I often get asked this question in different ways -
"What book or resource do you recommend for my middle schooler?"
"What is your most favourite resource?"
"My kid loves math and is very good at it. Can you recommend something challenging?"
So here's my answer to all these. My favourite book is Pre-Algebra from Art of Problem Solving by Richard Rusczyk, David Patrick, Ravi Boppana. And yes I've recommended this book to all my middle schoolers who love math and who wants to get trained for competitions like AMC8 or Math Counts. When I got my hands on this book, I just loved it. It mirrored my beliefs about the way math has to be taught.
Why do I love this so much?
I love the way the book makes you think. It's not plain concepts like you would find in any school text book. Every single example problem given in the book is a step towards learning something new. This book requires a change in mindset. You have to go from "here is the method and here is a problem and use this method to solve it" to "here is a problem - now generate ideas to solve it". It teaches you to solve problems that you do not know to solve.
In-fact if you want a single resource to coach your child for middle school math competitions, this is it. If your child solves these problems then AMC8 should be easy.
This book explains they why behind all the concepts. So most of us know the divisibility rule for 3. If the sum of the digits is divisible by 3, then the number is divisible by 3. But do you know why it works only for 3? Does it work for any other number? Do you know how they got the divisibility rules for most of the numbers? The book explains it in detail. You'll see that everything has a logical explanation and you won't have to memorise a bunch of formulae. You will truly start loving math.
The way it goes in the book is - a concept is explained, then a series of questions or problems are asked that makes you think about the topic. The solutions are provided after all the questions. At the end of each subchapter there are exercise problems. At the end of each chapter there are challenge problems that can be considered "interesting" even by seasoned problem solvers. (I never use the word "tough problem" with my kids. I always call them "interesting". My kids still laugh about that)
Even though this book is called Pre-Algebra, this is more like a fore runner for all the middle school topics. Exponents, geometry, probability are all discussed to a good depth here. You can expect to solve questions like these "A pair of 8-sided dice has the sides of each die numbered 1 through 8. Each side has the same probability of landing face up. What is the probability that the product of the two numbers on the sides that land face-up is greater than 36?" from probability.
Along with this book you also get access to an Online forum where the concepts and problems are discussed. So you get to be a part of a great online community that loves math and you can let loose all your geekiness here :)
If you want to get a copy of this book you can get it from their AOPS website or Amazon
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As you know I'm an Online Math Tutor. I train kids for all Elementary and Middle School Math Competitions. To know more about me and how I work click here.
I am an Amazon affiliate and I get a small percentage of the books cost if you order it through Amazon. However, I only recommend resources that I've personally used and loved. I've recommended this book to all my students long before I became an affiliate.