this book did the impossible.It taught me not only how to solve math problems but to understand how I solved them.I actually feel comfortable with math and want to go as far as I can learning it.Instead of being torture it is now an intriguing subject.I made it to Algebra II in high school ten years ago but I never knew what I was doing.I highly recommend this book to anyone who thinks they "can't do math".I think some people just learn differently than it is taught in most public schools.You CAN learn math (if I could, then you can too!).

4-0 out of 5 stars Very good book
It's a very good book that is easy to understand.

5-0 out of 5 stars This book is like having a personal tutor..that you like
To say this book helped me is an understatement. It not only helps me inmy college studies, but in every day situations.I am purchasing anothercopy today for my niece, who is experiencing some difficulty incomprehending math. Of course she is labeled with a "LearningDisability". Well after my husband & I helped her with herhomework, we realized "she doesn't have a disability"....it isthe way the school "explains" math concepts that is making math amystery to her. When I spoke to her and brought math "down toearth" as this book does....she is catching on quick. I am sendingthis book to her today, for I know it will help her through-out her life.To the authors I want say....Thank you for making math understandable.

5-0 out of 5 stars A WONDERFUL tool for students of ALL AGES!
I am a mom who graduated many years ago, who is having to freshen up on my math and algebra skills so I can help my teenage children understand their work in school.This book makes learning algebra for my 16 year old son,who suffers from a Learning Disability, easy to comprehend, whilerefreshing what I learned many years ago.It takes you through practicallyevery step imaginable to understand the rules, terms and equations ofalgebra.I never thought learning algebra could be so easy!My son, whohas ALWAYS struggled with math, now actually says that algebra is FUN!Just keeping him interested in a subject is challenging enough, but withthis book, he actually looks forward to the challenge!

Thanks for makingthis book available! ... Read more

11. Lessons for Introducing Multiplication, Grade 3 (Teaching Arithmetic)
by Marilyn Burns
Paperback: 208 Pages (2001-09-15)
list price: US$33.95 -- used & new: US$21.48
(price subject to change: see help)
Asin: 0941355411
Average Customer Review: 5.0 out of 5 stars
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Multiplication is one of the most important math topics in third grade, and the lessons in this book offer ways to make it accessible to all children. Students learn how multiplication relates to repeated addition and how it can be interpreted geometrically. They calculate products up to 12 × 12, engage in explorations about multiplication, and practice solving real-world problems. ... Read more

Customer Reviews (1)

5-0 out of 5 stars Great Book for Introducing Multiplication
Excellent book. FULL of ideas...I used to have a hard time searching for GREAT ideas to intro multiplication to my students. Not anymore. This book is a great tool - a great resource. I ordered, received it and have used it daily for the last week. I am planning on using it for a couple more weeks.
If you are looking for great, interesting and FUN math activities that have students think outside of the box - THIS IS IT! ... Read more

12. Pre-Nursing Reviews in Arithmetic
by Mary E. Stehman
Paperback: 32 Pages (1961-06-01)
list price: US$8.95 -- used & new: US$4.96
(price subject to change: see help)
Asin: 0803681402
Average Customer Review: 3.5 out of 5 stars
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Customer Reviews (6)

3-0 out of 5 stars Its Ok, but not enough
I'm an older adult student, who returned to college after dropping out 15 years ago.I purchased this book to refresh my memory on arithmetic.While this book was easy to read and provided explanations on fractions, decimals, percentage, ratio/porportion, and the metric system, it was not enough.The examples provided were easy problems, not the type I encountered today on my TEAS exam.Those math problems were more complex.There were some easy ones, but a good majority required some thought.I would give this book 2.5 stars.I suppose you can start off with this small book, and then try to answer more complex questions in another book.

5-0 out of 5 stars fantastic
a very helpful lil book that gets right to the root of the problem and helps you establish the basics in math

5-0 out of 5 stars Excellent Service
Product arrived sooner than expected and was in excellent condition.Would purchase from this seller in the future.

2-0 out of 5 stars Not Helpful
This is too outdated to be of much use to anyone, in my opinion. The book doesn't even have the answers to most of the problems, either! You can find much more information on fractions on the internet, for free!

