Table of Contents

Brief Contents

Chapter 1. Problem Solving
Chapter 2. Sets, Functions, and Reasoning
Chapter 3. Whole Numbers
Chapter 4. Number Theory
Chapter 5. Integers and Fractions
Chapter 6. Decimals and Rational Numbers
Chapter 7. Statistics
Chapter 8. Probability
Chapter 9. Geometric Figures
Chapter 10. Measurement
Chapter 11. Motions in Geometry

Detailed Contents:

To the Student
1.1 Introduction to Problem Solving Math Activity: Tower Puzzle Patterns
Making a Drawing; Guessing and Checking; Making a Table; Using a Model; Working Backward

1.2 Patterns and Problem Solving

Math Activity: Pattern Block Sequences
Patterns in Nature; Number Patterns; Inductive Reasoning; Problem-Solving Application

1.3 Problem Solving with Algebra

Math Activity: Extending Tile Patterns
Variables and Equations; Solving Equations; Solving Inequalities; Using Algebra for Problem Solving; Problem Solving Application

2.1 Sets and Counting

Math Activity: Sorting and Classifying Attribute Pieces
Sets and Their Elements; Relationships between Sets; Operations on Sets; Problem-Solving Application; Infinite Sets
2.2 Functions and Graphs Math Activity: Slopes of Geoboard Line Segments
Functions; Rectangular Coordinates; Linear Functions and Slope; Nonlinear Functions; Interpreting Graphs; Problem Solving Application
2.3 Introduction to Deductive Reasoning Math Activity: Deductive Reasoning Game
Deductive Reasoning; Venn Diagrams; Conditional Statements; Reasoning with Conditional Statements; Problem-Solving Application
3.1 Numeration Systems Math Activity: Numeration and Place Value with Base Five Pieces
Grouping and Number Bases; Ancient Numeration Systems; Reading and Writing Numbers; Rounding Numbers; Models for Numeration; Problem-Solving Application; Base Five Numeration
3.2 Addition and Subtraction Math Activity: Addition and Subtraction with Base Five Pieces
Models for Addition Algorithms; Number Properties; Inequality of Whole Numbers; Models for Subtraction Algorithms; Mental Calculations; Estimation of Sums and Differences; Problem Solving Application
3.3 Multiplication Math Activity: Multiplication with Base Five Pieces
Models for Multiplication Algorithms; Number Properties; Mental Calculations; Estimation of Products; Problem-solving Application
3.4 Division and Exponents Math Activity: Division with Base Five Pieces
Models for Division Algorithms; Division Theorem; Mental Calculations; Estimation of Quotients; Exponents; Order of Operations; Problem-Solving Application
4.1 Factors and Multiples Math Activity: Divisibility with Base Ten Pieces
Models for Factors and Multiples; Problem-Solving Application; Divisibility Tests; Prime and Composite Numbers; Prime Number Test; Sieve of Eratosthenes
4.2 Greatest Common Factor and Least Common Multiple Math Activity: Factors and Multiples from Tile Patterns
Prime Factorizations; Factors of Numbers; Problem-Solving Application; Greatest Common Factor; Least Common Multiple; Problem-Solving Application
5.1 Integers Math Activity: Addition and Subtraction with Black and Red Tile
Positive and Negative Integers; Uses of Integers; Models for Integers; Addition; Subtraction; Multiplication; Division; Inequality; Properties of Integers; Mental Calculations; Estimation; Problem-Solving Application
5.2 Introduction to Fractions Math Activity: Equality and Inequality with Fraction Bars
Fraction Terminology; Models for Fractions; Equality of Fractions; Common Denominators; Inequality; Density of Fractions; Mixed Numbers and Improper Fractions; Mental Calculations; Estimation; Problem-Solving Application
5.3 Operations with Fractions Math Activity: Operations with Fraction Bars
Addition; Subtraction; Multiplication; Division; Number Properties; Mental Calculations; Estimation; Problem-Solving Application
6.1 Decimals and Rational Numbers Math Activity: Decimal Place Value with Base Ten Pieces
Decimal Terminology and Notation; Models for Decimals; Equality of Decimals; Inequality of Decimals; Rational Numbers; Density of Rational Numbers; Estimation; Problem-Solving Application
6.2 Operations with Decimals Math Activity: Decimal Operations with Base Ten Pieces and Decimal Squares
Addition; Subtraction; Multiplication; Division; Order of Operations; Repeating Decimals; Properties of Rational Numbers; Mental Computation; Estimation; Problem-Solving Application
