Unit 2 Linear Functions and Systems of Linear Functions Algebra 1

Transcription

1 Number of Days: MS 44 10/16/17 12/22/17 HS 44 10/16/17 12/22/17 Unit Goals Stage 1 Unit Description: Unit 2 builds upon students prior knowledge of linear models. Students learn function notation and develop concepts of domain and range. Recognizing a linear function as having a constant rate of change, students will interpret the slope in the context of a situation. Arithmetic sequences will be referenced as a special type of linear function. Students expand their experience with functions to include more specialized functions absolute value, scatter plots with lines of fit, and those that are piecewise-defined. Students then use linear functions to explore systems of linear equations and inequalities. Materials: calculators, graph paper, Desmos Standards for Mathematical Practice SMP 1 SMP 2 SMP 3 SMP 4 SMP 5 SMP 6 SMP 7 SMP 8 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. Standards for Mathematical Content Clusters Addressed [m] A-CED.A Create equations that describe numbers or relationships. [a] A-REI.C Solve systems of equations. Transfer Goals Students will be able to independently use their learning to Make sense of never-before-seen problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Making Meaning UNDERSTANDINGS Students will understand that Functions can be represented in different ways, such as algebraically, graphically, numerically in tables, or by verbal descriptions. In function notation, the graph of the function f is the graph of the equation y = f (x). The graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Key features of linear functions can be applied to more specialized functions, including arithmetic sequences, absolute value functions, piecewise-defined functions, and scatter plots. The solution of a system of linear equations can be found algebraically or by graphing each line, approximating the point of intersection, and then checking the solution. A system of linear equations can be used to solve an equation with variables on both sides. Graphing linear inequalities in two variables is similar to graphing linear equations in two variables. For a linear inequality in two variables, the appropriate half-plane is shaded to represent the solution set. Solutions of a system of linear inequalities are the ordered pairs in the area where the corresponding half-planes intersect. ESSENTIAL QUESTIONS Students will keep considering What are the different ways to represent a function? How can linear equations be written in different, yet equivalent, forms? Explain how linear functions can be applied to specialized functions, including arithmetic sequences, absolute value, piecewise-defined functions, and scatter plots. How can systems of linear equations or inequalities be used to model and solve real-world problems? Compare and contrast solving a linear equation with variables on both sides using an algebraic method and a graphical method. LONG BEACH UNIFIED SCHOOL DISTRICT 1 Posted 10/17/17

2 [m] A-REI.D [m] F-IF.A [m] F-IF.B Represent and solve equations and inequalities graphically. Understand the concept of a function and use function notation. Interpret functions that arise in applications in terms of the context. [s] F-IF.C Analyze functions using different representations. [s] F-BF.A Build a function that models a relationship between two quantities. [a] F-BF.B Build new functions from existing functions. [s] S-ID.B Summarize, represent, and interpret data on two categorical and quantitative variables. [m] S-ID.C Interpret linear models. Unit Goals Stage 1 KNOWLEDGE Students will know The definition of academic vocabulary words, such as arithmetic sequence, domain, explicit rule, function notation, half-plane, inverse function, piecewise function, range, solution of a linear inequality in two variables, and system of linear inequalities. A function is a relationship that has exactly one output (range) for each input (domain). If f is a function and x is an element of its domain, then f (x) indicates the output of f corresponding to the input x. The equation y = mx + b defines a linear function with a graph that is a straight line. The graphs of nonlinear functions are not straight lines. A linear equation written in the form y - y1 = m( x - x1) is in point-slope form and ax + by = c is in standard form. Nonvertical lines are parallel if they have the same slope. Nonvertical lines are perpendicular if their slopes are negative reciprocals. Scatter plots visually represent quantitative data to determine if there is a positive correlation, negative correlation, or no correlation between two variables. Acquisition SKILLS Students will be skilled at and/or be able to Use function notation and evaluate functions. Graph linear equations in two variables on the coordinate plane and label the axes with appropriate scales. Interpret key features of a graph or a table representing a linear function that models a relationship between two quantities. Compare properties of two functions each represented in a different way (equations, tables, graphs, or written descriptions). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Calculate and interpret the slope (rate of change) of a function presented symbolically or as a table and estimate the rate of change from a graph. Identify the effects of transformations on the graphs of linear functions by replacing f(x) with f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k. Write linear functions in different forms to reveal different properties of the linear function. Graph absolute value equations on the coordinate plane and interpret the solutions. Represent data of two quantitative variables on a scatter plot and describe how the variables are related. Fit a linear function to a scatter plot that suggests a linear association. Recognize that sequences are functions. Write explicit functions to describe arithmetic sequences. Graph piecewise functions. Find the inverse of a linear function. Solve systems of linear equations in two variables using multiple methods, including solving by graphing, substituting, and eliminating. Solve linear equations with variables on both sides using a system of linear equations. Graph the solutions to a linear inequality in two variables as a half-plane and graph the solution set to a system of linear inequalities in two variables as the intersection of corresponding half-planes. LONG BEACH UNIFIED SCHOOL DISTRICT 2 Posted 10/17/17

