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Content Strand: Interpreting Functions Standard: A1.FIF.4 Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. (Limit to linear; quadratic; exponential.) Related Standards: SCCCR A1.AREI.10SCCCR A1.NQ.2SCCCR A1.FIF.2SCCCR A1.FIF.5SCCCR A1.FIF.7SCCCR A1.ACE.2CCSSM F.IF.4Vocabulary: function, quantities, graphical, tabular, coordinate plane, ordered pairs, intercepts, intervals, increasing, decreasing, constant, positive, negative, relative, maximums, minimums, symmetries, end behavior, periodicity, vertex, linear, quadratic, exponential, continuous, discrete, horizontal, vertical Example: A rocket is launched from 180 feet above the ground at time t = 0. The function that models this situation is given by h = – 16t2 + 96t + 180, where t is measured in seconds and h is height above the ground measured in feet.What is a reasonable domain restriction for t in this context?Determine the height of the rocket two seconds after it was launched.Determine the maximum height obtained by the rocket.Determine the time when the rocket is 100 feet above the ground.Determine the time at which the rocket hits the ground.How would you refine your answer to the first question based on your response to the second and fifth questions? Strategies/Activities: Unit 4 Linear FunctionsProcess Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Sections 3-1, 4-2 Exemplar Lessons: Sites: Videos:, Web Code: ate-0775, Chapter 1-4 Introduction to FunctionsChapter 5-1 Relating Graphs to EventsUSATESTPrep: Linear Equations: Finding Intercepts Sample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: 3-1 p. 168-169; 4-2 p. 242 Multiple Choice: Open Ended: Timmy goes to the fair with $40. Each ride costs $2. Using $40 as the y-intercept and -$2 as the slope, sketch a graph to show much money Timmy will have left after riding n rides? Content Strand: Interpreting Functions Standard: A1.FIF.1 Extend previous knowledge of a function to apply to general behavior and features of a function.Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. Related Standards: SCCCR A1.FIF.1 B and CSCCCR A1.FIF.2SCCCR A1.FIF.4SCCCR A1.FIF.5SCCCR A1.FIF.7SCCCR A1.FLEQ.2CCSSM F.IF.1 Vocabulary: function, input, output, domain, range, ordered pair, mapping, graphing, vertical line test Example: For numbers 1a – 1d, determine whether each relation is a function. Explain your answer.Solutions:1a. Yes – All x-coordinates are unique, so it meets the definition of a function.1b. No – An input of x = 1 has two corresponding outputs, y = 3 and y = 3, so it fails to meet the definition of a function.1c. Yes – This is a function since for each value chosen along the x-axis, there is exactly one y-value on the graph that corresponds to it.1d. No – This is not a function since the input of 5 has two corresponding output values, 3 and 2. Strategies/Activities: Unit 4 Linear FunctionsProcess Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Section 3-2, 3-2 Algebra Lab: The Vertical Line Test, 3-3, 3-4, 3-4 Technology Lab Exemplar Lessons: Sites:Relationships in 2 Variable : : Functions and Non-Functions: Graphically(01:47)Functions and Non-Functions:Algebraically (02:08), Patterns: Functions or Relations (01:34)Functions: Definitions and Examples (01:23), Relations: Definitions and Examples (02:14)Domain and Range of Functions, Graphing y=x (01:28), Graphing y=x2 (01:26), Graphing y=x3(01:23) , Web Code: ate-0775, Chapter 5-2 Relations and FunctionsSample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 175, 184-185, 191-192, 194 Choice: If f(x) = 4x - 2 and D = {-1, 0, 1}, what is the range?{-6, 2} {±2}{-6,±2}{-6, -2}Open Ended:Express the relation as a table, a graph, and a mapping. Then determine the domain and range.{(4, 3), (-1,4), (3, -2), (2, 3), (-2,1)}Content Strand: Interpreting Functions Standard: A1.FIF.1 Extend previous knowledge of a function to apply to general behavior and features of a function.B. Represent a function using function notation and explain that f(x) denotes the output of function that corresponds to the input x. Related Standards: SCCCR A1.FIF.2SCCCR A1.FIF.1 A and CSCCCR A1.FIF.4SCCCR A1.FIF.5SCCCR A1.FIF.7SCCCR A1.FLEQ.2CCSSM F.IF.1Vocabulary: function, function rule, function notation, output, input, domain, range, independent variable, dependent variable Example: Strategies/Activities: Unit 4 Linear FunctionsProcess Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Section 3-3, 3-4, 3-4 Technology Lab Exemplar Lessons: Web Sites:Videos: : Functions and Non-Functions: Graphically(01:47)Functions and Non-Functions:Algebraically (02:08), Patterns: Functions or Relations (01:34) Functions: Definitions and Examples (01:23), Relations: Definitions and Examples (02:14)Domain and Range of Functions, Graphing y=x (01:28), Graphing y=x2 (01:26), Graphing y=x3(01:23) , Web Code: ate-0775, Chapter 5-2 Relations and Functions Sample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 184-185, 191-192, 194 Choice: A florist delivers flowers to anywhere in town. d is the distance from the delivery address to the florist shop in miles. The cost to deliver flowers, based on the distance d, is given by C(d) = 0.04d3-0.65d2+3.5d+9.Evaluate C(d) for d=6 and d=11, and describe what the values of the function represent.C(6)=15.24; C(11)=22.09 C(6)represents the cost, $15.24, of delivering flowers to a destination that is 6 miles from the shop.C(11) represents