3-0 out of 5 stars Informative
I found this book to be very informative. I recommend it to someone who needs to brush up on their basic skills. ... Read more

13. Lessons for Addition and Subtraction: Grades 2-3 (Teaching Arithmetic)
by Bonnie Tank, Lynne Zolli
Paperback: 186 Pages (2001-09-01)
list price: US$33.95 -- used & new: US$9.97
(price subject to change: see help)
Asin: 0941355322
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The real-world problems, explorations with money, measurement activities, investigations, and games in this book capture students' interest, motivate their thinking, and increase their learning. Students learn basic facts, develop multiple strategies for computing, make estimates, and apply addition and subtraction to problem-solving situations. ... Read more

14. Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School
by Thomas P. Carpenter, Megan Loef Franke, Linda Levi
Paperback: 160 Pages (2003-01-15)
list price: US$33.75 -- used & new: US$26.00
(price subject to change: see help)
Asin: 0325005656
Average Customer Review: 4.5 out of 5 stars
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In this book the authors reveal how children's developing knowledge of the powerful unifying ideas of mathematics can deepen their understanding of arithmetic ... Read more

Customer Reviews (3)

5-0 out of 5 stars Excellent!!
I sent for this book the day before my classes started and didn't pay for fast shipping. I ordered on Aug. 17th, the book was shipped on the 19th and arrived on the 23rd. I was very pleased since the estimated arrival date was Sept. 9th! The book arrived in good shape other than a small fold on the upper corner. Since this book was half the price of a new book at my college book store I couldn't be happier with my purchase and would definitely order from this company again.

5-0 out of 5 stars A Must for Elementary Teachers
2+3=5+4???What kind of thinking would make a child think this is true?This book skillfully opens your mind to the kinds of erroneous thinking that trip young students up as they begin to study algebraic principles.It's a real eye-opener into common mathematical misconcepetions to watch for and help children through in the elementary grades.

4-0 out of 5 stars CGI Continuation Book
This book is great for an elementary teacher, middle school teacher, or junior high teacher.CGI incorporates differing problem solving strategies and relies heavily on class discussion in order to develop new mathematical concepts.

The best part of this book is the development of algebraical concepts in the early grades but is great for reviewing or new ways of presenting concepts in the latter grades.

I highly recommend this product if a teacher is willing to implement the total program and money involved.I am a second year teacher and I spent over $800 to implement this program in my classroom because I had none of the materials needed (snap cubes, cuisinaire rods, markers, or tubs to hold the materials.) ... Read more

15. A Course in Arithmetic (Graduate Texts in Mathematics)
by Jean Pierre Serre
Hardcover: 132 Pages (1973-04-18)
list price: US$64.95 -- used & new: US$44.78
(price subject to change: see help)
Asin: 0387900403
Average Customer Review: 4.5 out of 5 stars
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Jean-Pierre Serre is Professor at the Collège de France. He has written a number of books, including "Algebraic Groups and Class Fields", "Local Fields", "Complex Semisimple Lie Algebras", "Linear Representations of Finite Groups", Collected Papers (3 volumes), and "Trees" published by Springer-Verlag. ... Read more

Customer Reviews (6)

3-0 out of 5 stars A pleasure to read, but
This book is very elegant, a pleasure to read, but not a great textbook -- after reading you are likely not to remember anything other than having enjoyed it (this is particularly true of the proof of Dirichlet's theorem). For actually learning to work in the subject (of analytic number theory), Davenport's book Multiplicative Number Theory is VASTLY superior.

5-0 out of 5 stars An excellent book, and a great title!
Contrary to what many Americans may think of when they hear "arithmetic", this book is not about adding and multiplying (well, at least not at a basic level).Rather, this book covers several important topics in number theory - that of quadratic forms (the "algebraic" portion of the book), L-functions associated to Dirichlet characters, and modular forms (the "analytic" portion).

The section on quadratic forms is primarily devoted to a proof of the Hasse-Minkowski theorem, which is a type of "local-global" principle.This provides a natural opportunity to introduce p-adic numbers, which have become ubiquitous in the algebraic side of number theory.The analytic section starts with basic definitions and provides a proof of Dirichlet's theorem on primes in an arithmetic progression, which provides a natural opportunity to introduce an initial theory of L-functions.The last section provides an excellent introduction to the basic properties and theorems on modular forms.

