Bellwood-Antis S.D. Curriculum (Dec. 2011) Course: Algebra II Grade Level(s): 10-12 Department: Mathematics Topic: Solving Equations and Inequalities Chapter: 1 Big Ideas: Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms. Patterns exhibit relationships that can be extended, described, and generalized. Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations. Essential Questions: How can we show that algebraic properties and processes are extensions of arithmetic properties and processes, and how can we use algebraic properties and processes to solve problems? How do you write, solve, graph, and interpret linear equations and inequalities to model relationships between quantities? There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities. Mathematical functions are relationships that assign each member of one set (domain) to a unique member of another set (range), and the relationship is recognizable across representations. Families of functions exhibit properties and behaviors that can be recognized across representations. Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations.
Standards Keystone Anchors/Eligible Content A1.1.1.1.1 - Compare and/or order any real numbers. A1.1.1.3.1 - Simplify/evaluate expressions involving properties/laws of exponents, roots, and/or absolute values to solve problems. A1.1.2.1.1 - Write, solve, and/or apply a linear equation (including problem situations). A1.1.2.1.2 - Use and/or identify an algebraic property to justify any step in an equation solving process. A1.1.3.1.1 - Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities). A1.1.3.1.2 - Identify or graph the solution set to a linear inequality on a number line. Content/ Concepts Solving Equations and Inequalities Competencies/Skills 1-1 Expressions and Formulas Use the order of operations Use formulas 1-2 Properties of Real Numbers Classify real numbers Use the properties of real numbers to simplify expressions 1-3 Solving Equations Translate verbal expressions into algebraic expressions and equations, and vice versa Solve equations 1-4 Solving Absolute Value Equations Evaluate absolute value expressions Solve absolute value equations 1-5 Solving Inequalities Solve inequalities Solve real-world inequalities problems 1-6 Solving Compound and Absolute Value Inequalities Solve compound inequalities Solve absolute value inequalities Assessment Evidence FORMATIVE ASSESSMENTS Homework Board Work Worksheets Human # Line Quizzes 1.1-1.3 1.3-1.5 on pg. 39 SUMMATIVE ASSESSMENTS Chapter 1 Test Instructional Activities, Strategies, and INSTRUCTIONAL ACTIVITIES AND STRATEGIES Guided Notes Modeling Human # Line Board Work Graphic Organizer RESOURCES Glencoe Algebra2 Text Glencoe Algebra2 Teacher Resource Pack Teacher Generated Study Island Kuta Software A1.1.3.1.3 - Interpret solutions to problems in the context of the problem situation.
Bellwood-Antis S.D. Curriculum Course: Algebra II Grade Level(s): 10-12 Department: Mathematics Topic: Linear Relations and Functions Chapter: 2 Big Ideas: Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms. Patterns exhibit relationships that can be extended, described, and generalized. Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations. There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities. Essential Questions: How do you decide which functional representation to choose when modeling a real world situation, and how would you explain your solution to the problem? How do you write, solve, graph, and interpret linear equations and inequalities to model relationships between quantities? How can we use bivariate data to analyze relationships and make predictions? Mathematical functions are relationships that assign each member of one set (domain) to a unique member of another set (range), and the relationship is recognizable across representations. Families of functions exhibit properties and behaviors that can be recognized across representations. Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations. Bivariate data can be modeled with mathematical functions that approximate the data well and help us make predictions based on the data.