the cost, $22.09, of delivering flowers to a destination that is 11 miles from the shop. B. C(6)=62.04; C(11)=179.39 C(6)represents the cost, $62.04, of delivering flowers to a destination that is 6 miles from the shop.C(11)represents the cost, $179.39, of delivering flowers to a destination that is 11 miles from the shop. C. C(6)=23.43; C(11)=49.62 C(6)represents the cost, $23.43, of delivering flowers to a destination that is 6 miles from the shop.C(11)represents the cost, $49.62, of delivering flowers to a destination that is 11 miles from the shop. D. C(6)=22.09; C(11)=15.24 C(6)represents the cost, $22.09, of delivering flowers to a destination that is 6 miles from the shop.C(11)represents the cost, $15.24, of delivering flowers to a destination that is 11 miles from the shop. Open Ended: The base of a cardboard box is a square with side length c centimeters. The volume of the box in cubic centimeters is given by the function V(c)=c3- 3c2 . Hint: The formula for the volume of a rectangular prism is base * heightPart A: Show how to find all of the box’s dimension given that c = 4.Part B: Evaluate V(1), V(2), and V(3) for this function. Show your work. What do these values mean in the context of this problem?Part C: Should the domain for this function be restricted? If not, explain why not. If so, explain why and give the restricted domain. Content Strand: Interpreting Functions Standard: A1.FIF.1 Extend previous knowledge of a function to apply to general behavior and features of a function.C. Understand that the graph of a function labeled as f is the set of all ordered pairs (x,y) that satisfy the equation y = f(x). Related Standards: SCCCR A1.AREI.10SCCCR A1.FIF.1 A and BSCCCR A1.FIF.2SCCCR A1.FIF.4SCCCR A1.FIF.5SCCCR A1.FIF.7SCCCR A1.FLQE.2CCSSM F.IF.1Vocabulary: function, coordinate plate, ordered pair, vertical line test, function notation, function ruleExample: Strategies/Activities: down to The Vertical Line Test Unit 4 Linear FunctionsProcess Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Section 3-2, 3-3, 3-4, 3-4 Technology Lab Exemplar Lessons: Web Sites: Videos: : Functions and Non-Functions: Graphically(01:47)Functions and Non-Functions:Algebraically (02:08), Patterns: Functions or Relations (01:34)Functions: Definitions and Examples (01:23), Relations: Definitions and Examples (02:14), Function Notation(02:22), Evaluate Linear Functions (01:14), Web Code: ate-0775, Chapter 5-4 Writing a Function Rule Sample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 175, 184-185, 191-192, 194 Choice:The graph of function f is shown below:Which of the following equations represents the function? y = 2x + 3 y = 2x + 2 y = 3x + 3 y = 3x + 5 Open Ended:The directions on a turkey tell you to cook the turkey 20 minutes per pound.a. Write a function in function notation for this situation where x is the number of pounds.b. Describe the domain of this function. Assume turkeys can weigh up to 30 pounds.c. Graph this function and state the range.d. Use this graph to determine the cooking time for an 18 pound turkey.Content Strand: Interpreting Functions Standard: A1.FIF.2* Evaluate functions and interpret the meaning of expressions involving function notation from a mathematical perspective and in terms of the context when the function describes a real-world situation. Related Standards: SCCCR A1.FIF.1SCCCR A1.FIF.1 B and CSCCCR A1.FIF.4SCCCR A1.FIF.5SCCCR A1.FIF.7SCCCR A1.FLQE.2CCSSM F.IF.2Vocabulary: function, function notation, evaluate, interpret, expressionExample: Let . Find , , , and You put a yam in the oven. After 45 minutes, you take it out. Let f be the function that assigns to each minute after you placed the yam in the oven, its temperature in degrees Fahrenheit.A. Write a sentence explaining what f(0)=65 means in everyday language.B. Write a sentence explaining what f(5)<f(10) means in everyday language. C. Write a sentence explaining what f(40)=f(45) means in everyday language D. Write a sentence explaining what f(45)>f(60) means in everyday language. Sample Response:f(0)=65 means that when you placed the yam in the oven, its temperature was 65 degrees Fahrenheit.f(5)<f(10) means that the temperature of the yam 5 minutes after you placed it in the oven was less than its temperature 10 minutes after you placed it in the oven. This would be because the yam's temperature will increase from 65 degrees Fahrenheit during the first few minutes its in the oven.f(40)=f(45) means that the temperature of the yam 40 minutes after you placed it in the oven was the same as its temperature 45 minutes after you placed it in the oven. This would be because the temperature of the yam eventually plateaus.f(45)>f(60) means that the temperature of the yam 45 minutes after you placed it in the oven was greater than its temperature 60 minutes after you placed it in the oven. This would be because the yam began to cool down after you removed it from the oven. Strategies/Activities: Unit 4 Linear FunctionsProcess Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling.5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Sections 3-4, 4-2Exemplar Lessons: Sites: Videos: : Functions and Non-Functions: Graphically(01:47)Functions and Non-Functions:Algebraically (02:08), Patterns: Functions or Relations (01:34)Functions: Definitions and Examples (01:23), Relations: Definitions and Examples (02:14) Function Notation(02:22), Linear Equations: Finding Intercepts, Graphing