MATHEMATICS Mathematics Curriculum---Hanover County Public Schools Revised Summer Inequalities

Transcription

1 Number and MATHEMATICS Expressions AII.1 The student will identify field properties, axioms of equality and inequality, and properties of order that are valid for the set of real numbers and its subsets, complex numbers, and matrices. Hanover Objective(s): same Related Standard(s): Complex numbers are organized into a hierarchy of subsets with properties applicable to each subset. Complex numbers are a superset of real numbers and, as a system, contain solutions for equations that are not solvable over the set of real numbers. Identify examples of field properties: commutative, associative, identity, inverse, and distributive. Identify examples of axioms of equality: reflexive, symmetric, transitive, substitution, addition, and multiplication. Identify examples of axioms of inequality and order: trichotomy, transitive, addition, and multiplication. Place the following sets of numbers in a hierarchy of subsets: complex, pure imaginary, real, rational, irrational, integers, whole, and natural. Add and multiply matrices, and determine which field properties hold.

2 Textbook Correlation Glencoe Algebra II Chapter 1 p Expressions and Formulas Properties of Real Numbers Solving Equations Solving Absolute Value Equations Solving Solving Compound and Absolute Value Chapter 2 p Linear Equations Chapter 5 p Complex Numbers Noteables p p p MATHEMATICS Activities Properties of Real Numbers, Max A. Sobel, Norbert Lerner, Evan M. Matetsky, Louis s. Cohen, Harper & Row Algebra Two, Scribner Educational Publishers, New York, NY: 1985, p [Hereafter referred to as Sobel and number.] Norton Juster, Dot and Line, Random House, New York: (Now available in paperback: ISBN ) Using Matrices in Real-Life Settings, Roland E. Larson, Algebra 2, D.C. Heath and Company, 1993, p I Have/Who Has(Instructional Activity AII.1a.ACT) Patterns from Pascal s Triangle (Instructional Activity AII.1B.ACT). Fibonacci Sequence (Instructional Activity AII.1C.ACT) Worksheet Review WS 1 AII.1B Equation WS 1- AII.1C Equation WS 2 AII.1D Math Block Table-AII.1E Practice 1-3-AII.1F Math Tool Box Skills Review-AII.1G Properties AII.1H Lesson 3-3, Solving Equations AII.1I Lesson 3-3, Combining Like Terms AII.1J Lesson 3-4, Using the Distributive Property, Simplifying Variable Expressions AII.1K Lesson 3-4, Using the Distributive Property, Solving and Modeling Equations AII.1L Practice 3-3, Mixed Exercises AII.1M Practice 3-4, Example Exercises AII.1N Practice 4-7, Mixed Exercises, AII.1O Lesson 8-7, More Multiplication Properties of Exponents, Raising a Product to a Power AII.1P Lesson 8-7, More Multiplication Properties of Exponents, Raising a Power to a Power AII.1Q Lesson 8-6, A Multiplication Property of

3 Exponents, Multiplying Powers AII.1R Lesson 8-8, Division Properties of Exponents, Dividing Powers with the Same Base AII.1S Lesson 8-8, Division Properties of Exponents, Raising a Quotient to a Power AII.1T Powere Properties Chart- AII.1U Properties Table AII.1V Properties Worksheet-AII.1V Test Review AII.1X Textbook: Properties and Formulas of Advanced Algebra, p. T660, p

4 Number and Expressions AII.2 The student will add, subtract, multiply, divide, and simplify rational expressions, including complex fractions. Hanover Objective(s): same Computational skills applicable to numerical fractions also apply to rational expressions involving variables. Add, subtract, multiply, and divide rational expressions whose denominators are monomials or polynomial expressions in completely factored form. Simplify a rational expression with common monomial or binomial factors. Recognize a complex fraction, and simplify it as a quotient or product of simple fractions.