Standards Keystone Anchors/Eligible Content A1.1.2.1.1 - Write, solve, and/or apply a linear equation (including problem situations). A1.1.2.1.3 - Interpret solutions to problems in the context of the problem situation. A1.1.3.1.3 - Interpret solutions to problems in the context of the problem situation. A1.2.1.1.1 - Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically. A1.2.1.1.2 - Determine whether a relation is a function, given a set of points or a graph. A1.2.1.1.3 - Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table). A1.2.1.2.1 - Create, interpret, and/or use the equation, graph, or table of a linear function. A1.2.1.2.2 - Translate from one representation of a linear function to another Content/ Concepts Linear Relations and Functions Competencies/Skills 2-1 Relations and Functions Determine functions Identify domain and range Find functional values 2-2 Linear Equations Identify linear equations and functions Write linear equations in standard form Graph equations in standard form Find x- and y-intercepts 2-3 Slope Find and use the slope of a line Graph parallel and perpendicular lines 2-4 Writing Linear Equations Given the slope and a point on the line Given two points on the line Given a parallel or perpendicular line and a point 2-5 Scatter Plots Find and use prediction equations 2-6 Special Functions Identify and graph constant, identity, and absolute value functions 2-7 Graphing Inequalities Graph linear and absolute value inequalities 2-6 Special Functions Identify and graph step and piecewise functions Assessment Evidence FORMATIVE ASSESSMENTS Homework Board Work Worksheets Quizzes 2.1-2.4 Scatter Plot Project SUMMATIVE ASSESSMENTS Chapter 2 Test Instructional Activities, Strategies, and INSTRUCTIONAL ACTIVITIES AND STRATEGIES Guided Notes Modeling Board Work Written Conversations Scatter Plot Project RESOURCES Glencoe Algebra2 Text Glencoe Algebra2 Teacher Resource Pack Teacher Generated
(i.e., graph, table, and equation). A1.2.2.1.1 - Identify, describe, and/or use constant rates of change. A1.2.2.1.2 - Apply the concept of linear rate of change (slope) to solve problems. A1.2.2.1.3 - Write or identify a linear equation when given the graph of the line two points on the line the slope and a point on the line Note: Linear equation may be in point-slope, standard, and/or slope-intercept form. A1.2.2.2.1 - Draw, identify, find, and/or write an equation for a line of best fit for a scatter plot. A1.2.3.2.2 - Analyze data, make predictions, and/or answer questions based on displayed data (scatter plots) A1.2.3.2.3 - Make predictions using the equations or graphs of best-fit lines of scatter plots.
Bellwood-Antis S.D. Curriculum Course: Algebra II Grade Level(s): 10-12 Department: Mathematics Topic: Systems of Equations and Inequalities Chapter: 3 Big Ideas: Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms. Patterns exhibit relationships that can be extended, described, and generalized. Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations. There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities. Essential Questions: How can we show that algebraic properties and processes are extensions of arithmetic properties and processes, and how can we use algebraic properties and processes to solve problems? How do you decide which functional representation to choose when modeling a real world situation, and how would you explain your solution to the problem? How do you write, solve, and interpret systems of two linear equations and inequalities using graphing and algebraic techniques? Mathematical functions are relationships that assign each member of one set (domain) to a unique member of another set (range), and the relationship is recognizable across representations. Families of functions exhibit properties and behaviors that can be recognized across representations. Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations.
Standards Keystone Anchors/Eligible Content A1.1.2.2.1 - Write and/or solve a system of linear equations (including problem situations) using graphing, substitution, and/or elimination. A1.1.2.2.2 - Interpret solutions to problems in the context of the problem situation. A1.1.3.2.1 - Write and/or solve a system of linear inequalities using graphing. A1.1.3.2.2 - Interpret solutions to problems in the context of the problem situation. (US Standards Gr.11) E1.b - Express and solve systems of linear equations in three variables with and without the use of technology. Content/ Concepts Systems of Equations and Inequalities Competencies/Skills 3-1 Solving Systems of Equations by Graphing Determine whether a system of equations is: consistent and independent (intersecting lines; one solution), consistent and dependent (same line; infinitely many solutions), or inconsistent (parallel lines; no solution) 3-2 Solving Systems of Equations Algebraically Solve by using substitution Solve by using elimination Solve real-world problems using systems of linear equations in two variables 3-5 Solving Systems of Equations in Three Variables 3-3 Solving Systems of Inequalities by Graphing Determine the coordinates of the vertices of a region formed by the graph of a system of inequalities Assessment Evidence FORMATIVE ASSESSMENTS Homework Board Work Worksheets s SUMMATIVE ASSESSMENTS 3.1, 3.2, 3.5 Quiz 3.4 Partner Quiz Instructional Activities, Strategies, and INSTRUCTIONAL ACTIVITIES AND STRATEGIES Guided Notes Modeling s Board Work Reviews and Partner Work Use highlighters for section 3-3 RESOURCES Glencoe Algebra2 Text Glencoe Algebra2 Teacher Resource Pack Teacher Generated Kuta Software Worksheets E1.c - Solve systems of linear inequalities in two variables and graph the solution set. 3-4 Linear Programming Solve real-world problems with linear programming to identify maximum and minimum values of a function over a region
Bellwood-Antis S.D. Curriculum Course: Algebra II Grade Level(s): 10-12 Department: Mathematics Topic: Polynomials Chapter 5 Big Ideas: Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms. Patterns exhibit relationships that can be extended, described, and generalized. Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations. There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities. Essential Questions: How do you explain the benefits of multiple methods of representing polynomial functions (tables, graphs, equations, and contextual situations)? Are there times when radical notation is more productive than rational exponent notation? How can categorizing polynomials help in factoring? When is long division necessary? Why not just use synthetic division? What is the value of scientific notation? Families of functions exhibit properties and behaviors that can be recognized across representations. Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations.
