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Oroville Union High School District
Mathematics Curriculum
Mathematics - Advanced Algebra

Advanced Algebra Content Standards

Absolute Value
The learner will be able to solve equations and inequalities involving absolute value.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 1.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  Unit 4: Parabolas and Other Parent Graphs: PG-111-122, 145(a); Unit 5: Linear Systems and Matrices: LS-3, 4, 5, 12, 13, 22, 35, 63, 150(b); Unit 6: Logarithms and Other Inverses: CC-54, 115, 123, 165(c); Unit 7: Polynomials and General Systems: CF-46, 92; Unit 8: Circular Functions: CT-76(c,d), 131; Unit 9: More Triangles and Trigonometry: ST-7(ii), 136(c); Unit 10: Probability and Policy Making: PM-55, 75; Unit 11: Counting and Sampling: IC-32; Unit 12: Descriptive Statistics: DS-33, 34, 35, 37; Unit 13: Revisiting and Extending: RE-63, 89.
· PLATO Learning Inc., 2000, Modules: [Software].  Beginning Algebra: Solving Equations, Absolute Value, Graphing, Intervals Distance and Absolute Values.
  
Systems of Linear Equations
The learner will be able to solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 2.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  Unit 1: Exploring Functions: EF-18, 33, 34, 39, 52, 53, 95, 119; Unit 2: Sequences: BB-17, 27-29, 66, 95, 98; Unit 3: Exponential Functions: FX-11, 36, 50,108, 114(a,b), 125, 135, 140, 144; Unit 4: Parabolas and Other Parent Graphs: PG-10, 18, 54, 134; Unit 5: Linear Systems and Matrices: LS-1, 2, 6, 8, 19, 20, 23, 25, 26, 29, 30, 37, 38, 40, 42, 46, 48, 54?62, 66?73, 74, 77-88, 89, 90, 92-94, 101-103, 105. 106, 111, 112, 114?121, 125-136, 138-141, 143, 148, 149, 150, 152, 154, 156, 157; Unit 6: Logarithms and Other Inverses: CC-11, 13, 20, 22, 50, 86, 102, 135; Unit 7: Polynomials and General Systems: CF-7-9, 37-39, 41-43, 46, 51-54, 56, 65, 66, 72, 82, 100, 113, 133, 136, 145, 149, 153, 154; Unit 8: Circular Functions: CT-6, 41, 55, 117, 130, 131, 133, 142, 156; Unit 9: More Triangles and Trigonometry: ST-8, 12, 22, 38(b), 51, 77, 103(b), 108, 129; Unit 10: Probability and Policy Making: PM-20-22, 33, 51, 52, 54, 73, 88, 93, 105; Unit 11: Counting and Sampling: IC-13, 27, 31, 32, 94,109, 123, 128; Unit 12: Descriptive Statistics: DS-87, 143-146; Unit 13: Revisiting and Extending: RE-8,17, 73.
· PLATO Learning Inc., 2000, Modules: [Software].  Intermediate Algebra: Linear Systems of Equations and Inequalities: Linear Systems, Systems - Substitute, Systems - Addition, Word Problems, Review: Linear Systems. l
  