5 Textbook Correlation Glencoe Algebra II Chapter 1 p Properties of Real Numbers Solving Equations Chapter 2 p Modeling Real-World Data: Using Scatter Plots Chapter 5 p Monomials Chapter 9 p Multiplying and Dividing Rational Expressions Adding and Subtracting Rational Expressions Noteables p p p p MATHEMATICS Activities Resources * and / Rational Expressions Ronald E. Larson, Timothy D. Kanold, and Lee Stiff, Algebra 2, D. C. Heath and Company, Lesington, MA: 1993, p [Hereafter referred as Larson and page number] + and Rational Expressions Larson, p Worksheets Factoring Worksheet- AII.2A Operations with Fractions- AII.2B Rational Expressions-AII.2C Assessment: Simplifying Rational Expressions-AII.2A.ASMT Multiply/Divide Rational Exp (3 Forms)- AII.2B.ASMT Simplify Rational Exp with bonus-aii.2c.asmt Make Up Test AII.2D.ASMT Operations with Rational Exp- AII.2E.ASMT

6 Number and Expressions AII.3 The student will: add, subtract, multiply, divide, and simplify radical expressions containing positive rational numbers and variables and expressions containing rational exponents write radical expressions as expressions containing rational exponents, and vice versa. Hanover Objective(s): same The student will: add, subtract, multiply, divide, and simplify radical expressions containing positive rational numbers and variables and expressions containing rational exponents write radical expressions as expressions containing rational exponents, and vice versa. simplify radical expressions containing numbers and variables add radical expressions subtract radical expressions multiply radical expressions divide radical expressions write expressions with rational exponents in simplest radical form and vice versa. Simplify radical expressions containing positive rational numbers and variables. Convert from radical notation to exponential notation, and vice versa. Add and subtract radical expressions with like radicands. Multiply and divide radical expressions not requiring rationalizing the denominators. Textbook Correlation Activities

7 Glencoe Algebra II Chapter 5 p , p Dividing Polynomials Roots of Real Numbers Radical Expressions Rational Exponents Noteables: p p MATHEMATICS Properties Of Roots of Real Numbers Larson, p and Max A. Sobel, Norbert Lerner, Evan M. Maletsky, and Louis S. Cohen, Algebra 2, Harper & Row, 1985, p. 174, 214 [Hereafter referred to as Sobel and page number.] Worksheets: Radical WS 1 AII.3A Radical WS 2 AII. 3B Radical WS 3 AII.3C Radical WS 4 AII.3D Radical WS 5 AII.3E Lesson 9-4, Simplifying Radicals, Multiplications with Radicals AII.3F Lesson 9-4, Simplifying Radicals, Division with Radicals AII.3G Lesson 9-5, Adding and Subtracting Radicals AII.3H Reteaching 9-4 AII.3I Lesson 9-5, Adding and Subtracting Radicals AII.3J Reteaching 9-5 AII.3K Assessment: Radical Expressions/Equations AII.3A.ASMT Simplifying Radicals and Solving Equations (2 Forms) AII.3B.ASMT

8 Number and Expressions AII.4 The student will solve absolute value equations and inequalities graphically and algebraically. Graphing calculators will be used both as a primary method of solution and to verify algebraic solutions. Hanover Objective(s): same Absolute value equations and inequalities can be used to model practical problems. Solve absolute value equations in one variable algebraically and graphically, using a graphing calculator. Solve absolute value inequalities in one variable algebraically and graphically. Express the solutions to absolute value equations and inequalities in one variable graphically and as an algebraic inequality. Graph absolute value equations in two variables. Verify solutions to absolute value equations and inequalities in two variables, using a graphing calculator.

9 Textbook Correlation Glencoe Algebra II Chapter 1 p Solving Compound and Absolute Value Chapter 9 p Classes of Noteables: p p MATHEMATICS Activities Resources Solving Absolute Value Larson, p Worksheets: Practice 4-8, Absolute Value AII.4A Assessment Sample: Sobel, p. 78 and p. A8.

10 Number and Expressions AII.5 The student will identify and factor completely polynomials representing the difference of squares, perfect square trinomials, the sum and difference of cubes, and general trinomials. Hanover Objective(s): same The complete factorization of polynomials has occurred when each factor is a prime polynomial. Pattern recognition can be used to determine complete factorization of a polynomial. Determine the greatest monomial factor as a first step in complete factorization. Recognize squares and cubes of positive integers. Recognize examples of general patterns: difference of squares, sum and difference of cubes, and perfect square trinomials. Factor polynomials by applying general patterns.

