West Virginia Department of Education
Unit Plan for Math II Unit IIUnit Plan Title: Unit II Function JunctionGrade Level: High School Math IIUnit Overview:The physical world can be modeled mathematically and mathematical equations have solutions. Students will be presented with different applications and given the opportunity to determine which form of a function reveals the most pertinent information to find solutions to different applications. They will investigate patterns in representations of linear, quadratic and exponential models, and determine relationships that affect parameters of functions and key features of graphs. They will anticipate the graph of quadratic functions by interpreting various forms of the function and discover connections between factors, zeros, roots, solutions and x-intercepts. Students will construct and compare key characteristics of linear, exponential, and polynomial models in terms of context and determine both explicit and recursive representations. They will expand their experience with functions to include absolute value, step, piecewise-defined and inverse functions.Unit Calendar:Math II Unit II Quadratic Functions and Modeling CalendarWest Virginia College- and Career-Readiness Standards: Objectives Directly Taught or LearnedThrough Inquiry/DiscoveryEvidence of Student Mastery of ContentM.2HS.7 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Instructional Note: Focus on quadratic functions; compare with linear and exponential functions studied in Mathematics I.The student completes Getting Ready for a Pool Party, Floating Down the River, and Features of Functions explorations at a level of success designated by the teacher.The student meets the teacher set criteria on the Features of Functions Assessment.M.2HS.8 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. (e.g., if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.) Instructional Note: Focus on quadratic functions; compare with linear and exponential functions studied in Mathematics I.The student completes Getting Ready for a Pool Party, Floating Down the River, and Features of Functions explorations at a level of success designated by the teacher.The student meets the teacher set criteria on the Features of Functions Assessment.M.2HS.9 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Instructional Note: Focus on quadratic functions; compare with linear and exponential functions studied in Mathematics I. Students will demonstrate mastery by completing Lesson 2 - Vocabulary and Concept Development activity, Investigating Average Rate of Change activity and Rate of Change Applications activity at a level of success designated by the teacher.M.2HS.10 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 piecewise- defined functions, including step functions and absolute value functions. Instructional Note: Compare and contrast absolute value, step and piecewise defined functions with linear, quadratic, and exponential functions. Highlight issues of domain, range and usefulness when examining piecewise-defined functions.Instructional Note: Extend work with quadratics to include the relationship between coefficients and roots and that once roots are known, a quadratic equation can be factored. (CCSS.Math.Content.HSF-IF.C.7)The student completes the Function Flipbook at a level of success designated by the teacher.The student completes Getting Ready for a Pool Party, Floating Down the River, and Features of Functions explorations at a level of success designated by the teacher.The student meets the teacher set criteria on the Features of Functions Assessment.M.2HS.11 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values and symmetry of the graph and interpret these in terms of a context. b. Use the properties of exponents to interpret expressions for exponential functions. (e.g., Identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay. Instructional Note: This unit and, in particular, this standard extends the work begun in Mathematics I on exponential functions with integer exponents.Students will demonstrate mastery by completing Algebra 1 Workshop 5 - , Completing the Square Discovery activity, Discovering Quadratic Functions Key Features activity, Exponential Growth & Decay Investigation activity and Allowance Problem Revisited activity at a level of success designated by the teacher.M.2HS.12 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (e.g., Given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum). Focus on expanding the types of functions considered to include, linear, exponential and quadratic. Extend work with quadratics to include the relationship between coefficients and roots and that once roots are known, a quadratic equation can be factored.The student successfully completes the tutorial located at student meets the teacher set criteria on the Egg Launch Activity Sheet.The student meets the teacher set criteria on the Greenhouse Academic Prompt.M.2HS.13 Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process or steps for calculation from a context. b. Combine standard function types using arithmetic operations.