Gateways to Algebra and Geometry

by Bolciani

• ISBN13: 9780395771242
• ISBN10: 0395771242
• Edition: Student
• Format: Hardcover
• Copyright: 1996-03-01
• Publisher: MCDOUG-LITTELL

Table of Contents

A Letter to the Student	1	(1)
Patterns	2	(46)
A Tiling Problem	4	(6)
Number and Letter Patterns	10	(6)
Practical Patterns	16	(7)
A Family Tree
Other Applied Patterns
Probability	23	(6)
What is Probability?
Applying Probability
Tables and Spreadsheets	29	(7)
The Cost of Postage Stamps
Spreadsheets
Communicating Mathematics	36
Describing a Rectangle
Explaining the Rounding Process
Investigations
Escape Velocity	3	(6)
Tessellation	9	(6)
Patterns on a Telephone	15	(7)
Technology	22	(6)
Leap Year	28	(7)
Spreadsheets	35	(6)
Geometry	41	(1)
Chapter Summary	42	(1)
Chapter Review	43	(3)
Chapter Test	46	(1)
Puzzles and Challenges	47	(1)
Formulas and Percent	48	(44)
Operations on Numbers	50	(7)
Which Operation Comes First?
Operation Symbols
Powers and Roots	57	(7)
Exponents
Roots
Order of Operations
Geometric Formulas	64	(7)
Area and Circumference Formulas
The Pythagorean Theorem
Percent	71	(7)
What Is a Percent?
Percent Problems
More About Spreadsheets	78
Investigations
Selling Prices	49	(7)
Mental Math	56	(7)
Algebra	63	(7)
Volume	70	(7)
Decimals	77	(8)
Sports	85	(1)
Chapter Summary	86	(1)
Chapter Review	87	(3)
Chapter Test	90	(1)
Puzzles and Challenges	91	(1)
Measurement and Estimation	92	(56)
Linear Measurement	94	(7)
Linear Units
Measurement and Polygons
Scientific Notation	101	(6)
Scientific Notation and Large Numbers
Scientific Notation and Small Numbers
Estimation and Rounding	107	(7)
Accuracy
Rounding
Understanding Equations	114	(7)
Solving an Equation
Estimating Solutions
Inverse Operations
Angle Measurement	121	(8)
Rotations
Naming Angles
Measuring Angles
Constructions with Ruler and Protractor	129	(7)
Geometric Properties	136
Investigations
The Golden Rectangle	93	(7)
The English System	100	(6)
History	106	(7)
In the News	113	(7)
Merchandising	120	(8)
Early Civilization	128	(7)
Geometry	135	(6)
Geometry	141	(1)
Chapter Summary	142	(1)
Chapter Review	143	(3)
Chapter Test	146	(1)
Puzzles and Challenges	147	(1)
Ratio and Proportion	148	(50)
A Closer Look at Measurement	150	(8)
Attributes and Units
Metric Units
Operations with Measurements
Ratios of Measurements	158	(7)
Ratios
Rates
Unit Costs
More Applications of Ratios	165	(7)
Scale and Ratios
Density
Working with Units	172	(6)
Proportions	178	(7)
What is a Proportion?
