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Chapter 1. Whole Numbers
Activity 1.1. Education Pays
Objectives.
1. Read and write whole numbers.
2. Compare whole numbers using inequality symbols.
3. Round whole numbers to specified place values.
4. Use rounding for estimation.
5. Classify whole numbers as even or odd, prime, or composite.
6. Solve problems involving whole numbers.
Activity 1.2. Bald Eagle Population Increasing Again
Objectives.
1. Read tables.
2. Read bar graphs.
3. Interpret bar graphs.
4. Construct graphs.
Activity 1.3. Bald Eagles Revisited
Objectives.
1. Add whole numbers by hand and mentally.
2. Subtract whole numbers by hand and mentally.
3. Estimate sums and differences using rounding.
4. Recognize the associative property and the commutative property for addition.
5. Translate a written statement into an arithmetic expression.
Activity 1.4. Summer Camp
Objectives.
1. Multiply whole numbers and check calculations using a calculator.
2. Multiply whole numbers using the distributive property.
3. Estimate the product of whole numbers by rounding.
4. Recognize the associative and commutative properties for multiplication.
Activity 1.5. College Supplies
Objectives.
1. Divide whole numbers by "grouping."
2. Divide whole numbers "by hand" and by calculator.
3. Estimate the quotient of whole numbers by rounding.
4. Recognize noncommutative property for division.
Activity 1.6. Reach for the Stars
Objectives.
1. Use exponential notation.
2. Factor whole numbers.
3. Determine the prime factorization of a whole number.
4. Recognize square numbers and roots of square numbers.
5. Recognize cubed numbers.
6. Apply the multiplication rule for numbers in exponential form with the same base.
Activity 1.7. You and Your Calculator
Objectives.
1. Use order of operations to evaluate arithmetic expressions.
2. Use order of operations to evaluate formulas involving whole numbers.
What Have I Learned?
How Can I Practice?
Chapter 1 Summary
Chapter 1 Gateway Review
Chapter 2. Variables and Problem Solving
Activity 2.1. How Much Do I Need to Buy?
Objectives.
1. Recognize and understand the concept of a variable in context and symbolically.
2. Translate a written statement (verbal rule) into a statement involving variables (symbolic rule).
3. Evaluate variable expressions.
4. Apply formulas (area, perimeter, and others) to solve contextual problems.
Activity 2.2. How High Will It Go?
Objectives.
1. Recognize input/output relationship between variables in a formula or equation (two variables only).
2. Evaluate variable expressions in formulas and equations.
3. Generate a table of input and corresponding output values from a given equation, formula, or situation.
4. Read, interpret, and plot points in rectangular coordinates that are obtained from evaluating a formula or equation.
Activity 2.3. Are You Balanced?
Objectives.
1. Translate contextual situations and verbal statements into equations.
2. Apply the fundamental principle of equality to solve equations of the forms x + a = a + x = b and x - a = b.
Activity 2.4. How Far Will You Go? How Long Will It Take?
Objectives.
1. Apply the fundamental principle of equality to solve equations of the form ax = b, a ? 0.
2. Translate contextual situations and verbal statements into equations.
3. Use the formula rate x time = amount in various contexts.
Activity 2.5. Web Devices for Sale
Objectives.
1. Identify like terms.
2. Combine like terms using the distributive property.
3. Solve equations of the form ax + bx = c.
Activity 2.6. Make Me an Offer
Objectives.
1. Use the basic steps for problem solving.
2. Translate verbal statements into algebraic equations.
3. Use the basic principles of algebra to solve real-world problems.
What Have I Learned?
How Can I Practice?
Chapter 2 Summary
Chapter 2 Gateway Review
Chapter 3. Problem Solving with Rational Numbers. Addition and Subtraction of Integers, Fractions, and Decimals
Cluster 1. Adding and Subtracting Integers
Activity 3.1. On the Negative Side
Objectives.
1. Identify integers.
2. Represent quantities in real-world situations using integers.
3. Compare integers.
4. Calculate absolute value of integers.
Activity 3.2. Maintaining Your Balance
Objectives.