y=x,Graphing Linear Functions, Web Code: ate-0775, Chapter 1-4 Introduction to Functions Chapter 5-4 Writing a Function Rule Sample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 191-192, 194, 242 Choice: The following table represents a linear function f(x).xf(x)-5-30-2-12169? What is f(9)?14-345456Open Ended:The distance traveled (in meters) by the Oregon slug can be modeled by the function f(t) = 0.9t, where t is the time in minutes. Find the distance traveled in 27.5 minutes. Content Strand: Interpreting Functions Standard: A1.FIF.5* Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes. (Limit to linear; quadratic; exponential.) Related Standards: SCCCR A1.ACE.2SCCCR A1.RE1.10SCCCR A1.FIF.1 B and CSCCCR A1.FIF.2SCCCR A1.FIF.4SCCCR A1.FIF.7SCCCR A1.FLQE.2CCSSM F.IF.1CCSSM F.IF.2CCSSM F.IF.5 Vocabulary: function, domain, range, input, output, ordered pair, linear Example: Example 1: Oakland Coliseum, home of the Oakland Raiders, is capable of seating 63,026 fans. For each game, the amount of money that the Raiders' organization brings in as revenue is a function of the number of people,n, in attendance. If each ticket costs $30.00, find the domain and range of this function.Solution: Let r represent the revenue that the Raider's organization makes, so that r=f(n). Since n represents a number of people, it must be a nonnegative whole number. Therefore, since 63,026 is the maximum number of people who can attend a game, we can describe the domain of f as follows:Domain ={n:0≤n≤63,026 and n is an integer}The range of the function consists of all possible amounts of revenue that could be earned. To explore this question, note that r=0 if nobody comes to the game, r=30 if one person comes to the game, r=60 if two people come to the game, etc. Therefore, r must be a multiple of 30 and cannot exceed 30?63,026=1,890,780, so we see thatRange={r:0≤r≤1,890,780 and r is an integer multiple of 30}.Note that the representations used above are just sample ways of writing down the domain and range, using set-builder notation. Other options for writing down descriptions of the same sets abound.Example 2: Solution: Strategies/Activities: Unit 4 Linear FunctionsProcess Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text: Holt McDougal Algebra I Common Core Edition, Sections 3-2, 3-3, 3-4, 4-1, 4-1 Career Application, 4-2, 4-5Exemplar Lessons: Web Sites: Videos: : Function Notation (02:22), Evaluate Linear Functions (01:14), Functions and Non-Functions: Numerically (02:08),Functions and Non-Functions: Graphically (01:47), Functions: Definitions and Examples, (01:25), Recognizing Functions(03:34), Relations:Definitions and Examples (02:14) , Web Code: ate-0775, Chapter 1-4 Introducing Functions, Chapter 5-2, Relations and Functions Chapter 5-3 Writing a Function Rule Sample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 175, 184-185, 191-192, 194, 235-236, 242, 264-266 Choice: What is the range for the function, f (x), shown here?all real numbers{(0, 2), (1, 2), (–1, 2), (2, 2), (–2, 2)}{2}{(2, 2)}Open Ended:When Aidan had his picture taken, the photographer charged a $10 sitting fee and $6 for each sheet of pictures purchased.a. Write the function for the situation, where x is the number of sheets purchased.b. Graph this function.c. Explain how the graph of the function can be used to find the cost of pictures if Aidan bought 10 sheets of pictures. How could you use the function to check this answer? Content Strand: Interpreting Functions Standard: A1.FIF.6* Given a function in graphical, symbolic, or tabular form, determine the average rate of change of the function over a specified interval. Interpret the meaning of the average rate of change in a given context. (Limit to linear; quadratic; exponential.) Related Standards:SCCCR A1.ACE.2SCCCR A1.ASE.1SCCCR A1.FIF.7SCCCR A1.FLQE.2SCCCR A1.FLQE.5CCSSM F.IF.6Vocabulary: function, graphical, symbolic, tabular, average rate of change, slope, table of values, interval, linear, slope formula, slope-intercept form Example: Strategies/Activities: Unit 4 Linear Functions Lesson 2 and 3Process Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Section 4-3, 4-4, 4-6 Exemplar Lessons: Sites: Videos: : Linear Equations: Slope (01:21), Slope: 2 Points Coordinate Grid (01:50), Slope: Graphical and Algebraic (01:16), Slope: Rate of Change of Two Variables (01:44)Slope: Table of Values (01:20) , Web Code: ate-0775, Chapter 5-3,Functions Rules, Tables, and Graphs Chapter 6-1 Rate of Change Chapter 6-2 Slope-Intercept Form Sample Assessment-like Questions: Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 250-251, 259, 273-274 Choice: What is the average rate of change of the function in the table?x-2-10123f(x)-5-1371115543-1-4Open Ended: What is the average rate of change for the boiling point of water? 