Preface | p. xv |
Whole Numbers | p. 1 |
Education Pays | p. 1 |
Objectives | |
Read and write whole numbers | |
Compare whole numbers using inequality symbols | |
Round whole numbers to specified place values | |
Use rounding for estimation | |
Classify whole numbers as even or odd, prime, or composite | |
Solve problems involving whole numbers | |
Bald Eagle Population Increasing Again | p. 10 |
Objectives | |
Read tables | |
Read bar graphs | |
Interpret bar graphs | |
Construct graphs | |
Bald Eagles Revisited | p. 19 |
Objectives | |
Add whole numbers by hand and mentally | |
Subtract whole numbers by hand and mentally | |
Estimate sums and differences using rounding | |
Recognize the associative property and the commutative property for addition | |
Translate a written statement into an arithmetic expression | |
Summer Camp | p. 31 |
Objectives | |
Multiply whole numbers and check calculations using a calculator | |
Multiply whole numbers using the distributive property | |
Estimate the product of whole numbers by rounding | |
Recognize the associative and commutative properties for multiplication | |
College Supplies | p. 39 |
Objectives | |
Divide whole numbers by grouping | |
Divide whole numbers by hand and by calculator | |
Estimate the quotient of whole numbers by rounding | |
Recognize the noncommutative property for division | |
Reach for the Stars | p. 49 |
Objectives | |
Use exponential notation | |
Factor whole numbers | |
Determine the prime factorization of a whole number | |
Recognize square numbers and roots of square numbers | |
Recognize cubed numbers | |
Apply the multiplication rule for numbers in exponential form with the same base | |
You and Your Calculator | p. 59 |
Objectives | |
Use order of operations to evaluate arithmetic expressions | |
Use order of operations to evaluate formulas involving whole numbers | |
What Have I Learned? | p. 67 |
How Can I Practice? | p. 71 |
Summary | p. 77 |
Gateway Review | p. 83 |
Variables and Problem Solving | p. 91 |
How Much Do I Need to Buy? | p. 91 |
Objectives | |
Recognize and understand the concept of a variable in context and symbolically | |
Translate a written statement (verbal rule) into a statement involving variables (symbolic rule) | |
Evaluate variable expressions | |
Apply formulas (area, perimeter, and others) to solve contextual problems | |
How High Will It Go? | p. 101 |
Objectives | |
Recognize input/output relationship between variables in a formula or equation (two variables only) | |
Evaluate variable expressions in formulas and equations | |
Generate a table of input and corresponding output values from a given equation, formula, or situation | |
Read, interpret, and plot points in rectangular coordinates that are obtained from evaluating a formula or equation | |
Are You Balanced? | p. 110 |
Objectives | |
Translate contextual situations and verbal statements into equations | |
Apply the fundamental principle of equality to solve equations of the forms x + a = b, a + x = b and x - a = b | |
How Far Will You Go? How Long Will It Take? | p. 117 |
Objectives | |
Apply the fundamental principle of equality to solve equations of the form ax = b, a [NotEqual] 0 | |
Translate contextual situations and verbal statements into equations | |
Use the relationship rate [Middot] time = amount in various contexts | |
Web Devices for Sale | p. 24 |
Objectives | |
Identify like terms | |
Combine like terms using the distributive property | |
Solve equations of the form ax + bx = c | |
Make Me an Offer | p. 130 |
Objectives | |
Use the basic steps for problem solving | |
Translate verbal statements into algebraic equations | |
Use the basic principles of algebra to solve real-world problems | |
What Have I Learned? | p. 138 |
How Can I Practice? | p. 139 |
Summary | p. 143 |
Gateway Review | p. 147 |
Problem Solving with Rational Numbers: Addition and Subtraction of Integers, Fractions, and Decimals | p. 151 |
Adding and Subtracting Integers | |
On the Negative Side | p. 151 |
Objectives | |
Identify integers | |
Represent quantities in real-world situations using Integers | |
Compare integers | |
Calculate absolute value of integers | |
Maintaining Your Balance | p. 159 |
Objectives | |
Add and subtract integers | |
Identify properties of addition and subtraction of integers | |
What's the Bottom Line? | p. 168 |
Objectives | |
Write formulas from verbal statements | |
Evaluate expressions in formulas | |
Solve equations of the form X + b = c and b - x = c | |
Solve formulas for a given variable | |
Riding in the Wind | p. 175 |
Objectives | |
Translate verbal rules into equations | |
Determine an equation from a table of values | |
Use a rectangular coordinate system to represent an equation graphically | |
What Have I Learned? | p. 183 |
How Can I Practice? | p. 185 |
Adding and Subtracting Fractions | |
Are You Hungry? | p. 191 |
Objectives | |
Identify the numerator and denominator of a fraction | |
Determine the greatest common factor (GCF) | |
Determine equivalent fractions | |
Reduce fractions to equivalent fractions in lowest terms | |
Convert mixed numbers to improper fractions and improper fractions to mixed numbers | |
Determine the least common denominator (LCD) of two or more fractions | |
Compare fractions | |
Food for Thought | p. 203 |
Objective | |
Add and subtract fractions and mixed numbers with the same denominators | |
Math Is a Trip | p. 210 |
Objectives | |
Determine the least common denominator (LCD) for two or more fractions | |
Add and subtract fractions with different denominators | |
Solve equations in the form x + b = c and x - b = c that involve fractions | |
What Have I Learned? | p. 217 |
How Can I Practice? | p. 219 |
Adding and Subtracting Decimals | |
What Are You Made Of? | p. 223 |
Objectives | |
Identify place values of numbers written in decimal form | |
Convert a decimal to a fraction or a mixed number | |
Compare decimals | |
Read and write decimals | |
Round decimals | |
Think Metric | p. 231 |
Objectives | |
Know the metric prefixes and their decimal values | |
Convert measurements between metric quantities | |
Dive into Decimals | p. 235 |
Objectives | |
Add and subtract decimals | |
Compare and interpret decimal numbers | |
Boiling, Freezing, and Financial Aid | p. 240 |
Objectives | |
Add and subtract positive and negative decimal numbers | |
Interpret and compare decimal numbers | |
Solve equations of the type x + b = c and x - b = c involving decimal numbers | |
What Have I Learned? | p. 246 |
How Can I Practice? | p. 247 |
Summary | p. 251 |
Gateway Review | p. 255 |
Multiplication and Division of Rational Numbers | p. 263 |
Multiplying and Dividing Integers | |
Are You Physically Fit? | p. 263 |
Objectives | |
Multiply and divide integers | |
Perform calculations involving a sequence of operations | |
Apply exponents to integers | |
Identify properties of calculations involving multiplication and division with zero | |
Integers and Tiger Woods | p. 275 |
Objectives | |
Use order of operations with expressions involving integers | |
Apply the distributive property | |
Evaluate algebraic expressions and formulas using integers | |
Solve equations of the form ax = b, where a [NotEqual] 0, involving integers | |
What Have I Learned? | p. 283 |
How Can I Practice? | p. 285 |
Multiplying and Dividing Fractions | |
Get Your Homestead Land | p. 288 |
Objectives | |
Multiply and divide fractions | |
Recognize the sign of a fraction | |
Determine the reciprocal of a fraction | |
Solve equations of form ax = b, a [NotEqual] 0, that involve fractions | |
Tiling the Bathroom | p. 299 |
Objectives | |
Multiply and divide mixed numbers | |
Evaluate expressions with mixed numbers | |
Calculate the square root of a mixed number | |
What Have I Learned? | p. 309 |
How Can I Practice? | p. 310 |
Multiplying and Dividing Decimals | |
Quality Points and GPA: Tracking Academic Standing | p. 315 |
Objectives | |
Multiply and divide decimals | |
Estimate products and quotients involving decimals | |
Tracking Temperature | p. 325 |
Objectives | |
Use the order of operations to evaluate expressions that include decimals | |
Use the distributive property in calculations involving decimals | |
Evaluate formulas that include decimals | |
Solve equations of the form ax = b that include decimals | |
What Have I Learned? | p. 333 |
How Can I Practice? | p. 335 |
Summary | p. 339 |
Gateway Review | p. 343 |
Problem Solving with Ratios, Proportions, and Percents | p. 349 |
Everything Is Relative | p. 349 |
Objectives | |
Understand the distinction between actual and relative measure | |
Write a ratio in its verbal, fraction, decimal and percent formats | |
The Devastation of AIDS in Africa | p. 360 |
Objectives | |
Use proportional reasoning to apply a known ratio to a given piece of information | |
Write an equation using the relationship "ratio [Middot] total = part" and then solve the resulting equation | |
Who Really Did Better? | p. 365 |
Objectives | |
Define actual and relative change | |
Distinguish between actual and relative change | |
Don't Forget the Sales Tax | p. 370 |
Objectives | |
Define and determine growth factors | |
Use growth factors in problems involving percent increases | |
It's All on Sale! | p. 377 |
Objectives | |
Define and determine decay factors | |
Use decay factors in problems involving percent decreases | |
Take an Additional 20% Off | p. 384 |
Objective | |
Apply consecutive growth and/or decay factors to problems involving two or more percent changes | |
Fuel Economy | p. 391 |
Objectives | |
Apply rates directly to solve problems | |
Use unit analysis (dimensional analysis) to solve problems that involve consecutive rates | |
Four out of Five Dentists Prefer the Brooklyn Dodgers? | p. 399 |
Objectives | |
Recognize that equivalent fractions lead to proportions | |
Use proportions to solve problems involving ratios and rates | |
What Have I Learned? | p. 405 |
How Can I Practice? | p. 407 |
Summary | p. 411 |
Gateway Review | p. 413 |
Problem Solving with Geometry | p. 417 |
The Geometry of Two-Dimensional Plane Figures | |
Walking around Bases, Gardens, Trusses, and Other Figures | p. 417 |
Objectives | |
Recognize perimeter as a geometric property of plane figures | |
Write formulas for, and calculate perimeters of, squares, rectangles, triangles, parallelograms, trapezoids, and polygons | |
Use unit analysis to solve problems involving perimeter | |
Circles Are Everywhere | p. 429 |
Objectives | |
Measure lengths of diameters and circumferences of circles | |
Develop and use formulas for calculating circumferences of circles | |
Lance Armstrong and You | p. 433 |
Objectives | |
Calculate perimeters of many-sided plane figures using formulas and combinations of formulas | |
Use unit analysis to solve problems involving perimeters | |
Baseball Diamonds, Gardens, and Other Figures Revisited | p. 437 |
Objectives | |
Write formulas for areas of squares, rectangles, parallelograms, triangles, trapezoids, and polygons | |
Calculate areas of polygons using appropriate formulas | |
How Big Is That Circle Really? | p. 446 |
Objectives | |
Develop a formula for the area of a circle | |
Use the formula to determine areas of circles | |
A New Pool and Other Home Improvements | p. 452 |
Objectives | |
Solve problems in context using geometric formulas | |
Distinguish between problems that require area formulas and those that require perimeter formulas | |
How Big Is That Angle? | p. 457 |
Objectives | |
Measure sizes of angles with a protractor | |
Classify triangles as equiangular, equilateral, isosceles, or scalene | |
How About Pythagoras? | p. 464 |
Objectives | |
Develop and use the Pythagorean Theorem for right triangles | |
Calculate the square root of numbers other than perfect squares | |
Apply the Pythagorean Theorem in context | |
Moving Up with Math | p. 471 |
Objectives | |
Recognize the geometric properties of similar triangles | |
Use similar triangles in indirect measurement | |
What Have I Learned? | p. 475 |
How Can I Practice? | p. 477 |
The Geometry of Three-Dimensional Space Figures | |
Painting Your Way through Summer | p. 482 |
Objectives | |
Recognize geometric properties of three-dimensional figures | |
Write formulas for and calculate surface areas of boxes (rectangular prisms), cans (right circular cylinders), and balls (spheres) | |
Truth in Labeling | p. 486 |
Objectives | |
Write formulas for and calculate volumes of boxes and cans | |
Recognize geometric properties of three-dimensional figures | |
Analyzing an Ice Cream Cone | p. 491 |
Objectives | |
Write formulas for and calculate volumes of balls (spheres) and cones | |
Summertime | p. 497 |
Objectives | |
Use geometry formulas to solve problems | |
Use scale drawings in problem-solving | |
What Have I Learned? | p. 500 |
How Can I Practice? | p. 503 |
Summary | p. 507 |
Gateway Review | p. 513 |
More Problem Solving with Algebra and Mathematical Models | p. 519 |
Leasing a Copier | p. 519 |
Objectives | |
Describe a mathematical situation as a set of verbal statements | |
Translate verbal rules into symbolic equations | |
Solve problems involving equations of the form y = ax + b | |
Solve equations of the form y = ax + b for the input x | |
Evaluate expressions ax + b in equations of the form y = ax + b to obtain an output y | |
Windchill | p. 529 |
Objectives | |
Evaluate expressions to determine the output for a formula | |
Solve formulas for a specific variable | |
Comparing Energy Costs | p. 536 |
Objectives | |
Write symbolic equations from information organized in a table | |
Produce tables and graphs to compare outputs from two different mathematical models | |
Solve equations of the form ax + b = cx + d | |
Volume of a Storage Tank | p. 544 |
Objectives | |
Use property of exponents to multiply powers having the same base | |
Use property of exponents to raise a power to a power | |
Use the distributive property and properties of exponents to write an expression as an equivalent expression in expanded form | |
Math Magic | p. 550 |
Objectives | |
Recognize an algebraic expression as a code of instructions to obtain an output | |
Simplify algebraic expressions | |
Mathematical Modeling | p. 557 |
Objectives | |
Develop an equation to model and solve problems | |
Solve problems using formulas as models | |
Recognize patterns and trends between two variables using tables as models | |
Recognize patterns and trends between two variables using graphs as models | |
What Have I Learned? | p. 568 |
How Can I Practice? | p. 570 |
Summary | p. 577 |
Gateway Review | p. 579 |
Appendixes | |
Learning Math Opens Doors: Twelve Keys to Success | p. A-1 |
Selected Answers | p. A-15 |
Glossary | p. A-33 |
Index | p. I-1 |
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