11 Textbook Correlation Glencoe Algebra II Chapter 5 p Factoring Polynomials Chapter 6 p Solving Quadratic Equations by Graphing Solving Quadratic Equations by Factoring Noteables p p MATHEMATICS Activities Factoring Polynomials and Solving Polynomial Equations Larson, p Worksheets: Practice AII.5A Practice 10-4, Example Exercises- AII.5B Practice 10-5, Mixed Exercises AII.5C Practice 10-6, Example Exercises AII.5D Practice 10-6, Mixed Exercises AII.5E 10-2,Multiplying and Factoring with Monomials- AII.5F 10-4,Factoring Trinomials using Tiles AII.5G 10-4, Factoring Trinomials AII.5H 10-5, Factoring Special Cases AII.5I 10-6, Solve Equations by Factoring AII.5J

12 Number and Expressions AII.6 The student will select, justify, and apply a technique to solve a quadratic equation over the set of complex numbers. Graphing calculators will be used for solving and confirming algebraic solutions. Hanover Objective(s): same Related Standard(s): A quadratic equation whose graph does not intersect the x- axis has only complex solutions. Complex solutions occur in pairs (conjugates). The quadratic formula can be used to solve any quadratic equation. Recognize a quadratic equation. Select an appropriate strategy for solving a quadratic equation (factoring, using the quadratic formula, or graphing). Solve a quadratic equation over the set of complex numbers. Identify from a graph the real solutions to a quadratic equation. Find the real roots of a quadratic equation, using a graphing calculator.

13 Textbook Correlation Glencoe Algebra II Chapter 6 p Solving Quadratic Equations by Graphing Solving Quadratic Equations by Factoring Completing the Square The Quadratic Formula and the Discriminant Chapter 9 p Classes of Noteables p p MATHEMATICS Worksheets: Equation WS 1 AII.6A Equation WS 2 AII.6B Activities

14 Number and Expressions AII. 7 The student will solve equations containing rational expressions and equations containing radical expressions algebraically and graphically. Graphing calculators will be used for solving and confirming algebraic solutions. Hanover Objective(s): same A solution of an equation makes the equation true. Equations can be solved in a variety of ways. The solution of an equation in one variable can be found by graphing each side of the equation separately and finding the x-coordinate of the point of intersection. Practical problems can be interpreted, represented, and solved using equations. Solve equations containing rational expressions with monomial denominators algebraically and graphically. Solve equations containing a radical expression algebraically and graphically. The equation will contain a linear expression under the radical, and all terms outside the radical will be constants. Identify from a graph the solutions to an equation containing rational or radical expressions. Solve an equation containing rational or radical expressions, using a graphing calculator. Check possible solutions to an equation containing rational or radical expressions, using a graphing calculator.

15 Textbook Correlation Glencoe Algebra II Chapter 1 p Solving Equations Chapter 5 p Radical Chapter 9 p Classes of Solving Rational Noteables p p p MATHEMATICS Activities Exploring Rational (Instructional Activity AII.7A). Solving Radical Equations, Larson p Solving Rational Equations, Larson p Worksheets: Exploring Rational (2 Pages)-AII.7A 9-6,Solving Radical Equations-AII.7B 9-6, Solving Radical Equations w/extraneous solutions- AII.7C

16 Number and Expressions AII.8 The student will recognize multiple representations of functions (linear, quadratic, absolute value, step, and exponential functions) and convert between a graph, a table, and symbolic form. A transformational approach to graphing will be employed through the use of graphing calculators. Hanover Objective(s): same The graphs/equations for a family of functions can be determined using a transformational approach. Recognize graphs of parent functions for linear, quadratic, absolute value, step, and exponential functions. Given an equation of a function, identify the function as linear, quadratic, absolute value, step, or exponential. Write the equation of a linear (slope-intercept form), quadratic ([h, k] form), absolute value, step, or exponential function, given the graph of the parent function or an integral translation of a parent function. Given an equation, graph a linear, quadratic, absolute value, step, or exponential function with the aid of a graphing calculator.