3 Assessed Grade Level Standards Standards for Mathematical Practice SMP 1 Make sense of problems and persevere in solving them. SMP 2 Reason abstractly and quantitatively. SMP 3 Construct viable arguments and critique the reasoning of others. SMP 4 Model with mathematics. SMP 5 Use appropriate tools strategically. SMP 6 Attend to precision. SMP 7 Look for and make use of structure. SMP 8 Look for and express regularity in repeated reasoning. Standards for Mathematical Content [m] A-CED.A Create equations that describe numbers or relationships. [Linear, quadratic, and exponential (integer inputs only).] A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. [a] A-REI.C Solve systems of equations. [Linear-linear and linear-quadratic.] A-REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. A-REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. [m] A-REI.D Represent and solve equations and inequalities graphically. [Linear and exponential; learn as general principle.] A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. A-REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. [m] F-IF.A Understand the concept of a function and use function notation. [Learn as general principle; focus on linear and exponential and on arithmetic and geometric sequences.] F-IF.1 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. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. F-IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n 1. [m] F-IF.B Interpret functions that arise in applications in terms of the context. [Linear, exponential, and quadratic.] F-IF.4 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 LONG BEACH UNIFIED SCHOOL DISTRICT 3 Posted 10/17/17

4 Assessed Grade Level Standards the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, 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. F-IF.6 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. [s] F-IF.C Analyze functions using different representations. [Linear, exponential, quadratic, absolute value, step, piecewise-defined.] F-IF.7 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. F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. [s] F-BF.A Build a function that models a relationship between two quantities. [Linear, exponential, and quadratic.] F-BF.1 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. F-BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. [a] F-BF.B Build new functions from existing functions. [Linear, exponential, quadratic, and absolute value; for F-BF.4a, linear functions only.] F-BF.3 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. F-BF.4 Find inverse functions. a. 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) =2x 3 or f(x) = (x+1)/(x 1) for x 1. [s] S-ID.B Summarize, represent, and interpret data on two categorical and quantitative variables. [Linear focus, discuss general principle.] S-ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a linear function for a scatter plot that suggests a linear association. [m] S-ID.C Interpret linear models. S-ID.7 Interpret the slope and the intercept of a linear model in the context of the data. S-ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. S-ID.9 Distinguish between correlation and causation. Key: [m] = major clusters; [s] = supporting clusters, [a] = additional clusters Indicates a modeling standard linking mathematics to everyday life, work, and decision-making CA Indicates a California-only standard LONG BEACH UNIFIED SCHOOL DISTRICT 4 Posted 10/17/17

5 Assessment Evidence Unit Assessment Evidence of Learning Stage 2 Claim 1: Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Concepts and skills that may be assessed in Claim1: A-CED.A The student graphs equations or inequalities on coordinate axes with labels and scales to represent the solution to a contextual problem. The student creates equations in two or more variables to represent relationships between quantities. A-REI.C The student solves systems of linear equations in two variables using multiple methods. A-REI.D The student understands that the graph of an equation in two variables is the set of all its solutions in the coordinate plane, often forming a curve (which could be a line). The student finds solutions (either exact or approximate as appropriate) to the equation f ( x) = g( x) using technology to graph functions, make tables of values, or find their successive approximations. The student graphs the solutions to a linear inequality in two variables as a half-plane (excluding the boundary line in the case of a strict inequality). The student graphs the solution set to a system of linear inequalities in two variables as the intersection of corresponding half-planes. F-IF.A The student understands that a function from one set (the domain) to another set (the range) assigns to each element of the domain exactly one element of the range. The student recognizes any necessary restriction that needs to be placed on the domain in order for an equation to represent a function. The student understands that the graph of f is the graph of the equation y = f ( x). The student recognizes that sequences are functions whose domain is a subset of integers. F-IF.B The student interprets key features of a graph or a table representing a function modeling a relationship between two quantities. The student sketches graphs showing key features given a verbal description of a relationship between two quantities that can be modeled with a function. The student relates the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. The student calculates and interprets the average rate of change of a function presented symbolically or as a table and estimates the rate of change of a function from a graph. F-IF.C The student graphs functions expressed symbolically and shows key features of the graph. The student compares properties of two functions each represented in a different way. The student graphs absolute value equations on the coordinate plane and interprets the solutions. LONG BEACH UNIFIED SCHOOL DISTRICT 5 Posted 10/17/17

