Common Curriculum Map. Discipline: Math Course: Algebra 2

Transcription

1 Common Curriculum Map Discipline: Math Course: Algebra 2 Semester One: Standards: 6.A.3 - Represent fractions, decimals, percentages, exponents and scientific notation in equivalent forms. 6.A.4 - Identify and apply the associative, commutative, distributive and identity properties of real numbers, including special numbers such as pi and square roots 6.B.3b - Apply primes, factors, divisors, multiples, common factors and common multiples in solving problems. 6.B.3c - Identify and apply properties of real numbers including pi, squares, and square roots. 6.B.4 - Select and use appropriate arithmetic operations in practical situations including calculating wages after taxes, developing a budget and balancing a checkbook. 6.B.5 - Identify, represent and apply numbers expressed in exponential, logarithmic and scientific notation using contemporary technology. 6.C.3b - Show evidence that computational results using whole numbers, fractions, decimals, percents and proportions are correct and/or that estimates are reasonable. 7.A.4b - Apply formulas in a wide variety of theoretical and practical real-world measurement applications involving perimeter, area, volume, angle, time, temperature, mass, speed, distance, density and monetary values. 8.A.3a - Apply the basic properties of commutative, associative, distributive, transitive, inverse, identity, zero, equality and order of operations to solve problems. 8.A.3b - Solve problems using linear expressions, equations and inequalities. 8.B.3 - Use graphing technology and algebraic methods to analyze and predict linear relationships and make generalizations from linear patterns. 8.B.4a - Represent algebraic concepts with physical materials, words, diagrams, tables, graphs, equations and inequalities and use appropriate technology. 8.B.4b - Use the basic functions of absolute value, square root, linear, quadratic and step to describe numerical relationships. 8.B.5 - Use functions including exponential, polynomial, rational, parametric, logarithmic, and trigonometric to describe numerical relationships. 8.C.2 - Explain operations and number properties including commutative, associative, distributive, transitive, zero, equality and order of operations.

2 8.C.3 - Apply the properties of numbers and operations including inverses in algebraic settings derived from economics, business and the sciences. 8.D.3a - Solve problems using numeric, graphic or symbolic representations of variables, expressions, equations and inequalities. 8.D.3c - Apply properties of powers, perfect squares and square roots. 8.D.4 - Formulate and solve linear and quadratic equations and linear inequalities algebraically and investigate nonlinear inequalities using graphs, tables, calculators and computers. Essential Questions: Chapter 1: What are the sets of real numbers, and how do they relate to one another? What is the order of operations for real numbers? Why are they critical to the study of mathematics? What are the Basic Properties and Field Properties of Real Numbers? Chapter 2: How do you solve and graph inequalities in one variable? How do you solve combined inequalities? How do you use absolute value in relation to inequalities? In ways are solving and graph the above three items similar/different? Chapter 3: How do you solve and graph an equation in two variables? How do you solve and graph an inequality in two variables? How do you solve systems of equations and inequalities? What is a Relation? What is a Function? How are relations and functions similar/different? What are Domain and Range and what roles do they play in relations and functions? Chapter 4: What are the laws of exponents? How do you factor polynomials? How are factoring and the distributive property related? In what ways are quadratic functions and linear functions different? How do you solve polynomial equations? Chapter 5: What are rational algebraic expressions? How do you find the sum/difference/product/quotient of rational expressions? What are complex fractions? Content: Chapter 1: 1. Basic Concepts of Algebra Chapter 2: 2. Inequalities 3. Absolute Value Chapter 3: 4. Linear Equations and their Graphs 5. Systems of linear equations, inequalities

3 6. Relations, Functions Chapter 4: 7. Laws of exponents 8. Products of Polynomials 9. Factors of Polynomials 9. Factoring Chapter 5: 10. Rational Expressions Skills: Chapter 1 skills: 1. Graph real numbers on a number line. 2. Compare real numbers. 3. Find absolute value. 4. Simplify numerical expressions. 5. Evaluate numerical expressions. 6. Name properties of equality for real numbers. 7. Use properties of addition and multiplication of real numbers. 8. Adding/Subtracting and Multiplying/Dividing real numbers. 9. Solving equations with one variable. 10. Translate word phrases into mathematical expressions and translate word sentences into equations. 11. Solve word problems. Chapter 2 skills: 12. Solve and graph inequalities in one variable. 13. Solve and graph combined inequalities. 14. Understand difference between disjunction and conjunction. 15. Solve open sentences involving absolute value. Chapter 3 skills: 16. Solve open sentences in 2 variables. 17. Graph linear equations in 2 variables. 18. Find the slope of a line. 19. Draw a line given its slope and a point on the line. 20. Find the equation of a line given its slope and a point on a line, two points, or its slope and the y intercept. 21. Solve a system of linear equations and inequalities by graphing 22. Determine which Relations are also functions. 23. Graph Relations. Chapter 4 skills: 24. Simplify, add, and subtract polynomials 25. Use laws of exponents to multiply a polynomial by a monomial. 26. Multiply polynomials 27. Factor polynomials by using GCF, by recognizing special products, and by grouping terms. 28. Factoring quadratic expressions 29. Solving Polynomial equations Chapter 5 skills: 30. Use scientific notation 31. Simplify rational algebraic expressions.

