VIEWS: 57 PAGES: 5 POSTED ON: 7/3/2011
Course: Algebra 2 Austin ISD Curriculum Road Map 2010 – 2011 th 4 Six week – January 4 – February 17 (31 days) Concept (Big Idea): Square Root and Exponential Functions Concept Pacing: 5 days Enduring Understanding: Essential Questions: Real-life applications can be represented and solved using square root How are square root equations & inequalities different from the other types (radical) equations and inequalities, and solved using a variety of methods we have solved? (some similar to quadratic methods) What methods are most useful in solving square root equations & inequalities and how do we choose the best method? Unit: Square Root Functions Unit Pacing: 5 days Vocabulary: radical equation, radical inequality Resources: DC Algebra II Assessment, SATEC, Holt Matrix # Established Goals Established Goals Students Will Know… Students will be able to…. TEKS Knowledge & Skill TEKS Student Expectation 2A.9: The student formulates 2A.9D: determine solutions of square root essential vocabulary such as solve radical equations and 248 equations and inequalities equations using graphs, tables, and radical equation and radical inequalities using a graph and a based on square root algebraic methods; inequality table or using algebraic methods functions, uses a variety of 2A.9E: determine solutions of square root determine if the solution or 248A methods to solve them, and inequalities using graphs and tables solutions of a square root equation analyzes the solutions in is extraneous terms of the situation. 2A.9F: analyze situations modeled by square root functions, formulate equations 238 or inequalities, select a method, and solve problems Student Work Products/Assessment Evidence Other Evidence (i.e. unit tests, open ended exams, quiz, essay, student Performance Tasks work samples, observations, etc.) Algebra II Assessments (Charles A. Dana Center): I was going how fast? Review Inverses and Square Roots, SATEC Algebra 2 Just a Swingin’, SATEC Algebra 2, Radical Equations Matching Activity Learning Plan Lesson/Activity/Module Teacher Resource Student Resource Technology (Media, Other Assessment Name website, etc.) Square Root Functions Algebra II Assessment Dana Center I was going Graphing Calculators Dana Center I was going how fast? p. 227 Holt: power points how fast? SATEC: Review Inverses p. 228 – 230 and Square Roots SATEC: Review Inverses SATEC: Just Swinging and Square Roots Reflect and apply SATEC: Just Swingin’ Radical Equations Radical Equations Matching Activity Matching Activity Page 1 of 5 Course: Algebra 2 Austin ISD Curriculum Road Map 2010 – 2011 th 4 Six week – January 4 – February 17 (31 days) Concept (Big Idea): Exponential Functions Concept Pacing: 11 days Enduring Understanding: Essential Questions: Exponential functions grow (eventually) faster than linear functions and do In what ways is the exponential graph different from the other parent not increase at a constant rate of change (like linear functions); they have functions? numerous applications in growth with populations ( and decay) and How does the symbolic notation of quadratic transformations (shifts, monetary growth (loans, retirement plans, savings) stretches, compressions) connect to the exponential graph? Real-world problems involving growth, decay, and/or finances, can be How are transformations of the exponential function similar to modeled using exponential equations or inequalities and solved multiple transformations of the quad & absolute value function? How are they methods different? How does the function help to identify significant points to graph the function? How can exponential functions be used to analyze population growth/decay and make real-life decisions surrounding population rates? What methods can be used for exponential equations/ineqs and how do you choose which method is best? How do we know the answer makes sense? Unit: Exponential Functions Unit Pacing: 11 days Vocabulary: exponential function, base, asymptote, exponential growth, exponential decay Resources: SATEC, Holt Matrix Established Goals Established Goals Students Will Know… Students will be able to…. # TEKS Knowledge & Skill TEKS Student Expectation 2A.4: The student 2A.4A: identify and sketch graphs of Essential vocabulary such as write and evaluate exponential connects algebraic and parent functions, including linear (f(x) = exponential function, base, asymptote, expressions 2 geometric representations x), quadratic (f(x) = x ), exponential (f(x) exponential growth and exponential sketch (by hand) the graph of an x 262 of functions. = a ), and logarithmic (f(x) = logax) decay exponential function with functions, absolute value of x (f(x) = |x|), The similarities and differences of significant points (intercepts, square root of x (f(x) = √x), and transformations of exponential functions asymptotes…) and proper shape reciprocal of x (f(x) = 1/x). compared to other functions such as or direction 2A.4B: extend parent functions with quadratic and absolute value explain the parameter parameters such as a in f(x) = a/x and the general form of an exponential changes 321 describe the effects of the parameter equation and what each variable and graph both the parent and changes on the graph of parent represents transformed exponential x functions; exponential (f(x) = a ), function 2A.11: The student 2A.11D: determine solutions of Essential vocabulary such as write a function that models formulates equations and exponential and logarithmic equations exponential growth and exponential growth 249 inequalities based on using graphs, tables, and algebraic decay and decay situations exponential and methods be able to determine if the Page 2 of 5 Course: Algebra 2 Austin ISD Curriculum Road Map 2010 – 2011 th 4 Six week – January 4 – February 17 (31 days) Matrix Established Goals Established Goals Students Will Know… Students will be able to…. # TEKS Knowledge & Skill TEKS Student Expectation logarithmic functions, uses 2A.11E: determine solutions of exponential function shows 247A a variety