Standards Common Core Keystone Anchors/Eligible Content A2.1.1.1.1: Simplify square roots in terms of i. (e.g., 24 = 2i 6). A2.1.1.1.2: Simplify/evaluate expressions involving imaginary numbers powers of i (e.g., i 6 + i 3 = 1 + i). A2.1.1.2.1: Add and subtract complex numbers(e.g., (7 3i) (2 + i) = 5 4i). A2.1.1.2.2: Multiply and divide complex numbers (e.g., (7 3i)(2 + i) = 17 + i). A2.1.2.1.1: Use exponential expressions to represent rational numbers. A2.1.2.1.2: Simplify/evaluate expressions involving positive and negative exponents and/or roots (may contain all types of real numbers - exponents should not exceed power of 10). Content/Concepts Competencies/Skills Assessment Evidence Instructional Activities, Strategies, and Polynomials and Radical Equations and Inequalities 5.1 Multiply and Divide Monomials 5.1 Scientific Notation 5.2 Add, Subtract, and Multiply Polynomials 5.3 Divide Polynomials Long division Synthetic division 5.4 Factor Polynomials GCF Difference of Squares Sum of Cubes Difference of Cubes Trinomials in Quadratic Form Grouping 5.4 Simplify Quotients by Factoring 5.5 Simplify Radicals 5.5 Approximate Radicals Using a Calculator 5.6 Simplify Radical Expressions 5.6 Add, Subtract, Multiply, and Divide Radical Expressions 5.7 Radical Form and Rational Exponent Form 5.8 Solve Equations and Inequalities Containing Radicals 5.9 Add, Subtract, Multiply, and Divide Complex Numbers FORMATIVE ASSESSMENTS: Word Splash Sorting Activities Graphic Organizer I Can/Who Can BINGO SUMMATIVE ASSESSMENTS: Section Quizzes 5.1-5.3 5.4 5.5-5.7 5.8-5.9 Study Island Keystone Materials CommonCore Chapter Test INSTRUCTIONAL ACTIVITIES AND STRATEGIES: Word Splash Sorting Activities Graphic Organizer I Can/Who Can BINGO Guided Notes Modeling Think Alouds Cooperative Quad Work RESOURCES: Glencoe Algebra2 Text Glencoe Algebra2 Teacher Resource Pack Glencoe Algebra1 Teacher Resource Pack CH 9 Study Island Kuta Software Teacher Generated
A2.1.2.1.3: Simplify/evaluate expressions involving multiplying with exponents (e.g. x 6 * x 7 = x 13 ), powers of powers (e.g., (x 6 ) 7 =x 42 ) and powers of products (2x 2 ) 3 =8x 6 (limit to rational exponents). A2.1.2.2.1: Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax 2 +bx+c where a is not equal to 0). A2.1.3.1.2: Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x 2) = 1 or ( x 2 + 21x) = 14).
Bellwood-Antis S.D. Curriculum Course: Algebra II Grade Level(s): 10-12 Department: Mathematics Topic: Quadratic Functions and Inequalities Chapter: 6 Big Ideas: Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms. Patterns exhibit relationships that can be extended, described, and generalized. Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations. There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities. Essential Questions: How can you extend algebraic properties and processes to quadratic, exponential and polynomial expressions and equations and then apply them to solve real world problems? How do quadratic equations and their graphs and/or tables help us interpret events that occur in the world around us? Why is it necessary to have a variety of methods to solve a quadratic equation? Mathematical functions are relationships that assign each member of one set (domain) to a unique member of another set (range), and the relationship is recognizable across representations. Families of functions exhibit properties and behaviors that can be recognized across representations. Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations.