17 Textbook Correlation Glencoe Algebra II Chapter 2 p , Relations and Linear Equations Slope Writing Linear Equations Special Graphing Chapter 5 p Polynomials Chapter 6 p , Graphing Quadratic Solving Quadratic Equations by Graphing Analyzing Graphs of Quadratic Graphing Calculator Investigation p Chapter 7 p Polynomial Chapter 8 p Parabolas Chapter 9 p Classes of Chapter 10 p Exponential Noteables p p p p p p p p p MATHEMATICS Activities Worksheets: Piecewise (Activity AII.8A) Postage and the Greatest Integer Function (Instructional Activity AII.8B) Doubling Time Growth Model (Activity AII.8C) Investment Banking (Activity AII.8D) Algebra II Group Activity (Activity AII.8E) Rational AII.8F Graphing Step, Absolute Value and Linear AII.8G Building A Bridge (2 Pages) AII.8H Relationships and Graphs (Packet) AII.8I Assessment: AII Quiz-Lesson 1.7, 1.3 (4 Forms) AII.8A.ASMT Test on Review of Alg I and Chap 1 (4 Forms) AII.8B.ASMT Make up Test, Review of Alg I and Chap 1 (2 Forms) AII.8C.ASMT Quiz 2.1, 2.3- AII.8D.ASMT Test 2 (1-5) and Lesson 8.1- AII.8E.ASMT

18 Number and Expressions AII.9 The student will find the domain, range, zeros and inverse of a function, the value of a function for a given element in its domain, and the composition of multiple functions. will include exponential, logarithmic, and those that have domains and ranges that are limited those that have domains and ranges that are limited and/or discontinuous. The Graphing calculator will be used as a tool to assist in investigation of functions, including exponential and logarithmic. Hanover Objectives: same describe the relationship between two variables. Graphs of functions that are inverses of each other are reflections across the line y = x. The composition of a function and its inverse is the identity function. arise from practical situations. If (a, b) is an element of a function, then (b, a) is an element of the inverse of the function. Identify the domain, range, zeros, and inverse of a function presented algebraically or graphically. Distinguish between relations and functions that are expressed algebraically and graphically. Recognize restricted/discontinuous domains and ranges. Use interchange of variables to find the inverse of a function. Given the graphs, recognize that exponential and logarithmic functions are inverses of each other. Find the composition of two functions. Find the value of a function for a given element from the

19 domain. Investigate exponential and logarithmic functions, using the graphing calculator. Textbook Correlation Glencoe Algebra II Chapter 2 p Relations and Chapter 6 p Graphing Quadratic Chapter 7 p Operations on Inverse and Relations Chapter 9 p Classes of Noteables p p p p Activities Worksheets: Domain and Range (Instructional Activity AII.9A) WS Section 5-4 AII.9B WS Section 5-4 AII.9C WS Section 5-4 AII.9D Relations and (Packet) AII.9E Assessment Sample: Restrict your teaching to graphing logs on the calculator (example y = log x y = log 2x y= 2 log x.) Teach how to use the log button on the calculator. Emphasize domain and range on every graphing problem.

20 Number and Expressions AII.10 The student will investigate and describe the relationships between the solution of an equation, zero of a function, x-intercept of a graph, and factors of a polynomial expression through the use of graphs. Hanover objectives: same The Fundamental Theorem of Algebra states that, including complex and repeated solutions, an n th degree polynomial equation has exactly n roots (solutions). The following statements are equivalent: k is a zero of the polynomial function f; (x k) is a factor of f(x); k is a solution of the polynomial equation f(x) = 0; and k is an x-intercept for the graph of the polynomial. Identify the x-intercept(s) of a graph. Identify the zero(s) of a function, given a graph. Determine the linear factors of a polynomial expression when the zeros of the corresponding polynomial function are displayed on a graph.