1. Add and subtract integers.
2. Identify properties of addition and subtraction of integers.
Activity 3.3. What's the Bottom Line?
Objectives.
1. Write formulas from verbal statements.
2. Evaluate expressions in formulas.
3. Solve equations of the form x + b = c and b - x = c.
4. Solve formulas for a given variable.
Activity 3.4. Riding in the Wind
Objectives.
1. Translate verbal rules into equations.
2. Determine an equation from a table of values.
3. Use a rectangular coordinate system to represent an equation graphically.
What Have I Learned?
How Can I Practice?
Cluster 2. Adding and Subtracting Fractions
Activity 3.5. Are You Hungry?
Objectives.
1. Identify the numerator and the denominator of a fraction.
2. Determine the greatest common factor (GCF).
3. Determine equivalent fractions.
4. Reduce fractions to equivalent fractions in lowest terms.
5. Convert mixed numbers to improper fractions and improper fractions to mixed numbers.
6. Determine the least common denominator (LCD) of two or more fractions.
7. Compare fractions.
Activity 3.6. Food for Thought
Objective.
1. Add and subtract fractions and mixed numbers with the same denominators.
Activity 3.7. Math Is a Trip
Objectives.
1. Determine the least common denominator (LCD) for two or more fractions.
2. Add and subtract fractions with different denominators.
3. Solve equations in the form x + b = c and x - b = c that involve fractions.
What Have I Learned?
How Can I Practice?
Cluster 3. Adding and Subtracting Decimals
Activity 3.8. What Are You Made Of?
Objectives.
1. Identify place values of numbers written in decimal form.
2. Convert a decimal to a fraction or a mixed number.
3. Compare decimals.
4. Read and write decimals.
5. Round decimals.
Activity 3.9. Think Metric
Objectives.
1. Know the metric prefixes and their decimal values.
2. Convert between metric quantities.
Activity 3.10. Dive into Decimals
Objectives.
1. Add and subtract decimals.
2. Compare and interpret decimal numbers.
Activity 3.11. Boiling, Freezing, and Financial Aid
Objectives.
1. Add and subtract positive and negative decimal numbers.
2. Interpret and compare decimal numbers.
3. Solve equations of the type x + b = c and x - b = c involving decimal numbers.
What Have I Learned?
How Can I Practice?
Chapter 3 Summary
Chapter 3 Gateway Review
Chapter 4. Multiplication and Division of Rational Numbers
Cluster 1. Multiplying and Dividing Integers
Activity 4.1. Are You Physically Fit?
Objectives.
1. Multiply and divide integers.
2. Perform calculations involving a sequence of operations.
3. Apply exponents to integers.
4. Identify properties of calculations involving multiplication and division with zero.
Activity 4.2. Integers and Tiger Woods
Objectives.
1. Use order of operations with expressions involving integers.
2. Apply the distributive property.
3. Evaluate algebraic expressions and formulas using integers.
4. Solve equations of the form ax = b, where a does not equal 0, involving integers.
What Have I Learned?
How Can I Practice?
Cluster 2. Multiplying and Dividing Fractions
Activity 4.3. Get Your Homestead Land
Objectives.
1. Multiply and divide fractions.
2. Recognize the sign of a fraction.
3. Determine the reciprocal of a fraction.
4. Solve equations of form ax = b, where a does not equal 0, involving fractions.
Activity 4.4. Tiling the Bathroom
Objectives.
1. Multiply and divide mixed numbers.
2. Evaluate expressions with mixed numbers.
3. Calculate the square root of a mixed number.
What Have I Learned?
How Can I Practice?
Cluster 3. Multiplying and Dividing Decimals
Activity 4.5. Quality Points and GPA. Tracking Academic Standing
Objectives.
1. Multiply and divide decimals.
2. Estimate products and quotients involving decimals.
Activity 4.6. Tracking Temperature
Objectives.
1. Use the order of operations to evaluate expressions that include decimals.
2. Use the distributive property in calculations involving decimals.
3. Evaluate formulas that include decimals.
4. Solve equations of the form ax = c that include decimals.
What Have I Learned?