18166330 Content Strand: Interpreting Functions Standard: A1.FIF.7* Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases. Related Standards: SCCCR.ACE.2SCCCR.A1.AREI.10SCCCR.A1.ASE.1SCCCR A1.FIF.1 SCCCR A1.FIF.2SCCCR A1.FIF.4SCCCR A1.FIF.5SCCCR A1.FIF.6SCCCR A1.FLQE.1SCCCR A1.FLQE.2SCCCR A1.FLQE.5CCSSM F.IF.1CCSSM F.IF.7Vocabulary: function, quantities, graphical, symbolic, coordinate plane, intercepts, intervals, increasing, decreasing, constant, positive, negative, relative, maximums, minimums, symmetries, end behavior, periodicity, vertex, ordered pairs, slope intercept form, standard form Example: Graph the function f(x) = 2x by creating a table of values. Identify the key characteristics of the graph. Strategies/Activities: Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Section 3-4, 4-1, 4-2, 4-5, 4-6, 4-7, 4-9, Chapter 4 Extension Exemplar Lessons: Web Sites:: : Graphing Linear Functions (03:17), Functions: Definitions and Examples (01:25), Function Notation (02:22), Evaluate Linear Functions (01:14), Functions and Non-Functions: Numerically (02:08),Functions and Non-Functions: Graphically (01:47), Graphing y=x (01:28), Recognizing Functions(03:34), Relations:Definitions and Examples (02:14), Slope: 2 points Coordinate Grid(01:50), Slope: Graphical and Algebraic (01:16), Slop: Rate of Change of Two Variables (01:44), Slope: Table of Two Values (01:20), Slope of Parallel and Perpendicular Lines (02:31), Parallel and Perpendicular Lines (01:42), Direct Variation (01:48), Direct Variation II (3:00) , Web Code: ate-0775, Chapter 5-2 Relations and Functions Chapter 5-3 Functions, Tables and Graphs Chapter 5-5 Direct Variation Chapter 5-6 Inverse Variation Chapter 6-1 Rate of Change and Slope Chapter 6-2 Slope-Intercept Form Chapter 6-4 Standard Form Chapter 6-5 Point-Slope Form and Writing Linear Functions Chapter 6-6 Parallel and Perpendicular Lines Sample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 191-192, 194, 235-236, 242, 264-266, 273-274, 281-282, 298-299 Multiple Choice: Which of the following could be the graph of f(x) = 23x-5? Open Ended: Graph by making a table of values: Content Strand: Interpreting Functions Standard: A1.FIF.8* Translate between different but equivalent forms of a function equation to reveal and explain different properties of the function. (Limit to linear; quadratic; exponential.) Related Standards: SCCCR.ACE.2SCCCR.A1.ASE.1SCCCR A1.FIF.7SCCCR A1.FLQE.2SCCCR A1.FLQE.5CCSSM F.IF.8Vocabulary: function, translate, equivalent, equation, linear, slope-intercept form, point-slope form, standard form Example: Write the function y -3=23(x-4)in the equivalent form most appropriate for identifying the slope and y-intercept of the function.Solution: y = 2/3x + 1/3 Strategies/Activities: Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Sections 4-7, 4-9 Exemplar Lessons: Sites: Videos: an Equation of a Line- Slope and 1 point(01:04) , Web Code: ate-0775, Chapter 6-5 Point Slope Form and Writing Linear Equations Chapter 6-6 Parallel and Perpendicular Lines Sample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 281-282, 298-299 Multiple Choice: Joshua wants to check to see if the point (2,3) is on a line. Which of the following equations of the line would most easily answer his question?y = 5x-7 B. 5x-y=7 C. y-3=5(x-2)D. -y=-5x+7Open Ended:Find the slope and intercepts of the line -8x + 5y = 36. Content Strand: Interpreting Functions Standard: A1.FIF.9* Compare properties of two functions given in different representations such as algebraic, graphical, tabular, or verbal. (Limit to linear; quadratic; exponential.) Related Standards: SCCCR A1.FIF.6SCCCR.ACE.2SCCCR.A1.ASE.1SCCCR A1.FIF.6SCCCR A1.FIF.7SCCCR A1.FLQE.2SCCCR A1.FLQE.5CCSSM F.IF.9Vocabulary: function, algebraic, graphical, tabular, verbal, properties, slope, intercept Example: Strategies/Activities: Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Section 4-3, 4-4, 4-6 Exemplar Lessons: Web Sites:Videos: : Linear Equations: Slope (01:21), Slope: 2 Points Coordinate Grid (01:50), Slope: Graphical and Algebraic (01:16), Slope: Rate of Change of Two Variables (01:44)Slope: Table of Values (01:20) , Web Code: ate-0775, Chapter 5-3,Functions Rules, Tables, and Graphs Chapter 6-1 Rate of Change Chapter 6-2 Slope-Intercept FormSample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 250-251, 259, 264-266, 273-274 Multiple Choice: Function A: y = 32x+4 Function B:Which of the following can be said about the relationship between function A and B?They have the same slope.They have the same x-intercept.They have the same y-intercept. IB. IIC. III D. I, II, IIIOpen Ended: Arrange the 4 functions in order from greatest to least slope.381000The slope of a ski run that descends 15 feet for every horizontal change of 24 feet. y = -12x+7 1771650228600Content Strand: Creating Equations Standard: A1.ACE.2* Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales. (Limit to linear; quadratic; exponential with integer exponents; direct and indirect variation.) Related Standards: SCCCR.A1.AREI.10SCCCR.A1.ASE.1SCCCR A1.FIF.2SCCCR A1.FIF.4SCCCR A1.FIF.5SCCCR A1.FIF.6SCCCR A1.FIF.7SCCCR A1.FLQE.1SCCCR A1.FLQE.2SCCCR A1.FLQE.5CCSSM CED.2Vocabulary: equation, variables, constants, quantities, linear, direct variation, indirect (inverse) variation, coordinate plate, ordered pairs, axes, units, scales, independent variable, dependent variable, proportion, slope intercept form, standard form, point-slope form Example: David compares the sizes and costs of photo books offered at an online store. The table below shows the cost for each size photo book. 1. Write an equation to represent the relationship between the cost, y, in dollars, and the number of pages, x, for each book size. Be sure to place each equation next to the appropriate book size. Assume that x is at least 20 pages. -190499381002. What is the cost of a 12-in. by 12-in. book with 28 pages?3. How many pages are in an 8-in. by 11-in. book that costs $49? Strategies/Activities: Unit 4 Linear Functions Lesson 