6 Evidence of Learning Stage 2 Assessment Evidence F-BF.A The student writes explicit functions to describe relationships between two quantities from a context. The student understands a function as a model of the relationship between two quantities. F-BF.B The student identifies the effects of transformations on the graphs of linear functions by replacing f(x) with f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative) and finds the value of k given the graphs. The student finds the inverse of a linear function. S-ID.B The student represents data on two quantitative variables on a scatter plot and describes how the variables are related. The student fits a linear function for a scatter plot that suggests a linear association. S-ID.C The student interprets the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. The student interprets the correlation coefficient of a linear fit. The student distinguishes between correlation and causation. Claim 2: Students can solve a range of wellposed problems in pure and applied mathematics, making productive use of knowledge and problem-solving strategies. Standard clusters that may be assessed in Claim 2: A.CED.A A-REI.D F-IF.A F-IF.B F-IF.C F-BF.A S-ID.C Other Evidence Formative Assessment Opportunities Informal teacher observations Checking for understanding using active participation strategies Exit slips/summaries Tasks Claim 3: The student can clearly and precisely construct viable arguments to support their own reasoning and critique the reasoning of others. Standard clusters that may be assessed in Claim 3: A-REI.D F-IF.A F-IF.B F-IF.C F-BF.B Modeling Lessons (SMP 4) Formative Assessment Lessons (FAL) Quizzes / Chapter Tests SBAC Interim Assessment Blocks Claim 4: The student can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems. Standard clusters that may be assessed in Claim 4: A-CED.A F-IF.B F-IF.C F-BF.A S-ID.B Access Using Formative Assessment for Differentiation for suggestions. Located on the LBUSD website M Mathematics Curriculum Documents LONG BEACH UNIFIED SCHOOL DISTRICT 6 Posted 10/17/17

7 1 day I will explore linear functions by participating in the Opening Task. OPENING TASK How Do I See The Pattern Growing? This Opening Task asks students to think about how they see a pattern growing. Give students time to work independently and then have them work with a partner. Next, facilitate a class discussion utilizing Talk Moves about how they see the pattern growing. This task is a gateway into the entire unit. How Do I See The Pattern Growing? 3-4 I will define and evaluate functions by Identifying relationships that are functions from mapping diagrams, tables, and graphs. Explaining that a function assigns each element of the domain to exactly one element in the range. (SMP 3) Determining if a function is linear or nonlinear from graphs, tables, and equations. (SMP 7) Using function notation to explain that if f is a function and x is an element in the domain, then f(x) denotes the output of f corresponding to the input x. (SMP 3) Graphing function f using the equation y = f (x). Constructing a linear function to model a relationship between two quantities. Relating the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. (SMP 2) Answering questions such as o How can you tell if a relationship is a function? o Describe how to use function notation. o Explain how to compare functions that are represented in different ways. o How do you evaluate a function? o Describe a context in which the domain would be discrete? Continuous? Section 3.1 Section 3.2 Section 3.3 STEM Video: Speed of Light Desmos: Function Carnival and Part 2 Desmos: Graphing Stories Desmos: Card Sort Linear or Nonlinear Domain and Range Task The Customers Task Points on a Graph Task Linear Functions Sorting Activity Recognizing functions Inputs and outputs of a function Interpreting function notation Linear and nonlinear functions Oakland Coliseum Task STEM Video Performance Task: Speed of Light LONG BEACH UNIFIED SCHOOL DISTRICT 7 Posted 10/17/17