(e.g., Build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. Instructional Note: Focus on situations that exhibit a quadratic or exponential relationship.Students will demonstrate mastery by completing Lesson 5 - Vocabulary and Concept Development activity, Identifying Linear Quadratic and Cubic Functions activity, Linear, Quadratic and Cubic Equations Assessment activity, Investigating Quantity Relationships and Inverse Functions activity and Quantity Relationships and Inverse Functions Application activity at a level of success designated by the teacher.M.2HS.14 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Instructional Note: Focus on quadratic functions and consider including absolute value functions.The student completes the Function Transformation Vocabulary handout at a level of success designated by the teacher.The student meets the teacher set criteria on the Even or Odd Function Respond Sheet.The student meets the teacher set criteria on the Even or Odd Function Assessment.The student meets the teacher set criteria on the Logo Design Performance Assessment.M.2HS.15 Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x)= 2 x3 or f(x) = (x+1)/(x-1) for x ≠ 1. Instructional Note: Focus on linear functions but consider simple situations where the domain of the function must be restricted in order for the inverse to exist, such as f(x) = x2, x>0.Students will demonstrate mastery by completing Lesson 5 - Vocabulary and Concept Development activity, Investigating Quantity Relationships and Inverse Functions activity and Quantity Relationships and Inverse Functions Application activity at a level of success designated by the teacher.M.2HS.16 Using graphs and tables, observe that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically; or (more generally) as a polynomial function. Instructional Note: Compare linear and exponential growth studied in Mathematics I to quadratic growth.Students will demonstrate mastery by completing Lesson 2 - Vocabulary and Concept Development activity and Investigating Average Rate of Change activity at a level of success designated by the teacher.Mathematical Practices:Mathematical Habits of MindEvidence of Student Engagement in Mathematical PracticesMake sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.Proficient students clarify the meaning of real world problems and identify entry points to their solution. They choose appropriate tools and make sense of quantities and relationships in problem situations. Students use assumptions and previously-established results to construct arguments and explore them. They justify conclusions, communicate using clear definitions, and respond to arguments, deciding if the arguments make sense. They ask clarifying questions. Students reflect on solutions to decide if outcomes make sense. They discern a pattern or structure and notice if calculations are repeated, while looking for both general methods and shortcuts. As they monitor and evaluate their progress, they will change course if necessary. Focus/Driving Question: How can various forms of functions be useful in modeling real world applications?Student will Know:The average rate of change over an interval is the slope of the secant line for the endpoints of that intervalOne form of a polynomial expression may be more useful than anotherThe zeroes of a polynomial equation are the x-intercepts of the graphThe connection between the factored form of a polynomial and the graphical representationThe relationships among the graph, equation, factors and zeroes of a quadratic functionSome real life situations that exhibit characteristics of change can be modeled by quadratics and exponential functionsTypes of functions such as linear, quadratic, cubic and etc. can be determined from the values of their common first, second, third and etc. differencesAn independent variable in a functional relation is the variable that determines the value of the functionA dependent variable in a functional relation is the value that is determined by the variables of the function. It is the value of the functionAn explicit function is a function whose value may be computed from the independent variableA recursive function is a function that determines the next term of a sequence from one or more of the preceding termsThe inverse function for a function f is a function g whose domain is the range of f and whose range is the domain of fNot all functions are invertibleThe graph of an even or odd function will show symmetries that can be created using reflections.The effect parameter changes have on the graph of a functionStudent will Do:Compare average rates of change of linear, exponential and quadratic functionsDetermine the regression representation for a given set of dataTransform quadratic expressionsApply the techniques of factoring and completing the square in various situationsUse various forms of quadratics to find the graphical representation and vice versaInterpret key featuresFind interceptsFind maximums, minimums, symmetries, periodicity and end behaviorFind intervals where functions are increasing, decreasing, positive or negativeSketch graphsUse words, graphs, tables, and equations to generate solutions to practical problemsGeneralize the results to make a conclusionModel real life situations that exhibit characteristics of changeDetermine the type of functions such as linear, quadratic, cubic and etc. from the values of their common first, second, third and etc. differencesFind an explicit form of a function from other representationsFind a recursive form of a function from other representationsFind an inverse of a function from other representationsUse interval notationGraph square root, cube root, piecewise-defined, step and absolute value functionsInterpret domain and range in the context of a situationClassify functions as even, odd or neitherPerform transformations on quadratic and absolute value functionsRelate the transformations of functions graphically to real-world applications.Resources/Websites:Unlined paperMarkers or colored pencilsRulersGraph paperGraphing calculator and/or CAS (Computer Algebra System)Chart paper and markersCard stock or recycled folders to make study cardsScissorsColor TilesAlgebra Tiles and/or Algebra Tiles - Linear Data - 1 Workshop 5 - Recursion to Explore Real World Problems – : Line of Best Fit - Math - Jobs That Use Quadratic Equations - - Math Jobs - Use Math - Vision Project | MVP – Mathematics Vision Project (MVP) - HYPERLINK "" - - Quadratic Formula: Solutions and the Discriminant - Illuminations: Egg Launch Contest - of Functions (Verbally) - Activities: Transformers – Texas Instruments – US and Canada - online graphing utility: ? Curriculum Pathways? - (Quick Launch #93)Assessment Plan:Major Projects: (Group) or (Individual)Features of Functions AssessmentGreenhouse Academic PromptLinear, Quadratic and Cubic Equations AssessmentEven or Odd Function AssessmentLogo Design Performance AssessmentUnit Reflection:The teacher will reflect on how the unit went and determine the parts from the entire unit that need to be revised or revisited.Career Connections:Worker in all careers use fundamentals and applications of functions. Careers in the Science, Technology, Engineering and Mathematics Cluster that use quadratics and exponential functions are actuaries, aerospace engineers, chemical engineers, civil engineers, computer software engineers, electrical engineers, environmental engineers, industrial engineers, mathematicians, nuclear engineers and statisticians. For more information, see XP Math - Jobs That Use Quadratic Equations - . Careers in the Science, Technology, Engineering and Mathematics cluster that use rates of change and exponential growth are actuaries, data analysts, mathematicians and statisticians along with several research careers in the Health Science cluster including biotechnology research and development. Careers in the Science, Technology, Engineering and Mathematics cluster that use quantity relationships and inverse functions are actuaries, data analysts, mathematicians, computer programmers and statisticians along with several research careers in the Health Science cluster including biotechnology research and development. For more information on mathematics jobs and careers, see XP - Math Jobs - and We Use Math - Plan Outline (Lesson Plans link):Lesson 1 - How Do I Look NowLesson 2 - The Changing Rate of ChangeLesson 3 - My, You Look DifferentLesson 4 - I See Where You Are Coming FromLesson 5 - Decision Making FactorsLesson 6 - How Does That Affect MeKey Words:average rate of change, contextual situations, exponential functions, function transformations, growth, inverse functions, key features, modeling with quadratics, multiple representations, parabola, quadratic functions, recursionNote: Italicized documents can be found in the corresponding lesson plans.Planning CalendarMath II Unit II Function Junction (Quadratic Functions and Modeling)Day 1Lesson 1 - How Do I Look Now (Key Features of Functions)Step 1DQ: How do I relate key features of functions and their graphs to the real world?WVCCRS: M.2HS.7, M.2HS.8, M.2HS.10MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Compare shapes of basic functions with real-world phenomena V: radical, polynomial, absolute value, step, piecewise-defined, exponential, intercepts, relative maximum, relative minimum, zeros, end behavior, increasing intervals, decreasing intervalsSE: Students create function flipbookS: Whole class discussion on the connection between graphs of functions and the world outside of the classroomR: Describe a context where the domain of the function would be:Real numbers? Whole numbers? Rational numbers? Day 2Lesson 1 - How Do I Look Now (Key Features of Functions)Step 2DQ: How do I relate key features of functions and their graphs to the real world?WVCCRS: M.2HS.7, M.2HS.8, M.2HS.10MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Compare shapes of basic functions with real-world phenomena V: radical, polynomial, absolute value, step, piecewise-defined, exponential, intercepts, relative maximum, relative minimum, zeros, end behavior, increasing intervals, decreasing intervalsSE: Students interpret key features of functions using graphs and tablesS: Whole class discussion on the connection between graphs of functions and the world outside of the classroomR: Describe a context where the domain of the function would be:Real numbers? Whole numbers? Rational numbers? Day 3Lesson 1 - How Do I Look Now (Key Features of Functions)Step 3DQ: How do I relate key features of functions and their graphs to the real world?WVCCRS: M.2HS.7, M.2HS.8, M.2HS.10MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Compare shapes of basic functions with real-world phenomena V: radical, polynomial, absolute value, step, piecewise-defined, exponential, intercepts, relative maximum, relative minimum, zeros, end behavior, increasing intervals, decreasing intervalsSE: Informal assessment of student's understanding of interpreting key features of functionsS: Whole class discussion on the connection between graphs of functions and the world outside of the classroomR: Describe a context where the domain of the function would be:Real numbers? Whole numbers? Rational numbers? Day 4Lesson 2 - The Changing Rate of ChangeStep 1DQ: How can the rate of change of functions be useful in interpreting physical world situations?WVCCRS: M.2HS.9, M.2HS.16MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Explore rate of change with linear data V: average rate of change,decreasing function, exponential function, increasing function, line of best fit, linear function, polynomial function, quadratic function, scatterplots, secant lineSE: Launch/Introduction, vocabulary and concept development activitiesS: Whole class discussion on rate of change to interpretations R: Daily journal entry Day 5Lesson 2 - The Changing Rate of ChangeStep 2DQ: How can the rate of change of functions be useful in interpreting physical world situations?WVCCRS: M.2HS.9, M.2HS.16MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Explore rate of change with linear data V: average rate of change,decreasing function, exponential function, increasing function, line of best fit, linear function, polynomial function, quadratic