21 Textbook Correlation Glencoe Algebra II Chapter 2 p Linear Equations Slope Writing Linear Equations Chapter 5 p Factoring Polynomials Chapter 6 p Solving Quadratic Equations by Graphing Solving Quadratic Equations by Factoring Chapter 7 p Polynomial Noteables p p p p MATHEMATICS Activities Worksheets: Relationships and Graphs (Packet) AII.10A

22 Number and Expressions AII. 11 The student will use matrix multiplication to solve practical problems. Graphing calculators or computer programs with matrix capabilities will be used to find the product. Hanover Objective(s): same Matrices can be used to model and solve practical problems. Recognize matrices that can be multiplied. Perform matrix multiplication with a graphing calculator or a computer program with matrix capabilities. Use matrix multiplication to solve practical problems.

23 Textbook Correlation Glencoe Algebra II Chapter 4 p , , Introduction to Matrices Operations with Matrices Multiplying Matrices Determinants Identity and Inverse Matrices Using Matrices to Solve of Equations Noteables p p p MATHEMATICS Activities Worksheets: Assignment Sheet for Chapter 3 (2 pages) AII.11A Assessment: Test , 3.6 (2 Forms)-No Calculator-AII.11A.ASMT Quiz AII.11B.ASMT Test Chap 3 (w/calc) AII.11C.ASMT Make Up Test 3 (w/calc) AII.11D.ASMT

24 Number and Expression AII.12 The student will represent problem situations with a system of linear equations and solve the system using the inverse matrix method. Graphing calculators of computer programs with matrix capability will be used to perform computations. Hanover Objective(s): same Matrices are a convenient shorthand for solving systems of equations. Matrices can model a variety of linear systems. Solutions of a linear system are values that satisfy every equation in the system. Model problems with a system of no more than three linear equations. Represent a system of no more than three linear equations in matrix form. Solve a matrix equation using a graphing calculator or computer program with matrix capability. Find the inverse of a matrix with a graphing calculator. Express a system of linear equations as a matrix equation.

25 Textbook Correlation Glencoe Algebra II Chapter 3 p Solving of Equations by Graphing Solving of Equations Algebraically Noteables p MATHEMATICS Activities Linear, Larson, p of Equations & AII.12A Matrices for Problems in Manufacturing AII.12B Using Matrices to Organize Data AII.12C

26 Number and Expression AII.13 The student will solve systems of linear inequalities and linear programming problems and describe the results both orally and in writing. A graphing calculator will be used to facilitate solutions to linear programming problems. Hanover Objective(s): same Linear programming models an optimization process. A linear programming model consists of a system of constraints and an objective quantity that can be maximized or minimized. Any maximum or minimum value will occur at a corner point of a feasible region. Model practical problems with systems of linear inequalities. Solve systems of linear inequalities. Identify the feasibility region of a system of linear inequalities with no more than five constraints. Identify the coordinates of the corner points of a feasibility region. Find the maximum or minimum value for the function defined over the feasibility region. Describe the meaning of the maximum or minimum value.

27 Textbook Correlation Glencoe Algebra II Chapter 3 p Solving of by Graphing Linear Programming MATHEMATICS Activities Algebra II Activity (Instructional Activity AII.13A) Linear Programming AII.13B Graphing AII.13C Noteables p UCSMP: of Linear, Section 5.7 Linear Programming I, Section 5.8 Linear Programming II, Section 5.9 Concepts of Linear Programming, Bellman, p , 313, 561.

28 Number and Expression AII. 14 The student will solve nonlinear systems of equations, including linear-quadratic and quadratic-quadratic, algebraically and graphically. The graphing calculator will be used as a tool to visualize graphs and predict the number of solutions. Hanover Objective(s): same Solutions of a nonlinear system of equations are numerical values that satisfy every equation in the system. The coordinates of points of intersection in nonlinear systems are solutions to the system. Identify nonlinear systems of equations as linear-quadratic or quadratic-quadratic. Visualize a nonlinear system of two equations, and predict the number of solutions, using the graphing calculator. Solve a linear-quadratic system of two equations algebraically and graphically. Solve a quadratic-quadratic system of two equations algebraically and graphically.

