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Just an absolutely outstanding set of problems ranging from introductory to Olympiad level problems to challenge all types of kids looking to learn from their books.We ran across a really nice challenge problem in the chapter about congruence today that made lots great math conversation.
That said, they are intended for dedicated students who will work hard and learn relatively quickly.
They do not have many routine practice problems, and instead have mainly more challenging problems which force students to think hard and explore the concepts more deeply.
Ao PS Track: The Ao PS track is built for the exceptional mathematics student who is both capable and interested in exploring and executing the Mathematics curriculum from the perspective of depth.
The Ao PS approach favors very, very deep analytical approaches to topics in Mathematics, sometimes moving more slowly than Honors because of the depth of analysis expected from the student.
To get the most out of an Ao PS book (or pretty much any other math book), do the problems. Do the exercises at the end of each section, and the review and challenge problems at the end of each chapter.
There are a lot of problems, and some of them are quite difficult, so you should not expect to be able to solve every single one of them.
A weaker student may prefer a more traditional textbook, to use either instead of or in conjunction with an Ao PS book.
Ao PS books also tend to be less useful as definitive references than traditional textbooks: you will find fewer well-organized statements of important facts and identities and theorems in them (though I think this is more relevant to the more advanced books than it is to Prealgebra). Spend a good chunk of time trying all the problems at the beginning of each section, before you move on to read their solutions.
Both the problem itself and the more advanced theorem from “Geometry Revisited” that it hinted at were super fun to talk through with my son.
Here’s us doing a quick review of the problem itself tonight: The Art of Problem Solving problems are so great to begin with and it is sort of doubly fun to be able to use them as stepping stones to show some more advanced geometry.