How Can I Practice?
Chapter 4 Summary
Chapter 4 Gateway Review
Chapter 5. Problem Solving with Ratios, Proportions, and Percents
Activity 5.1. Everything is Relative
Objectives.
1. Understand the distinction between absolute and relative measure.
2. Write a ratio in its fraction, decimal, and percent formats.
Activity 5.2. The Devastation of AIDS in Africa
Objectives.
1. Use proportional reasoning to apply a known ratio to a given piece of information.
2. Write an equation using the relationship "ratio x total = part" and then solve the resulting equation.
Activity 5.3. Who Really Did Better?
Objectives.
1. Define actual and relative change.
2. Distinguish between actual and relative change.
Activity 5.4. Don't Forget the Sales Tax
Objectives.
1. Define and determine growth factors.
2. Use growth factors in problems involving percent increases.
Activity 5.5. It's All on Sale!
Objectives.
1. Define and determine decay factors.
2. Use decay factors in problems involving percent decreases.
Activity 5.6. Take an Additional 20% Off
Objective.
1. Apply consecutive growth and/or decay factors to problems involving two or more percent changes.
Activity 5.7. Fuel Economytives.
1. Apply rates directly to solve problems.
2. Use u
Objecnit analysis or dimensional analysis to solve problems that involve consecutive rates.
Activity 5.8. Four out of Five Dentists Prefer the Brooklyn Dodgers?
Objectives.
1. Recognize that equivalent fractions lead to proportions.
2. Use proportions to solve problems involving ratios and rates.
What Have I Learned?
How Can I Practice?
Chapter 5 Summary
Chapter 5 Gateway Review
Chapter 6. Problem Solving with Geometry
Cluster 1. The Geometry of Two-Dimensional Plane Figures
Activity 6.1. Walking around Bases, Gardens, Trusses, and Other Figures
Objectives.
1. Recognize perimeter as a geometric property of plane figures.
2. Write formulas for, and calculate perimeters of, squares, rectangles, triangles, parallelograms, trapezoids, and polygons.
3. Use unit analysis to solve problems involving perimeter.
Activity 6.2. Circles Are Everywhere
Objectives.
1. Measure the lengths of the diameter and circumference of circles.
2. Develop and use formulas for the circumference of a circle.
Activity 6.3. Lance Armstrong and You
Objectives.
1. Calculate perimeters of many-sided plane figures using formulas and combinations of formulas.
2. Use unit analysis to solve problems involving perimeters.
Activity 6.4. Baseball Diamonds, Gardens, and Other Figures Revisited
Objectives.
1. Write formulas for areas of squares, rectangles, parallelograms, triangles, trapezoids, and polygons.
2. Calculate the areas of polygons using appropriate formulas.
Activity 6.5. How Big Is That Circle Really?
Objectives.
1. Develop formulas for the area of a circle.
2. Use formulas to determine areas of circles.
Activity 6.6. A New Pool and Other Home Improvements
Objectives.
1. Solve problems in context using geometric formulas.
2. Distinguish between problems requiring area formulas and perimeter formulas.
Laboratory Activity 6.7. How Big Is That Angle?
Objectives.
1. Measure the size of an angle with a protractor.
2. Classify triangles as equiangular, equilateral, isosceles, or scalene.
Laboratory Activity 6.8. How About Pythagoras?
Objectives.
1. Develop and use the Pythagorean Theorem for right triangles.
2. Calculate the square root of numbers other than perfect squares.
3. Apply the Pythagorean Theorem in context.
Activity 6.9. Moving Up with Math
Objectives.
1. Recognize the geometric properties of similar triangles.
2. Use similar triangles in indirect measurement.
What Have I Learned?
How Can I Practice?
Cluster 2. The Geometry of Three-Dimensional Space Figures
Activity 6.10. Painting Your Way through the Summer
Objectives.
1. Recognize geometric properties of three-dimensional figures.
2. Write formulas for and calculate surface areas of boxes (rectangular prisms), cans (right circular cylinders), and balls (spheres).