Standards Keystone Anchors/Eligible Content A2.1.1.1.1 Simplify/write square roots in terms of i (e.g., -24 = 2i 6). A2.1.2.2.1 Factor algebraic expressions, including difference of squares and trinomials. A2.1.3.1.1 Write and/or solve quadratic equations (including factoring and using the Quadratic Formula). A2.2.1.1.4 Identify and/or determine the characteristics of an exponential, quadratic, or polynomial function (e.g., intervals of increase/decrease, intercepts, zeros, and asymptotes). A2.2.2.1.1 Create, interpret, and/or use the equation, graph, or table of a polynomial function (including quadratics). Content/ Concepts Quadratic Functions and Inequalities Competencies/Skills 6-1 Graphing Quadratic Functions Find and interpret the maximum and minimum values of a quadratic function 6-2 Solving Quadratic Equations by Graphing 6-3 Solving Quadratic Equations by Factoring Write a quadratic equation given the roots 6-4 Completing the Square Solve quadratic equations by using the Square Root Property and by Completing the Square 6-5 The Quadratic Formula and Discriminant Solve quadratic equations using the Quadratic Formula Use the discriminant to determine the number and type of roots of a quadratic equation 6-6 Analyzing Graphs of Quadratic Functions Write quadratic equations in vertex form Assessment Evidence FORMATIVE ASSESSMENTS Homework Board Work Worksheets s 6.1-6.6 Activity (in quads) Quizzes 6.1 6.3 6.3 6.5 SUMMATIVE ASSESSMENTS Chapter 6 Test Instructional Activities, Strategies, and INSTRUCTIONAL ACTIVITIES AND STRATEGIES Guided Notes Modeling s Warm-Ups Board Work Reviews and Partner Work 6.1-6.6 Quad Activity Geometry Sketchpad Activity RESOURCES Glencoe Algebra2 Text Glencoe Algebra2 Teacher Resource Pack Teacher Generated Kuta Software Worksheets Geometer Sketchpad A2.2.2.1.3 Determine, use, and/or interpret minimum and maximum values over a specified interval of a 6-7 Graphing and Solving Quadratic Inequalities
graph of a polynomial, exponential, or logarithmic function. A2.2.2.2.1 Identify or describe the effect of changing parameters within a family of functions (e.g., y = x 2 and y = x 2 + 3, or y = x 2 and y = 3x 2 ).
Bellwood-Antis S.D. Curriculum Course: Algebra II Grade Level(s): 10-12 Department: Mathematics Topic: Polynomial Functions Marking Period: Chapter 7 Big Ideas: Essential Questions: Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms. Patterns exhibit relationships that can be extended, described, and generalized. Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations. There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities. How do you explain the benefits of multiple methods of representing polynomial functions (tables, graphs, equations, and contextual situations)? What does the degree of a polynomial function reveal? How can synthetic division be used to find the roots of a polynomial equation? Why is it beneficial to depress a polynomial function? What is the benefit of rewriting expressions and equations in quadratic format? Families of functions exhibit properties and behaviors that can be recognized across representations. Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations.
Standards Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root, cube root, and piecewisedefined functions, including step functions and absolute value functions. c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior Keystone Anchors/Eligible Content A2.2.1.1.4 - Identify and/or determine the characteristics of an exponential, quadratic, or polynomial function (e.g., intervals of increase/decrease, intercepts, zeros, and asymptotes). A2.2.2.1.1 - Create, interpret, and/or use the equation, graph, or table of a polynomial function (including quadratics). A2.2.2.1.3 - Determine, use, and/or interpret minimum and maximum values over a specified interval of a graph of a polynomial, exponential, or log function. A2.2.2.1.4 - Translate a polynomial, exponential, or logarithmic function from one representation of a function to another (graph, table, and equation). Content/Concepts Competencies/Skills Assessment Evidence Instructional Activities, Strategies, and Polynomials and Radical Equations and Inequalities 7.1 Identify and Evaluate Polynomial Functions 7.2 Graph Polynomial Functions Identify Extrema 7.3 Quadratic Techniques for Solving Equations 7.4 Evaluate Functions Using Synthetic Substitution 7.4 Use the Factor Theorem to Identify Binomial Factors 7.5 Roots and Zeros of a Polynomial Function 7.9 Graph and Analyze Square Root Functions and Inequalities FORMATIVE ASSESSMENTS: SUMMATIVE ASSESSMENTS: Section Quizzes Study Island Keystone Materials CommonCore INSTRUCTIONAL ACTIVITIES AND STRATEGIES: Guided Notes Modeling Think Alouds Cooperative Quad Work RESOURCES: Glencoe Algebra2 Text Glencoe Algebra2 Teacher Resource Pack Study Island Kuta Software Teacher Generated
Bellwood-Antis S.D. Curriculum Course: Algebra II Grade Level(s): 10-12 Department: Mathematics Topic: Conic Sections Marking Period: Chapter 8 Big Ideas: Essential Questions: Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms. Some geometric relationships can be described and explored as functional relationships. What real world scenarios can be modeled using conic sections? How do the various conic sections originate? What are the features that distinguish the conic sections? Patterns exhibit relationships that can be extended, described, and generalized. Conic Sections are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations. There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities. Spatial reasoning and visualization are ways to orient thinking about the physical world. Objects can be transformed in an infinite number of ways. Transformations can be described and analyzed mathematically.
