New Progress in Mathematics

by McDonnell, Rose A.; Le Tourneau, Catherine D.; Burrows, Anne V.; Ford, Elinor R.

• ISBN13: 9780821517079
• ISBN10: 0821517074
• Edition: Revised
• Format: Hardcover
• Copyright: 1996-01-01
• Publisher: William H Sadlier

Table of Contents

Introduction: Problem Solving
NPM's Problem-Solving Model	vi
Some Problem-Solving Strategies
Substituting Simpler Numbers	viii
Working Backwards	ix
Make a Table/Find a Pattern	x
Writing a Question	xi
Using a Frequency Table and Graph	xii
Numbers and Numeration
Working with Whole Numbers	2	(1)
Place Value	3	(1)
Working with Decimals	4	(2)
Whole Numbers and Expanded Form	6	(1)
Decimals and Expanded Form	7	(1)
Comparing Whole Numbers and Decimals	8	(1)
Ordering Whole Numbers and Decimals	9	(1)
Rounding Whole Numbers	10	(2)
Rounding Decimals	12	(2)
Technology: Software Tools	14	(2)
Problem-Solving Strategy: Guess and Test	16	(2)
Problem-Solving Applications	18	(6)
More Practice	20	(1)
Math Probe: Ancient Numerals	21	(1)
Check Your Mastery	22	(2)
Addition and Subtraction
Adding Whole Numbers	24	(2)
Subtracting Whole Numbers	26	(2)
Estimating Sums for Whole Numbers	28	(1)
Estimating Differences for Whole Numbers	29	(1)
Mental Math Computation: Compensation	30	(1)
Adding Decimals	31	(1)
Subtracting Decimals	32	(2)
Estimating Sums and Differences for Decimals	34	(2)
Problem-Solving Strategy: Missing Information	36	(2)
Problem-Solving Applications	38	(8)
More Practice	40	(1)
Math Probe: Short Word Form	41	(1)
Check Your Mastery	42	(1)
Cumulative Review	43	(3)
Multiplication and Division
Multiplying with Multiples of 10, 100, or 1000	46	(1)
Estimating Whole-Number Products	47	(1)
Multiplying by Two or Three Digits	48	(2)
Multiplying Decimals	50	(1)
Estimating Decimal Products	51	(1)
Dividing with Multiples of 10, 100, or 1000	52	(1)
Estimating Whole-Number Quotients	53	(1)
One-Digit Divisors and Short Division	54	(1)
Two-Digit Divisors	55	(1)
Three-Digit Divisors	56	(1)
Zero in the Quotient	57	(1)
Dividing a Decimal by a Whole Number	58	(2)
Multiplying and Dividing by Powers of Ten	60	(2)
Dividing by a Decimal	62	(2)
Technology: It All Adds Up to Computers	64	(2)
Problem-Solving Strategy: Identifying Extra Information	66	(2)
Problem-Solving Applications	68	(6)
More Practice	70	(1)
Math Probe: Be A Mathlete! Use Pattern Power	71	(1)
Check Your Mastery	72	(2)
Expressions, Equations, and Inequalities
Mathematical Expressions	74	(2)
Translating Expressions	76	(2)
Equations and Inequalities	78	(2)
Properties of Addition and Multiplication	80	(1)
Inverse Operations	81	(1)
Solving Addition and Subtraction Equations	82	(2)
Solving Multiplication and Division Equations	84	(2)
Order of Operations	86	(2)
Formulas	88	(2)
Problem-Solving Strategy: Writing and Using Equations	90	(2)
Problem-Solving Applications	92	(8)
More Practice	94	(1)
Math Probe: Mathematical Systems	95	(1)
Check Your Mastery	96	(1)
Cumulative Review	97	(3)
Integers
Using Integers	100	(2)
Comparing and Ordering Integers	102	(4)
Adding Integers	106	(1)
Subtracting Integers	106	(2)
Multiplying Integers	108	(2)
Dividing Integers	110	(2)
Technology: Computation	112	(2)
Problem-Solving Strategy: Working Backwards	114	(2)
Problem-Solving Applications	116	(6)
More Practice	118	(1)
Math Probe: Absolute Value	119	(1)
Check Your Mastery	120	(2)
Number Theory
Facts About Groups	122	(2)
Working with Number Groups	124	(2)
Solving Inequalities	126	(2)
Exponents: Powers of Ten	128	(2)
Expanded Form: Powers of Ten	130	(2)
Divisibility	132	(2)