Activity 6.11. Truth in Labeling
Objectives.
1. Write formulas for and calculate volumes of boxes and cans.
2. Recognize geometric properties of three-dimensional figures.
Activity 6.12. Analyzing an Ice Cream Cone
Objective.
1. Write formulas for and calculate volumes of balls (spheres) and cones.
Laboratory Activity 6.13. Summertime
Objectives.
1. Use geometry formulas to solve problems.
2. Use scale drawings in the problem-solving process.
What Have I Learned?
How Can I Practice?
Chapter 6 Summary
Chapter 6 Gateway Review
Chapter 7. More Problem Solving with Algebra and Mathematical Models
Activity 7.1. Leasing a Copier
Objectives.
1. Describe a mathematical model as a set of verbal statements.
2. Translate verbal rules into symbolic equations.
3. Solve problems involving equations of the form y = ax + b.
4. Solvve equations of the form y = ax + b for the input x.
5. Evaluate expressions ax + b in the equations of the form y = ax + b to obtain an output y.
Activity 7.2. Windchill
Objectives.
1. Evaluate formulas to determine an output.
2. Solve formulas for a specific variable.
Activity 7.3. Comparing Energy Costs
Objectives.
1. Write symbolic equations from information organized in a table.
2. Produce tables and graphs to compare outputs from two different mathematical models.
3. Solve equations of the form ax + b = cx + d.
Activity 7.4. Volume of a Storage Tank
Objectives.
1. Use property of exponents to multiply powers having the same base.
2. Use property of exponents to raise a power to a power.
3. Use the distributive property and properties of exponents to write an expression as an equivalent expression in expanded form.
Activity 7.5. Math Magic
Objectives.
1. Recognize an algebraic expression as a code of instructions to obtain an output.
2. Simplify algebraic expressions.
Activity 7.6. Mathematical Modeling
Objectives.
1. Develop an equation to model and solve problems.
2. Solve problems using formulas as models.
3. Recognize patterns and trends between two variables using tables as models.
4. Recognize patterns and trends between two variables using graphs as models
Table of Contents
Chapter 1. Whole Numbers
Activity 1.1. Education Pays
Objectives.
1. Read and write whole numbers.
2. Compare whole numbers using inequality symbols.
3. Round whole numbers to specified place values.
4. Use rounding for estimation.
5. Classify whole numbers as even or odd, prime, or composite.
6. Solve problems involving whole numbers.
Activity 1.2. Bald Eagle Population Increasing Again
Objectives.
1. Read tables.
2. Read bar graphs.
3. Interpret bar graphs.
4. Construct graphs.
Activity 1.3. Bald Eagles Revisited
Objectives.
1. Add whole numbers by hand and mentally.
2. Subtract whole numbers by hand and mentally.
3. Estimate sums and differences using rounding.
4. Recognize the associative property and the commutative property for addition.
5. Translate a written statement into an arithmetic expression.
Activity 1.4. Summer Camp
Objectives.
1. Multiply whole numbers and check calculations using a calculator.
2. Multiply whole numbers using the distributive property.
3. Estimate the product of whole numbers by rounding.
4. Recognize the associative and commutative properties for multiplication.
Activity 1.5. College Supplies
Objectives.
1. Divide whole numbers by "grouping."
2. Divide whole numbers "by hand" and by calculator.
3. Estimate the quotient of whole numbers by rounding.
4. Recognize noncommutative property for division.
Activity 1.6. Reach for the Stars
Objectives.
1. Use exponential notation.
2. Factor whole numbers.
3. Determine the prime factorization of a whole number.
4. Recognize square numbers and roots of square numbers.
5. Recognize cubed numbers.
6. Apply the multiplication rule for numbers in exponential form with the same base.
Activity 1.7. You and Your Calculator
Objectives.
1. Use order of operations to evaluate arithmetic expressions.
2. Use order of operations to evaluate formulas involving whole numbers.
What Have I Learned?
How Can I Practice?
Chapter 1 Summary
Chapter 1 Gateway Review
Chapter 2. Variables and Problem Solving
Activity 2.1. How Much Do I Need to Buy?