Operations on Polynomials
The learner will be able to are adept at operations on polynomials, including long division.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 3.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  Unit 1: Exploring Functions: EF-7, 54; 65; Unit 2: Sequences: BB-4, 5, 35(a,b,d), 50-52, 70, 96, 107; Unit 3: Exponential Functions: FX-13, 14(a-d), 25(a-d), 34, 38, 51(a-d), 66, 83(a-d), 86(a-d), 95(a-d), 98(a-d), 111(b), 112(a-d), 115(a-d), 122(a-d), 128, 139(a-d); Unit 4: Parabolas and Other Parent Graphs: PG-22-24, 27, 28, 30(a,c,d), 34, 38(a), 40(b), 46-51, 62, 63, 66, 71, 72, 77(a,b,c), 91(a), 92, 103, 109, 132, 135(b), 136, 144(a?d), 148, 163; Unit 5: Linear Systems and Matrices: LS-44, 45(a?d), 50(e), 64, 97, 100, 123, 124, 144, 153; Unit 6:Logarithms and Other Inverses CC-3(a-d), 12(a), 16(a-d), 26(a-d), 38(a-d), 42(a-d), 49(a-d), 63, 68, 76, 79, 93, 104, 124(a-d), 158(a-d); Unit 7: Polynomials and General Systems CF-4, 6, 12, 13, 14(a,b), 20, 23, 32, 50, 53(a), 76, 82, 98, 106(a), 107(b), 111(a), 120(a-c), 131; 149, 155; 157; Unit 8: Circular Functions: CT-5, 7(a), 19, 29, 56, 66; 118(a), 144, 156; Unit 9: More Triangles and Trigonometry: ST-22, 38(b), 63, 65(b), 93(b), 131, 133(b), 134; Unit 10:Probability and Policy Making PM-5(c), 7, 10, 19(a,b), 20(b), 21, 25(a-f), 32, 45, 46, 49, 51(b), 65(c,d), 67(a-b), 72, 73, 94(e); Unit 11: Counting and Sampling: IC-9, 13, 25, 28, 29, 79, 80, 92, 106, 110-113, 116, 117, 122, 127, 139, 156; Unit 12: Descriptive Statistics: DS-81(a), 86, 94(a-f), 95(a-f), 96(a-c), 97, 107-109, 116, 120, 128, 141, 143; Unit 13: Revisiting and Extending: RE-5, 26-28, 42(b,c), 44, 53(b,c), 57-60, 70, 79-85, 89, 90. Unit 3: Exponential Functions: FX?14, 83(c,d), 95(d), 115(a?c), 122(b,c), 139(a,b) Unit 4: Parabolas and Other Parent Graphs: PG?34(c,f), 132(a), 144(a?c) Unit 5: Linear Systems and Matrices: LS?44, 45(c,d), 124(a,b), 137(c) Unit 6: Logarithms and Other Inverses: CC?26(b), 42(b?d), 68(a?c), 93(d) Unit 7: Polynomials and General Systems: CF?4(b), 49, 53(a), 76, 98, 107(b), 111(a) Unit 10: Probability and Policy Making: PM?10(c), 67(a,b) Unit 11: Counting and Sampling: IC?80, 106(a) Unit 12: Descriptive Statistics: DS?95(a?f), 96(a?c), 97 Unit 13: Revisiting and Extending: RE?32, 42(b,c), 53(b,c)
· PLATO Learning Inc., 2000, Modules: [Software].  Beginning Algebra: Monomial Sum and Difference, Monomial Product and Quotient, Binomial Sum and Difference, Polynomial Sum and Difference, Polynomial Product, Polynomial Quotient.
  
Factoring Polynomials
The learner will be able to factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 4.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  
· PLATO Learning Inc., 2000, Modules: [Software].  Beginning Algebra: Common Factors, Factoring II, Factoring Special Cases, Factoring Trinomials I, Factoring Trinomials II, Review: Polynomials/Factoring; Advanced Algebra: Factoring.
  
Real and Complex Numbers
The learner will be able to 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.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 5.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  Unit 7: Polynomials and General Systems: CF-65, 66, 68-74, 77, 78, 81-86, 100, 101, 105-109, 113-117, 130, 131, 140, 141, 143(b,c,d), 148, 149, 151, 152, 154; Unit 8: Circular Functions: CT-34, 53(b), 54(b), 57, 156; Unit 9: More Triangles and Trigonometry: ST-9, 35, 64; Unit 10: Probability and Policy Making: PM-8, 21(b,c), 52, 63, 77(b,c,d), 95, 98(d,f); Unit 11: Counting and Sampling: IC-16, 67; Unit 13: Revisiting and Extending: RE-60.
· PLATO Learning Inc., 2000, Modules: [Software].  No PLATO modules are available for this learning expectation at this time.
  
Complex Numbers
The learner will be able to add, subtract, multiply, and divide complex numbers.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 6.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  Unit 7: Polynomials and General Systems: CF-70, 74, 78(c,d), 85, 87, 88, 15-117, 121, 140; Unit 8: Circular Functions: CT-11, 34, 57, 101; Unit 9: More Traingles and Trigonometry: ST-9, 53; Unit 10: Probability and Policy Making: PM-52, 53, 77(a-d), 86; Unit 11: Counting and Sampling: IC-16, 46, 67; Unit 13: Revisiting and Extending: RE-3, 31, 60.
· PLATO Learning Inc., 2000, Modules: [Software].  No PLATO modules are available for this learning expectation at this time.
  