Prime and Composite Numbers	134	(1)
Prime Factorization	135	(1)
Greatest Common Factor	136	(2)
Least Common Multiple	138	(2)
Scientific Notation	140	(2)
Problem-Solving Strategy: Using Tables and Drawings	142	(2)
Problem-Solving Applications	144	(8)
More Practice	146	(1)
Math Probe: Square Root	147	(1)
Check Your Mastery	148	(1)
Cumulative Review	149	(3)
Fractions: Addition, Subtraction
Fractions, Mixed Numbers, Equivalent Fractions	152	(2)
Fractions, Simplest Form	154	(1)
Changing Improper Fractions to Mixed Numbers	155	(1)
Comparing and Ordering Fractions	156	(2)
Fraction Sense	158	(2)
Adding Fractions	160	(2)
Subtracting Fractions	162	(2)
Mixed Numbers to Improper Fractions	164	(1)
Subtracting Fractions from Whole Numbers	165	(1)
Mixed Numbers: Rounding and Estimating	166	(1)
Adding Mixed Numbers	167	(1)
Subtracting Mixed Numbers	168	(2)
Technology: Using Spreadsheets	170	(2)
Problem-Solving Strategy: Logical Reasoning	172	(2)
Problem-Solving Applications	174	(6)
More Practice	176	(1)
Math Probe: Mobius Strip	177	(1)
Check Your Mastery	178	(2)
More Fractions and Decimals
Multiplying Fractions	180	(1)
Multiplying Fractions and Whole Numbers	181	(1)
Multiplying Mixed Numbers	182	(2)
Multiplying Using Cancellation	184	(2)
Reciprocals	186	(1)
Dividing a Whole Number by a Fraction	187	(1)
Dividing a Fraction by a Fraction or a Whole Number	188	(1)
Simplifying Complex Fractions	189	(1)
Dividing Mixed Numbers	190	(2)
Finding Parts of a Number and the Number	192	(2)
Changing Fractions and Mixed Numbers to Decimals	194	(2)
Terminating and Repeating Decimals	196	(2)
Changing Decimals to Fractions and Mixed Numbers	198	(2)
Problem-Solving Strategy: Interpreting the Remainder	200	(2)
Problem-Solving Applications	202	(10)
More Practice	204	(1)
Math Probe: Continued Fractions	205	(1)
Check Your Mastery	206	(1)
Cumulative Review	207	(2)
Cumulative Test	209	(3)
Measurement
Measuring Length in Metric Units	212	(2)
Changing Metric Units	214	(2)
Measuring Capacity in Metric Units	216	(1)
Measuring Mass in Metric Units	217	(1)
Relating Metric Units	218	(1)
Precision in Measurement	219	(1)
Length: in Customary Units	220	(2)
Capacity: in Customary Units	222	(1)
Weight: in Customary Units	223	(1)
Temperature (°C and °F)	224	(2)
Technology: Calculator Key--IN	226	(2)
Problem-Solving Strategy: Maps and Charts	228	(2)
Problem-Solving Applications	230	(6)
More Practice	232	(1)
Math Probe: Networks	233	(1)
Check Your Mastery	234	(2)
Plane Geometry
Geometric Concepts	236	(2)
Using a Protractor	238	(2)
Constructing a Congruent Segment	240	(1)
Constructing a Congruent Angle	241	(1)
Bisecting a Segment	242	(1)
Bisecting an Angle	243	(1)
Constructing Parallel Lines	244	(1)
Constructing Perpendicular Lines	245	(1)
Line Symmetry	246	(1)
Rotational Symmetry	247	(1)
Problem-Solving Strategy: Making an Organized List or Chart	248	(2)
Problem-Solving Applications	250	(8)
More Practice	252	(1)
Math Probe: ``Saw'' and ``Ladder'' Angles	253	(1)
Check Your Mastery	254	(1)
Cumulative Review	255	(3)
Polygons and Circles
Classifying Polygons	258	(2)
Circles	260	(2)
Perimeter	262	(2)
Perimeter and a Missing Dimension	264	(1)
Congruent Figures	265	(1)
Area of a Rectangle and a Square	266	(2)
Area of a Parallelogram	268	(1)
Area of a Triangle	269	(1)
Area of a Trapezoid	270	(2)
Solving for Missing Dimensions	272	(2)
Circumference of a Circle	274	(2)
Area of a Circle	276	(2)
Technology: Welcome to BASIC Training	278	(2)
Problem-Solving Strategy: Use Simpler Numbers	280	(2)
Problem-Solving Applications	282	(6)