Objectives.
1. Recognize and understand the concept of a variable in context and symbolically.
2. Translate a written statement (verbal rule) into a statement involving variables (symbolic rule).
3. Evaluate variable expressions.
4. Apply formulas (area, perimeter, and others) to solve contextual problems.
Activity 2.2. How High Will It Go?
Objectives.
1. Recognize input/output relationship between variables in a formula or equation (two variables only).
2. Evaluate variable expressions in formulas and equations.
3. Generate a table of input and corresponding output values from a given equation, formula, or situation.
4. Read, interpret, and plot points in rectangular coordinates that are obtained from evaluating a formula or equation.
Activity 2.3. Are You Balanced?
Objectives.
1. Translate contextual situations and verbal statements into equations.
2. Apply the fundamental principle of equality to solve equations of the forms x + a = a + x = b and x - a = b.
Activity 2.4. How Far Will You Go? How Long Will It Take?
Objectives.
1. Apply the fundamental principle of equality to solve equations of the form ax = b, a ? 0.
2. Translate contextual situations and verbal statements into equations.
3. Use the formula rate x time = amount in various contexts.
Activity 2.5. Web Devices for Sale
Objectives.
1. Identify like terms.
2. Combine like terms using the distributive property.
3. Solve equations of the form ax + bx = c.
Activity 2.6. Make Me an Offer
Objectives.
1. Use the basic steps for problem solving.
2. Translate verbal statements into algebraic equations.
3. Use the basic principles of algebra to solve real-world problems.
What Have I Learned?
How Can I Practice?
Chapter 2 Summary
Chapter 2 Gateway Review
Chapter 3. Problem Solving with Rational Numbers. Addition and Subtraction of Integers, Fractions, and Decimals
Cluster 1. Adding and Subtracting Integers
Activity 3.1. On the Negative Side
Objectives.
1. Identify integers.
2. Represent quantities in real-world situations using integers.
3. Compare integers.
4. Calculate absolute value of integers.
Activity 3.2. Maintaining Your Balance
Objectives.
1. Add and subtract integers.
2. Identify properties of addition and subtraction of integers.
Activity 3.3. What's the Bottom Line?
Objectives.
1. Write formulas from verbal statements.
2. Evaluate expressions in formulas.
3. Solve equations of the form x + b = c and b - x = c.
4. Solve formulas for a given variable.
Activity 3.4. Riding in the Wind
Objectives.
1. Translate verbal rules into equations.
2. Determine an equation from a table of values.
3. Use a rectangular coordinate system to represent an equation graphically.
What Have I Learned?
How Can I Practice?
Cluster 2. Adding and Subtracting Fractions
Activity 3.5. Are You Hungry?
Objectives.
1. Identify the numerator and the denominator of a fraction.
2. Determine the greatest common factor (GCF).
3. Determine equivalent fractions.
4. Reduce fractions to equivalent fractions in lowest terms.
5. Convert mixed numbers to improper fractions and improper fractions to mixed numbers.
6. Determine the least common denominator (LCD) of two or more fractions.
7. Compare fractions.
Activity 3.6. Food for Thought
Objective.
1. Add and subtract fractions and mixed numbers with the same denominators.
Activity 3.7. Math Is a Trip
Objectives.
1. Determine the least common denominator (LCD) for two or more fractions.
2. Add and subtract fractions with different denominators.
3. Solve equations in the form x + b = c and x - b = c that involve fractions.
What Have I Learned?
How Can I Practice?
Cluster 3. Adding and Subtracting Decimals
Activity 3.8. What Are You Made Of?
Objectives.
1. Identify place values of numbers written in decimal form.
2. Convert a decimal to a fraction or a mixed number.
3. Compare decimals.
4. Read and write decimals.
5. Round decimals.
Activity 3.9. Think Metric
Objectives.
1. Know the metric prefixes and their decimal values.
2. Convert between metric quantities.
Activity 3.10. Dive into Decimals
Objectives.
1. Add and subtract decimals.
2. Compare and interpret decimal numbers.
Activity 3.11. Boiling, Freezing, and Financial Aid
Objectives.
