Curriculum Design Template Content Area: Mathematics Course Title: Algebra I Grade Level: 8-9 Review of Statistics and Solving Equations Solving Inequalities An Intro to Functions Marking Period 1 An Intro to Functions Linear Functions Systems of Equations and Inequalities Marking Period 2 Exponents and Exponential Functions Polynomials and Factoring Marking Period 3 Polynomials and Factoring Quadratic Functions and Equations Radical Expressions Marking Period 4 Date Created: June 2014 Board Approved on: August 25, 2014
Algebra 1 Pacing Guide Unit Title Lessons to Include Time Common Core Standards Math Statistics Solving Equations Solving Inequalities Functions Review: Dot Plots, Histograms, Box and Whisker Plots, Interquartile Range, Outliers, Standard Deviation (Concept Byte Chapter 12), Median, Mean, Frequency Tables, Joint Frequencies, Marginal Frequencies, Conditional Relative Frequencies Review: Solving: One Step, Two Step, Multi Step, Variables on Both Sides, Literal Equations, Absolute Value Eqns Graphing Inequalities, solving linear inequalities, absolute value inequalities Review: Relating two quantities, patterns, linear vs. non-linear, graphing a function rule, writing a function rule 2 days S.ID.1, S.ID.2, S.ID.3, S.ID.5, N.NQ.1, N.NQ.2 4 days A.REI.1, A.REI.3, A.CED.1, A.CED.3, A.CED.4, N.Q.1, N.NQ.2, A.SSE.1 1 day A.CED.1, A.CED.3, N.Q.2, A.SSE.1, A.REI.3 2 days A.REI.10, F. IF. 4, N.Q.1, N.Q.2, F.IF.5, A.SSE.1, A.CED.2 4.6 Formalizing Relations and Functions 3 days F.IF.1, F.IF.2 Linear Functions Systems of Equations and Inequalities Exponents and Exponential Functions 4.7 Arithmetic Sequences 2 days A.SSE.1, F.IF.3, F.BF.1, F.BF.2, F.LE.2 Review: Rate of change, slope, direct variation, Slope-Intercept, Point-Slope, Standard form, parallel, perpendicular lines 5 days F.IF.6, F.LE.1, N.Q.2, A.CED.2, A.SSE.1, A.SSE.2, F.IF.4, F.IF.7, F.BF.1., F.BF.2, F.LE.2, F.LE.5, F.IF.9, G.GPE.5 5.7 Scatter Plots 2 days N.Q.1, F.LE.5, S.ID.6, S.ID.7, S.ID.8, S.ID.9 6.1 Solving Systems by Graphing 1 day A.REI.6 6.2 Solving Systems by Substitution 3 days A.REI.6 6.3 Solving Systems by Elimination 3 days A.REI.6, A.REI. 5 6.4 Applications of Linear Systems 3 days A.REI.6, N.Q.2, N.Q.3, A.CED.2, A.CED.3 6.5 Linear Inequalities 3 days A.CED.3, A.REI.12 6.6 Systems of Linear Inequalities 7.2 & 7.3 Multiplication Properties of Exponents 1 day N.RN.1 7.4 Division Properties of Exponents 1 day N.RN.1 7.1 Zero and Negative Properties of Exponents 2 days N.RN.1, N.RN.2 7.5 Rational Exponents 2 days N.RN.2 7.6 Exponential Functions 3 days A.CED.2, A.REI.11, F.IF.4, F.IF.5, F.IF.7, FIF.9, F.LE.2, F.LE.3
Exponents and Exponential Functions (continued) Polynomials & Functions Quadratic Functions & Equations 7.7 Exponential Growth and Decay 3 days A.SSE.1, A.SSE.3, A.CED.2, F.IF.4, F.IF.8, F.BF.3, F.LE.1, F.LE.5 8.1 Adding and Subtracting Polynomials 2 days A.APR.1 8.2 Multiplying and Factoring 1 day A.APR.1 8.3 Multiplying Binomials 3 days A.APR.1 8.4 Multiplying Special Cases 8.5 Factoring 1 day A.SSE.1 8.6 Factoring 3 days A.SSE.1 8.7 Factoring Special Cases 1 day A.SSE.1, A.SSE.2 9.1 Quadratic Graphs & Properties 2 days A.CED.2, F.IF.4, F.IF.5, F.IF.7, F.BF.3 9.3 Solving Quadratic Equations 1 day N.Q.2, A.CED.1, A.CED.4, A.APR.3, A.REI.4, F.BF.4 9.4 Factoring to Solve Quadratic Equations 3 days A.SSE.3, A.CED.1, A.REI.4, F.IF.8 9.6 The Quadratic Formula and Discriminant (Also mention N.RN.3) 3 days N.Q.3, A.CED.1, A.REI.4, N.RN.3 9.2 Graphing Quadratic Functions 4 days A.CED.2, F.IF.4, F.IF.7, F.IF.8, F.IF.9, F.BF.3 9.5 Completing the Square 2 days N.Q.3, A.SSE.1, A.SSE.3, A.CED.1, A.REI.1, A.REI.4, F.IF.8 9.7 Linear, Quadratic and Exponential Models 5 days F.IF.4, F.BF.1, F.LE.1, F.LE.2, F.LE.3, S.ID.6 9.8 Systems of Linear and Quadratic Functions 4 days A.CED.3, A.REI.7, A.REI.11 Radical Expressions and Equations 10.2 Simplifying Radicals 4 days A.REI.2 10.3 Operations with Radical Expressions 2 days A.REI.2 10.4 Solving Radical Equations 3 days A.REI.2
Course Title: Algebra 1 Grade Level: 9 th Overarching What is the Real Number System? How can we use statistics to extrapolate information? What are single-variable equations and how do we solve them? What are single-variable inequalities and how do we solve and graph them? What are functions? What is slope? What is an equation of a line? How do we graph linear equations? How do we solve systems of linear equations? How do we solve and graph systems of linear inequalities? What are exponents and their properties? What is a polynomial? What is a quadratic equation? What is a radical? How can we solve radical equations? Overarching Enduring Understanding Students in Algebra 1 will learn about the real number system, equations, inequalities, functions, linear systems and how they are used in everyday life. They will also become fluent with simple quadratic, polynomial, and exponential functions. Course Description Algebra 1 covers all basic components of algebra, including the exploration of expressions, equations, and functions, rational numbers, solving and analyzing linear equations and inequalities, discrete math, graphing relations and functions, polynomials, quadratic and exponential functions, rational expressions and equations, and radical expressions and equations. Graphing calculators and other technology are used when appropriate. This course is designed for the college bound student who intends to attend a 4-year college and/or a STEM career. Life Skills Standards 9.1.12.A.1 - Apply critical thinking and problem-solving strategies during structured learning experiences. 9.1.12.B.1 - Present resources and data in a format that effectively communicates the meaning of the data and its implications for solving problems, using multiple perspectives. 9.4.12.A.2 - Demonstrate mathematics knowledge and skills required to pursue the full range of postsecondary education and career opportunities. 9.4.12.O.(2).1 - Develop an understanding of how science and mathematics function to provide results, answers, and algorithms for engineering activities to solve problems and issues in the real world. 9.4.12.O.(2).2 - Apply science and mathematics when developing plans, processes, and projects to find solutions to real world problems.
Technology Standards 8.1.12 A 3 - Construct a spreadsheet, enter data, use mathematical or logical functions to manipulate and process data, generate charts and graphs, and interpret the results. 8.1.12 B 9 - Create and manipulate information, independently and/or collaboratively, to solve problems and design and develop products. Statistics Different measures can be used to interpret and compare sets of data Separating data into subsets is a useful way to summarize and compare data sets Key Terms Frequency tables, histograms, box and whisker plots, dot plots, quartiles, percentiles, standard deviation, measures of central tendency (mean, median, mode). Students will be able to: To make and interpret frequency tables, histograms, and dot plots To find mean, median, mode, and range To make and interpret box and whisker plots To find quartiles and percentiles To calculate and compare standard deviations of data sets MA.9-12.HSS-ID.1 - Represent data with plots on the real number line (dot plots, histograms, and box plots). MA.9-12.HSS-ID.2 - Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. MA.9-12.HSS-ID.3 - Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). MA.9-12.HSS-ID.5 -Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. MA.9-12.HSN-Q.1 - Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. MA.9-12.HSN-Q.2 - Define appropriate quantities for the purpose of descriptive modeling. Have students collect data (such as age, height, weight, etc) within the classroom or school setting and have them calculate the measures of central tendency. Have students find their pulse and make a dot plot of class data Have students make a histogram and frequency table out of classroom preferences (such as favorite food, best TV genre, etc) Have students use Journal or Interactive Notebook
Differentiation /Customizing learning (strategies) Work in groups or stations Enrichment worksheets Allow students to choose topics Do a RAFT activity (Role, Audience, Format, Topic) Equations Can equations that appear to be different be equivalent? How can you solve equations? How can equations be used to model real-world problems? Key Terms Inverse operations, equivalent equations, literal equations Students will be able to: Solve equations using addition, subtraction, multiplication and division. Use the distributive property to simplify expressions and solve equations. Combine like terms to simplify expressions and solve equations. Solve equations involving rational numbers. Write and solve an equation to represent a real-world situation. Solve absolute value equations. Rearrange formulas for an indicated variable. MA.9-12.A-REI.1 - Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. MA.9-12.A-REI.3 - Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. MA.9-12.A-CED.1 - Create equations and inequalities in one variable and use them to solve problems. MA.9-12.HSA-CED.3 - Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. MA.9-12.A-CED.4 - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. MA.9-12.HSA-SSE.1 - Interpret expressions that represent a quantity in terms of its context. MA.9-12.HSN-Q.1 - Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. MA.9-12.HSN-Q.2 - Define appropriate quantities for the purpose of descriptive modeling. Use websites on Smart Board to play equation games. Refer to Algebra Supplemental Binder for various worksheets. Have students create tutorial videos using imovie.
Algebra tiles. Have students use Journal or Interactive Notebook Differentiation /Customizing learning (strategies) Give students specific criteria to create their own equation. Have students create tutorial videos using imovie. Write a short news article that includes numbers and a range around the n umbers to introduce absolute value equations. Tiered Instruction Stations and Groups Interactive Word Wall Solving Inequalities How do you represent relationships between quantities that are not equal? Can inequalities that appear to be different be equal? How can you solve and graph inequalities? Key Terms Number line, compound inequality, no solution, intersection Students will be able to Solve inequalities using addition, subtraction, multiplication and division. Use the distributive property to simplify expressions and solve inequalities. Combine like terms to simplify expressions and solve inequalities. Solve inequalities involving rational numbers. Write and solve an inequality to represent a real-world situation. Graph solutions to inequalities. Recognize when to switch the inequality symbol. MA.9-12.A-REI.3 - Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.. MA.9-12.A-CED.1 - Create equations and inequalities in one variable and use them to solve problems. MA.9-12.HSA-CED.3 - Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. MA.9-12.HSA-SSE.1 - Interpret expressions that represent a quantity in terms of its context. MA.9-12.HSN-Q.2 - Define appropriate quantities for the purpose of descriptive modeling. Use websites on Smart Board to play inequality games. Refer to Algebra Supplemental Binder for various worksheets. Have students create tutorial videos using imovie. Modeling using inequalities. Have students create a chart showing what words mean less than and greater than. Have students use Journal or Interactive Notebook
Differentiation /Customizing learning (strategies) Give students specific criteria to create and graph their own inequality. Have students create tutorial videos using imovie. Tiered Instruction Stations/Groups Menu Activity (Choose 2-3 problems per section) Functions What is a function? What is the difference between dependent and independent variables? What is function notation? What are three ways to represent a function? How can you represent and describe functions? How can you determine a graph is a function? Key Terms Function, dependent and independent variables, domain, range, relation, function table, linear function, non-linear function, function table, vertical line test. Students will be able to: Represent functions using tables, graphs, and equations. Use function notation. Use function rules to describe a table. Graph a function involving two quantities. Model real-world situations using a function. Use the vertical line test to determine if a graph is a function or not. MA.9-12.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). MA.9-12.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. MA.9-12.HSF-IF.3 - Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. MA.9-12.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. MA.9-12.F-IF.5 - Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. MA.9-12.HSF-BF.1 - Write a function that describes a relationship between two quantities. MA.9-12.HSF-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. MA.9-12.HSF-LE.2 - Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
MA.9-12.HSA-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). MA.9-12.HSA-SSE.1 - Interpret expressions that represent a quantity in terms of its context. MA.9-12.HSA-CED.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. MA.9-12.HSN-Q.1 - Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. MA.9-12.HSN-Q.2 - Define appropriate quantities for the purpose of descriptive modeling. Have students create a two-step function, create its function table, and write it on the board. The rest of the class has to find what the functions rule is. Divide class into groups; give each group 3 index cards one with an equation, one with a table, one with a graph. For each card the group must come up with the other 2 ways to represent the function. Divide class into groups; give each group several cards with functions listed. Have students group into three categories: linear, quadratic, and absolute value. Explain similarities and differences in graphs (Use graphing calculator to graph functions). Have students use Journal or Interactive Notebook Differentiation /Customizing learning (strategies) Divide class into groups; give each group 3 index cards one with an equation, one with a table, one with a graph. For each card the group must come up with the other 2 ways to represent the function. Do a RAFT activity (Role, Audience, Format, Topic) Graphing and Writing Linear Equations What does the slope of a line indicate about the line? How are slope and rate of change related? What information does the equation of a line give you? How can you make predictions based upon a scatter plot? What information do you need to know about a line in order to write its equation? How do you determine the equations of a line? How do you determine if two lines are parallel, perpendicular or just intersecting? How do the intercepts of a line help us to graph the line? Key Terms Slope, point-slope form, linear equations, slope-intercept form, rate of change, standard from, line of best fit, intercept. Students will be able to: Find slope using a formula. Find slope using a graph.
Analyze various slopes and describe their meaning. Use an equation to find a slope and y-intercept. Find a line of best fit. Analyze scatter plots. Identify the equations and the slopes of both horizontal and vertical lines. Switch between point-slope form, slope-intercept form and standard form. Use slope to determine if lines are parallel, perpendicular or neither. Determine the intercepts of an equation and use them to graph the line. MA.9-12.S-ID.6 - Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. MA.9-12.S-ID.7 - - Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. MA.9-12.S-ID.8 - Compute (using technology) and interpret the correlation coefficient of a linear fit. MA.9-12.HSS-ID.9 - Distinguish between correlation and causation. MA.9-12.A-CED.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. MA.9-12.HSA-SSE.1 - Interpret expressions that represent a quantity in terms of its context. MA.9-12.HSA-SSE.2 - Use the structure of an expression to identify ways to rewrite it. MA.9-12.HSF-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. MA.9-12.HSF-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. MA.9-12.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. MA.9-12.HSF-IF.9 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). MA.9-12.HSF-BF.1 - Write a function that describes a relationship between two quantities. MA.9-12.HSF-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. MA.9-12.HSF-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. MA.9-12.HSF-LE.1 - Distinguish between situations that can be modeled with linear functions and with exponential functions. MA.9-12.HSF-LE.2 - Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). MA.9-12.HSF-LE.5 - Interpret the parameters in a linear or exponential function in terms of a context.
MA.9-12.G-GPE.5 - - Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). MA.9-12.HSN-Q.1 - Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. MA.9-12.HSN-Q.2 - Define appropriate quantities for the purpose of descriptive modeling. Use the Communicators for graphing lines with a given slope. Use the graphing calculators to analyze what changing the slope does to a line. Use the graphing calculators to analyze equations of parallel and perpendicular lines. Have students find lines of various slopes in magazine pictures Have students use Journal or Interactive Notebook Differentiation /Customizing learning (strategies) Use the motion sensor and Vernier Graphing App on ipads to have students walk a line: to match a given slope. Have students graph 5 random lines and then have them determine the slope, intercepts, and equations of the lines. Menu Activity (Choose 2-3 Problems per section) Tiered Instruction Systems of Equations and Inequalities Name and show how to use the methods for solving systems of equations. What is the best way to check your solutions to a given system of equations? When graphing a set of lines, how close is it feasible to get to a given solution? Can systems of equations model real-world situations? How do you graph a linear inequality? How do you graph a system of linear inequalities? How can we use linear inequalities to solve linear programming problems? How do we know where to shade on the graph of a linear inequality? Can systems of inequalities model real-world situations? Can a linear inequality have no solution? Key Terms System of equations, elimination method, substitution method, graphing method, solution to a system, no solution, infinitely many solutions, Linear inequality, solution of the inequality, system of linear inequality, solution of the system, linear programming, constraints, feasible region Students will be able to: Solve systems of linear equations by graphing, substitution, and elimination method.
Write and solve systems of linear equations from real-world problems. Determine if a given point is a solution to a given system of linear equations. Determine if there is no solution or infinitely many solutions. Graph a linear inequality. Graph a system of linear inequalities. Know how to determine where to shade on the graph of a linear inequality. Write inequalities to represent real-world situations. Use given constraints to write a system of linear inequalities, use the constraints to graph the feasible region of a system, and then solve the system. MA.A.CED.2- Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. MA.A.CED.3- Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. MA.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 MA.A.REI.6- Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. MA.9-12.HSA-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. MA.9-12.HSN-Q.2 - Define appropriate quantities for the purpose of descriptive modeling. MA.9-12.HSN-Q.3 - Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Have students graph systems by hand to determine a solution. Use technology to solve for solutions to systems of equations graphically. Have a discussion on when it is best to use which method. YouTube video instruction. Have students write a short paragraph describing the difference between a solution to a system of linear equations and a system of linear inequalities. Have students graph inequalities and systems of inequalities on the Communicators while one student models it on the Smart Board with Geometer s Sketchpad. Divide the class into groups and give them several systems of equations and systems of inequalities and have them find the solutions to determine that equations will generate a point for a solution and inequalities will generate a plane for a solution. Have students compare graphing two-variable and one-variable inequalities. Have students use Journal or Interactive Notebook Differentiation /Customizing learning (strategies) Have students write their own word problems, swap problems and solve each other s problem.
Use group work as a tool to let students of varying abilities to learn in a cooperative environment. Have students develop a system of 3-4 inequalities whose feasible region would generate a specific quadrilateral (trapezoid, parallelogram, square, rectangle, etc.) Exponents and Exponential Functions How can you represent numbers less than 1 using exponents? How can you simplify expressions involving exponents? What are the characteristics of exponential functions? How are rational exponents related to radicals? Key Terms Exponent, base, power, compound interest, growth factor, decay factor, exponential functions, exponential growth and decay, scientific notation, rational exponent, radical Students will be able to: Represent numbers using negative exponents. Define and use 0 and negative exponents. Learn the rules for multiplying and dividing powers. Use rational exponents to represent radicals. Apply the power to a power rule. Convert flexibly between scientific and standard notation and use them to calculate values. Evaluate and graph exponential functions. Model exponential growth and decay. Recognize that exponential functions show growth or decay. Recognize that exponential functions grow/decay faster than linear and quadratic functions. MA.9-12.HSF-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. MA.9-12.HSF-IF.5 - Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. MA.9-12.HSF-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. MA.9-12.HSF-IF.8 - Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. MA.9-12.HSF-IF.9 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). MA.9-12.HSF-LE.1 - Distinguish between situations that can be modeled with linear functions and with exponential functions. MA.9-12.HSF-LE.2 - Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship,
or two input-output pairs (include reading these from a table). MA.9-12.HSF-LE.3 - Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. MA.9-12.HSF-LE.5 - Interpret the parameters in a linear or exponential function in terms of a context MA.9-12.HSF-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. MA.9-12.HSN-RN.1 - Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. MA.9-12.HSN-RN.2 - Rewrite expressions involving radicals and rational exponents using the properties of exponents. MA.9-12.HSA-SSE.1- Interpret expressions that represent a quantity in terms of its context. MA.9-12.HSA-SSE.3 - Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. MA.9-12.HSA-CED.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. MA.9-12.HSA-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. Have students create tutorial videos using imovie. Have students find expressions for area and perimeter of polygons whose sides are expressions rather than numbers. Have students use Journal or Interactive Notebook Tower of Hanoi Differentiation /Customizing learning (strategies) Look for fun activities on the web to differentiate lesson. (i.e. Number Balls and M&M activity) Stations and Group work Anchor Activities Use graphing calculator to assist with graphing exponential functions Polynomials Can two algebraic expressions that appear to be different be equivalent? How are the properties of real numbers related to polynomials? (Adding, Subtracting, Multiplying, Factoring) How can you solve a quadratic function? What are the characteristics of a quadratic function?
Key Terms Coefficients, monomial, binomial, trinomial, polynomial, degree, terms, difference of two squares, factoring, perfect square trinomial, standard form, factored form, binomial factors Students will be able to: Add, subtract, and multiply polynomials. Factor polynomials. Write polynomials in standard form. Identify the degree of a polynomial. Solve a quadratic trinomial by factoring. Identify quadratic expressions that cannot be factored. MA.A.SSE.1 - Interpret expressions that represent a quantity in terms of its context. MA.9-12.HSA-SSE.2 - Use the structure of an expression to identify ways to rewrite it. MA.9-12.A-APR.1 - Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Work examples together on the Communicators and/or Smart Board. Have students create their own adding, subtracting, and multiplying problems and then swap with a partner. Use Lattice Method to show how to multiply binomials, trinomials and polynomials. Have students use Journal or Interactive Notebook Differentiation /Customizing learning (strategies) Allow students of differing abilities to work collaboratively to do complex factoring problems. There are at least 4 different ways to factor a quadratic polynomial try other methods if a student is struggling with one method. Attributes Chart Graphic Organizers Parallel Modeling Activity Quadratic Equations and Functions What are the characteristics of quadratic functions? How do you solve a quadratic equation? How can you use quadratic equations to model real-world situations? How do you graph a quadratic equation? Key Terms Parabola, vertex, intercepts, axis of symmetry, maximum, minimum, quadratic equation Students will be able to: Solve a quadratic equation by factoring to find the x-intercepts. Determine the axis of symmetry of a quadratic equation. Calculate the vertex.
Find the y-intercept. Graph a parabola. Identify if a parabola has a maximum or a minimum. MA.9-12.HSA-CED.1 - Create equations and inequalities in one variable and use them to solve problems MA.9-12.HSA-CED.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. MA.9-12.HSA-CED.3 - Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. MA.9-12.HSA-CED.4 - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. MA.9-12.HSA-REI.1 - Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. MA.9-12.A-REI.4 - Solve quadratic equations in one variable. MA.9-12.HSA-REI.7 - Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. MA.9-12.HSA-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. MA.9-12.HSA-SSE.1 - Interpret expressions that represent a quantity in terms of its context. MA.9-12.HSA-SSE.3 - Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. MA.9-12.HSA-APR.3 - Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. MA.9-12.HSF-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. MA.9-12.HSF-IF.5 - Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. MA.9-12.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. MA.9-12.HSF-IF.8 - Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. MA.9-12.HSF-IF.9 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). MA.9-12.HSF-BF.1 - Write a function that describes a relationship between two
quantities. MA.9-12.HSF-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. MA.9-12.HSF-LE.1 - Distinguish between situations that can be modeled with linear functions and with exponential functions. MA.9-12.HSF-LE.2 - Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). MA.9-12.HSF-LE.3 - Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. MA.9-12.HSS-ID.6 - Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. MA.9-12.HSN-Q.2 - Define appropriate quantities for the purpose of descriptive modeling. MA.9-12.HSN-Q.3 - Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Use the graphing calculator and/or Geometer s Sketchpad to show how the a value determines if the parabola opens up or down. Have students use the Communicators to graph parabolas. Watch YouTube videos to see models of parabolas (i.e. basketball and skateboard half-pipes) Have students use Journal or Interactive Notebook Differentiation /Customizing learning (strategies) Pair students up; have one student develop the criteria for the parabola and have the other student graph it. Team Problem Solving Anticipation/Reaction Guide Sequence Chart Radical Expressions and Equations How are radical expressions represented? What are the characteristics of square root functions? How can you solve a radical equation? Key Terms Radical expression, square root, rationalize the denominator, like radicals, unlike radicals, conjugates, radical equation, extraneous solutions Students will be able to: Simplify radicals involving products and quotients Simplify sums and differences of radical expressions Simplify products and quotients of radical expressions
Solve equations containing radicals Identify extraneous solution MA.9-12.HSA-REI.2 - Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Have students use Journal or Interactive Notebook Use the Solve It Applet from Pearson Webpage Use the Dynamic Activity Applet from Pearson Webpage Have students create problems and swap to solve Use Find the Buried Treasure WS from Chapter 10-3 in textbook resources Differentiation /Customizing learning (strategies) Stations and Group Activities RAFT activity Parallel Modeling Cause/Effect Organizer