Rational Expressions
The learner will be able to 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.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 7.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  Unit 6: Logarithms and Other Inverses: CC-4, 10(e,d), 26(a-d), 38(c), 40(a-b), 42(a-d), 49(d), 68(a-d), 76(c,d), 93(a-d), 105, 124(a-d), 146(a,b) 158(c,d); Unit 7: Polynomials and General Systems: CF-14(a,b), 49, 63; Unit 8: Circular Functions: CT-29, 33, 43, 66, 98; Unit 9: More Triangles and Trigonometry: ST-34, 36, 65(a,b), 76, 93(a,b), 133; Unit 10: Probability and Policy Making: PM-10(a-d), 19(a,b), 20(b), 25(b,e,f), 45, 46, 65(b), 67(a,b), 73, 78(a,b); Unit 11: Counting and Sampling: IC-13, 28, 29, 64(c), 65, 78, 91(a,b), 92, 104, 106(a,b); Unit 12: Descriptive Statistics: DS-28, 30(a,b), 70(b) 86, 101(a), 130; Unit 13: Revisiting and Extending: RE-12,,19, 20, 21, 23, 26, 44, 57, 58, 60, 73.
· PLATO Learning Inc., 2000, Modules: [Software].  Intermediate Algebra: Rational Expressions, Evaluating, Equivalent Forms, Rational Sum and Difference, Rational Product and Quotient, Unlike Denominators, Review: Rational Expression; Advanced Algebra: Algebraic Fractions.
  
Quadratic Equations
The learner will be able to 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.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 8.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  Unit 1: Exploring Functions: EF-8(c), 54, 82, 109, 110(a,b) quadratic formula, 118(d-f); Unit 2: Sequences: BB-33, 49, 62; Unit 3: Exponential Functions: FX-9, 12(a), 37, 53, 64, 69; Unit 4: Parabolas and Other Parent Graphs: PG?16, 22-25, 27(a-e), 28, 38(a), 43, 46-51, 62-64, 66, 71(a-d), 72, 92, 103, 131?133, 148, 158, 159(g), 163; Unit 5: Linear Systems and Matrices: LS-50, 100, 123, 157; Unit 6: Logarithms and Other Inverses: CC-38(b,d), 49(c), 76(b,d), 79; Unit 7: Polynomials and General Systems: CF-4(a,b,c), 9, 14, 19, 23, 30, 65?68, 70, 72, 83, 88, 101, 103, 106, 111, 112, 114, 131, 140, 141, 143(a?d), 148, 149, 152(c), 153; Unit 8: Circular Functions: CT?5, 53, 54, 66(b), 75, 87, 118(a), 142, 156; Unit 9: More Triangles and Trigonometry: ST-35, 38(b), 63, 64, 117, 118, 131, 133(b); Unit 10: Probability and Policy Making: PM-4, 6(a,b), 7, 8, 19(a), 21, 25(c,d), 32, 48, 51(b), 63, 65, 71, 73, 87, 93, 94; Unit 11: Counting and Sampling: IC-31, 79, 87, 122; Unit 12: Descriptive Statistics: DS?13, 78, 81(b), 86, 87, 116, 143; Unit 13: Revisiting and Extending: RE-17, 31, 33, 45, 57, 58, 59, 60, 70, 71(c), 79, 87.
· PLATO Learning Inc., 2000, Modules: [Software].  Beginning Algebra: Quadratic Equations, Quadratic Formula, Word Problems II.
  
Coefficients and Quadratic Functions
The learner will be able to 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.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 9.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  
· PLATO Learning Inc., 2000, Modules: [Software].  Advanced Algebra: Parabolas.
  
Graphing Quadratic Functions
The learner will be able to graph quadratic functions and determine the maxima, minima, and zeros of the function.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 10.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  
· PLATO Learning Inc., 2000, Modules: [Software].  Not available on the Web Learning Network.
  