of methods to exponential and logarithmic inequalities growth or decay without solve them, and analyzes using graphs and tables graphing it the solutions in terms of 2A.11F: analyze a situation modeled by be able to solve an exponential the situation an exponential function, formulate an equation by using the same 236 base equation of inequality, and solve the problem Student Work Products/Assessment Evidence Other Evidence (i.e. unit tests, open ended exams, quiz, essay, student work Performance Tasks samples, observations, etc.) Starbuck’s Exponential Growth; Graphing Exponential functions, SATEC Algebra 2; Graphing Exponential Functions Parameter Changes, SATEC Algebra 2 Learning Plan Lesson/Activity/Module Teacher Resource Student Resource Technology (Media, website, etc.) Other Assessment Name Exponential Functions Starbuck’s Starbuck’s Unit Test Exponential Growth Exponential Growth SATEC: Graphing SATEC: Graphing Exponential Functions Exponential Functions SATEC: Graphing SATEC: Graphing Exponential Functions Exponential Functions Parameter Changes Parameter Changes Page 3 of 5 Course: Algebra 2 Austin ISD Curriculum Road Map 2010 – 2011 th 4 Six week – January 4 – February 17 (31 days) Concept (Big Idea): Logarithmic Functions Concept Pacing: 14 days Enduring Understanding: Essential Questions: Logarithmic Functions, Inverses, & Transformations In what ways is the logarithmic function similar to the exponential function? Logarithmic functions are inverses of exponential functions; they have How are they different? applications similar to that of the exponential functions; the graphing of log How does the symbolic notation of quadratic transformations (shifts, functions follows our predetermined rules of transformations for all parent stretches, compressions) connect to the logarithmic graph? functions How are transformations of the logarithmic function similar to transformations of the other parent functions? How are they different? How does the function help to identify significant points to graph the function? Unit: Exponential Functions Unit Pacing: 7 days Vocabulary: asymptote, horizontal and vertical shifts, domain and range, logarithm, restricted domain, inverse functions Resources: Holt, TEXTEAMS Matrix # Established Goals Established Goals Students Will Know… Students will be able to…. TEKS Knowledge & Skill TEKS Student Expectation 2A.4: The student 2A.4A: identify and sketch graphs of The relationship between the Graph (without a calculator) the connects algebraic and parent functions, including linear (f (x) = exponential and logarithmic function exponential and logarithmic parent 2 geometric representations x), quadratic (f (x) = x ), exponential (f graphs function (with correct asymptotes x 262 of functions. (x) = a ), and logarithmic (f (x) = logax) the asymptote of the exp and log and intercepts) functions, absolute value of x (f (x) = graphs and what they represent on |x|), square root of x (f (x) = x ), and the graph reciprocal of x (f (x) = 1/x); 2A.4B: extend parent functions with The affects of “a” on the Graph a logarithmic function, by parameters such as a in f(x) = a/x and logarithmic graph hand, with a shift on the asymptote 321 describe the effects of the parameter The affects of “h” & “k” on the and x-intercept (horizontal & vertical) changes on the graph of parent horizontal & vertical shifts of Identify the domain and range for a functions; logarithmic functions logarithmic graph that has been transformed 2A.4C: describe and analyze the The relationship between the Graph the inverse function given an relationship between a function and its graph of an exponential and exponential or log function inverse logarithmic function Identify the domain and range for a 327 The relationship between the log or exp function and its inverse domain and range of inverse functions (exp & log) Page 4 of 5 Course: Algebra 2 Austin ISD Curriculum Road Map 2010 – 2011 th 4 Six week – January 4 – February 17 (31 days) Matrix # Established Goals Established Goals Students Will Know… Students will be able to…. TEKS Knowledge & Skill TEKS Student Expectation 2A.11: The student 2A.11B: use the parent function to -The affects of parameter changes Graph a log function with parameter formulates equations and investigate, describe, and predict the (without a calculator) changes (without a calculator) inequalities based on effects of parameter changes on the - the limitations of domain and Identify the domain and range of a exponential and graphs of exponential and logarithmic range on the log function (and its transformed log function 326 logarithmic functions, uses functions, describe limitations on the inverse) Restrict the domain to make a a variety of methods to domain and range, and examine - the definition of a restricted function one-to-one and find its solve them, and analyzes asymptotic behavior; domain inverse the solutions in terms of - the domain of a log function - determine the reasonableness of a the situation (positive values of x for log x) solution to exponential and log 2A.11C: determine the reasonable - the definition of a logarithm as equations and inequalities domain and range values of exponential related to exponents - solve log and exp equations & and logarithmic functions, as well as inequalities using calculator and 256 interpret and determine the algebraic methods reasonableness of solutions to - identify the relationship between exponential and logarithmic equations logs and exponents and inequalities Student Work Products/Assessment Evidence Performance Tasks Other Evidence (i.e. unit tests, open ended exams, quiz, essay, student work samples, observations, etc.) Quizzes, unit test, 6wks test, texteams: energy of earthquakes pg 166 Learning Plan Lesson/Activity/Module Teacher Resource Student Resource Technology (Media, website, etc.) Other Assessment Name Inverse functions- Holt 7-7, 7-8 Holt powerpoint 7.3 logarithms and texteams: energy of exponential functions earthquakes pg 166; & transformations exploring inverseslogsexp Page 5 of 5