4Process Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Sections 4-1, 4-2, 4-5, 4-6, 4-7, 4-9Holt McDougal Algebra 2 Common Core Edition, Section 5-1 Exemplar Lessons: Web Sites: Videos: : USATestPrep: Graphing Linear Functions (03:17), Functions: Definitions and Examples (01:25), Function Notation (02:22), Evaluate Linear Functions (01:14), Functions and Non-Functions: Numerically (02:08),Functions and Non-Functions: Graphically (01:47), Graphing y=x (01:28), Recognizing Functions(03:34), Relations:Definitions and Examples (02:14), Slope: 2 points Coordinate Grid(01:50), Slope: Graphical and Algebraic (01:16), Slop: Rate of Change of Two Variables (01:44), Slope: Table of Two Values (01:20), Slope of Parallel and Perpendicular Lines (02:31), Parallel and Perpendicular Lines (01:42), Direct Variation (01:48), Direct Variation II (3:00) , Web Code: ate-0775, Chapter 5-2 Relations and Functions Chapter 5-3 Functions, Tables and Graphs Chapter 5-5 Direct Variation Chapter 5-6 Inverse Variation Chapter 6-1 Rate of Change and Slope Chapter 6-2 Slope-Intercept Form Chapter 6-3 Applying Linear Functions Chapter 6-4 Standard Form Chapter 6-5 Point-Slope Form and Writing Linear Functions Chapter 6-6 Parallel and Perpendicular Lines Sample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 235-236, 242, 264-266, 273-274, 281-282, 298-299Holt Algebra 2 Test Prep: p. 319-320 Multiple Choice: 19812000-190499257175Open Ended: Wheelchair ramps for access to public buildings are allowed a maximum of one inch of vertical increase for every one foot of horizontal distance. Create an equation to model this guideline. (Hint: 1 foot = 12 inches) Graph your equation to determine if a ramp that is 10 feet long and 8 inches tall would meet this guideline.Content Strand: Reasoning with Equations and Inequalities Standard: A1.AREI.10* Explain that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane. Related Standards: SCCCR A1.FIF.5SCCCR A1.FIF.7SCCCR A1.ACE.2SCCCR A1.ASE.1SCCCR A1.FLQE.2CSSM AREI.10CVocabulary: equation, set, solution, coordinate plate, ordered pairs Example: Strategies/Activities: Unit 4 Linear FunctionsProcess Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Section 4-1Exemplar Lessons: Sites: Videos: Prep: Graphing Linear Functions (02:49), Graphing y=x (01:28), Recognizing Functions, Web Code: ate-0775, Chapter 6-3 Applying Linear Functions Sample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 235-236 Choice: 1. Which equation best represents the table below? x 2 3 4 5 6 y 13 11 9 7 5 A y = x – 2B y = –2x +17C y = 2x + 13D y = 2x + 17Jessie needs to solve the equation y = 14x-20. Which of the following would allow Jessie to show all the solutions to the equation? The equation written in standard form A table of values for the equation A written situation explaining the equation The graph of the equationOpen Ended: The graph above shows all the solutions to what equation? Content Strand: Reasoning with Equations and Inequalities Standard: A1.AREI.12* Graph the solutions to a linear inequality in two variables. Related Standards: CCSSM REI.12Vocabulary: inequality, solution, coordinate plane, ordered pair, point, intersection, dashed line, solid line, shading above, shading below, slope-intercept form, standard form, point-slope form, half-plane Example: Strategies/Activities: Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Section 5-5 Exemplar Lessons: Web Sites:Videos: : Solving Linear Inequalities (02:43), Word Problems: Linear Inequalities (02:58), Interpret Solutions: Inequalities (01:18) , Web Code: ate-0775, Chapter 7-5 Linear Inequalities Sample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 365-366 Choice: Open Ended:Content Strand: Structure and Expressions Standard: A1.ASE.1* Interpret the meanings of coefficients, factors, terms, and expressions based on their real-world contexts. Interpret complicated expressions as being composed of simpler expressions. (Limit to linear; quadratic; exponential.) Related Standards: SCCCR A1.ACE.2SCCCR A1.FIF.5SCCCR.A1.FIF.6SCCCR A1.FIF.7SCCCR A1.FLQE.2SCCCR A1.FLQE.5CCSSM A.SSE.1Vocabulary: coefficient, factors, variable, terms, expressions, numerical expression, algebraic expression, verbal expression, sum, difference, product, quotient, less than, more than, is (equal), double, triple, half, third, reduced by, increased by, decreased by, twice, in groups of, power, exponent, per, ratio, order of operations, slope, x-intercept, y-intercept, slope intercept form, standard form, point-slope form Example: Suppose the cost of cell phone service for a month is represented by the expression 0.40s + 12.95. Students can analyze how the coefficient of 0.40 represents the cost of one minute (40?), while the constant of 12.95 represents a fixed, monthly fee, and s stands for the number of cell phone minutes used in the month. Similar real-world examples, such as tax rates, can also be used to explore the meaning of expressions. -1523990 Strategies/Activities: Unit 4 Linear Functions Lesson 4Process Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Section 4-6 Exemplar Lessons: Sites:Videos: : Writing Equation of a Line Slope and a Point , Web Code: ate-0775, Chapter 6 Lesson 2 Slope-Intercept Form Sample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 273-274Textbook Pg. 10 #36, Pg. 11 #48-50 Choice: Which equation shows in slope-intercept form? B. C. D. Open Ended:The cost to produce a movie is $100. The movie producer earns $2 for each ticket the movie sells. What is the equation for the money earned by the movie producer? What does y mean? What does 2x mean? What does 10 mean? Content Strand: Linear, Quadratic, and Exponential Standard: A1.FLQE.1* Distinguish between situations that can be modeled with linear functions or exponential functions by recognizing situations in which one quantity changes at a constant rate per unit interval as opposed to those in which a quantity changes by a constant percent rate per unit interval.?