Exponents and Logarithms
The learner will be able to understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 11.1.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  
· PLATO Learning Inc., 2000, Modules: [Software].  Advanced Algebra: Exponential and Logarithmic Functions.
  
Validity of an Argument
The learner will be able to judge the validity of an argument according to whether the properties of real numbers, exponents, and logarithms have been applied correctly at each step.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 11.2.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  
· PLATO Learning Inc., 2000, Modules: [Software].  Advanced Algebra Exponential and Logarithmic Functions.
  
Laws of Fractional Exponents
The learner will be able to know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 12.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  
· PLATO Learning Inc., 2000, Modules: [Software].  Advanced Algebra: Exponents and Radicals, Exponential and Logarithmic Functions, Exponential Growth and Decay.
  
Definition of Logarithms
The learner will be able to use the definition of logarithms to translate between logarithms in any base.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 13.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  
· PLATO Learning Inc., 2000, Modules: [Software].  No PLATO modules are available for this learning expectation at this time.
  
Properties of Logarithms
The learner will be able to understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 14.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  
· PLATO Learning Inc., 2000, Modules: [Software].  No PLATO modules are available for this learning expectation at this time.
  
Truth of Algebraic Statements
The learner will be able to determine whether a specific algebraic statement involving rational expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always true, or never true.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 15.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  
· PLATO Learning Inc., 2000, Modules: [Software].  Advanced Algebra: Numbers and Their Properties: Exponents and Radicals, Algebraic Operations, Factoring, Algebraic Fractions.
  
Geometry of a Graph: Conic Section
The learner will be able to 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.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 16.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  
· PLATO Learning Inc., 2000, Modules: [Software].  Advanced Algebra: Ellipses and Hyperbolas.
  
Graphing a Quadratic Equation
The learner will be able to ,given a quadratic equation of the form ax 2 + by 2 + cx + dy + e = 0, 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 then graph the equation.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 17.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  
· PLATO Learning Inc., 2000, Modules: [Software].  Advanced Algebra (partial): Parabolas, Ellipses and Hyperbolas.
  
Combinations and Permutations
The learner will be able to use fundamental counting principles to compute combinations and permutations.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 18.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  No PLATO modules are available for this learning expectation at this time.
· PLATO Learning Inc., 2000, Modules: [Software].  
  
Computing Probabilities
The learner will be able to use combinations and permutations to compute probabilities.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 19.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  
· PLATO Learning Inc., 2000, Modules: [Software].  No PLATO modules are available for this learning expectation at this time.
  
Binomial Theorem and Expressions
The learner will be able to know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 20.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  
· PLATO Learning Inc., 2000, Modules: [Software].  No PLATO modules are available for this learning expectation at this time.
  
Method of Mathematical Induction
The learner will be able to apply the method of mathematical induction to prove general statements about the positive integers.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 21.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  
· PLATO Learning Inc., 2000, Modules: [Software].  No PLATO modules are available for this learning expectation at this time.
  
Arithmetic & Geometric Series
The learner will be able to find the general term and the sums of arithmetic series and of both finite and infinite geometric series.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 22.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  
· PLATO Learning Inc., 2000, Modules: [Software].  Calculus 2: Introduction to Series.
  
Summation Formulas
The learner will be able to derive the summation formulas for arithmetic series and for both finite and infinite geometric series.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 23.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  
· PLATO Learning Inc., 2000, Modules: [Software].  Not available on the Web Learning Network.
  
Problem Solving: Functional Concepts
The learner will be able to solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 24.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  
· PLATO Learning Inc., 2000, Modules: [Software].  Advanced Algebra: Composite and Inverse Functions, Applications of Functions.
  
Combining & Simplifying Functions
The learner will be able to use properties from number systems to justify steps in combining and simplifying functions.
Strand Scope Source
Algebra II Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra II, 25.0.
  Instructional Resources
 
· CPM Mathematics 3, (Algebra 2), 2nd Ed., v. 5.0, 2000., Problems: [Textbook].  
· PLATO Learning Inc., 2000, Modules: [Software].  No PLATO modules are available for this learning expectation at this time.
  
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