function, scatterplots, secant lineSE: Review linear data activitiesS: Whole class discussion on rate of change to interpretations R: Daily journal entry Day 6Lesson 2 - The Changing Rate of ChangeStep 3DQ: How can the rate of change of functions be useful in interpreting physical world situations?WVCCRS: M.2HS.9, M.2HS.16MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Explore rate of change with linear data V: average rate of change,decreasing function, exponential function, increasing function, line of best fit, linear function, polynomial function, quadratic function, scatterplots, secant lineSE: Investigate average rate of change activityS: Whole class discussion on rate of change to interpretations R: Daily journal entry Day 7Lesson 2 - The Changing Rate of ChangeStep 4DQ: How can the rate of change of functions be useful in interpreting physical world situations?WVCCRS: M.2HS.9, M.2HS.16MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Explore rate of change with linear data V: average rate of change,decreasing function, exponential function, increasing function, line of best fit, linear function, polynomial function, quadratic function, scatterplots, secant lineSE: Rate of change applications activityS: Whole class discussion on rate of change to interpretations R: Daily journal entry Day 8Lesson 3 - Decision Making Factors (Analyzing Quadratic and Exponential Functions)Step 1DQ: How can different forms of quadratic and exponential functions be useful in modeling physical world applications?WVCCRS: M.2HS.11MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Compare linear and exponential functions V: coefficient, constant, constant function, exponential decay, exponential growth, factor, parabola, perfect square, vertexSE: Launch/Introduction and factoring activitiesS: Whole class discussion on analyzing functions using different representations R: Daily journal entryDay 9Lesson 3 - Decision Making Factors (Analyzing Quadratic and Exponential Functions)Step 2DQ: How can different forms of quadratic and exponential functions be useful in modeling physical world applications?WVCCRS: M.2HS.11MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Compare linear and exponential functions V: coefficient, constant, constant function, exponential decay, exponential growth, factor, parabola, perfect square, vertexSE: Completing the square activityS: Whole class discussion on analyzing functions using different representations R: Daily journal entryDay 10Lesson 3 - Decision Making Factors (Analyzing Quadratic and Exponential Functions)Step 3DQ: How can different forms of quadratic and exponential functions be useful in modeling physical world applications?WVCCRS: M.2HS.11MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Compare linear and exponential functions V: coefficient, constant, constant function, exponential decay, exponential growth, factor, parabola, perfect square, vertexSE: Quadratic functions key features activityS: Whole class discussion on analyzing functions using different representations R: Daily journal entryDay 11Lesson 3 - Decision Making Factors (Analyzing Quadratic and Exponential Functions)Step 4DQ: How can different forms of quadratic and exponential functions be useful in modeling physical world applications?WVCCRS: M.2HS.11MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Compare linear and exponential functions V: coefficient, constant, constant function, exponential decay, exponential growth, factor, parabola, perfect square, vertexSE: Investigate exponential growth & decay activityS: Whole class discussion on analyzing functions using different representations R: Daily journal entryDay 12Lesson 3 - Decision Making Factors (Analyzing Quadratic and Exponential Functions)Step 5DQ: How can different forms of quadratic and exponential functions be useful in modeling physical world applications?WVCCRS: M.2HS.11MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Compare linear and exponential functions V: coefficient, constant, constant function, exponential decay, exponential growth, factor, parabola, perfect square, vertexSE: Revisit comparing linear and exponential functions activityS: Whole class discussion on analyzing functions using different representations R: Daily journal entryDay 13Lesson 4 - My, You Look Different (Comparing Different Representations) Step 1DQ: How can similar information about two functions be garnered from different representations of those functions?WVCCRS: M.2HS.7, M.2HS.8, M.2HS.12MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Discussion of projectile motion problems V: projectile, trajectory SE: Launch/Introduction and quadratic formula activitiesS: Whole class discussion on comparing properties of functions using different representations R: Which representation do you feel most comfortable with and why? Day 14Lesson 4 - My, You Look Different (Comparing Different Representations) Step 2DQ: How can similar information about two functions be garnered from different representations of those functions?WVCCRS: M.2HS.7, M.2HS.8, M.2HS.12MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Discussion of projectile motion problems V: projectile, trajectory SE: Students compare functions given different representations activityS: Whole class discussion on comparing properties of functions using different representations R: Which representation do you feel most comfortable with and why?Day 15Lesson 4 - My, You Look Different (Comparing Different Representations) Step 3DQ: How can similar information about two functions be garnered from different representations of those functions?WVCCRS: M.2HS.7, M.2HS.8, M.2HS.12MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Discussion of projectile motion problems V: projectile, trajectory SE: Students compare functions