The Art of Problem Solving Prealgebra
by Richard Rusczyk Author
(From Amazon): Prealgebra prepares students for the rigors of algebra, and also teaches students problem-solving techniques to prepare them for prestigious middle school math contests such as MATHCOUNTS, MOEMS, and the AMC 8. Topics covered in the book include the properties of arithmetic, exponents, primes and divisors, fractions, equations and inequalities, decimals, ratios and proportions, unit conversions and rates, percents, square roots, basic geometry (angles, perimeter, area, triangles, and quadrilaterals), statistics, counting and probability, and more! The text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, giving the student a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which algebraic techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains well over 1000 problems. The solutions manual (sold separately) contains full solutions to all of the problems, not just answers. This book can serve as a complete Prealgebra course. This text is supplemented by free videos and a free learning system at the publisher's website.
Additional Details
- Resource Type
- Book
- ISBN
- 9781934124215
- Print Status
- In Print
- Chapters
- 83
- Pages
- 608
- Suggested Grades
- 7th - 8th
- Publisher
- AoPS Incorporated
- Copyright
- 2011
Chapters
- 1.1 Why Start with Arithmetic
- 1.2 Addition
- 1.3 Multiplication
- 1.4 Negation
- 1.5 Subtraction
- 1.6 Reciprocals
- 1.7 Division
- 1.8 Summary
- 2.1 Squares
- 2.2 Higher Exponents
- 2.3 Zero as an Exponent
- 2.4 Negative Exponents
- 2.5 Summary
- 3.1 Multiples
- 3.2 Divisibility Tests
- 3.3 Prime Numbers
- 3.4 Prime Factorization
- 3.5 Least Common Multiple
- 3.6 Divisors
- 3.7 Greatest Common Divisor
- 3.8 Summary
- 4.1 What is a Fraction?
- 4.2 Multiplying Fractions
- 4.3 Dividing by a Fraction
- 4.4 Raising Fractions to Powers
- 4.5 Simplest Form of a Fraction
- 4.6 Comparing Fractions
- 4.7 Adding and Subtracting Fractions
- 4.8 Mixed Numbers
- 4.9 Summary
- 5.1 Expressions
- 5.2 Solving Linear Equations I
- 5.3 Solving Linear Equations II
- 5.4 Word Problems
- 5.5 Inequalities
- 5.6 Summary
- 6.1 Arithmetic with Decimals
- 6.2 Rounding
- 6.3 Decimals and Fractions
- 6.4 Repeating Decimals
- 6.5 Summary
- 7.1 What is a Ratio?
- 7.2 Multi-way Ratios
- 7.3 Proportions
- 7.4 Conversions
- 7.5 Speed
- 7.6 Other Rates
- 7.7 Summary
- 8.1 What is a Percent?
- 8.2 Word Problems
- 8.3 Percent Increase and Decrease
- 8.4 Summary
- 9.1 From Squares to Square Roots
- 9.2 Square Roots of Non-square Integers
- 9.3 Arithmetic with Square Roots
- 9.4 Summary
- 10.1 Measuring Angles
- 10.2 Parallel Lines
- 10.3 Angles in Polygons
- 10.4 Summary
- 11.1 Measuring Segments
- 11.2 Area
- 11.3 Circles
- 11.4 Summary
- 12.1 The Pythagorean Theorem
- 12.2 Some Special Triangles
- 12.3 Types of Quadrilaterals
- 12.4 Summary
- 13.1 Basic Statistics
- 13.2 Limits of Basic Statistics
- 13.3 Tables, Graphs, and Charts
- 13.4 Summary
- 14.1 Counting with Addition and Subtraction
- 14.2 The Multiplication Principle
- 14.3 Casework
- 14.4 Counting Pairs
- 14.5 Probability
- 14.6 Summary
- 15.1 Find a Pattern
- 15.2 Make a List
- 15.3 Draw a Picture
- 15.4 Work Backwards
- 15.5 Summary
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