Solving Proportions
Similarity	185
Enlargements and Reductions
Similar Geometric Figures
Investigations
Lift-to-Drag Ratios	149	(8)
Mass and Weight	157	(7)
Radar Guns	164	(7)
Auto Trip	171	(6)
Water Consumption	177	(7)
Floor Plans	184	(7)
Similar Polygons	191	(1)
Chapter Summary	192	(1)
Chapter Review	193	(3)
Chapter Test	196	(1)
Puzzles and Challenges	197	(1)
Data Analysis	198	(52)
Circle Graphs	200	(7)
Reading a Circle Graph
Drawing a Circle Graph
Bar Graphs and Line Graphs	207	(6)
Reading Bar Graphs and Line Graphs
Drawing Bar Graphs and Line Graphs
Other Data Displays	213	(8)
Scattergrams
Histograms
Pictographs
Artistic Graphs
Averages	221	(7)
The Mean
The Median
The Mode
Organizing Data	228	(6)
Stem-and-Leaf Plots
Box-and-Whisker Plots
Matrices	234
Organizing Data in a Matrix
Dimensions of a Matrix
Equal Matrices
Investigations
History	199	(7)
Communications	206	(6)
Sports	212	(8)
Data Analysis	220	(7)
Baseball	227	(6)
Statistics	233	(8)
Language Arts	241	(1)
Chapter Summary	242	(1)
Chapter Review	243	(4)
Chapter Test	247	(2)
Puzzles and Challenges	249	(1)
Signed Numbers	250	(66)
The Number Line	252	(8)
Number Lines and Signed Numbers
Opposites
Origin and Coordinates
Inequalities	260	(7)
Graphing and Writing Inequalities and Inequalities and or Inequalities
Adding Signed Numbers	267	(8)
Adding Signed Numbers on the Number Line
Using a Calculator to Add Signed Numbers
Multiplying and Dividing Signed Numbers	275	(7)
Multiplication of Signed Numbers
Scalar Multiplication
Powers of Signed Numbers
Division of Signed Numbers
Matrix Multiplication	282	(8)
Subtracting Signed Numbers	290	(6)
Definition of Subtraction
Subtracting Matrices
Absolute Value	296	(6)
Distance from Zero
Distance Between Two Numbers
Two-Dimensional Graphs	302
The Rectangular Coordinate System
Graphing Geometric Figures
Investigations
Map Coloring	251	(8)
Temperature Scales	259	(7)
Equilibrium	266	(8)
Banking	274	(7)
Physics	281	(8)
Using a Matrix	289	(6)
Time Differences	295	(6)
Gasoline Mileage	301	(8)
Floor Plan	309	(1)
Chapter Summary	310	(1)
Chapter Review	311	(3)
Chapter Test	314	(1)
Puzzles and Challenges	315	(1)
Exploring Geometry	316	(52)
Line and Angle Relationships	318	(7)
Parallel and Perpendicular Lines
Adjacent and Vertical Angles
Quadrilaterals	325	(7)
Squares, Rectangles, and Parallelograms
Rhombuses and Trapezoids
Symmetry	332	(7)
What is Symmetry?
Reflection Symmetry
Rotation Symmetry
Rigid Transformations	339	(8)
Reflections
Rotations
Translations
Discovering Properties	347	(7)
Transformations and Matrices	354
The Vertex Matrix
Translations
Reflections and Rotations
Investigations
Equipment Design	317	(7)
Architecture	324	(7)
Tessellations	331	(7)
Logos	338	(8)
M. C. Escher	346	(7)
Playing-Card Symmetries	353	(8)
Origami	361	(1)
Chapter Summary	362	(1)
Chapter Review	363	(3)
Chapter Test	366	(1)
Puzzles and Challenges	367	(1)
The Language of Algebra	368	(58)
Simplifying Expressions	370	(8)
Equivalent Expressions
Adding and Subtracting Like Terms
The Distributive Property
Using Variables	378	(7)
Expressions to Describe Phrases
Expressions to Describe Situations
Equations to Represent Problems
Solving Equations	385	(7)
Inverse Operations
Equations with Several Operations
Some Special Equations	392	(7)
Absolute-Value Equations
Equations with Square Roots
Simplifying to Solve Equations
Solving Inequalities	399	(7)
Adding and Subtracting
Multiplying and Dividing
Substitution	406	(7)
Special Substitutions
Variables for Expressions
Functions	413
What is a Function?
