Mathematics in Action

<p><strong>Chapter 1. Whole Numbers</strong></p> <p>Activity 1.1 Education Pays</p> <p>Objectives:</p> <p>1. Read and write whole numbers.</p> <p>2. Compare whole numbers using inequality symbols.</p> <p>3. Round whole numbers to specified place values.</p> <p>4. Use rounding for estimation.</p> <p>5. Classify whole numbers as even or odd, prime, or composite.</p> <p>6. Solve problems involving whole numbers.</p> <p>Activity 1.2 Bald Eagle Population Increasing Again</p> <p>Objectives:</p> <p>1. Read tables.</p> <p>2. Read bar graphs.</p> <p>3. Interpret bar graphs.</p> <p>4. Construct graphs.</p> <p>Activity 1.3 Bald Eagles Revisited</p> <p>Objectives:</p> <p>1. Add whole numbers by hand and mentally.</p> <p>2. Subtract whole numbers by hand and mentally.</p> <p>3. Estimate sums and differences using rounding.</p> <p>4. Recognize the associative property and the commutative property for addition.</p> <p>5. Translate a written statement into an arithmetic expression.</p> <p>Activity 1.4 Summer Camp</p> <p>Objectives:</p> <p>1. Multiply whole numbers and check calculations using a calculator.</p> <p>2. Multiply whole numbers using the distributive property.</p> <p>3. Estimate the product of whole numbers by rounding.</p> <p>4. Recognize the associative and commutative properties for multiplication.</p> <p>Activity 1.5 College Supplies</p> <p>Objectives:</p> <p>1. Divide whole numbers by grouping.</p> <p>2. Divide whole numbers by hand and by calculator.</p> <p>3. Estimate the quotient of whole numbers by rounding.</p> <p>4. Recognize that division is not commutative.</p> <p>Activity 1.6 Reach for the Stars</p> <p>Objectives:</p> <p>1. Use exponential notation.</p> <p>2. Factor whole numbers.</p> <p>3. Determine the prime factorization of a whole number.</p> <p>4. Recognize square numbers and roots of square numbers.</p> <p>5. Recognize cubed numbers.</p> <p>6. Apply the multiplication rule for numbers in exponential form with the same base.</p> <p>Activity 1.7 You and Your Calculator</p> <p>Objective:</p> <p>1. Use order of operations to evaluate arithmetic expressions.</p> <p>What Have I Learned?</p> <p>How Can I Practice?</p> <p>Chapter 1 Summary</p> <p>Chapter 1 Gateway Review</p> <p><strong>Chapter 2. Variables and Problem Solving</strong></p> <p>Activity 2.1 How Much Do I Need to Buy?</p> <p>Objectives:</p> <p>1. Recognize and understand the concept of a variable in context and symbolically.</p> <p>2. Translate a written statement (verbal rule) into a statement involving variables (symbolic rule).</p> <p>3. Evaluate variable expressions.</p> <p>4. Apply formulas (area, perimeter, and others) to solve contextual problems.</p> <p>Activity 2.2 How High Will It Go?</p> <p>Objectives:</p> <p>1. Recognize input/output relationship between variables in a formula or equation (two variables only).</p> <p>2. Evaluate variable expressions in formulas and equations.</p> <p>3. Generate a table of input and corresponding output values from a given equation, formula, or situation.</p> <p>4. Read, interpret, and plot points in rectangular coordinates that are obtained from evaluating a formula or equation.</p> <p>Activity 2.3 Are You Balanced?</p> <p>Objectives:</p> <p>1. Translate contextual situations and verbal statements into equations.</p> <p>2. Apply the fundamental principle of equality to solve equations of the forms x + a = |||em/em|||, a + x = |||em/em||| and x - a = |||em/em|||.</p> <p>Activity 2.4 How Far Will You Go? How Long Will It Take?</p> <p>Objectives:</p> <p>1. Apply the fundamental principle of equality to solve equations of the form ax = |||em/em|||, a ≠ 0.</p> <p>2. Translate contextual situations and verbal statements into equations.</p> <p>3. Use the relationship rate · time = amount in various contexts.</p> <p>Activity 2.5 Web Devices for Sale</p> <p>Objectives:</p> <p>1. Identify like terms.</p> <p>2. Combine like terms using the distributive property.</p> <p>3. Solve equations of the form ax + bx = c.</p> <p>Activity 2.6 Make Me an Offer</p> <p>Objectives:</p> <p>1. Use the basic steps for problem solving.</p> <p>2. Translate verbal statements into algebraic equations.</p> <p>3. Use the basic principles of algebra to solve real-world problems.</p> <p>What Have I Learned?</p> <p>How Can I Practice?</p> <p>Chapter 2 Summary</p> <p>Chapter 2 Gateway Review</p> <p><strong>Chapter 3. Problem Solving with Integers</strong></p> <p>Activity 3.1 On the Negative Side</p> <p>Objectives:</p> <p>1. Recognize integers.</p> <p>2. Represent quantities in real-world situations using integers.