(Note: A1.FLQE.1a is not a Graduation Standard.) a. Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. Related Standards: SCCCR A1.FIF.5SCCCR A1.FIF.6SCCCR A1.ACE.2SCCCR A1.ASE.1SCCCR A1.SPID.7SCCCR A1.FLQE.2CCSSM F.LQE.1 Vocabulary: linear, constant rate of change, unit interval, slope, difference Example: Strategies/Activities: Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Section 4-5, 4-3 Algebra Lab Exemplar Lessons: Web Sites: Videos: : Direct Variation (01:48), Direct Variation II ( 3:00), Slope: Rate of Change of Two Variables , Web Code: ate-0775, Chapter 5-5 Direct VariationChapter 6-1 Rate of Change and Slope Sample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 264-266Multiple Choice: Compare the tables of Function 1 and Function 2 above. Which of the following statements are true? (Choose all that apply.)Function 1 is linear because x and y are changing by equal differences over equal intervals.Function 1 is nonlinear because x is increasing over equal intervals and y is decreasing over equal intervals.Function 2 is linear because x and y are both increasing over equal intervals.Function 2 is nonlinear because x and y are changing by different intervals over equal intervals. 40386004010025Open Ended: The table shows the number of hand painted t-shirts Mi-Ling can make after a given number of days. Is the relationship between x and y linear? Justify your answer. Content Strand: Linear, Quadratic, and Exponential Standard: A1.FLQE.2* Create symbolic representations of linear and exponential functions, including arithmetic and geometric sequences, given graphs, verbal descriptions, and tables. (Limit to linear; exponential.) Related Standards: SCCCR A1.ACE.2SCCCR.A1.AREI.10SCCCR.A1.ASE.1SCCCR A1.FIF.2SCCCR A1.FIF.4SCCCR A1.FIF.5SCCCR A1.FIF.6SCCCR A1.FIF.7SCCCR A1.FLQE.5CCSSM A.CED.2CCSSM F.LE.2 Vocabulary: linear, symbolic, arithmetic sequence, geometric sequence, coordinate plane, table of values, constant rate of change, variables, slope-intercept form, standard form, all verbal operation words, term, common difference Example: Albuquerque boasts one of the longest aerial trams in the world. The tram transports people up to Sandia Peak. The table shows the elevation of the tram at various times during a particular ride. Write an equation for a function that models the relationship between the elevation of the tram and the number of minutes into the ride. Justify your choice.What was the elevation of the tram at the beginning of the ride?If the ride took 15 minutes, what was the elevation of the tram at the end of the ride? Strategies/Activities: Unit 4 Linear Functions Lesson 2-4Process Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Sections 3-3, 3-6, 4-5, 4-6, 4-7 Exemplar Lessons: Web Sites: Videos: : Write Linear Equations to Model Problems (01:50), Writing Equation of a Line -Slope and 1 point (01:04), Direct Variation (01:48), Direct Variation (3:00) , Web Code: ate-0775, Chapter 6-3 Applying Linear FunctionsChapter 5-7 Describing Number Patterns, Chapter 8-6 Geometric Sequences Sample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 184-185, 210-212, 264-266, 273-274, 281-282 Choice: Renting a canoe costs an initial $10 as well as $8 per hour. If c represents the cost of a canoe rental and t represents the number of hours of the rental, which of the following equations best models this scenario?B. C. D. Line RS represents a bike ramp. Which equation represents the bike ramp?-400049361950y = 13x+2B. y = 13x-6C. y =3x+2D. y = 3x-6Open Ended:At sea level, the speed of sound in air is linearly related to the air temperature. If the temperature is 35?℃, sound will travel at a speed of 352 meters per second. If the temperature is 15℃ sound will travel at a speed of 340 meters per second. Write an equation to model the relationship between temperature, x, and speed of sound, y. Content Strand: Linear, Quadratic, and Exponential Standard: A1.FLQE.5* Interpret the parameters in a linear or exponential function in terms of the context. (Limit to linear.) Related Standards: SCCCR A1.ACE.2SCCCR A1.ASE.1SCCCR A1.FIF.6SCCCR A1.FIF.7SCCCR A1.FLQE.2CCSSM F.LE.5Vocabulary: linear, parameters, domain, range Example: 1. The total cost for a plumber who charges $50 for a house call and $85 per hour would be expressed as the function y = 85x + 50. If the rate were raised to $90 per hour, how would the function change? 