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Prealgebra, by Richard Rusczyk, David Patrick, Ravi Boppana
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Prealgebra prepares students for the rigors of algebra, and also teaches students problem-solving techniques to prepare them for prestigious middle school math contests such as MATHCOUNTS, MOEMS, and the AMC 8. Topics covered in the book include the properties of arithmetic, exponents, primes and divisors, fractions, equations and inequalities, decimals, ratios and proportions, unit conversions and rates, percents, square roots, basic geometry (angles, perimeter, area, triangles, and quadrilaterals), statistics, counting and probability, and more! The text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, giving the student a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which algebraic techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains well over 1000 problems. The solutions manual (sold separately) contains full solutions to all of the problems, not just answers. This book can serve as a complete Prealgebra course. This text is supplemented by free videos and a free learning system at the publisher's website.
- Sales Rank: #16734 in Books
- Published on: 2011-08-10
- Binding: Paperback
- 608 pages
About the Author
Richard Rusczyk is the founder of Art of Problem Solving. He is co-author of the Art of Problem Solving, Volumes 1 and 2 and Intermediate Algebra, and author of Introduction to Algebra, Introduction to Geometry, and Precalculus. He was a national MATHCOUNTS participant in 1985, a three-time participant in the Math Olympiad Summer Program, and a USA Mathematical Olympiad winner in 1989. He is also the co-founder of the Mandelbrot Competition. Mr. Rusczyk is a graduate of Princeton University. David Patrick is an instructor and curriculum developer at Art of Problem Solving. He is the author of Art of Problem Solvings Introduction to Counting & Probability, Intermediate Counting & Probability, and Calculus textbooks. He had the sole perfect score in North America on the 1988 American High School Mathematics Examination, was a USA Mathematical Olympiad winner, and was a top-10 finisher on the William Lowell Putnam Mathematics Competition. Dr. Patrick is a graduate of Carnegie Mellon University and has a Ph.D. in Mathematics from MIT. He taught mathematics at the University of Washington before joining Art of Problem Solving in 2004. Ravi Boppana is the Director of Mathematics at Advantage Testing, as well as the co-founder and co-director of the national Math Prize for Girls competition, sponsored by the Advantage Testing Foundation. He was 27th in the country on the William Lowell Putnam Mathematics Competition. Dr. Boppana received a Ph.D. in Computer Science from MIT at the age of 22. He was a tenured professor at NYU, where he received the Presidential Young Investigator Award for Excellence in Research and the Golden Dozen Award for Excellence in Teaching. His daughter Meena finished second in New York State at MATHCOUNTS and was a USA Math Olympiad qualifier.
Most helpful customer reviews
84 of 86 people found the following review helpful.
Excellent, excellent math instruction for the Mathematically inclined youngster
By Amazon Customer
First, some context, so you can decide if my opinion is useful to you. I'm a working electrical engineer who always enjoyed math as a student -- I almost majored in Applied Math in college; my son is a bright kid going into 5th grade who gets bored easily in math class and needs extra challenge. My goal with this book was not just to teach him faster than the school is teaching (although it is that, too,) but to teach him math to a greater *depth.* I wanted to make sure he learns *why* stuff works, and not just blindly memorize formulas for the test; I wanted to help him develop his problem-solving and critical thinking skills. In my view, Math instruction is not just about teaching Math, it's about teaching how to really *think.*
This book has met and exceeded all my expectations, and I cannot recommend it highly enough: the philosophy behind the 'Art of Problem Solving' -- the folks who wrote this book and others in the series, is that you learn more when you wrestle with ideas and try to figure them out for yourself than having them spoon-fed to you. So their approach is to begin each unit with problems for the student to sit down and try to solve for herself, using what she already knows. The problems help lead the student to discover (for example,) *why* the product of the square of two numbers is equal to the square of their product.
After attempting those problems, the student reads on and compares her solution with the one in the book, and a lot of the learning happens from reading and really *understanding* how and why the authors solved the problems the way they did. Along the way, the text will 'lecture' a bit, and point out important rules the students have 'proven', as well as introduce any unfamiliar terms needed for the next section.
Next, there are exercises at the end of each unit, for the student to practice what has been learned. These are NOT 'worksheet'-style problems like in elementary texts, where you have pages of basically the same problem over and over. These exercises seem to be hand-crafted to guide the student from simpler to harder problems, step by step, and they do a great job. Finally, at the end of each chapter (there are 5 or so units per chapter) there are whole-chapter review exercises of increasing difficulty, followed by 'challenge problems'.
The main difference between 'exercises' and 'challenge problems' is that it is expected that most students will be able to get most for the 'exercises' correctly by working through the chapter and working through the other examples. The challenge problems require more 'thinking outside the box' and some are really very challenging, even for folks like me, who survived differential equations in college. NOBODY should expect to figure them all out, certainly not without a LOT of effort, but everybody can learn from *trying* to solve them. Nobody *ever* asked me questions like this in my middle school classes, even in the honors classes, and yet my son, by trying to solve them (and he certainly can't solve all of them,) is gaining a *much* deeper understanding of the material than I ever had at his age. (To be honest, I've had fun wrestling with the harder ones myself, after he goes to bed. But I'm weird like that.)