</p> <p>3. Represent integers on the number line.</p> <p>4. Compare integers.</p> <p>5. Calculate absolute values of integers.</p> <p>Activity 3.2 Maintaining Your Balance</p> <p>Objectives:</p> <p>1. Add and subtract integers.</p> <p>2. Identify properties of addition and subtraction of integers.</p> <p>Activity 3.3 Whats the Bottom Line?</p> <p>Objectives:</p> <p>1. Write formulas from verbal statements.</p> <p>2. Evaluate expressions in formulas.</p> <p>3. Solve equations of the form x + |||em/em||| = c and |||em/em||| - x = c.</p> <p>4. Solve formulas for a given variable.</p> <p>Activity 3.4 Riding in the Wind</p> <p>Objectives:</p> <p>1. Translate verbal rules into equations.</p> <p>2. Determine an equation from a table of values.</p> <p>3. Use a rectangular coordinate system to represent an equation graphically.</p> <p>Activity 3.5 Are You Physically Fit?</p> <p>Objectives:</p> <p>1. Multiply and divide integers.</p> <p>2. Perform calculations involving a sequence of operations.</p> <p>3. Apply exponents to integers.</p> <p>4. Identify properties of calculations that involve multiplication and division with zero.</p> <p>Activity 3.6 Integers and Tiger Woods</p> <p>Objectives:</p> <p>1. Use order of operations with expressions that involve integers.</p> <p>2. Apply the distributive property.</p> <p>3. Evaluate algebraic expressions and formulas using integers.</p> <p>4. Combine like terms.</p> <p>5. Solve equations of the form ax = |||em/em|||, where a ≠ 0, that involve integers.</p> <p>6. Solve equations of the form ax + bx = c, where a + |||em/em||| ≠ 0, that involve integers.</p> <p>What Have I Learned?</p> <p>How Can I Practice?</p> <p>Chapter 3 Summary</p> <p>Chapter 3 Gateway Review</p> <p><strong>Chapter 4. Problem Solving with Fractions</strong></p> <p>Activity 4.1 Are You Hungry?</p> <p>Objectives:</p> <p>1. Identify the numerator and the denominator of a fraction.</p> <p>2. Determine the greatest common factor (GCF).</p> <p>3. Determine equivalent fractions.</p> <p>4. Reduce fractions to equivalent fractions in lowest terms.</p> <p>5. Determine the least common denominator (LCD) of two or more fractions.</p> <p>6. Compare fractions.</p> <p>Activity 4.2 Get Your Homestead Land</p> <p>Objectives:</p> <p>1. Multiply and divide fractions.</p> <p>2. Recognize the sign of a fraction.</p> <p>3. Determine the reciprocal of a fraction.</p> <p>4. Solve equations of the form ax = |||em/em|||, a ≠ 0, that involve fractions.</p> <p>Activity 4.3 On the Road with Fractions</p> <p>Objectives:</p> <p>1. Add and subtract fractions and with the same denominators.</p> <p>2. Add and subtract fractions and with different denominators.</p> <p>3. Solve equations in the form x + |||em/em||| = c, and x - |||em/em||| = c that involve fractions.</p> <p>Activity 4.4 Hanging With Fractions</p> <p>Objectives:</p> <p>1. Calculate powers and square roots of fractions.</p> <p>2. Evaluate equations that involve powers.</p> <p>3. Evaluate equations that involve square roots.</p> <p>4. Use order of operations to calculate numerical expressions that involve fractions.</p> <p>5. Evaluate algebraic expressions that involve fractions.</p> <p>6. Use the distributive property with fractions.</p> <p>7. Solve equations of the form ax + bx = c with fraction coefficients.</p> <p>What Have I Learned?</p> <p>How Can I Practice?</p> <p>Chapter 4 Summary</p> <p>Chapter 4 Gateway Review</p> <p><strong>Chapter 5. Problem Solving with Mixed Numbers and Decimals</strong></p> <p>Cluster 1 Mixed Numbers and Improper Fractions</p> <p>Activity 5.1 Food for Thought</p> <p>Objectives:</p> <p>1. Determine equivalent fractions.</p> <p>2. Add and subtract fractions and mixed numbers with the same denominators.</p> <p>3. Convert mixed numbers to improper fractions and improper fractions to mixed numbers.</p> <p>Activity 5.2 Mixing with Denominators</p> <p>Objectives:</p> <p>1. Determine the least common denominator (LCD) for two or more mixed numbers.</p> <p>2. Add and subtract mixed numbers with different denominators.</p> <p>3. Solve equations in the form x + |||em/em||| = c and x - |||em/em||| = c that involve mixed numbers.</p> <p>Activity 5.3 Tiling the Bathroom</p> <p>Objectives:</p> <p>1. Multiply and divide mixed numbers.</p> <p>2. Evaluate expressions with mixed numbers.</p> <p>3. Calculate the square root of a mixed number.</p> <p>4. Solve equations of the form ax + |||em/em||| = 0, a ≠ 0, that involve mixed numbers.</p> <p>Cluster 1 What Have I Learned?</p> <p>Cluster 1 How Can I Practice?</p> <p>Cluster 2 Decimals</p> <p>Activity 5.4 What Are You Made Of?