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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 contains full solutions to all of the problems, not just answers. This book can serve as a complete Prealgebra course.

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Additional Details

Resource Type: Book
ISBN: 9781934124215
Print Status: In Print
Lessons: 83
Pages: 608
Publisher: AoPS Incorporated
Copyright: 2011

Lessons

1 1.1 Why Start with Arithmetic? (Chapter 1: Properties of Arithmetic)
2 1.2 Addition (Chapter 1: Properties of Arithmetic)
3 1.3 Multiplication (Chapter 1: Properties of Arithmetic)
4 1.4 Negation (Chapter 1: Properties of Arithmetic)
5 1.5 Subtraction (Chapter 1: Properties of Arithmetic)
6 1.6 Reciprocals (Chapter 1: Properties of Arithmetic)
7 1.7 Division (Chapter 1: Properties of Arithmetic)
8 1.8 Summary (Chapter 1: Properties of Arithmetic)
9 2.1 Squares (Chapter 2: Exponents)
10 2.2 Higher Exponents (Chapter 2: Exponents)
11 2.3 Zero as an Exponent (Chapter 2: Exponents)
12 2.4 Negative Exponents (Chapter 2: Exponents)
13 2.5 Summary (Chapter 2: Exponents)
14 3.1 Multiples (Chapter 3: Number Theory)
15 3.2 Divisibility Tests (Chapter 3: Number Theory)
16 3.3 Prime Numbers (Chapter 3: Number Theory)
17 3.4 Prime Factorization (Chapter 3: Number Theory)
18 3.5 Least Common Multiple (Chapter 3: Number Theory)
19 3.6 Divisors (Chapter 3: Number Theory)
20 3.7 Greatest Common Divisor (Chapter 3: Number Theory)
21 3.8 Summary (Chapter 3: Number Theory)
22 4.1 What is a Fraction? (Chapter 4: Fractions)
23 4.2 Multiplying Fractions (Chapter 4: Fractions)
24 4.3 Dividing by a Fraction (Chapter 4: Fractions)
25 4.4 Raising Fractions to Powers (Chapter 4: Fractions)
26 4.5 Simplest Form of a Fraction (Chapter 4: Fractions)
27 4.6 Comparing Fractions (Chapter 4: Fractions)
28 4.7 Adding and Subracting Fractions (Chapter 4: Fractions)
29 4.8 Mixed Numbers (Chapter 4: Fractions)
30 4.9 Summary (Chapter 4: Fractions)
31 5.1 Expressions (Chapter 5: Equations and Inequalities)
32 5.2 Solving Linear Equations I (Chapter 5: Equations and Inequalities)
33 5.3 Solving Linear Equations II (Chapter 5: Equations and Inequalities)
34 5.4 Word Problems (Chapter 5: Equations and Inequalities)
35 5.5 Inequalities (Chapter 5: Equations and Inequalities)
36 5.6 Summary (Chapter 5: Equations and Inequalities)
37 6.1 Arithmetic with Decimals (Chapter 6: Decimals)
38 6.2 Rounding (Chapter 6: Decimals)
39 6.3 Decimals and Fractions (Chapter 6: Decimals)
40 6.4 Repeating Decimals (Chapter 6: Decimals)
41 6.5 Summary (Chapter 6: Decimals)
42 7.1 What is a Ratio? (Chapter 7: Ratios, Conversions, and Rates)
43 7.2 Multi-way Ratios (Chapter 7: Ratios, Conversions, and Rates)
44 7.3 Proportions (Chapter 7: Ratios, Conversions, and Rates)
45 7.4 Conversions (Chapter 7: Ratios, Conversions, and Rates)
46 7.5 Speed (Chapter 7: Ratios, Conversions, and Rates)
47 7.6 Other Rates (Chapter 7: Ratios, Conversions, and Rates)
48 7.7 Summary (Chapter 7: Ratios, Conversions, and Rates)
49 8.1 What is a Percent? (Chapter 8: Percents)
50 8.2 Word Problems (Chapter 8: Percents)
51 8.3 Percent Increase and Decrease (Chapter 8: Percents)
52 8.4 Summary (Chapter 8: Percents)
53 9.1 From Squares to Square Roots (Chapter 9: Square Roots)
54 9.2 Square Roots of Non-square Integers (Chapter 9: Square Roots)
55 9.3 Arithmetic with Square Roots (Chapter 9: Square Roots)
56 9.4 Summary (Chapter 9: Square Roots)
57 10.1 Measuring Angles (Chapter 10: Angles)
58 10.2 Parallel Lines (Chapter 10: Angles)
59 10.3 Angles in Polygons (Chapter 10: Angles)
60 10.4 Summary (Chapter 10: Angles)
61 11.1 Measuring Segments (Chapter 11: Perimeter and Area)
62 11.2 Area (Chapter 11: Perimeter and Area)
63 11.3 Circles (Chapter 11: Perimeter and Area)
64 11.4 Summary (Chapter 11: Perimeter and Area)
65 12.1 The Pythagorean Theorem (Chapter 12: Right Triangles and Quadrilaterals)
66 12.2 Some Special Triangles (Chapter 12: Right Triangles and Quadrilaterals)
67 12.3 Types of Quadrilaterals (Chapter 12: Right Triangles and Quadrilaterals)
68 12.4 Summary (Chapter 12: Right Triangles and Quadrilaterals)
69 13.1 Basic Statistics (Chapter 13: Data and Statistics)
70 13.2 Limits of Basic Statistics (Chapter 13: Data and Statistics)
71 13.3 Tables Graphs and Charts (Chapter 13: Data and Statistics)
72 13.4 Summary (Chapter 13: Data and Statistics)
73 14.1 Counting with Addition and Subtraction (Chapter 14: Counting)
74 14.2 The Multiplication Principle (Chapter 14: Counting)
75 14.3 Casework (Chapter 14: Counting)
76 14.4 Counting Pairs (Chapter 14: Counting)
77 14.5 Probability (Chapter 14: Counting)
78 14.6 Summary (Chapter 14: Counting)
79 15.1 Find a Pattern (Chapter 15: Problem-Solving Strategies)
80 15.2 Make a List (Chapter 15: Problem-Solving Strategies)
81 15.3 Draw a Picture (Chapter 15: Problem-Solving Strategies)
82 15.4 Work Backwards (Chapter 15: Problem-Solving Strategies)
83 15.5 Summary (Chapter 15: Problem-Solving Strategies)

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