IMPORTANT NOTES:
(1) If you are using this book as a private text -- as opposed to a middle-school classroom with an instructor -- YOU ABSOLUTELY NEED THE SOLUTIONS MANUAL; it's not just an answer key, it actually details *how* to solve every single problem in this book. Without it, there's no way for the student to check his work on the exercises, and they won't learn nearly as much; it's published as a separate volume mostly to let it be used as a classrom text, but most buyers should think of the two books as one indivisible item.
(2) THERE ARE OTHER, FREE SUPPLEMENTAL MATERIALS AVAILABLE -- the authors have a web site, artofproblemsolving.com, which also hosts literally *hundreds* of short youtube videos, many aligned to specific topics in the textbooks, and there's a pretty cool (currently free) tool called 'Alcumus' that challenges you with math problems of increasing difficulty in a quiz-game format. [solutions are shown after you answer, so you can learn even from the problem you don't solve.] They also host free online math competitions [quiz style] and paid online classes aligned with the text, but I can't comment on those because we haven't tried them - yet.
UPDATE: we tried the online PreAlgebra I class (covers the first half of the book) -- it is an excellent class, but be aware that it is generally aimed at kids who 'get math' and like it, and who are mature and disciplined enough to work hard at difficult things until they 'get it' -- if your kid requires a lot of hand-holding to get him to do the work, you will hate this class, but if he/she likes math and enjoys a challenge, they will learn a LOT. The format is more like a college class than a typical middle-school classroom; there's a through syllabus given out before the class starts, there are assigned reading and problems you are expected to solve, preferably before the weekly class meeting, and the content moves *fast* [generally one or at most two weeks per topic.] If your kid takes this seriously, I think you will get your money's worth out of the classes and then some, but it requires hard work and dedication.
(3) THIS BOOK IS NOT FOR EVERYBODY -- although I firmly believe this philosophy of learning through solving problems is a *better* way to teach math than what most kids get in school, the level and pacing in this textbook seems clearly and deliberately aimed at the mathematically inclined or gifted reader.
(3a) Kids who don't "get" math or don't like it will, in my opinion, be enormously frustrated by this book, and kids whose parents don't "get" math may be unable to help them; of course that's true for any textbook; you have to know the subject, at least a little, to help your kids with their homework, right? :^)
(3b) [This caveat is aimed at a small group of people with truly exceptional kids - the 99.9+ %-ers] Kids who are very bright sometimes get freaked out when they have to struggle, if they can't easily get 100% scores on everything without really trying. Your child should *expect* to struggle with parts of this book, and come out knowing more at the end, but I don't think *anybody* is going to breeze through this book and get all the challenge problems correct. I believe it is critical to expose kids like this to 'insolvable' challenges so they can *learn* how to struggle with, and master difficult material. But some young, exceptionally gifted kids who are homeschooling might get overly frustrated and quit if they lack the emotional maturity to deal with the setbacks and the challenges productively.
45 of 49 people found the following review helpful.
It don't get no better.
By Tumblemark
I used to think that Rusczyk's *Algebra* was the best math text I had ever read. That was until *Prealgebra* came out last summer. Wow! It's brilliant!
*Algebra* was written just right for a (very sharp) high school mind. *Prealgebra* is perfectly dialed in to the (better be very sharp) middle school mind. The book is very challenging. It teaches with the most scientifically-proven effective technique there is: worked examples. There's almost nothing else. No photos, no cartoons, no distractions of any kind (cognitive load theory explains that these reduce learning). Just very straightforward working through of examples and a few bullet points. There are actually very few problems, and certainly not page after page of work sheets. And the problems themselves (most are word problems) are mind stretching. Then you move on.
I doubt if this book could be a text for a middle school class; the teaching would be too challenging (you definitely want to get the Solutions Manual, if only to see how the authors solve the problems). But for a kid who finds math boring, this will present all the challenge and engagement you could ask for. I suspect that it will take more than a school year to go through it, because it is so thorough. I use it with a small group of PG tweens (IQ > 145) and it is perfect for them after finishing Singapore Math 6A/B. They find it challenging and rewarding, insightful, engaging, and doesn't talk down to them. They know it's hard, but it's fun hard, and it's never boring.
I should mention: there are free step-by-step videos on the Art of Problem Solving dot com web site where Rusczyk teaches each point. You can go back and replay parts, stop the video, etc. I don't use them, because I find interacting with each of my students personally and addressing their issues individually works better. (My daughter snidely remarked on one: "He's doing it the hard way.") But I can certainly see how a parent would be happy to turn their math whiz over to the master himself. Find him on YouTube too.
This book will build a solid foundation for discrete math and combinatorics, sadly lacking in math education these days. I have but a single criticism: many times a problem could be solved using a pair of simultaneous linear equations but instead a more convoluted method is suggested. I suppose there's a reason for that. I'll have to ask Rusczyk the next time I see him -- after thanking him profusely for this fantastic text.
0 of 0 people found the following review helpful.
good book.
By Xin Zhang
It arrived in time, good book.
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