8 7-8 I will examine the Section 3.4 characteristics of Section 3.5 linear functions and Section 3.6 their graphs by Section 3.7 Graphing linear functions from tables and equations showing key features. Explaining that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). (SMP 3) Comparing properties of linear functions represented in different ways (algebraically, graphically, numerically in tables, or by verbal descriptions). Calculating the slope (rate of change) of a linear function from a table, equation, or graph. Interpreting the slope (rate of change) and y-intercept (the initial value) of a linear function in the terms of the situation it models. (SMP 2) Transforming parent linear functions to create new functions. Identifying the effect of transformations on parent linear functions. (SMP 7) Graphing absolute value functions. Applying knowledge of transformations to absolute value functions. (SMP 7) Answering questions such as o Are horizontal and vertical lines examples of functions? Why? o How do you graph a linear function using key features? o The slope of a line is 3 2. Provide coordinates for two points on the line and justify your reasoning. o Compare and contrast the effect of transformations on the graphs of linear functions with the graphs of absolute value functions. o How does changing the value of a affect the graph of f(x)=a x? o Synergy Item Bank: Item ID 54491, 56188, 55051, 54995, 53381, 56187, 68954, Desmos: Sketchy Lines Line Builders mypd Course #3054: Building Conceptual Understanding of Functions Using Desmos Finding Intercepts Task Line Builders Task Graphs of Linear Functions Which One Doesn t Belong? Desmos: Cart Sort Linear Functions Desmos: Polygraph Lines mypd Course #3059: Desmos Activity Polygraph Graphing Absolute Value Functions x-intercepts and y-intercepts Slope Comparing linear functions Graphs of absolute value functions Conference Tables Task Modeling: How Much Does a 100x100 In-N-Out Burger Cost? (SMP 4) LONG BEACH UNIFIED SCHOOL DISTRICT 8 Posted 10/17/17

9 I will write linear equations in two variables by 4-5 Writing linear functions in different, yet equivalent, forms to reveal different properties of the function (e.g., slope-intercept form, standard form, pointslope form). Constructing a linear function to represent a relationship between two quantities. (SMP 2) Answering questions such as o Given the graph of a linear function, how can you write the equation of the line? o What features of linear functions do slopeintercept form, standard form, and point-slope form reveal? o Compare and contrast the slope of parallel and perpendicular lines. o Synergy Item Bank: Item ID Section 4.1 Section 4.2 Section 4.3 STEM Video: Future Wind Power Desmos: Match My Line Desmos: Land the Plane Writing Linear Equations Task Linear Graphs Task Writing slope-intercept equations Point-slope form Summary: Forms of two-variable linear equations Interpreting linear functions and equations Constructing linear models for real-world relationships STEM Video Performance Task: Future Wind Power Modeling: Walk Out (SMP 4) Modeling: Walk Out Sequel with Desmos (SMP 4) 2-3 I will check my understanding of linear functions by participating in the FAL. OPTION 1: FORMATIVE ASSESSMENT LESSON Classifying Equations of Parallel and Perpendicular Lines (SMP 1, 2, 3, 4, 5, 6, 7, 8) LONG BEACH UNIFIED SCHOOL DISTRICT 9 Posted 10/17/17

10 I will apply linear function models by Representing data on two quantitative variables on a scatter plot and describing how the variables are related as a correlation. Fitting a linear function trend line to the data in a scatter plot that suggests linear association. Interpreting the slope and the y-intercept of the linear model in the context of the data and interpreting the correlation coefficient of a trend line. (SMP 2) Recognizing that arithmetic sequences are linear functions. Writing explicit rules for arithmetic sequences and translating between forms. Graphing and writing piecewise-defined functions. Finding the inverse of linear functions. Answering questions such as o How can you make predictions from a scatter plot using a linear model? o What is the difference between correlation and causation? o Why is an arithmetic sequence a function? (SMP 3) o Why is the domain of arithmetic sequences the set of positive integers? o How are piecewise functions and their graphs different from other linear functions? o How are a function and its inverse related? o If the ordered pair (1, 3) satisfies the original function, what ordered pair satisfies the inverse function? Explain your reasoning. (SMP 3) o Synergy Item Bank: Item ID 54706, 54707, 54709, 55248, 50626, 55684, 73053, 54859, 56186, Section 4.4 Section 4.5 Section 4.6 Section 4.7 Section 10.4 (Only Examples 1, 2, 3) Scatter Plots Desmos: Line of Best Fit Scatter Plot Task Creating and interpreting scatterplots Estimating with trend lines Barbie Bunge Jump Activity with Lines of Fit Desmos: Charge! Exploring Linear Data Pizza Sales Task Speeding Tickets Task Arithmetic Sequences Introduction to arithmetic sequences Constructing arithmetic sequences Snake on a Plane Task Piecewise Functions Desmos: Piecewise Linear Functions Function Notation: What s My Story? Desmos: Marbleslides mypd Course #3006: Desmos Activity Marbleslides Piecewise functions Text Messaging Task The Parking Lot Task LONG BEACH UNIFIED SCHOOL DISTRICT 10 Posted 10/17/17

11 7-8 I will solve systems of linear equations by 2-3 I will check my understanding of systems of linear equations by participating in the FAL. Graphing. Using substitution. Using elimination. Solving special systems with no solutions or infinitely many solutions. Writing and solving systems of linear equations to represent real-world situations. (SMP 2) Using a system to solve a linear equation with variables on both sides. (SMP 7) Answering questions such as o What does it mean to be a solution to a system of linear equations? o How can you estimate a solution to a system of linear equations by graphing? o When is it most appropriate to solve a system of linear equations by graphing? By substitution? By elimination? o Describe the graph of a system of linear equations with no solutions or infinitely many solutions. o How do you use a system of linear equations to solve an equation in one variable with variables on both sides of the equal sign? o Synergy Item Bank: Item ID 50627, 54655, OPTION 2: FORMATIVE ASSESSMENT LESSON (choose one) Solving Linear Equations in Two Variables (SMP 1, 2, 3, 4, 5, 6, 7, 8) Comparing Value for Money: Baseball Jerseys (SMP 1, 2, 3, 4, 5, 6, 8) Classifying Solutions to Systems of Equations (SMP 1, 2, 3, 4, 5, 6, 7, 8) Section 5.1 Section 5.2 Section 5.3 Section 5.4 Section 5.5 Create a System of Two Equations Task Understanding Elimination Through Discovery Find A System Task Desmos: Card Sort Linear Systems System of equations overview Baseball Jerseys Task Cash Box Task Concession Stand Prices Task Desmos: Playing Catch Up Printing Tickets Task Modeling: Is It Cheaper to Pay Annually or Monthly? (SMP 4) Modeling: Stacking Cups (SMP 4) Modeling: Piling Up Systems of Linear Equations (SMP 4) mypd Course #7669: Implementing FAL Solving Linear Equations in Two Variables LONG BEACH UNIFIED SCHOOL DISTRICT 11 Posted 10/17/17

12 I will solve linear Section 5.6 inequalities in two Section 5.7 variables and STEM Video: Setting systems of linear Fisher Limits inequalities by I will check my understanding of systems of linear inequalities by participating in the FAL. Graphing the solutions to a linear inequality in two variables as a half-plane. Writing a linear inequality given a graph. Solving systems of linear inequalities. Answering questions such as o What does a solution of a linear inequality mean? o How do you graph a linear inequality in two variables? o How do you determine if the boundary line is solid or dashed? What does a solid boundary line mean verses a dashed boundary line? o How do you graph a system of linear inequalities? o Synergy Item Bank: Item ID OPTION 3: FORMATIVE ASSESSMENT LESSON Representing Inequalities Graphically (SMP 1, 2, 5, 6, 7, 8) Exploring Inequalities Using Desmos Desmos: Point Collector Lines Linear Inequalities in Two Variables Task Linear Inequalities Which One Doesn t Belong? System of Linear Inequalities Task Desmos: Polygraph Linear Inequalities Desmos: Polygraph Systems of Linear Inequalities Graphing two-variable inequalities Modeling with linear inequalities STEM Video Performance Task: Fishing Limits Modeling: How Can You Win Every Prize at Chuck E. Cheese s? (SMP 4) LONG BEACH UNIFIED SCHOOL DISTRICT 12 Posted 10/17/17

13 I will prepare for the Incorporating the Standards for Mathematical Ch. 3 Review unit assessment on Practice (SMPs) along with the content standards (p ) linear functions and to review the unit. Ch. 4 Review systems of linear 1-2 (p ) functions by Ch. 5 Review (p ) 1 day Unit Assessment Students will take the Synergy Online Unit Assessment. Unit Assessment Resources (Word or PDF) can be used throughout the unit. At this point, all standards addressed in the High School SBAC Interim Assessment Block Linear Functions have been covered. This block may now be administered. LONG BEACH UNIFIED SCHOOL DISTRICT 13 Posted 10/17/17