1. Add and subtract positive and negative decimal numbers.
2. Interpret and compare decimal numbers.
3. Solve equations of the type x + b = c and x - b = c involving decimal numbers.
What Have I Learned?
How Can I Practice?
Chapter 3 Summary
Chapter 3 Gateway Review
Chapter 4. Multiplication and Division of Rational Numbers
Cluster 1. Multiplying and Dividing Integers
Activity 4.1. Are You Physically Fit?
Objectives.
1. Multiply and divide integers.
2. Perform calculations involving a sequence of operations.
3. Apply exponents to integers.
4. Identify properties of calculations involving multiplication and division with zero.
Activity 4.2. Integers and Tiger Woods
Objectives.
1. Use order of operations with expressions involving integers.
2. Apply the distributive property.
3. Evaluate algebraic expressions and formulas using integers.
4. Solve equations of the form ax = b, where a does not equal 0, involving integers.
What Have I Learned?
How Can I Practice?
Cluster 2. Multiplying and Dividing Fractions
Activity 4.3. Get Your Homestead Land
Objectives.
1. Multiply and divide fractions.
2. Recognize the sign of a fraction.
3. Determine the reciprocal of a fraction.
4. Solve equations of form ax = b, where a does not equal 0, involving fractions.
Activity 4.4. Tiling the Bathroom
Objectives.
1. Multiply and divide mixed numbers.
2. Evaluate expressions with mixed numbers.
3. Calculate the square root of a mixed number.
What Have I Learned?
How Can I Practice?
Cluster 3. Multiplying and Dividing Decimals
Activity 4.5. Quality Points and GPA. Tracking Academic Standing
Objectives.
1. Multiply and divide decimals.
2. Estimate products and quotients involving decimals.
Activity 4.6. Tracking Temperature
Objectives.
1. Use the order of operations to evaluate expressions that include decimals.
2. Use the distributive property in calculations involving decimals.
3. Evaluate formulas that include decimals.
4. Solve equations of the form ax = c that include decimals.
What Have I Learned?
How Can I Practice?
Chapter 4 Summary
Chapter 4 Gateway Review
Chapter 5. Problem Solving with Ratios, Proportions, and Percents
Activity 5.1. Everything is Relative
Objectives.
1. Understand the distinction between absolute and relative measure.
2. Write a ratio in its fraction, decimal, and percent formats.
Activity 5.2. The Devastation of AIDS in Africa
Objectives.
1. Use proportional reasoning to apply a known ratio to a given piece of information.
2. Write an equation using the relationship "ratio x total = part" and then solve the resulting equation.
Activity 5.3. Who Really Did Better?
Objectives.
1. Define actual and relative change.
2. Distinguish between actual and relative change.
Activity 5.4. Don't Forget the Sales Tax
Objectives.
1. Define and determine growth factors.
2. Use growth factors in problems involving percent increases.
Activity 5.5. It's All on Sale!
Objectives.
1. Define and determine decay factors.
2. Use decay factors in problems involving percent decreases.
Activity 5.6. Take an Additional 20% Off
Objective.
1. Apply consecutive growth and/or decay factors to problems involving two or more percent changes.
Activity 5.7. Fuel Economytives.
1. Apply rates directly to solve problems.
2. Use u
Objecnit analysis or dimensional analysis to solve problems that involve consecutive rates.
Activity 5.8. Four out of Five Dentists Prefer the Brooklyn Dodgers?
Objectives.
1. Recognize that equivalent fractions lead to proportions.
2. Use proportions to solve problems involving ratios and rates.
What Have I Learned?
How Can I Practice?
Chapter 5 Summary
Chapter 5 Gateway Review
Chapter 6. Problem Solving with Geometry
Cluster 1. The Geometry of Two-Dimensional Plane Figures
Activity 6.1. Walking around Bases, Gardens, Trusses, and Other Figures
Objectives.
1. Recognize perimeter as a geometric property of plane figures.
2. Write formulas for, and calculate perimeters of, squares, rectangles, triangles, parallelograms, trapezoids, and polygons.
