Art of Problem Solving Introduction to Number Theory Set

Art of Problem Solving Introduction to Number Theory Set


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Item #: INTNMT
Grades: 7-10

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This is an outstanding math program for the math-gifted student. It is rigorous and oriented to the independent problem-solver. The texts are based on the premise that students learn math best by solving problems - lots of problems - and preferably difficult problems that they don't already know how to solve. Most sections, therefore, begin by presenting problems and letting students intuit solutions BEFORE explaining ways to solve them. Even if they find ways to answer the problems, they should read the rest of the section to see if their answer is correct and if theirs is the best or most efficient way to solve that type of problem. Textual instruction, then, is given in the context of these problems, explaining how to best approach and solve them.

Throughout the text there are also special, blue-shaded boxes highlighting key concepts, important things to retain (like formulas), warnings for potential problem-solving pitfalls, side notes, and bogus solutions (these demonstrate misapplications). There are exercises at the end of most sections to see if the student can apply what's been learned. Review problems at the end of each chapter test understanding for that chapter. If a student has trouble with these, he should go back and re-read the chapter. Each chapter ends with a set of Challenge Problems that go beyond the learned material. Successful completion of these sets demonstrates a high degree of mastery.

A unique feature in this series is the hints section at the back of the book. These are intended to give a little help to selected problems, usually the very difficult ones (marked with stars). In this way, students can get a little push in the right direction, but still have to figure out the solution for themselves. The solution manuals do contain complete solutions and explanations to all the exercises, review problems and challenge problems. It is best for students not to access these until they have made several attempts to solve the problems first. I particularly like one of the motivating boxes in the text that coaches, "If at first you don't know how to solve a problem, don't just stare at it. Experiment!". That pretty much sums up the philosophy of the course, encouraging children to take chances, become aggressive problem solvers, and attack problems with confidence. I wonder how far some children would go if they were encouraged this way instead of being spoon fed?

Though this course is used in classroom settings, the texts are student-directed, making them perfect for the independent learner or homeschooler. Students should start the introductory sequence with the Prealgebra book. Afterwards, begin the Introduction to Algebra. Students will be prepared for both the Introduction to Counting and Probability and Introduction to Number Theory courses after completing the first 11 chapters of Algebra. It won't matter whether they do these along with Algebra, put aside Algebra and complete the other two or finish Algebra first and then do them. All of them should be completed prior to the Introduction to Geometry book. If you are coming into this course from another curriculum, you will probably want to take a placement test to decide where to enter this program. Even if your student has finished Algebra 2 elsewhere, you will want to make sure that all of the material from this series has been covered before continuing on to the Intermediate series.

Taken together, these constitute a complete curriculum for outstanding math students in grades 6-10 and one that prepares them for competitions such as MATHCOUNTS and the American Mathematics Competitions. The material is challenging and in-depth; this is not a course for the mathematically faint of heart. If your child loves math, is genuinely math-gifted, or is interested in participating in math competitions, you definitely need to give this one serious consideration.

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Why did you choose this?
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For my children to study math - supplemenation materials
Usha A on Apr 30, 2021
To learn about number theory
Kavita S. on Dec 8, 2020
For my children to study math - supplemenation materials
Usha A on Apr 30, 2021
attend math count
qing z on Dec 25, 2020
To learn about number theory
Kavita S. on Dec 8, 2020
Excellent curriculum that makes think
Jim G on Feb 21, 2020
My kid love math.
kabita n on Jan 14, 2019
for my kids
kai z on Aug 16, 2017
Extension of algebra and geometry for advanced student.
Tina F on Feb 24, 2017
My son has completed Algebra I, but as a rising 7th grader, I wanted him to have a gap before moving on to the logic and proofs of Geometry. Art of Problem Solving is the only publisher that is producing math content which is truly rigorous and thought-provoking, most of the rest is over-simplified.
Karen S on Jun 25, 2016
good book
Sandra T on Oct 15, 2015
attend math count
qing z on Dec 25, 2020
Excellent curriculum that makes think
Jim G on Feb 21, 2020
5.0 / 5.0
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Rated 5 out of 5
Curious about numbers?
My sons have used the Art of Problem Solving curricula for part of their middle school math requirements and enjoyed the curricula. This was our first purchase of a book that is not in the usual sequence of math taught in American schools (PreAlgebra -> Algebra -> Geometry) My oldest son (age 14) enjoys thinking about math problems and ideas and requested this book to learn more about Number Theory. This Art of Problem Solving book is substantially shorter than the books we have purchased previously. My son is working through this book in his free time (he is currently taking Algebra II/Trig for school) He says it is a fun way to think about numbers and to learn more. He would recommend it to anyone who wants to learn about Number Theory.
January 12, 2018
over 3 years ago

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