29 Glencoe Algebra II Chapter 8 p Solving Quadratic Noteables p Textbook Correlation MATHEMATICS Activities Nonlinear, Sobel, p , AII.14A UCSMP: Quadratic-Linear, Section 12.9 Quadratic-Quadratic, Section Linear-Quadratic, Sobel, p Quadratic, Sobel, p with Nonlinear Equations, Bellman, p

30 Number and Expression AII. 15 The student will recognize the general shape of polynomial, exponential, and logarithmic functions. The graphing calculator will be used as a tool to investigate the shape and behavior of polynomial functions. Hanover Objective(s): same Shapes and behavior of graphs of polynomials can be determined by analyzing transformations of parent functions. Using graphing calculators is a strategy for investigating the shape and behavior of polynomial functions. The Fundamental Theorem of Algebra (Carl Fredrich Gauss) states that in the complex number system, an n th degree polynomial equation has n zeros. Exponential and logarithmic functions are either strictly increasing or strictly decreasing. Investigate the shape and behavior of linear, quadratic, and cubic functions. Behaviors will include intercepts, number of turning points, and end behavior. Investigate the shape and behavior of exponential (a x = y) and logarithmic (log b x = y) functions, including intercepts and end behavior. Using the general shape of the graph of a function, identify the family of graphs to which a particular graph belongs. Characteristics of a graph may include the x- and y-intercepts, number and location of turning points, and end behaviors.

31 Textbook Correlation Glencoe Algebra II Chapter 6 p , Graphing Quadratic Analyzing Graphs of Quadratic Chapter 9 p Classes of Chapter 10 p Exponential Logarithms and Logarithmic Noteables p p p p MATHEMATICS Activities Circle (Instructional Activity AII.15A) Ellipses (Instructional Activity AII.15B) Hyperbolas (Instructional Activity AII.15C) Parabolas (Instructional Activity AII.15D) Projectile Motion (Instructional Activity AII.15E) Identifying Conics, Kenneth J. Travers, Leroy C. Dalton and Vincent F. Brunner, Using Advanced Algebra, Laidlaw Brothers, River Forest, Illinois, 1975, p UCSMP: Polynomial Models, Section 11.1, Chapter 7 The Factor Theorem, Section 11.4 Quadratic-Linear, Section 12.9 Quadratic-Quadratic, Section 12.10

32 Number and Expression AII. 16 The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve problems, including writing the first n terms, finding the nth term, and evaluating summation formulas. Notation will include Σ and a n. Hanover Objective(s): same Sequences and series arise from practical situations. The study of sequences and series is an application of investigation of patterns. Distinguish between a sequence and a series. Recognize patterns in a sequence. Distinguish between arithmetic and geometric sequences. Use and interpret the notations, n, n th term, and a n. Write the first n terms in an arithmetic or geometric sequence. Given the formula, find a n (the n th term) for an arithmetic or a geometric sequence. Given formulas, find the sum, S n, of the first n terms of an arithmetic or geometric series, including infinite series.

33 Glencoe Algebra II Chapter 11 p Arithmetic Sequences Arithmetic Series Geometric Sequences Geometric Series Noteables p Textbook Correlation MATHEMATICS Activities Seating Capacity, Roland E. Larson, Timothy D. Kanold, and Lee Stiff, Algebra 2, D.C. Heath and Company, Lesington, MA: 1993, p Sharing Ideas Larson, p Sharing Ideas Larson, p Zooming Inn Larson, p UCSMP: Explicit Formulas for Sequences, Section 1-3 Recursive Formulas for Sequences, Section 1-4 Arithmetic Sequences: Explicit Formulas, Section 3.6 Arithmetic Sequences: Recursive Formulas Section 3.7 Geometric Sequences, Section 8.3 Series, Combinations, and, Sections

34 Number and Expression AII.17 The student will perform operations on complex numbers and express the results in simplest form. Simplifying results will involve using patterns of the powers of i. Hanover Objective(s): same Complex numbers are a superset of real numbers. Recognize that the square root of 1 is represented as i. Define and identify a complex number. Apply the definition of i to simplify square roots of negative numbers. Simplify powers of i. Add, subtract, and multiply complex numbers. Textbook Correlation Glencoe Algebra II Chapter 5 p Complex Numbers Noteables p Activities Simplifying Expressions Containing Complex Numbers AII.17A UCSMP: The Imaginary Number i, Section 6..8 Complex Numbers, Section 6.9 Complex Numbers, Sobel, p