Evaluating Functions
Investigations
Fuel Efficiency	369	(8)
The Fibonacci Sequence	377	(7)
Science	384	(7)
Consumer Mathematics	391	(7)
Science	398	(7)
The Triangle Inequality	405	(7)
Decimals vs. Fractions	412	(7)
Rent Costs	419	(1)
Chapter Summary	420	(1)
Chapter Review	421	(3)
Chapter Test	424	(1)
Puzzles and Challenges	425	(1)
Real Numbers	426	(58)
Sets	428	(7)
Describing Sets
Subsets
Intersection and Union	435	(7)
Intersections and Unions of Sets
Venn Diagrams
Important Sets of Numbers	442	(6)
The Rational Numbers
The Real Numbers
Pi and the Circle	448	(7)
The Meaning of π
A Property of Circles
Properties of Real Numbers	455	(7)
Associative Properties
Commutative Properties
The Zero Product Property
Two Coordinate Formulas	462	(7)
The Distance Formula
The Midpoint Formula
Graphs of Equations	469
Investigations
Optical Illusion	427	(7)
Infinite Sets	434	(7)
Limits	441	(6)
Fractions	447	(7)
Approximating π	454	(7)
Language	461	(7)
Geography	468	(8)
Data Analysis	476	(1)
Chapter Summary	477	(1)
Chapter Review	478	(4)
Chapter Test	482	(1)
Puzzles and Challenges	483	(1)
Topics of Number Theory	484	(58)
Techniques of Counting	486	(8)
The Fundamental Counting Principle Counting Applications
Primes, Composites, and Multiples	494	(7)
Prime Numbers and Composite Numbers
Multiples
Divisibility Tests	501	(6)
Tests for 2, 3, 4, 5, 6, 8, 9, 10, and 12
Divisibility Test for 11
Prime Factorization	507	(6)
Prime-Factorization Form
Prime-Factorization Techniques
General Prime-Factorization Procedure
Factors and Common Factors	513	(8)
Factors of a Natural Number
Abundant, Deficient, and Perfect Numbers
Greatest Common Factors
LCM and GCF Revisited	521	(7)
Using Venn Diagrams
Simplifying Fractions
Equations Containing Fractions
Number-Theory Explorations	528
Symmetric Primes
Goldbach's Conjectures
Figurate Numbers
Pythagorean Triples
Investigations
Farming	485	(8)
Lotteries	493	(7)
Tile Arrangements	500	(6)
Numeric Palindrome	506	(6)
Number Game	512	(8)
Relatively Prime Numbers	520	(7)
Lattice Points	527	(8)
Prime Numbers	535	(1)
Chapter Summary	536	(1)
Chapter Review	537	(3)
Chapter Test	540	(1)
Puzzles and Challenges	541	(1)
Solving Problems with Algebra	542	(60)
Mathematics in Words	544	(2)
Presenting Solutions to Problems	546	(7)
Equations with Variables on Both Sides	553	(6)
More Word Problems	559	(7)
Equations with Several Variables	566	(7)
Polyhedra	573	(8)
Prisms
Pyramids
Solids with Circular Cross Sections	581	(8)
Cylinders
Cones
Spheres
Reading Information from Graphs	589
Investigations
Water Conservation	543	(9)
Language	552	(6)
Balance	558	(7)
The Teeter-totter Principle	565	(7)
Chemistry	572	(8)
Polyhedra	580	(8)
Ratio	588	(7)
Graphs	595	(1)
Chapter Summary	596	(1)
Chapter Review	597	(3)
Chapter Test	600	(1)
Puzzles and Challenges	601	(1)
Looking Ahead: Iterations and Fractals	602	(44)
Iterations	604	(8)
Repeated Calculations
Iteration Diagrams
More About Iterations	612	(8)
Rules Involving the Iteration Counter
Function Notation for Iteration
Geometric Iterations	620	(5)
Convergent Iterations	625	(9)
Convergence
Limiting Values
Introduction to Fractals	634
Investigations
Music	603	(8)
The Calendar	611	(8)
Mental Math	619	(5)
Snowflake Curve	624	(9)
Consumer Math	633	(6)
Technology	639	(1)
Chapter Summary	640	(1)
Chapter Review	641	(3)
Chapter Test	644	(1)
Puzzles and Challenges	645	(1)
Handbook of Arithmetic Skills	646	(14)
Tables and Charts	660	(6)
Glossary	666	(7)
Answers to Odd-Numbered Problems	673	(22)
Index	695	(8)
Credits	703