Standards Common Core Translate between the geometric description and the equationfor a conic section 1. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. 2. Derive the equation of a parabola given a focus and directrix. 3. (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. Use coordinates to prove simple geometric theorems algebraically. Keystone Anchors/Eligible Content G.2.1.2.1 - Calculate the distance and/or midpoint between two points on a number line or on a coordinate plane. Content/Concepts Competencies/Skills Assessment Evidence Instructional Activities, Strategies, and Advanced Functions and Relations 8.1 Midpoint and Distance Formulas 8.2 Parabolas Vertex Form 8.3 Circles 8.4 Ellipses 8.5 Hyperbolas 8.6 Conic Sections Identify Write in Standard Form 8.7 Quadratic Equations and Inequalities FORMATIVE ASSESSMENTS: 3-2-1 SUMMATIVE ASSESSMENTS: Section Quizzes Study Island Keystone Materials CommonCore INSTRUCTIONAL ACTIVITIES AND STRATEGIES: 3-2-1 Guided Notes Modeling Think Alouds Graphic Organizers Cooperative Quad Work RESOURCES: Glencoe Algebra2 Text Glencoe Algebra2 Teacher Resource Pack Study Island Kuta Software Teacher Generated
Bellwood-Antis S.D. Curriculum Course: Algebra II Grade Level(s): 10-12 Department: Mathematics Topic: Rational Expressions and Equations Marking Period: Chapter 9 Big Ideas: Essential Questions: Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms. Patterns exhibit relationships that can be extended, described, and generalized. Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations. There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities. Families of functions exhibit properties and behaviors that can be recognized across representations. Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations. What real world scenarios can be modeled by rational expressions? What are the implications of extraneous roots? What distinguishing qualities do direct, inverse, and joint variation equations possess? How does the identification of asymptotes assist in graphing rational functions? What distinguishes a factor representing a vertical asymptote from one that depicts a hole in the graph?
Standards Common Core Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Keystone Anchors/Eligible Content A2.1.2.2.2 - Simplify rational algebraic expressions. A2.1.3.1.2 - Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x - 2) = 1 or (x2 + 21x) = 14). Content/Concepts Competencies/Skills Assessment Evidence Instructional Activities, Strategies, and Advanced Functions and Relations 9.1 Multiply and Divide Rational Expressions 9.2 Add and Subtract Rational Expressions 9.3 Graph Rational Functions Identify Asymptotes Identify Holes 9.4 Recognize and Solve Direct, Inverse, and Joint Variations 9.5 Identify Different Function Graphically Equations 9.6 Solve Rational Equations and Inequalities FORMATIVE ASSESSMENTS: SUMMATIVE ASSESSMENTS: Section Quizzes Study Island Keystone Materials CommonCore INSTRUCTIONAL ACTIVITIES AND STRATEGIES: Guided Notes Modeling Think Alouds Graphic Organizers Cooperative Quad Work RESOURCES: Glencoe Algebra2 Text Glencoe Algebra2 Teacher Resource Pack Study Island Kuta Software Teacher Generated
Bellwood-Antis S.D. Curriculum Course: Algebra II Grade Level(s): 10-12 Department: Mathematics Topic: Advanced Functions and Relations Chapter 10 Big Ideas: Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms. Patterns exhibit relationships that can be extended, described, and generalized. Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations. There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities. Families of functions exhibit properties and behaviors that can be recognized across representations. Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations. Essential Questions: Why are calculators programmed to work in base 10 and base e only? How can you extend algebraic properties and processes to exponential and logarithmic expressions and equations and then apply them to solve real world problems? What are the advantages/disadvantages of the various methods to represent exponential functions (table, graph, equation) and how do we choose the most appropriate representation? How do you use lines and curves of best fit to model real world situations and to provide predictions based on a sample? When should common logarithms be used instead of a natural logarithm? Degree and direction of linear association between two variables is measurable.