More Practice	284	(1)
Math Probe: Tangrams or Polygonal Puzzles	285	(1)
Check Your Mastery	286	(2)
Ratio and Proportion
Ratios	288	(2)
Equal Ratios	290	(2)
Proportions	292	(2)
Solving Proportions	294	(2)
Scale Drawings	296	(2)
Map Distances	298	(2)
Similar Figures	300	(2)
Using Similar Right Triangles	302	(2)
Problem-Solving Strategy: Models	304	(2)
Problem-Solving Applications	306	(8)
More Practice	308	(1)
Math Probe: Proportional Puzzles	309	(1)
Check Your Mastery	310	(1)
Cumulative Review	311	(3)
Percent
Changing Decimals and Fractions to Percents	314	(2)
Changing Percents to Decimals and Fractions	316	(1)
Changing Percents Greater than 100%	317	(1)
Changing More Difficult Decimals and Fractions to Percents	318	(1)
Changing More Difficult Percents to Decimals and Fractions	319	(1)
Using Percents	320	(2)
Finding Percentage	322	(2)
Finding the Percent	324	(2)
Finding the Original Number	326	(2)
Technology: Patterns, Conjectures, and Calculations	328	(2)
Problem-Solving Strategy: Hidden Information	330	(2)
Problem-Solving Applications	332	(6)
More Practice	334	(1)
Math Probe: Logic	335	(1)
Check Your Mastery	336	(2)
Consumer Mathematics
Discount	338	(2)
Sales Tax	340	(2)
Commission	342	(2)
Earning Interest	344	(2)
Borrowing Money	346	(2)
Comparing Unit Prices	348	(2)
Checking Accounts	350	(2)
Budgets and Circle Graphs	352	(2)
Problem-Solving Strategy: Multi-Step Problems Using Formulas	354	(2)
Problem-Solving Applications	356	(8)
More Practice	358	(1)
Math Probe: Energy Expert	359	(1)
Check Your Mastery	360	(1)
Cumulative Review	361	(3)
Surface Area and Volume
Space Figures	364	(2)
Surface Area of a Rectangular Prism and a Cube	366	(2)
Surface Area of a Triangular Prism	368	(2)
Surface Area of a Cylinder	370	(2)
Volume of a Rectangular Prism and a Cube	372	(1)
Volume of a Triangular Prism	373	(1)
Volume of a Cylinder	374	(2)
Technology: Spreadsheets	376	(2)
Problem-Solving Strategy: Combining Strategies	378	(2)
Problem-Solving Applications	380	(6)
More Practice	382	(1)
Math Probe: Square Faces	383	(1)
Check Your Mastery	384	(2)
Probability, Statistics, and Graphing
Identifying Outcomes	386	(2)
Finding Probability	388	(2)
Probability of Compound Events	390	(2)
Counting Principle	392	(2)
Graphing Sense	394	(2)
Single Bar Graphs	396	(1)
Double Bar Graphs	397	(1)
Single Line Graphs	398	(1)
Double Line Graphs	399	(1)
Circle Graphs	400	(2)
Central Tendency	402	(2)
Graphing Ordered Pairs	404	(2)
Graphing Equations	406	(2)
Problem-Solving Strategy: Organized List	408	(2)
Problem-Solving Applications	410	(10)
More Practice	412	(1)
Math Probe: Slides and Flips	413	(1)
Check Your Mastery	414	(1)
Cumulative Review	415	(2)
Cumulative Test	417	(3)
OPTIONAL: Algebra Readiness
Algebra and Rational Number Topics
Classifying Algebraic Expressions	420	(2)
Evaluating Algebraic Expressions	422	(2)
Addition and Subtraction of Monomials	424	(2)
The Laws of Exponents	426	(2)
Addition and Subtraction of Polynomials	428	(2)
Multiplying Polynomials	430	(2)
Dividing Polynomials by Monomials	432	(2)
Addition and Subtraction of Signed Rational Numbers	434	(2)
Multiplication and Division of Signed Rational Numbers	436	(2)
Problem-Solving Strategy: Using More Than One Equation	438	(2)
Problem-Solving Applications	440	(7)
More Practice	442	(3)
Math Probe: Original Operations	445	(1)
Check Your Mastery	446	(1)
End of Book Material
Still More Practice	447	(18)
Brain Builders	465	(6)
Drill and Mental Math	471	(14)
Glossary	485	(4)
Index	489	(6)
Selected Odd-Numbered Answers	495