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I'm wondering if there are some good book/textbooks that were designed with algebraic logic in mind (ie. building intuition rather than rote learning).

As an example of what I mean, consider this question I found on Khan Academy: Given that $c<d<b$, is $\frac{b}{b+c+d}$ greater than, less than, or equal to $1/3$? Solving this problem myself really helped with my math intuition (sometimes I'm appalled with how bad my math intuition is) and I'd love to work through more things like this.

Edit: I have read How to Solve It and I'm looking for something more textbook-y. Reason being that I'm a tutor and I would love to use it with my students as well.

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Perhaps you can review and peruse the list I included in this answer math.stackexchange.com/questions/187340/… –  Amzoti Dec 20 '13 at 1:50
    
Wow, I'll definitely check that out. Thanks! –  dserver Dec 20 '13 at 1:55

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@Amzoti has given you a great list, but another book I think you should consider, especially given that you mentioned How to Solve It, is "Mathematical Discovery" by Polya. This book comes packaged various ways, either two separate volumes or the two volumes combined into one. I also see on Amazon that there is a new edition (2009) which lists Sam Sloan as a co-author, but I haven't seen that one. From the back cover of my copy: "Problem solving strategies and principles are taken from the standard precalculus curriculum of arithmetic, algebra, and geometry, plus combinatorics."

On a much more advanced level, there are also the two volumes of "Problems and Theorems in Analysis" by Polya and Szego, but that's way too advanced for high school, if that's what you are tutoring.

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Cool beans, I'll check that out. Thanks! –  dserver Dec 20 '13 at 18:58

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