What's the common theme in this book?We have the opportunity to see the origins of essential ideas in modern number theory (local-global principle, modular forms, L-functions) in a natural way.On the one hand, this book (as the other reviewers have mentioned) can be quite difficult for the beginner to read, since the exposition is sparse (but superb) and the material quite non-trivial.On the other hand, modern number theory (and much of modern mathematics) is incredibly abstract and advanced, and to see these ideas presented by a master is perhaps the best way to be introduced to the modern practice of number theory.Ultimately, with respect to difficulty it doesn't matter who or what you read to learn number theory.The subject will always be daunting to all but the most talented students, but any effort you put into reading this book is well worth it.

In summary, any aspiring number theorist (or person interested in modern number theory) needs to read this book.It can serve as an introductory text (I read it as such), but it is also an excellent reference, both for the mathematical material inside as well as the outstanding mathematical exposition.It's rare nowadays to see a mathematician of Serre's caliber also excel as an expository writer/teacher, so this book is a true gem.

5-0 out of 5 stars not to be confused with an "arithmetic" book
In french, "arithmétique" means elementary study of rational numbers... You will not learn how to add or substract rational numbers here. An easy book to begin with this kind of maths is Andrew's: number theory (from Dover): well explained with a lot of examples...I guess that the author meant something like: "arithmetic of quadratic forms..." The truth is contained in the book's introduction: the text is made of lessons given to second-year "normaliens" from the "rue d'Ulm": those were (and still are) among the most gifted mathematic students in France; (post-graduate level...) therefore any reader without a really sharp mind and a very good level of knowledge in algebra will hardly grasp anything from the book which is really demanding; in the first ten pages, you will find a study of finite fields aimed at proving the celebrated "law of quadratic reciprocity"; it is already well beyond classical elementary arithmetic as it was taught in "classe terminale" thirty years ago and furthermore nowdays.
Then it tackles with p-adic fields, entire quadratic forms and then Dirichlet Theorem on primes in arithmetic sequences in a mere 20 pages (to set things up, this theorem is not proven in Hardy an Wright's: "introduction to the theory of numbers" because it is not an elementary theorem as mathematicians go since any proof of it requires use of advanced complex variable methods...) and at last modular forms; as you can expect, everything in the book is connected; so it looks like (it is...) an impressive piece of mathematics; it is a daunting but not impossible task to go through the whole book; let say that such hard work is rewarding and the chapter on modular forms is really a fascinating one ( and a first step towards Wiles' proof of Fermat's last theorem albeit so many more steps have to be climbed to achieve that precise aim...) ; moreover, the chapters using "analytic methods" can be read independantly; "un tour de force".

5-0 out of 5 stars Breathtaking
Serre's work could best be summarized in one word - Elegance.
The book comprises of two distinct parts.
The first one is the 'algebraic' part. Serre's goal in this section is to give a complete classification of the quadratic forms over the rationals. As preliminaries to reaching this goal, he introduces the reader to quadratic reciprocity, p-adic fields and the Hilbert Symbol. After these three, he spends the next chapter detailing the properties of quadratic forms over Q and Q_p (the p-adic field). The reason to work over Q_p is the Hasse-Minkowski Theorem (which says that if you have a quadratic form, it has solutions in Q if and only if it has solutions in Q_p). Using Hensels Lemma, checking for solutions in Q_p is (almost) as easy as checking for solutions in Z/pZ. After doing that, he spends yet another chapter talking about the quadratic forms over the integers. (Note: the classification goal is already achieved in previous chapter).
The second half of the book is the 'analytic' one. The first chapter in this section gives a complete proof of Dirichlet's theorem while the second one studies the properties of modular forms (these are good!)
Due to the extreme elegance, the book is sometimes hard to read. This might sound like a paradox, but it's not and I'll explain why. The book takes some effort to read because it's terse and it often takes a while to figure out why something is 'obvious'. However, once you see it all, you'll realize that a great mind was guiding you through the pursuit. The choice of topics is just right to achieve the goals that the author sets out for himself. Also, I'd rather think for myself and read a smaller book than be given a huge fat tome where the author details his own thought process.
This book was my first foray into number theory and I absolutely enjoyed it. If you're considering reading it, I wish you joy in your pursuits.

5-0 out of 5 stars Very Demanding
The book is divided into two parts -- algebraic and analytic. I've only worked through the analytic part. Anything by Serre is worth its weight in gold and this book is no exception; everything Serre covers is of the utmost importance. But Serre's style is extremely condensed and spare, and he makes no concessions to the reader in terms of motivation or examples. I can't digest more than half a page of Serre a day; however if one wants to understand the structure of a theory, Serre is ideal.