</p> <p>Objectives:</p> <p>1. Identify place values of numbers written in decimal form.</p> <p>2. Convert a decimal to a fraction or a mixed number and vice versa.</p> <p>3. Classify decimals.</p> <p>4. Compare decimals.</p> <p>5. Read and write decimals.</p> <p>6. Round decimals.</p> <p>Activity 5.5 Dive into Decimals</p> <p>Objectives:</p> <p>1. Add and subtract decimals.</p> <p>2. Compare and interpret decimal numbers.</p> <p>3. Solve equations of the type x + |||em/em||| = c and x - |||em/em||| = c that involve decimals.</p> <p>Activity 5.6 Quality Points and GPA: Tracking Academic Standing</p> <p>Objectives:</p> <p>1. Multiply and divide decimals.</p> <p>2. Estimate products and quotients involving decimals.</p> <p>Activity 5.7 Tracking Temperature</p> <p>Objectives:</p> <p>1. Use the order of operations to evaluate expressions that include decimals.</p> <p>2. Use the distributive property in calculations that involve decimals.</p> <p>3. Evaluate formulas that include decimals.</p> <p>4. Solve equations of the form ax = c and ax + bx = c that involve decimals.</p> <p>Activity 5.8 Think Metric</p> <p>Objectives:</p> <p>1. Know the metric prefixes and their decimal values.</p> <p>2. Convert measurements between metric quantities.</p> <p>Cluster 2 What Have I Learned?</p> <p>Cluster 2 How Can I Practice?</p> <p>Chapter 5 Summary</p> <p>Chapter 5 Gateway Review</p> <p><strong>Chapter 6. Problem Solving with Ratios, Proportions, and Percents</strong></p> <p>Activity 6.1 Everything is Relative</p> <p>Objectives:</p> <p>1. Understand the distinction between absolute and relative measure.</p> <p>2. Write a ratio in its verbal, fraction, decimal, and percent formats.</p> <p>Activity 6.2 Four out of Five Dentists Prefer the Brooklyn Dodgers?</p> <p>Objectives:</p> <p>1. Recognize that equivalent fractions lead to a proportion.</p> <p>2. Use a proportion to solve a problem that involves ratios.</p> <p>Activity 6.3 The Devastation of AIDS in Africa</p> <p>Objectives:</p> <p>1. Use proportional reasoning to apply a known ratio to a given piece of information.</p> <p>2. Write an equation using the relationship ratio · total = part and then solve the resulting equation.</p> <p>Activity 6.4 Who Really Did Better?</p> <p>Objectives:</p> <p>1. Define actual and relative change.</p> <p>2. Distinguish between actual and relative change.</p> <p>Activity 6.5 Dont Forget the Sales Tax</p> <p>Objectives:</p> <p>1. Define and determine growth factors.</p> <p>2. Use growth factors in problems that involve percent increases.</p> <p>Activity 6.6 Its All on Sale!</p> <p>Objectives:</p> <p>1. Define and determine decay factors.</p> <p>2. Use decay factors in problems that involve percent decreases.</p> <p>Activity 6.7 Take an Additional 20% Off</p> <p>Objective:</p> <p>1. Apply consecutive growth and/or decay factors to problems that involve two or more percent changes.</p> <p>Activity 6.8 Fuel Economy</p> <p>Objectives:</p> <p>1. Apply rates directly to solve problems.</p> <p>2. Use proportions to solve problems involving rates.</p> <p>3. Use unit analysis or dimensional analysis to solve problems that involve consecutive rates.</p> <p>What Have I Learned?</p> <p>How Can I Practice?</p> <p>Chapter 6 Summary</p> <p>Chapter 6 Gateway Review</p> <p><strong>Chapter 7. Problem Solving with Geometry</strong></p> <p>Activity 7.1 Walking around Bases, Gardens, and Other Figures</p> <p>Objectives:</p> <p>1. Recognize perimeter as a geometric property of plane figures.</p> <p>2. Write formulas for, and calculate perimeters of, squares, rectangles, triangles, parallelograms, trapezoids, and</p> <p>ygons.</p> <p>3. Use unit analysis to solve problems that involve perimeter.</p> <p>Activity 7.2 Circles Are Everywhere</p> <p>Objectives:</p> <p>1. Measure the lengths of the diameter and circumference of circles.</p> <p>2. Develop and use formulas for calculating circumferences of circles.</p> <p>Activity 7.3 Lance Armstrong and You</p> <p>Objectives:</p> <p>1. Calculate perimeters of many-sided plane figures using formulas and combinations of formulas.</p> <p>2. Use unit analysis to solve problems that involve perimeters.</p> <p>Activity 7.4 Baseball Diamonds, Gardens, and Other Figures Revisited</p> <p>Objectives:</p> <p>1. Write formulas for areas of squares, rectangles, parallelograms, triangles, trapezoids, and polygons.</p> <p>2. Calculate areas of polygons using appropriate formulas.</p> <p>Activity 7.5 How Big Is That Circle?</p> <p>Objectives:</p> <p>1. Develop formulas for the area of a circle.</p> <p>2. Use formulas to determine areas of circles.</p> <p>Activity 7.6 A New Pool</p>