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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 | |