2. Lauren keeps records of the distances she travels in a taxi and what she pays: a. If you graph the ordered pairs (d,F) from the table, they lie on a line. How can you tell this without graphing them?b. Show that the linear function in part a. has equation F = 2.25d + 1.5.c. What do the 2.25 and the 1.5 in the equation represent in terms of taxi rides? Strategies/Activities: Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Section 4-6, 4-7 Exemplar Lessons: Sites: Videos: : Writing Equation of a Line -Slope and 1 point (01:04) , Web Code: ate-0775, Chapter 6-2 Slope-Intercept Form, Chapter 6-5 Point-Slope Form and Writing Linear Equations Sample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 273-274, 281-282 Multiple Choice: Open Ended: Jordan buys a new forklift for his business. It will cost $140,000 and will decrease in value each year. The value, V, of the forklift can be modeled by , where t is the number of years. If the forklift’s value decreases $30,000 each year, explain how the model would change. Content Strand: Quantities Standard: A1.NQ.1* Use units of measurement to guide the solution of multi-step tasks. Choose and interpret appropriate labels, units, and scales when constructing graphs and other data displays. Related Standards: SCCCR A1.SPID.6SCCCR A1.SPID.7SCCCR A1.SPID.8CCSSM N.Q.1Vocabulary: scatterplot, independent variable, dependent variable, x-axis, y-axis, labels, units, scale, interval Example: The table shows the average monthly outside temperature and the corresponding average monthly heating cost for a two story home during the fall and winter of 2000. If you were to create a scatter plot of the data, identify your independent and dependent variables.which axis would you label “Temperature”?what scale would you use for the y-axis? what scale would you use for the x-axis?Strategies/Activities Unit 4 Linear Functions Lesson 6 Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Sections 3-5, 3-5 Technology Lab, 4-8 Exemplar Lessons: Web Sites: Videos: : Scatterplots and Correlations (02:07) , Web Code: ate-0775, Chapter 1-5 Scatter Plots Chapter 6-7 Scatter Plots and Equations of Lines Sample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 202-203, 292 Multiple Choice: The scatterplot below shows the relationship between weight and eye color. According to the graph, the independent variable should be labeled _____. A. eye color on the x-axis-190499438150B. eye color on the y-axisC. weight on the x-axisD. weight on the y-axisOpen Ended: Based on the scatterplot, what information was used to create this graph? Be specific. -19049947625 Content Strand: Quantities Standard: A1.NQ.2* Label and define appropriate quantities in descriptive modeling contexts. Related Standards: SCCCR A1.SPID.6SCCCR A1.SPID.7SCCCR A1.SPID.8CCSSM N.Q.2CCSSM N.Q.3Vocabulary: scatterplot, independent variable, dependent variable, x-axis, y-axis, labels, units, scale, interval, margin of error, tolerance Example: Fawn is trying to improve her reading skills by taking a speed reading class. She is measuring how many words per minute (wpm) she can read after each week of the class. If you were to create a scatterplot of Fawn’s data, how would you label the axes? Explain.Explain how knowing that the class lasts 9 weeks would impact your scatterplot.Explain how knowing that Fawn read 220 words per minute would impact your scatterplot.Using the data from the table below, what calculator window would you use to predict how many words per minute Fawn would be reading by week 8 of the class? Explain. Strategies/Activities: Unit 4 Linear Functions Lesson 6 Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Sections 3-1, 3-5, 3-5 Technology Lab, 4-8 Exemplar Lessons: Sites: Videos: : Scatterplots and Correlations (02:07) : Web Code: ate-0775, Chapter 1 -5 Scatter Plots Chapter 6-7 Scatter Plots and Equations of LinesSample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 202-203, 292 Multiple Choice: Open Ended: Use the table that shows the average and maximum longevity of various animals in captivity to draw a scatter plot. Determine what relationship exists. Predict the maximum longevity of an animal with an average longevity of 33 years.Content Strand: Interpreting Data Standard: A1.SPID.6* Using technology, create scatterplots and analyze those plots to compare the fit of linear, quadratic, or exponential models to a given data set. Select the appropriate model, fit a function to the data set, and use the function to solve problems in the context of the data. Related Standards: SCCCR A1.SPID.7SCCCR A1.SPID.8SCCCR A1.FLQE.1SCCCR A1.NQ.1SCCCR A1.NQ.2CCSSM S.ID.6Vocabulary: scatterplot, points, coordinate plane, table of values, linear regression, line of best fit, outlier Example: Strategies/Activities: = Love: Fun With Linear Regression Labs Bungee: Unit 4 Linear Functions Unit 6Process Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Sections 3-5, 3-5 Technology Lab, 4-8 Exemplar Lessons: Web Sites:: : Scatterplots and Correlations (02:07) : Web Code: ate-0775, Chapter 1 -5 Scatter Plots Chapter 6-7 Scatter Plots and Equations of Lines Sample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 202-203, 292 Multiple Choice: Open Ended: The table shows the relationship between the size of a painting by a particular artist, and the price they charge for the painting. Painting Size(in2)486414448100Price(dollars)10015030085200 A. Use the calculator to write a linear equation to model the relationship between the painting size and price of a painting. Key Strokes: Use STAT key to enter in the table; Use [2nd] [Y =] to turn on the PLOT; ZOOM9 to graph the relation; STAT, then CALC #4 to write the LinReg equation. B. Make a graph of the table. Put the painting size along the x-axis and price along the y-axis. Use a scale of 20’s along both axes. Content Strand: Interpreting Data Standard: A1.SPID.7* Create a linear function to graphically model data from a real-world problem and