given different representations activity and Greenhouse Academic Prompt assessment.S: Whole class discussion on comparing properties of functions using different representations R: Which representation do you feel most comfortable with and why?Day 16Lesson 5 - I See Where You Are Coming From (Building Linear, Quadratic, Exponential and Inverse Functions) Step 1DQ: How can different representations of functions be useful in investigating patterns?WVCCRS: M.2HS.13, M.2HS.15MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Introduction to recursion with a real-world application V: common first, second, third, etc. differences, dependent variable, explicit function, independent variable, inverse function, invertible function, recursive function SE: Launch/Introduction, vocabulary and concept development activitiesS: Whole class discussion on explicit, recursive and inverse functions R: Daily journal entryDay 17Lesson 5 - I See Where You Are Coming From (Building Linear, Quadratic, Exponential and Inverse Functions) Step 2DQ: How can different representations of functions be useful in investigating patterns?WVCCRS: M.2HS.13, M.2HS.15MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Introduction to recursion with a real-world application V: common first, second, third, etc. differences, dependent variable, explicit function, independent variable, inverse function, invertible function, recursive function SE: Explore linear, quadratic and cubic equations activityS: Whole class discussion on explicit, recursive and inverse functions R: Daily journal entryDay 18Lesson 5 - I See Where You Are Coming From (Building Linear, Quadratic, Exponential and Inverse Functions) Step 3DQ: How can different representations of functions be useful in investigating patterns?WVCCRS: M.2HS.13, M.2HS.15MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Introduction to recursion with a real-world application V: common first, second, third, etc. differences, dependent variable, explicit function, independent variable, inverse function, invertible function, recursive function SE: Linear, quadratic and cubic equations assessmentS: Whole class discussion on explicit, recursive and inverse functions R: Daily journal entryDay 19Lesson 5 - I See Where You Are Coming From (Building Linear, Quadratic, Exponential and Inverse Functions) Step 4DQ: How can different representations of functions be useful in investigating patterns?WVCCRS: M.2HS.13, M.2HS.15MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Introduction to recursion with a real-world application V: common first, second, third, etc. differences, dependent variable, explicit function, independent variable, inverse function, invertible function, recursive function SE: Investigate quantity relationships and inverse functions activityS: Whole class discussion on explicit, recursive and inverse functions R: Daily journal entryDay 20Lesson 5 - I See Where You Are Coming From (Building Linear, Quadratic, Exponential and Inverse Functions) Step 5DQ: How can different representations of functions be useful in investigating patterns?WVCCRS: M.2HS.13, M.2HS.15MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Introduction to recursion with a real-world application V: common first, second, third, etc. differences, dependent variable, explicit function, independent variable, inverse function, invertible function, recursive function SE: Quantity relationships and inverse functions application activityS: Whole class discussion on explicit, recursive and inverse functions R: Daily journal entryDay 21Lesson 6 - I How Does That Affect Me (Transforming Functions) Step 1DQ: What does the equation tell me about the graph of the transformed function?WVCCRS: M.2HS.14MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Introduction to transformations with a real-world application V: even function, odd function, rigid transformation, dilation, symmetry, translation SE: Explore family of functions activityS: Whole class discussion on transformation of functions R: Study cards reviewDay 22Lesson 6 - I How Does That Affect Me (Transforming Functions) Step 2DQ: What does the equation tell me about the graph of the transformed function?WVCCRS: M.2HS.14MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Introduction to transformations with a real-world application V: even function, odd function, rigid transformation, dilation, symmetry, translation SE: Recognizing even and odd functions activityS: Whole class discussion on transformation of functions R: Study cards reviewDay 23Lesson 6 - I How Does That Affect Me (Transforming Functions) Performance TaskDQ: What does the equation tell me about the graph of the transformed function?WVCCRS: M.2HS.14MHM: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.L: Introduction to transformations with a real-world application V: even function, odd function, rigid transformation, dilation, symmetry, translation SE: Logo Design Performance TaskS: Whole class discussion on transformation of functions R: Study cards review DQ – Driving Question, WVCCRS – West Virginia College- and Career-Readiness Standards, MHM – Mathematical Habits of Mind, L– Launch, V – Vocabulary, SE – Student Engagement, S – Summary, R – Reflection ................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- virginia department of financial services
- virginia department of treasury
- virginia department of treasury unclaimed
- virginia department of education statistics
- virginia department of the treasury
- virginia department of education licensure
- virginia department of education website
- virginia department of education renewal
- west virginia division of banking
- west virginia department of banking
- virginia department of health office of licensure
- west virginia statistics of poverty