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San Bernardino City Unified School District Scope and Sequence High School Algebra 2 – Holt Semester 1 Pacing Weeks 1-3 CA Standard Number 7AF1.2** Content (Standard Component) • 2A 12.0* 1A 16.0 • • • • 1A 17.0 • 1A 18.0 • Week 4 2A 24.0 1A 5.0** • • Week 5 1A 6.0** 1A 7.0** 1A 6.0 • • • • • 1A2.0** 2A 2.0* Students use the correct order of operations to evaluate algebraic expressions. Students understand and use such operations as taking a root. Students understand and use the rules of exponents. Students know the laws of fractional exponents. Students understand the concept of a function and give pertinent information about given function. Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression. Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion. Students solve problems involving functional concepts. Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable. Students graph a linear equation and compute the x- and y-intercepts. Students are able to derive linear equations Students graph a linear equation. Students are able to sketch the region defined by a linear inequality. Students solve systems of linear equations and inequalities (in two variables) by substitution or with graphs. Holt Chapter and Section 1.1** – 1.5** 8.6 1.6 – 1.7 Support Resources Power Presentation One-Stop Planner Multilingual Glossary Chapter Resource File Alternate Openers 2.1, 2.3, 2.4 3.1, 3.2 2.5**, 3.3 Mathematics Framework for California Public Schools, California Department of Education, © 2006 Algebra 2 (CA Edition), Holt, Rinehart, and Winston, © 2008 6 = 6th Grade Standard, 7 = 7th Grade Standard, 1A = Algebra 1 Standard, G = Geometry Standard 2A = Algebra 2 Standard, TR = Trigonometry Standard * Key Standard ** Not an essential standard component. Page 1 Secondary Education Revised August 2012 San Bernardino City Unified School District Scope and Sequence High School Algebra 2 – Holt Semester 1 Week 6 CA Standard Number 2A 2.0* • Weeks 7-8 2A 22.0 2A 23.0* • • Week 9 G 22.0 • 2A 9.0* • Week 10 2A 10.0* 2A 1.0* 2A 9.0* • • • Week 11 1A 16.0 G 22.0 • • 2A 9.0* • 2A 10.0* • Pacing Content (Standard Component) Holt Chapter and Section Students solve systems of linear equations and inequalities (in two or three variables) Students find the general term and the sums of arithmetic series. Students derive the summation formulas for arithmetic series. 3.4 – 3.6 12.1 – 12.3 Week 9 & 10 Benchmark #1 Students know the effect of rigid motions on figures in the coordinate plane and space. Students demonstrate and explain the effect that changing a coefficient has on the graph. Students graph quadratic functions. Students solve equations and inequalities involving absolute value. Students demonstrate and explain the effect that changing a coefficient has on the graph. Students understand the concept of a function. Students know the effect of rigid motions on figures in the coordinate plane and space. Students demonstrate and explain the effect that changing a coefficient has on the graph. Students graph quadratic functions and determine the maxima and minima of the function. Support Resources Power Presentation One-Stop Planner Multilingual Glossary Chapter Resource File Alternate Openers 1.8, 1.9 2.6, 2.8, 2.9 9.1, 9.3 Mathematics Framework for California Public Schools, California Department of Education, © 2006 Algebra 2 (CA Edition), Holt, Rinehart, and Winston, © 2008 6 = 6th Grade Standard, 7 = 7th Grade Standard, 1A = Algebra 1 Standard, G = Geometry Standard 2A = Algebra 2 Standard, TR = Trigonometry Standard * Key Standard ** Not an essential standard component. Page 2 Secondary Education Revised August 2012 San Bernardino City Unified School District Scope and Sequence High School Algebra 2 – Holt Semester 1 Pacing Weeks 12-13 Week 14 CA Standard Number 2A 8.0* • 2A 9.0* • • 2A 10.0* • Content (Standard Component) 1A 23.0** • 2A 5.0* • 2A 6.0* 2A 24.0 • • • 2A 25.0 • Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students solve quadratic equations in the complex number system. Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions; that is, students can determine how the graph of a parabola changes as a, b and c vary in the equation y = a ( x − b) 2 − c Students graph quadratic functions and determine the maxima, minima, and zeros of the function. Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity. Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically. Students can plot complex numbers as points in the plane. Students add, subtract, multiply and divide complex numbers. Students solve problems involving functional concepts, such as composition and performing arithmetic operations on functions. Students use properties from number systems to justify steps in combining and simplifying functions. Holt Chapter and Section Support Resources 5.1 – 5.6 5.9, 5.8** 9.4 Mathematics Framework for California Public Schools, California Department of Education, © 2006 Algebra 2 (CA Edition), Holt, Rinehart, and Winston, © 2008 6 = 6th Grade Standard, 7 = 7th Grade Standard, 1A = Algebra 1 Standard, G = Geometry Standard 2A = Algebra 2 Standard, TR = Trigonometry Standard * Key Standard ** Not an essential standard component. Page 3 Secondary Education Revised August 2012 San Bernardino City Unified School District Scope and Sequence High School Algebra 2 – Holt Semester 1 Pacing Weeks 15-16 CA Standard Number 2A 11.1* • 2A 11.2* • 2A 12.0* • 2A 13.0 • 2A 14.0 • 2A 15.0* • 2A 24.0 • Content (Standard Component) Students understand the inverse relationship between exponents and logarithms, and use this relationship to solve problems involving logarithms and exponents. Students judge the validity of an argument according to whether the properties of exponents and logarithms have been applied correctly at each step. Students understand exponential functions and use these functions in problems involving exponential growth and decay. Students use the definition of logarithms to translate between logarithms in any base. Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values. Students determine whether a specific algebraic statement involving rational expressions, radical expressions, logarithmic functions, or exponential functions is sometimes true, always true, or never true. Students solve problems involving functional concepts, such as composition and defining the inverse function. Holt Chapter and Section 7.1, 7-2, 9.5, 7.3 – 7-8 Support Resources Power Presentation One-Stop Planner Multilingual Glossary Chapter Resource File Alternate Openers Week 17 & 18 BENCHMARK #2 Weeks 17-18 1.0*, 2.0*, 5.0*, 6.0*, 8.0*, 9.0*, 10.0*, 12.0*, 13.0, 14.0, 15.0*, 22.0, 23.0*, 24.0, 25.0 Review and take Final Exams ExamView Test Generator Assessment Resources MindPoint Quiz Show END OF SEMESTER 1 Mathematics Framework for California Public Schools, California Department of Education, © 2006 Algebra 2 (CA Edition), Holt, Rinehart, and Winston, © 2008 6 = 6th Grade Standard, 7 = 7th Grade Standard, 1A = Algebra 1 Standard, G = Geometry Standard 2A = Algebra 2 Standard, TR = Trigonometry Standard * Key Standard ** Not an essential standard component. Page 4 Secondary Education Revised August 2012 San Bernardino City Unified School District Scope and Sequence High School Algebra 2 – Holt Semester 2 Pacing Week 1 Weeks 2-4 Week 5 CA Standard Number 2A 21.0 • 2A 22.0 • 2A 23.0* • 2A 3.0* • 2A 4.0* • 2A 10.0* • 2A 20.0* • 7AF4.2** 2A 7.0* • • 2A 15.0* • Content (Standard Component) Students apply the method of mathematical induction to prove general statements about the positive integers. Students find the general term and the sums of both finite and infinite geometric series. Students derive the summation formulas for both finite and infinite geometric series. Students are adept at operations on polynomials, including long division. Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes. Students graph quadratic functions and determine the maxima, minima, and the zeros of the function. Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers. Solve multistep problems involving variation problems. Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions. Students determine whether a specific algebraic statement involving rational expressions is sometimes true, always true, or never true. Holt Chapter and Section 12.4, 12.5 Support Resources Power Presentation One-Stop Planner Multilingual Glossary Chapter Resource File Alternate Openers 6.1 – 6.8 6.9** 8.1** 8.2 – 8.3 Mathematics Framework for California Public Schools, California Department of Education, © 2006 Algebra 2 (CA Edition), Holt, Rinehart, and Winston, © 2008 6 = 6th Grade Standard, 7 = 7th Grade Standard, 1A = Algebra 1 Standard, G = Geometry Standard 2A = Algebra 2 Standard, TR = Trigonometry Standard * Key Standard ** Not an essential standard component. Page 5 Secondary Education Revised August 2012 San Bernardino City Unified School District Scope and Sequence High School Algebra 2 – Holt Semester 2 Pacing Weeks 6-7 CA Standard Number 2A 12.0* 2A 15.0* • • Content (Standard Component) Holt Chapter and Section Students know the laws of fractional exponents Students determine whether a specific algebraic statement involving rational expressions, radical expressions or logarithmic or exponential functions is sometimes true, always true, or never true. 8.4, 8.5** 8.6 – 8.8 Support Resources Power Presentation One-Stop Planner Multilingual Glossary Chapter Resource File Alternate Openers Week 8 - 10 Benchmark #3 (Emphasizes standards 6.0, 7.0, 8.0, 9.0, 13.0, 14.0) Weeks 8-10 6SDAP1.1 • 6SDAP3.5 • 2A 18.0* • 2A 19.0* 2A 20.0* • • Students compute the range, mean, median, and mode of data sets. Understand the difference between independent and dependent events. Students use fundamental counting principles to compute combinations and permutations. Students use combinations and permutations to compute probabilities. Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers. 11.1 – 11.6 Mathematics Framework for California Public Schools, California Department of Education, © 2006 Algebra 2 (CA Edition), Holt, Rinehart, and Winston, © 2008 6 = 6th Grade Standard, 7 = 7th Grade Standard, 1A = Algebra 1 Standard, G = Geometry Standard 2A = Algebra 2 Standard, TR = Trigonometry Standard * Key Standard ** Not an essential standard component. Page 6 Secondary Education Revised August 2012 San Bernardino City Unified School District Scope and Sequence High School Algebra 2 – Holt Semester 2 Pacing CA Standard Number Weeks 11-12 2A 1.0* 2A 2.0* • • 2A 3.0* 2A 4.0* • • 2A 5.0* • 2A 6.0* 2A 7.0* • • 2A 8.0* • 2A 9.0* • 2A 10.0* • Content (Standard Component) Holt Chapter and Section CST Review Students solve equations and inequalities involving absolute value. Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices. Students are adept at operations on polynomials, including long division. Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes. Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically. In particular, they can plot complex numbers as points in the plane. Students add, subtract, multiply, and divide complex numbers. Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator. Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system. Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions; that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y = a ( x − b) 2 − c . Students graph quadratic functions and determine the maxima, minima, and zeros of the function. Support Resources ExamView Test Generator Assessment Resources MindPoint Quiz Show Mathematics Framework for California Public Schools, California Department of Education, © 2006 Algebra 2 (CA Edition), Holt, Rinehart, and Winston, © 2008 6 = 6th Grade Standard, 7 = 7th Grade Standard, 1A = Algebra 1 Standard, G = Geometry Standard 2A = Algebra 2 Standard, TR = Trigonometry Standard * Key Standard ** Not an essential standard component. Page 7 Secondary Education Revised August 2012 San Bernardino City Unified School District Scope and Sequence High School Algebra 2 – Holt Semester 2 Pacing Weeks 11-12 (cont.) CA Standard Number 2A 11.1* • Students understand the inverse relationship between exponents and logarithms, and use this relationship to solve problems involving logarithms and exponents. 