4 32. Simplify quotients using the laws of exponents. 33. Simplify expressions involving the exponent of zero and negative integral exponents. 34. Multiply and Divide rational expressions. 35. Add and subtract rational expressions. Assessment: 1. Assignments from textbook. 2. Observation during group work/individual work in class. 3. Class discussions, formal and informal. 4. Tests and Quizzes. Semester Two: Standards: 6.A.3 Represent fractions, decimals, percentages, exponents and scientific notation in equivalent forms. 6.A.4 Identify and apply the associative, commutative, distributive and identity properties of real numbers, including special numbers such as pi and square roots. 6.A.5 Perform addition, subtraction and multiplication of complex numbers and graph the results in the complex plane. 6.B.3a Solve practical computation problems involving whole numbers, integers and rational numbers 6.B.5 Identify, represent and apply numbers expressed in exponential, logarithmic and scientific notation using contemporary technology. 6.B.3b Apply primes, factors, divisors, multiples, common factors and common multiples in solving problems. 6.B.3c Identify and apply properties of real numbers including pi, squares, and square roots. 6.C.3a Select computational procedures and solve problems with whole numbers, fractions, decimals, percents and proportions. 6.C.5 Determine the level of accuracy needed for computations involving measurement and irrational numbers. 6.D.3 Apply ratios and proportions to solve practical problems. 6.D.4 Solve problems involving recipes or mixtures, financial calculations and geometric similarity using ratios, proportions and percents. 6.D.5 Solve problems involving loans, mortgages and other practical applications involving geometric patterns of growth. 8.A.3a Apply the basic properties of commutative, associative, distributive, transitive, inverse, identity, zero, equality and order of operations to solve problems. 8.A.4a Use algebraic methods to convert repeating decimals to fractions. 8.A.3b Solve problems using linear expressions, equations and inequalities.

5 8.A.4b Represent mathematical patterns and describe their properties using variables and mathematical symbols. 8.B.4a Represent algebraic concepts with physical materials, words, diagrams, tables, graphs, equations and inequalities and use appropriate technology. 8.B.5 Use functions including exponential, polynomial, rational, parametric, logarithmic, and trigonometric to describe numerical relationships. 8.B.4b Use the basic functions of absolute value, square root, linear, quadratic and step to describe numerical relationships. 8.C.3 Apply the properties of numbers and operations including inverses in algebraic settings derived from economics, business and the sciences. 8.C.4a Analyze and report the effects of changing coefficients, exponents and other parameters on functions and their graphs. 8.C.5 Use polynomial, exponential, logarithmic and trigonometric functions to model situations. 8.D.3a Solve problems using numeric, graphic or symbolic representations of variables, expressions, equations and inequalities. 8.D.4 Formulate and solve linear and quadratic equations and linear inequalities algebraically and investigate nonlinear inequalities using graphs, tables, calculators and computers. 8.D.5 Formulate and solve nonlinear equations and systems including problems involving inverse variation and exponential and logarithmic growth and decay. 8.D.3b Propose and solve problems using proportions, formulas and linear functions. 8.D.3c Apply properties of powers, perfect squares and square roots. Essential Questions: Chapter 6: What is the nth root? What is an imaginary Number? What are the properties of the imaginary unit i? What makes a number complex? Chapter 7: What makes something a quadratic equation? What are the ways to solve a quadratic equation? How do you create the quadratic formula from a quadratic equation? How do you graph a quadratic equation? Chapter 9: How do you apply the distance formula and the midpoint formula? How do you use the Pythagorean Theorem to find the distance formula? How do you use the distance formula to find the equation of a circle? Chapter 10:

6 How do you cancel out an exponent that is a variable? How can you find an unknown exponent if you know the base and the answer? What is a log? How do you use logs? What is e? Chapter 8: What does it mean to vary directly vs. jointly or inversely? How is long division related to dividing polynomials? Content: Chapter 6: Irrational and Complex Numbers Chapter 7: Quadratic Equations and Functions Chapter 9: Distance Formula, Midpoint formula, Circles. Chapter 10: Exponential and Logarithmic functions. Chapter 8: Direct, inverse, and joint variation. dividing polynomial equations. Skills: Chapter 6: 1. Define and work with roots (square, cube, nth) 2. Discuss and work with properties of radicals 3. Work with product and quotient properties of radicals 4. Solve problems including the sums of radicals 5. Work with binomials containing radicals 6. Define and discuss conjugates 7. Solve equations with radicals 8. Define rational and irrational numbers 9. Identify rational and irrational numbers based on properties of numbers 10. Define and discuss the imaginary unit i 11. Define and discuss the complex number system 12. Define complex conjugates Chapter 7: 1. Work with completing the square 2. Discuss, derive, and use the quadratic formula 3. Define and discuss the Discriminant and its use in determining the nature of the roots of a quadratic equation 4. Discuss equations in quadratic form 5. Solve quadratic equations using substitution 6. Graph basic quadratic equations using vertex, stretch, and points 7. Put equations in quadratic form by algebraic manipulation and completing the square 8. Discuss minimum and maximum values of a quadratic function

7 Chapter 9: 1. Find the distance between any two points and the midpoint of the line segment joining them. 2. Learn the relationship between the center and radius of a circle and the equation of a circle. Chapter 10: 1. Extend the understanding of exponents to include rational numbers. 2. Find the composite of two given functions. 3. Find the inverse of a given functions. 4. Define a logarithmic function and learn how they are related to exponential functions. 5. Apply the basic properties of logarithms. 6. Use common logs to solve equations involving powers and evaluate logarithms with any given base. 7. Use exponential and logarithmic functions to solve growth and decay problems. 8. Define and use the natural logarithm function. Chapter 8: 1. Solve problems involving direct variation. 2. Solve problems involving inverse and joint variation. 3. Divide one polynomial by another polynomial. Assessment: Homework Quizzes Tests Think, Pair, Share Formal and informal discussions with class