interpret the meaning of the slope and intercept(s) in the context of the given problem. Related Standards: SCCCR A1.SPID.6SCCCR A1.SPID.8SCCCR A1.ASE.1SCCCR A1.FIF.4CCSSM S.ID.7Vocabulary: linear, slope, x-intercept, y-intercept, coordinate plane, ordered pairs, slope-intercept form, function notation Example: Lisa lights a candle and records its height in inches every hour. The results recorded as (time, height) are:(0, 20), (1, 18.3), (2, 16.6), (3, 14.9), (4, 13.2), (5, 11.5), (7, 8.1), (9, 4.7), and (10, 3)Express the candle’s height (h) as a function of time (t).State the meaning of the slope and the intercept in terms of the burning candle.Solution:h = 1.7t + 20Slope: The candle’s height decreases by 1.7 inches for each hour it is burning. Intercept: Before the candle begins to burn, its height is 20 inches.Strategies/Activities: Unit 4 Linear Functions Lesson 4 Process Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Sections 4-6, 3-5, 3-5 Technology Lab, 4-8 Exemplar Lessons: Sites: Videos: USATestPrep: Scatterplots and Correlations (02:07) : Web Code: ate-0775, Chapter 1 -5 Scatter Plots Chapter 6-7 Scatter Plots and Equations of Lines Sample Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 202-203, 273-274, 292 Multiple Choice:-180974219075Jamal is choosing between two moving companies. The first, U-Haul, charges an up-front fee of $20, then 59 cents a mile. The second, Budget, charges an up-front fee of $16, then 63 cents a mile[1]. When will U-Haul be the better choice for Jamal?If Jamal is moving 20 miles away.If Jamal is moving 50 miles away.If Jamel is moving 100 miles away.If Jamel is moving 200 miles away. Open Ended:The Viera family is traveling from Philadelphia, Pennsylvania, to Orlando, Florida, for vacation. The equation y = 1,000 - 65x represents the distance remaining in their trip after x hours.Graph the equation to find the distance remaining after 6 hours.What do the slope and y-intercept represent?Is the distance remaining proportional to the hours driven? Explain. Emily saved up $3500 for her summer visit to Seattle. She anticipates spending $400 each week on rent, food, and fun. Write a function and create a graph to show how long Emily’s summer visit can last. Content Strand: Interpreting Data Standard: A1.SPID.8* Using technology, compute and interpret the correlation coefficient of a linear fit. Related Standards: SCCCR A1.SPID.6SCCCR A1.SPID.7CCSSM S.ID.8Vocabulary: scatterplot, correlation, correlation coefficient, linear regression, vertical distance, residues, best fit line, magnitude, variable, table of values Example: 1. The following data presents the SAT score and GPA for 8 students. What is the correlation coefficient for the assumption that SAT score is dependent on GPA?Explain what the correlation coefficient means in terms of SAT score and GPA. Strategies/Activities: Unit 4 Linear Functions Lesson 6Process Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Section 3-5, 3-5 Technology, 4-8 Exemplar Lessons: Sites: Videos: : Scatterplots and Correlations (02:07) , Web Code: ate-0775, Chapter 1 -5 Scatter Plots Chapter 6-7 Scatter Plots and Equations of Lines Assessment-like Questions: Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 202-203, 292 Multiple Choice: Open Ended:The correlation coefficient of a given data set is 0.97. List three specific things this tells you about the data. Content Strand: Building Functions Standard: A1.FBF.3* Describe the effect of the transformations kf(x), f(x) + k, f(x+k), and combinations of such transformations on the graph of ? = ?(?) for any real number ?. Find the value of ? given the graphs and write the equation of a transformed parent function given its graph. (Limit to linear; quadratic; exponential with integer exponents; vertical shift and vertical stretch.)Related Standards:SCCCR A1.FIF.5SCCCR A1.FIF.7SCCCR A1.ACE.2SCCCR A1.ASE.1SCCCR A1.FLQE.2CCSSM F.BF.3Vocabulary: transformations, effect, real number, equation, parent function, graph, linear, vertical, horizontal, shift, reflection, stretch, compression, dilation, slope, intercepts Example: Compare the graphs of f(x) = 3x with those of g(x) = 3x + 2 and h(x) = 3x - 1 to see that parallel lines have the same slope and to explore the effect of the transformation of the function, f(x) = 3x such that g(x) = f(x) + 2 and h(x) = f(x)- 1. Strategies/Activities:: Matching Cards: Standards1. Make sense of problems and persevere in solving them. 2. Reason both contextually and abstractly. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.6. Communicate mathematically and approach mathematical situations with precision.7. Identify and utilize structure and patterns. Resources:Text:Holt McDougal Algebra I Common Core Edition, Section 4-10, Chapter 4 Extension Exemplar Lessons: Web Sites: (Section B) Videos: Assessment-like Questions:Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, ObservationsHolt Algebra 1 Test Prep: p. 306-308 Multiple Choice: The function for a graph reflected and translated up is: A. y = -x + 5 B. y = -(x + 5) C. y = -(x – 5) D. y = -x – 5Open Ended: Renaldo opened a savings account with the $300 he earned mowing yards over the summer. Each week he withdraws $20 for expenses. The graph shows this situation. -190499609600Explain how the graph has been transformed from y = f(x).Write the new equation to reflect the situation. ................
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