2A 11.2* • 2A 12.0* • 2A 15.0* • 2A 18.0* 2A 19.0* 2A 20.0* • • • 2A 23.0* • Students judge the validity of an argument according to whether the properties of real numbers, exponents, and logarithms have been applied correctly at each step. Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay. Students determine whether a specific algebraic statement involving rational expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always true, or never true. Students use fundamental counting principles to compute combinations and permutations. Students use combinations and permutations to compute probabilities. Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers. Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series. Content (Standard Component) Holt Chapter and Section Support Resources ExamView Test Generator Assessment Resources MindPoint Quiz Show Mathematics Framework for California Public Schools, California Department of Education, © 2006 Algebra 2 (CA Edition), Holt, Rinehart, and Winston, © 2008 6 = 6th Grade Standard, 7 = 7th Grade Standard, 1A = Algebra 1 Standard, G = Geometry Standard 2A = Algebra 2 Standard, TR = Trigonometry Standard * Key Standard ** Not an essential standard component. Page 8 Secondary Education Revised August 2012 San Bernardino City Unified School District Scope and Sequence High School Algebra 2 – Holt Semester 2 Pacing Weeks 13-15 Week 16 CA Standard Number 16.0** • 17.0** • G 19.0 • • G 20.0 • TR 2.0 • TR 8.0 • TR 9.0 • TR 13.0 • Content (Standard Component) Students demonstrate and explain how the geometry of the graph of a conic section (e.g., asymptotes, foci, eccentricity) depends on the coefficients of the quadratic equation representing it. Given a quadratic equation of the form ax 2 + by 2 + cx + dy + e = 0 , students can use the method for completing the square to put the equation into standard form and can recognize whether the graph of the equation is a circle, ellipse, parabola, or hyperbola. Students can graph an equation of the form ax 2 + by 2 + cx + dy + e = 0 . Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side. Students know and are able to use angle and side relationships in problems with special right triangles, such as 30°, 60°, and 90° triangles and 45°, 45°, and 90° triangles. Students know the definition of sine and cosine as y- and x- coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions. Students know the definitions of the inverse trigonometric functions and can graph the functions. Students compute, by hand, the values of the trigonometric functions and the inverse trigonometric functions at various standard points. Students know the law of sines and the law of cosines and apply those laws to solve problems. Holt Chapter and Section 10.1 – 10.6 Support Resources Power Presentation One-Stop Planner Multilingual Glossary Chapter Resource File Alternate Openers 13.1 – 13.6 Mathematics Framework for California Public Schools, California Department of Education, © 2006 Algebra 2 (CA Edition), Holt, Rinehart, and Winston, © 2008 6 = 6th Grade Standard, 7 = 7th Grade Standard, 1A = Algebra 1 Standard, G = Geometry Standard 2A = Algebra 2 Standard, TR = Trigonometry Standard * Key Standard ** Not an essential standard component. Page 9 Secondary Education Revised August 2012 San Bernardino City Unified School District Scope and Sequence High School Algebra 2 – Holt Semester 2 Pacing Weeks 17-18 CA Content Standard (Standard Component) Number Algebra 2: 1.0*, 2.0*, 3.0*, 4.0*, 5.0*, 6.0*, 7.0*, 8.0*, 9.0*, 10.0*, 12.0*, 13.0, 14.0, 15.0*, 16.0, 17.0, 18.0*, 19.0*, 20.0*, 22.0, 23.0*, 24.0, 25.0 Probability & Statistics: 1.0, 2.0 Review and take Final Exams END OF SEMESTER 2 Holt Chapter and Section Support Resources ExamView Test Generator Assessment Resources MindPoint Quiz Show Mathematics Framework for California Public Schools, California Department of Education, © 2006 Algebra 2 (CA Edition), Holt, Rinehart, and Winston, © 2008 6 = 6th Grade Standard, 7 = 7th Grade Standard, 1A = Algebra 1 Standard, G = Geometry Standard 2A = Algebra 2 Standard, TR = Trigonometry Standard * Key Standard ** Not an essential standard component. Page 10 Secondary Education Revised August 2012