6.3 Ratio, Percent, and Scientific Notation Math Activity: Percents with Decimal Squares
Ratios; Proportions; Percent; Calculations with Percents; Mental Calculations with Percents; Estimation; Scientific Notation; Problem-Solving Application
6.4 Irrational and Real Numbers Math Activity: Irrational Numbers on Geoboards
Pythagorean Theorem; Square Roots and Other Roots; Real Numbers; Properties of Real Numbers; Operations with Irrational Numbers; Problem-Solving Application
7.1 Describing and Analyzing Data Math Activity: Averages with Columns of Tile
Measures of Central Tendency; Problem-Solving Application; Box and Whisker Plots; Measures of Variability
7.2 Graphing Data and Making Predictions Math Activity: Graphing Bell-Shaped Distributions
Bar Graphs; Pie Graphs; Pictographs; Line Plots; Stem and Leaf Plots; Histograms; Line Graphs; Scatter Plots; Problem-Solving Application
7.3 Sampling, Predictions, and Simulations Math Activity: Simulations in Statistics
Sampling; Skewed and Symmetric Distributions; Normal Distributions; Measures of Relative Standing; Simulations; Problem-Solving Application
8.1 Single-Stage Experiments Math Activity: Experimental Probabilities from Simulations
Probabilities of Outcomes; Probabilities of Events; Mutually Exclusive Events; Odds; Experimental Probability; Simulations; Problem-Solving Application
8.2 Multistage Experiments Math Activity: Determining Fairness of Games
Probabilities of Outcomes; Probabilities of Events; Problem-Solving Application; Complementary Events; Problem-Solving Application; Expected Value
9.1 Plane Figures Math Activity: Angles in Pattern Block Figures
Mathematical Systems; Points, Lines, and Planes; Half-Planes, Segments, Rays, and Angles; Problem-Solving Application; Angle Measurements; Perpendicular and Parallel Lines; Problem-Solving Application; Curves and Convex Sets; Polygons; Problem-Solving Application
9.2 Polygons and Tessellations Math Activity: Tessellations with Polygons
Angles in Polygons; Congruence; Regular Polygons; Drawing Regular Polygons; Tessellations with Polygons; Problem-Solving Application
9.3 Space Figures Math Activity: Nets for Three-Dimensional Figures
Planes; Polyhedra; Regular Polyhedra; Pyramids and Prisms; Cones and Cylinders; Spheres and Maps*; Problem-Solving Application
9.4 Symmetric Figures Math Activity: Symmetries of Pattern Block Figures
Reflection Symmetry for Plane figures; Rotation Symmetry for Plane Figures; Reflection Symmetry for Space Figures; Rotation Symmetry for Space Figures; Problem-Solving Application
10.1 Systems of Measurement Math Activity: Perimeters of Pattern Block Figures
Nonstandard Units of Length; English Units; Metric Units; Precision and Small Measurements; International System of Units; Problem-Solving Application
10.2 Area and Perimeter Math Activity: Areas of Pattern Blocks Using Different Units
Nonstandard Units of Area; Standard Units of Area; Perimeter; Areas of Polygons; Circumferences and Areas of Circles; Problem-Solving Application
10.3 Volume and Surface Area Math Activity: Making Cylinders and Comparing Volumes
Nonstandard Units of Volume; Standard Units of Volume; Surface Area; Volumes of Space Figures; Irregular Shapes; Creating Surface Area*; Problem-Solving Application
11.1 Congruence and Constructions Math Activity: Tracing Figures from Motions with Tile
Mappings; Constructing Segments and Angles; Constructing Triangles; Constructing Bisectors; Constructing Perpendicular and Parallel Lines; Circumscribing Circles about Triangles; Constructions with a Mira; Problem-Solving Application
11.2 Congruence Mappings Math Activity: Rotating, Reflecting, and Translating Figures on Grids
Translations; Reflections; Rotations; Composition of Mappings; Congruence; Mapping Figures onto Themselves; Escher-Type Tessellations*; Problem-Solving Application
11.3 Similarity Mappings Math Activity: Enlargements with Pattern Blocks
Similarity and Scale Factors; Similar Polygons; Similar Triangles; Problem-Solving Application; Scale Factors with Area and Volume; Sizes and Shapes of Living Things*
Answers to Selected Math Activities
Answers to Puzzlers
Answers to Odd-Numbered Exercises and Problems and Chapter Tests


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