Standards Keystone Anchors/Eligible Content A2.1.2.1.2 - Simplify/evaluate expressions involving positive and negative exponents and/or roots (may contain all types of real numbers exponents should not exceed power of 10). A2.1.2.1.4 - Simplify or evaluate expressions involving logarithms and exponents (e.g., log28 = 3 or log42 = 1/2). A2.1.3.1.3 - Write and/or solve a simple exponential or logarithmic equation (including common and natural logarithms). A2.1.3.1.4 - Write, solve, and/or apply linear or exponential growth or decay (including problem situations). A2.2.1.1.4 - Identify and/or determine the characteristics of an exponential, quadratic, or polynomial function (e.g., intervals of increase/decrease, intercepts, zeros, and asymptotes). Content/Concepts Competencies/Skills Assessment Evidence Exponential and Logarithmic Relations 10.1 Exponential Functions Graph Solve Equations and Inequalities 10.2 Logarithms and Logarithmic Functions Evaluate Logarithmic Expressions Solve Logarithmic Equations and Inequalities 10.3 Properties of Logarithms Simplify and Evaluate Expressions Solve Logarithmic Equations 10.4-10.5 Common and Natural Logarithms Solve Equations and Inequalities Evaluate Expressions 10.6 Exponential Growth and Decay Become Familiar with the Formulas Solve real world problems using formulas FORMATIVE ASSESSMENTS: Homework SUMMATIVE ASSESSMENTS: Section Quizzes Study Island Keystone Materials CommonCore Chapter Test Instructional Activities, Strategies, and INSTRUCTIONAL ACTIVITIES AND STRATEGIES: Guided Notes Modeling Think Aloud Cooperative Quad Work RESOURCES: Glencoe Algebra2 Text Glencoe Algebra2 Teacher Resource Pack Study Island Kuta Software Teacher Generated
A2.2.2.1.2 - Create, interpret, and/or use the equation, graph, or table of an exponential or logarithmic function (including common and natural logarithms). A2.2.2.1.3 - Determine, use, and/or interpret minimum and maximum values over a specified interval of a graph of a polynomial, exponential, or logarithmic function. A2.2.2.1.4 - Translate a polynomial, exponential, or logarithmic function from one representation of a function to another (graph, table, and equation). A2.2.3.1.1 - Draw, identify, find, interpret, and/or write an equation for a regression model (lines and curves of best fit) for a scatter plot. A2.2.3.1.2 - Make predictions using the equations or graphs of regression models (lines and curves of best fit) of scatter plots.
Bellwood-Antis S.D. Curriculum Course: Algebra II Grade Level(s): 10-12 Department: Mathematics Topic: Probability and Statistics Marking Period: Chapter 12 Big Ideas: Essential Questions: Bivariate data can be modeled with mathematical functions that approximate the data well and help us make predictions based on the data. How do you differentiate between two independent events and two dependent events and how do you calculate the probabilities for each situation? What is the difference between an odds scenario and a probability scenario? If one is known, how do you calculate the other?
. Standards Common Core Keystone Anchors/Eligible Content A2.2.3.2.1: Use combinations, permutations, and the fundamental counting principle to solve problems. A2.2.3.2.2: Use odds to find probability and/or use probability to find odds. A2.2.3.2.3: Use probability for independent, dependent or compound events to predict outcomes Content/Concepts Competencies/Skills Assessment Evidence Instructional Activities, Strategies, and Discrete Mathematics 12.1 Fundamental Counting Principle Recognize and Solve Problems Involving Independent Events Dependent Events 12.2 Identify and Solve Permutation and Combination Problems 12.3 Probability and Odds 12.4 Multiply Probabilities Independent Events Dependent Events 12.5 Adding Probabilities Distinguish between Mutually Exclusive and Inclusive Events FORMATIVE ASSESSMENTS: SUMMATIVE ASSESSMENTS: Section Quizzes Study Island Keystone Materials CommonCore INSTRUCTIONAL ACTIVITIES AND STRATEGIES: Guided Notes Modeling Think Alouds Graphic Organizers Cooperative Quad Work RESOURCES: Glencoe Algebra2 Text Glencoe Algebra2 Teacher Resource Pack Study Island Kuta Software Teacher Generated