3. Use unit analysis to solve problems involving perimeter.
Activity 6.2. Circles Are Everywhere
Objectives.
1. Measure the lengths of the diameter and circumference of circles.
2. Develop and use formulas for the circumference of a circle.
Activity 6.3. Lance Armstrong and You
Objectives.
1. Calculate perimeters of many-sided plane figures using formulas and combinations of formulas.
2. Use unit analysis to solve problems involving perimeters.
Activity 6.4. Baseball Diamonds, Gardens, and Other Figures Revisited
Objectives.
1. Write formulas for areas of squares, rectangles, parallelograms, triangles, trapezoids, and polygons.
2. Calculate the areas of polygons using appropriate formulas.
Activity 6.5. How Big Is That Circle Really?
Objectives.
1. Develop formulas for the area of a circle.
2. Use formulas to determine areas of circles.
Activity 6.6. A New Pool and Other Home Improvements
Objectives.
1. Solve problems in context using geometric formulas.
2. Distinguish between problems requiring area formulas and perimeter formulas.
Laboratory Activity 6.7. How Big Is That Angle?
Objectives.
1. Measure the size of an angle with a protractor.
2. Classify triangles as equiangular, equilateral, isosceles, or scalene.
Laboratory Activity 6.8. How About Pythagoras?
Objectives.
1. Develop and use the Pythagorean Theorem for right triangles.
2. Calculate the square root of numbers other than perfect squares.
3. Apply the Pythagorean Theorem in context.
Activity 6.9. Moving Up with Math
Objectives.
1. Recognize the geometric properties of similar triangles.
2. Use similar triangles in indirect measurement.
What Have I Learned?
How Can I Practice?
Cluster 2. The Geometry of Three-Dimensional Space Figures
Activity 6.10. Painting Your Way through the Summer
Objectives.
1. Recognize geometric properties of three-dimensional figures.
2. Write formulas for and calculate surface areas of boxes (rectangular prisms), cans (right circular cylinders), and balls (spheres).
Activity 6.11. Truth in Labeling
Objectives.
1. Write formulas for and calculate volumes of boxes and cans.
2. Recognize geometric properties of three-dimensional figures.
Activity 6.12. Analyzing an Ice Cream Cone
Objective.
1. Write formulas for and calculate volumes of balls (spheres) and cones.
Laboratory Activity 6.13. Summertime
Objectives.
1. Use geometry formulas to solve problems.
2. Use scale drawings in the problem-solving process.
What Have I Learned?
How Can I Practice?
Chapter 6 Summary
Chapter 6 Gateway Review
Chapter 7. More Problem Solving with Algebra and Mathematical Models
Activity 7.1. Leasing a Copier
Objectives.
1. Describe a mathematical model as a set of verbal statements.
2. Translate verbal rules into symbolic equations.
3. Solve problems involving equations of the form y = ax + b.
4. Solvve equations of the form y = ax + b for the input x.
5. Evaluate expressions ax + b in the equations of the form y = ax + b to obtain an output y.
Activity 7.2. Windchill
Objectives.
1. Evaluate formulas to determine an output.
2. Solve formulas for a specific variable.
Activity 7.3. Comparing Energy Costs
Objectives.
1. Write symbolic equations from information organized in a table.
2. Produce tables and graphs to compare outputs from two different mathematical models.
3. Solve equations of the form ax + b = cx + d.
Activity 7.4. Volume of a Storage Tank
Objectives.
1. Use property of exponents to multiply powers having the same base.
2. Use property of exponents to raise a power to a power.
3. Use the distributive property and properties of exponents to write an expression as an equivalent expression in expanded form.
Activity 7.5. Math Magic
Objectives.
1. Recognize an algebraic expression as a code of instructions to obtain an output.
2. Simplify algebraic expressions.
Activity 7.6. Mathematical Modeling
Objectives.
1. Develop an equation to model and solve problems.
2. Solve problems using formulas as models.
3. Recognize patterns and trends between two variables using tables as models.
4. Recognize patterns and trends between two variables using graphs as models