35 Number and MATHEMATICS Expression AII.18 The student will identify conic sections (circle, ellipse, parablola, and hyperbola) from his/her equations. Given the equations in (h, k) form, students will sketch graphs of conic sections, using transformations. Hanover Objective(s): same Changing parameters (h, k) affects the graph of a conic section in a predictable pattern. Conic sections can be distinguished by their equations. Identify types of conic sections, given (h, k) form of an equation. Identify types of conic sections from a graph. Sketch the graph of a conic section in (h, k) form, using knowledge of transformations. Textbook Correlation Glencoe Algebra II Chapter 8 p Parabolas Circles Ellipses Hyperbolas Conic Sections Noteables p Activities Golden Gate Bridge, Ronald E. Larson, Timothy D. Kanold, and Lee Stiff, Algebra 2, D.C. Heath and Company, Lesington, MA: 1993, p.241. Sleepy Hare Restaurant Larson, p. 275 Gateway Arch Larson, p Circles, [Instructional Activity AII.15A] Ellipses, [Instructional Activity AII.15B] Hyperbolas, [Instructional Activity AII.15C] Parabolas, [Instructional Activity AII.15D] UCSMP: Parabolas and Quadratic Equations, Chapter 6 (omit 6.3) Quadratic Relations, Chapter 12, Sections

36 Number and Expression AII.19 The student will collect and analyze data to make predictions, write equations, and solve practical problems. Graphing calculators will be used to investigate scatter plots to determine the equation for a curve of best fit. Models will include linear, quadratic, exponential, and logarithmic functions. Hanover Objective(s): same Data and scatterplots may indicate patterns that can be modeled with an algebraic equation. Graphing calculators can be used to collect, organize, picture, and create an algebraic model of the data. Data that fit linear, quadratic, exponential, and logarithmic models arise from practical situations. Collect and analyze data. Investigate scatterplots to determine if patterns exist, and then identify the patterns. Find an equation for the curve of best fit for data, using a graphing calculator. Models will include linear, quadratic, exponential, and logarithmic functions. Make predictions, using data, scatterplots, or curve of best fit. Given a set of data, determine the model that would best describe the data.

37 Textbook Correlation Glencoe Algebra II Chapter 2 p. 87 Graphing Calculator Investigation Chapter 6 p. 300 Graphing Calculator Investigation Chapter 7 p. 359 Graphing Calculator Investigation MATHEMATICS Pulse Rate and Child s Age (Instructional Activity AII.19A) Scatter Plots, Rubenstein, p Scatter Plots II, Rubenstein, p. 13. TI-82/83 Procedure 23: Fining Best-Fit Models AII.19B Scatter plot AII.19C Scatter plot and Line of Best Fit AII.19D UCSMP: Fitting a Model to Data I, Section 2.8 Fitting a Model to Data II, Section 2.9

38 Number and Expression AII.20 The student will identify, create, and solve practical problems involving inverse variation and a combination of direct and inverse variations. Hanover Objective(s): same Practical problems can be modeled and solved by using direct and/or inverse variations. Joint variation is a combination of direct variations. Translate y is directly proportional to x as y = kx. Translate y is inversely proportional to x as y = k x. Translate y varies jointly as x and z as y = kxz. Determine the value of the constant of proportionality, k, given initial conditions for x and y. Set up and solve practical problems, using combinations of direct and inverse variation.

39 Textbook Correlation Glencoe Algebra II Chapter 9 p Direct, Joint, and Inverse Variation Classes of Noteables: p Activities Distance to a Thunderstorm (Instructional Activity AII.20A) Temperature Determines Chirps (Instructional Activity AII.20B) Direct, Inverse, and Joint Variations AII.20C Direct, Inverse, and Joint Variations AII.20D Direct Variation AII.20E Inverse Variation AII.20F Variation Review AII.20G UCSMP: Variation and Graphs, Chapter