I worked through "A Course in Arithmetic" over a decade back. As I recall I covered Riemann's zeta function and the Prime Number Theorem, the proof of Dirichlet's theorem on primes in arithmetical progressions using group characters in the context of arithmetical functions, and some of the basic theory of modular functions. All of this material is also covered in Apostol's two books on analytic number theory ("Introduction to Analytic Number Theory", and "Dirichlet Series and Modular Functions in Number Theory"); Apostol goes further than Serre in the analytic part -- which is only to be expected since he is devoting two whole texts to the subject. ... Read more

16. Ray's New Primary Arithmetic For Young Learners (1877)
by Joseph Ray
 Hardcover: 100 Pages (2010-09-10)
list price: US$27.16 -- used & new: US$25.65
(price subject to change: see help)
Asin: 1169069665
Average Customer Review: 4.0 out of 5 stars
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Product Description
This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

Customer Reviews (1)

4-0 out of 5 stars Great Price.Great Curriculum.
I purchased this book (Primary) and the parent guide for my 1st grade daughter to use as our homeschool curriculum for math.It is much different than the typical worksheet curriculum.Having used McGruffy, Math U See and K12 curriculum with my 4th grader over the years, Ray's required a complete paradigm shift for me to use effectively.Don't tell any one, but I didn't touch it with my daughter for the first month because I was intimated without my workbook safety net.

There are no workbooks, work sheets or standard manipulatives (Lord knows I already have more than enough of those from other programs).Rather than teach a concept and shove a worksheet it requires a little more effort.Ray's focuses heavily on practical application (word problems) and mental math which my daughter is very good at.I will teach her the concept sometimes using manipulatives - sometimes not then she works the problem in her head usually but will sometimes use the manipulates. Sometimes I'll have her write the answer in a spiral but typically not.When you think about it, it makes much more sense to teach this way when possible.When we're out in the real world, no one hands us a worksheet to figure out if we're going to have enough cash to pay for all the stuff we're buying at the grocery, right.

My father is a wiz at mental math and I think it's because he was taught with a similar approach.We are finishing up with subtraction and the next step is multiplication - yes - multiplication!It is a logical progression with lots of oral drilling.The other wonderful note about this curriculum is the price.You can buy the entire set through year 8 for less than one year of most other curriculums.That's a deal!

My only beef is with the illustrations.A very few of the lessons are based on looking at an illustration and making calculations - but the illustrations are very bad quality to the point that I skip those entirely.It is bothersome but would in no way deter me from recommending.

The only caveat to recommending is to consider your learner.While my daughter is thriving and learning skills not typically learned until the end of 3rd grade - it is not a curriculum I think I would use with my son who is doing quite well with Math U See.Completely different learners need entirely different approach.If you have a child inclined to mental processing, and you're okay with shifting from the worksheet mentality - don't hesitate.
... Read more

17. Introduction to Arithmetic for Digital Systems Designers
by Shlomo Waser, Michael J. Flynn
Hardcover: 336 Pages (1995-06-08)
list price: US$54.00
Isbn: 0030605717
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18. How to Solve Word Problems inArithmetic
by Phyllis Pullman
Paperback: 150 Pages (2000-12-13)
list price: US$9.95 -- used & new: US$99.13
(price subject to change: see help)
Asin: 0071362711
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Nothing strikes fear into the hearts of math students more than word problems. In How to Solve Word Problems in Arithmetic, noted math teacher Phyllis Pullman defangs the dreaded word problem for 5th through 8th grade-level arithmetic students by emphasizing the mechanics and grammar of problem-solving, and focusing on problems involving arithmetic skills, area, percent, basic geometry, measurement, and statistics. ... Read more

19. Arithmetic 1 Work-text Teacher Edition (Traditional Arithmetic Series)
by A Beka Book
Spiral-bound: Pages (2009)

Asin: B003YCGJYM
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Using delightful themes and full-color illustrations, Arithmetic 1 presents concepts in an orderly manner, building on prior learning and including consistent year-long review. Concepts include counting, writing and reading numbers, place value, addition and subtraction, money, graphs, measurement, time, temperature, and fractions. Applications to real world situations and daily Thinking Caps stretch students' thinking ability. The 342-page workbook is perforated and includes classwork and seatwork pages for every day based areound themes of the zoo, ocean, farm, and springtime. ... Read more

20. Arithmetic we need
by Guy T Buswell
 Hardcover: Pages (1959)

Asin: B0007FSDA2
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