Curriculum Design Template Content Area: Mathematics Course Title: Algebra I Grade Level: 8-9 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 Radial Expressions Data Analysis and Probability Marking Period 4 Date Created: May 2012 Board Approved on: August 27, 2012
Unit Title Lessons to include Time Foundations for Algebra Solving Equations Solving Inequalities An Introduction to Functions Linear Functions (test after 5.3 and after 5.7) Common Core Standards Math 1.2 Order of Operations and Evaluations Expressions A.SSE.1, A.SSE.1a 1.3 1.6 Real Numbers Prepares for N.RN.3 1.7 Distributive Property A.SSE.1.a 1.8 An Intro to Functions A.CED.1 1.9 Patterns, Equations and Graphs A.CED.2, A.REI.10 2.4 Solving Eq w/variables both sides A.CED1, A.REI1, A.REI.3 2.5 Literal Equations and Formulas 3weeks N.Q.1, A.CED.1, A.CED.4, A.REI.1, A.REI.3 3.7 Absolute Value equations A.SSE.1, A.SSE.1b, A.CED.1 3.1 Inequalities and their graphs Prepares for A.REI.3 3.2 Solving Inequalities using addition and subtraction A.CED.1, A.REI.3 3.3 Solving Inequalities using 3 weeks multiplication and division N.Q.2, A.CED.1, A.REI.3 3.4 Solving Mulit-step Inequalities A.CED.1, A.REI.3 3.7 Absolute Value Inequalities A.SSE.1, A.SSE.1b, A.CED.1 4.1 Using Graphs to Relate two Quantities Prepares for F.IF.4 4.2 Patterns and Linear Functions A.REI.10, F.IF.4 4.3 Patterns and Nonlinear Functions A.REI.10, F.IF.4 4.4 Graphing a Function Rule N.Q.1, A.REI.10, F.IF.5 4.5 Writing a Function Rule 4 weeks N.Q.2, A.SSE.1, A.SSE.1.a, A.CED.2 4.6 Formalizing relations and functions F.IF.1, F.IF.2 A.SSE.1, A.SSE.1.a, A.SSE.1.b, 4.7 Arithmetic Sequence F.IF.3, F.BF.1, F.BF.1.a. F.BF.2, F.LE.2 5.1 Rate of Change and Slope F.IF.6, F.LE. 1.b 5.2 Direct Variation N.Q.2, A.CED.2 A.SSE.1, A.SSE.1.a, A.SSE.2, 5.3 Slope-Intercept Form A.CED.2, F.IF.4, F.IF.7, F.IF.7a, F.BF.1, F.BF.1a, F.BF.3, F.LE.2, 3 weeks F.LE.5 N.Q.2, A.SSE.1, A.SSE.2, 5.5 Standards Form A.CED.2, F.IF.4, F.IF.7, F.IF.7a, F.IF.9, F.BF.1, F.BF.1a, F.BF.3, F.LE.2, F.LE.5 5.6 Parallel and Perpendicular Lines G.GPE.5 5.7 Scatter plots and trend lines N.Q.1, F.LE.5, S.ID.6, S.ID.6a,
Systems of Equations and Inequalities (test after 6.4 and after 6.6) Midterm Review & exam weeks Exponents and Exponential Functions (test after 7.1 and 7.7) