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Preface | |

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Whole Numbers | |

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Education Pays | |

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Objectives | |

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Read and write whole numbers | |

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Compare whole numbers using inequality symbols | |

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Round whole numbers to specified place values | |

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Use rounding for estimation | |

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Classify whole numbers as even or odd, prime, or composite | |

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Solve problems involving whole numbers | |

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Bald Eagle Population Increasing Again | |

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Objectives | |

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Read tables | |

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Read bar graphs | |

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Interpret bar graphs | |

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Construct graphs | |

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Bald Eagles Revisited | |

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Objectives | |

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Add whole numbers by hand and mentally | |

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Subtract whole numbers by hand and mentally | |

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Estimate sums and differences using rounding | |

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Recognize the associative property and the commutative property for addition | |

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Translate a written statement into an arithmetic expression | |

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Summer Camp | |

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Objectives | |

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Multiply whole numbers and check calculations using a calculator | |

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Multiply whole numbers using the distributive property | |

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Estimate the product of whole numbers by rounding | |

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Recognize the associative and commutative properties for multiplication | |

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College Supplies | |

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Objectives | |

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Divide whole numbers by grouping | |

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Divide whole numbers by hand and by calculator | |

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Estimate the quotient of whole numbers by rounding | |

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Recognize the noncommutative property for division | |

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Reach for the Stars | |

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Objectives | |

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Use exponential notation | |

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Factor whole numbers | |

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Determine the prime factorization of a whole number | |

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Recognize square numbers and roots of square numbers | |

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Recognize cubed numbers | |

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Apply the multiplication rule for numbers in exponential form with the same base | |

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You and Your Calculator | |

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Objectives | |

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Use order of operations to evaluate arithmetic expressions | |

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Use order of operations to evaluate formulas involving whole numbers | |

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What Have I Learned? | |

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How Can I Practice? | |

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Summary | |

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Gateway Review | |

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Variables and Problem Solving | |

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How Much Do I Need to Buy? | |

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Objectives | |

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Recognize and understand the concept of a variable in context and symbolically | |

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Translate a written statement (verbal rule) into a statement involving variables (symbolic rule) | |

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Evaluate variable expressions | |

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Apply formulas (area, perimeter, and others) to solve contextual problems | |

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How High Will It Go? | |

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Objectives | |

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Recognize input/output relationship between variables in a formula or equation (two variables only) | |

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Evaluate variable expressions in formulas and equations | |

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Generate a table of input and corresponding output values from a given equation, formula, or situation | |

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Read, interpret, and plot points in rectangular coordinates that are obtained from evaluating a formula or equation | |

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Are You Balanced? | |

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Objectives | |

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Translate contextual situations and verbal statements into equations | |

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Apply the fundamental principle of equality to solve equations of the forms x + a = b, a + x = b and x - a = b | |

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How Far Will You Go? How Long Will It Take? | |

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Objectives | |

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Apply the fundamental principle of equality to solve equations of the form ax = b, a [NotEqual] 0 | |

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Translate contextual situations and verbal statements into equations | |

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Use the relationship rate [Middot] time = amount in various contexts | |

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Web Devices for Sale | |

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Objectives | |

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Identify like terms | |

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Combine like terms using the distributive property | |

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Solve equations of the form ax + bx = c | |

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Make Me an Offer | |

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Objectives | |

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Use the basic steps for problem solving | |

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Translate verbal statements into algebraic equations | |

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Use the basic principles of algebra to solve real-world problems | |

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What Have I Learned? | |

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How Can I Practice? | |

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Summary | |

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Gateway Review | |

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Problem Solving with Rational Numbers: Addition and Subtraction of Integers, Fractions, and Decimals | |

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Adding and Subtracting Integers | |

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On the Negative Side | |

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Objectives | |

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Identify integers | |

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Represent quantities in real-world situations using Integers | |

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Compare integers | |

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Calculate absolute value of integers | |

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Maintaining Your Balance | |

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Objectives | |

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Add and subtract integers | |

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Identify properties of addition and subtraction of integers | |

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What's the Bottom Line? | |

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Objectives | |

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Write formulas from verbal statements | |

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Evaluate expressions in formulas | |

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Solve equations of the form X + b = c and b - x = c | |

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Solve formulas for a given variable | |

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Riding in the Wind | |

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Objectives | |

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Translate verbal rules into equations | |

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Determine an equation from a table of values | |

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Use a rectangular coordinate system to represent an equation graphically | |

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What Have I Learned? | |

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How Can I Practice? | |

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Adding and Subtracting Fractions | |

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Are You Hungry? | |

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Objectives | |

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Identify the numerator and denominator of a fraction | |

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Determine the greatest common factor (GCF) | |

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Determine equivalent fractions | |

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Reduce fractions to equivalent fractions in lowest terms | |

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Convert mixed numbers to improper fractions and improper fractions to mixed numbers | |

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Determine the least common denominator (LCD) of two or more fractions | |

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Compare fractions | |

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Food for Thought | |

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Objective | |

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Add and subtract fractions and mixed numbers with the same denominators | |

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Math Is a Trip | |

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Objectives | |

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Determine the least common denominator (LCD) for two or more fractions | |

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Add and subtract fractions with different denominators | |

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Solve equations in the form x + b = c and x - b = c that involve fractions | |

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What Have I Learned? | |

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How Can I Practice? | |

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Adding and Subtracting Decimals | |

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What Are You Made Of? | |

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Objectives | |

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Identify place values of numbers written in decimal form | |

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Convert a decimal to a fraction or a mixed number | |

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Compare decimals | |

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Read and write decimals | |

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Round decimals | |

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Think Metric | |

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Objectives | |

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Know the metric prefixes and their decimal values | |

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Convert measurements between metric quantities | |

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Dive into Decimals | |

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Objectives | |

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Add and subtract decimals | |

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Compare and interpret decimal numbers | |

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Boiling, Freezing, and Financial Aid | |

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Objectives | |

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Add and subtract positive and negative decimal numbers | |

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Interpret and compare decimal numbers | |

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Solve equations of the type x + b = c and x - b = c involving decimal numbers | |

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What Have I Learned? | |

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How Can I Practice? | |

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Summary | |

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Gateway Review | |

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Multiplication and Division of Rational Numbers | |

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Multiplying and Dividing Integers | |

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Are You Physically Fit? | |

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Objectives | |

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Multiply and divide integers | |

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Perform calculations involving a sequence of operations | |

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Apply exponents to integers | |

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Identify properties of calculations involving multiplication and division with zero | |

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Integers and Tiger Woods | |

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Objectives | |

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Use order of operations with expressions involving integers | |

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Apply the distributive property | |

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Evaluate algebraic expressions and formulas using integers | |

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Solve equations of the form ax = b, where a [NotEqual] 0, involving integers | |

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What Have I Learned? | |

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How Can I Practice? | |

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Multiplying and Dividing Fractions | |

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Get Your Homestead Land | |

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Objectives | |

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Multiply and divide fractions | |

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Recognize the sign of a fraction | |

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Determine the reciprocal of a fraction | |

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Solve equations of form ax = b, a [NotEqual] 0, that involve fractions | |

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Tiling the Bathroom | |

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Objectives | |

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Multiply and divide mixed numbers | |

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Evaluate expressions with mixed numbers | |

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Calculate the square root of a mixed number | |

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What Have I Learned? | |

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How Can I Practice? | |

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Multiplying and Dividing Decimals | |

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Quality Points and GPA: Tracking Academic Standing | |

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Objectives | |

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Multiply and divide decimals | |

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Estimate products and quotients involving decimals | |

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Tracking Temperature | |

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Objectives | |

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Use the order of operations to evaluate expressions that include decimals | |

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Use the distributive property in calculations involving decimals | |

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Evaluate formulas that include decimals | |

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Solve equations of the form ax = b that include decimals | |

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What Have I Learned? | |

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How Can I Practice? | |

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Summary | |

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Gateway Review | |

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Problem Solving with Ratios, Proportions, and Percents | |

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Everything Is Relative | |

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Objectives | |

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Understand the distinction between actual and relative measure | |

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Write a ratio in its verbal, fraction, decimal and percent formats | |

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The Devastation of AIDS in Africa | |

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Objectives | |

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Use proportional reasoning to apply a known ratio to a given piece of information | |

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Write an equation using the relationship "ratio [Middot] total = part" and then solve the resulting equation | |

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Who Really Did Better? | |

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Objectives | |

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Define actual and relative change | |

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Distinguish between actual and relative change | |

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Don't Forget the Sales Tax | |

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Objectives | |

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Define and determine growth factors | |

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Use growth factors in problems involving percent increases | |

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It's All on Sale! | |

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Objectives | |

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Define and determine decay factors | |

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Use decay factors in problems involving percent decreases | |

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Take an Additional 20% Off | |

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Objective | |

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Apply consecutive growth and/or decay factors to problems involving two or more percent changes | |

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Fuel Economy | |

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Objectives | |

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Apply rates directly to solve problems | |

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Use unit analysis (dimensional analysis) to solve problems that involve consecutive rates | |

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Four out of Five Dentists Prefer the Brooklyn Dodgers? | |

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Objectives | |

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Recognize that equivalent fractions lead to proportions | |

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Use proportions to solve problems involving ratios and rates | |

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What Have I Learned? | |

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How Can I Practice? | |

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Summary | |

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Gateway Review | |

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Problem Solving with Geometry | |

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The Geometry of Two-Dimensional Plane Figures | |

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Walking around Bases, Gardens, Trusses, and Other Figures | |

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Objectives | |

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Recognize perimeter as a geometric property of plane figures | |

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Write formulas for, and calculate perimeters of, squares, rectangles, triangles, parallelograms, trapezoids, and polygons | |

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Use unit analysis to solve problems involving perimeter | |

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Circles Are Everywhere | |

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Objectives | |

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Measure lengths of diameters and circumferences of circles | |

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Develop and use formulas for calculating circumferences of circles | |

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Lance Armstrong and You | |

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Objectives | |

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Calculate perimeters of many-sided plane figures using formulas and combinations of formulas | |

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Use unit analysis to solve problems involving perimeters | |

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Baseball Diamonds, Gardens, and Other Figures Revisited | |

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Objectives | |

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Write formulas for areas of squares, rectangles, parallelograms, triangles, trapezoids, and polygons | |

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Calculate areas of polygons using appropriate formulas | |

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How Big Is That Circle Really? | |

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Objectives | |

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Develop a formula for the area of a circle | |

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Use the formula to determine areas of circles | |

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A New Pool and Other Home Improvements | |

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Objectives | |

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Solve problems in context using geometric formulas | |

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Distinguish between problems that require area formulas and those that require perimeter formulas | |

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How Big Is That Angle? | |

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Objectives | |

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Measure sizes of angles with a protractor | |

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Classify triangles as equiangular, equilateral, isosceles, or scalene | |

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How About Pythagoras? | |

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Objectives | |

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Develop and use the Pythagorean Theorem for right triangles | |

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Calculate the square root of numbers other than perfect squares | |

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Apply the Pythagorean Theorem in context | |

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Moving Up with Math | |

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Objectives | |

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Recognize the geometric properties of similar triangles | |

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Use similar triangles in indirect measurement | |

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What Have I Learned? | |

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How Can I Practice? | |

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The Geometry of Three-Dimensional Space Figures | |

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Painting Your Way through Summer | |

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Objectives | |

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Recognize geometric properties of three-dimensional figures | |

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Write formulas for and calculate surface areas of boxes (rectangular prisms), cans (right circular cylinders), and balls (spheres) | |

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Truth in Labeling | |

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Objectives | |

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Write formulas for and calculate volumes of boxes and cans | |

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Recognize geometric properties of three-dimensional figures | |

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Analyzing an Ice Cream Cone | |

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Objectives | |

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Write formulas for and calculate volumes of balls (spheres) and cones | |

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Summertime | |

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Objectives | |

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Use geometry formulas to solve problems | |

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Use scale drawings in problem-solving | |

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What Have I Learned? | |

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How Can I Practice? | |

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Summary | |

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Gateway Review | |

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More Problem Solving with Algebra and Mathematical Models | |

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Leasing a Copier | |

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Objectives | |

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Describe a mathematical situation as a set of verbal statements | |

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Translate verbal rules into symbolic equations | |

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Solve problems involving equations of the form y = ax + b | |

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Solve equations of the form y = ax + b for the input x | |

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Evaluate expressions ax + b in equations of the form y = ax + b to obtain an output y | |

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Windchill | |

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Objectives | |

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Evaluate expressions to determine the output for a formula | |

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Solve formulas for a specific variable | |

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Comparing Energy Costs | |

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Objectives | |

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Write symbolic equations from information organized in a table | |

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Produce tables and graphs to compare outputs from two different mathematical models | |

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Solve equations of the form ax + b = cx + d | |

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Volume of a Storage Tank | |

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Objectives | |

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Use property of exponents to multiply powers having the same base | |

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Use property of exponents to raise a power to a power | |

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Use the distributive property and properties of exponents to write an expression as an equivalent expression in expanded form | |

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Math Magic | |

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Objectives | |

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Recognize an algebraic expression as a code of instructions to obtain an output | |

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Simplify algebraic expressions | |

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Mathematical Modeling | |

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Objectives | |

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Develop an equation to model and solve problems | |

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Solve problems using formulas as models | |

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Recognize patterns and trends between two variables using tables as models | |

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Recognize patterns and trends between two variables using graphs as models | |

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What Have I Learned? | |

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How Can I Practice? | |

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Summary | |

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Gateway Review | |

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Appendixes | |

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Learning Math Opens Doors: Twelve Keys to Success | |

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Selected Answers | |

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Glossary | |

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Index | |