Introduction to Number Theory Text (AOPS)

SKU
007602
ISBN
9781934124123
Grade 7-10
Neutral
Low Teacher Involvement
Multi-Sensory
No other materials needed
Sequential
Teaching Method
Traditional
Teacher-centered curriculum commonly used in classrooms that may include a text, teacher manual, tests, etc.
Charlotte Mason
A methodology based on the work of a 19th century educator who maintained that children learn best from literature (Living Books), not textbooks.
Classical
A methodology based on the Latin Trivium (three stages of learning), including the grammar stage (memorization and facts), logic stage (critical thinking), and rhetoric stage (developing/defending ideas).
Unit Study
A thematic or topical approach centered around one topic that integrates multiple subject areas.
Montessori (Discovery)
A methodology based on the work of a 20th century educator that emphasizes student and sensory-driven discovery learning and real-life applications.
Other
Other methodologies
Religious Content
Secular
Contains content contrary to common Christian beliefs (i.e. evolution).
Neutral
Avoids religious or theoretical topics or presents multiple viewpoints without preference.
Christian/Religious
Faith-based or including instructional religious content.
Learning Modality
Auditory
Learns through listening, talking out loud or reading out loud.
Visual
Learns through seeing, prefers written instructions and visual materials.
Kinesthetic/Tactile (Hands-On)
Learns through moving, doing and touching.
Multi-Sensory
Curriculum that employ a variety of activities/components.
Presentation
Sequential
Curriculum progresses through well-defined learning objectives. Emphasizes mastery before moving to the next topic.
Spiral
Topics and concepts are repeated from level to level, adding more depth at each pass and connecting with review.
Conceptual/Topical
Focus is on the “why,” often with a unifying concept as well as specific skills; coverage may be broader.
Teacher Involvement
Low Teacher Involvement
Student-led materials; parent acts as a facilitator.
Medium Teacher Involvement
A mix of teacher-led time and independent student work.
High Teacher Involvement
Teacher-led lessons; may utilize discussions, hands-on activities and working together.
Additional Materials Required
No other materials needed
Everything you need is included.
Other Materials Required
There are additional required resources that are a separate purchase.
Other Materials Optional
There are additional resources mentioned or recommended but are not absolutely necessary.
Consumable
Consumable
Designed to be written in; not reusable.
Non-Consumable
Not designed to be written in; reusable.
Our Price
$49.00
Description

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. complete solutions and explanations to all the exercises, review problems and challenge problems are found in the separate solution manual (007601).

Publisher's Description of Introduction to Number Theory Text (AOPS)

A thorough introduction for students in grades 7-10 to topics in number theory such as primes & composites, multiples & divisors, prime factorization and its uses, base numbers, modular arithmetic, divisibility rules, linear congruences, how to develop number sense, and more.

Learn the fundamentals of number theory from former MATHCOUNTS, AHSME, and AIME perfect scorer Mathew Crawford. Topics covered in the book include primes & composites, multiples & divisors, prime factorization and its uses, base numbers, modular arithmetic, divisibility rules, linear congruences, how to develop number sense, and much more.

The text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, so the student has a chance to solve them without help before proceeding. The text then includes motivated solutions to these problems, through which concepts and curriculum of number theory are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains hundreds of problems. The solutions manual contains full solutions to nearly every problem, not just the answers.

This book is ideal for students who have mastered basic algebra, such as solving linear equations. Middle school students preparing for MATHCOUNTS, high school students preparing for the AMC, and other students seeking to master the fundamentals of number theory will find this book an instrumental part of their mathematics libraries.

Paperback. Text: 336 pages. Solutions: 144 pages.

Category Description for Art Of Problem Solving
This is an outstanding math program for the math-gifted student. It is rigorous and oriented to the independent problem-solver. The Texts are student-directed, making them perfect for the independent learner or homeschooler. Based on the premise that students learn math best by solving problems – and preferably problems that they don’t already know how to solve - most sections begin by presenting problems and letting students intuit solutions before explaining ways to solve them.  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 are found at the end of each chapter. The Solution Manuals 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. One motivating box in the text 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 become aggressive problem solvers. Students should start the introductory sequence with the Prealgebra book and continue through the series. 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. The introduction and intermediate series together constitute a complete curriculum for outstanding math students in grades 6-12.

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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More Information
Product Format:Softcover Book
Brand:Art of Problem Solving
Author:Mathew Crawford
Grades:7-10
ISBN:9781934124123
Length in Inches:11
Width in Inches:8.4375
Height in Inches:0.5
Weight in Pounds:1.75
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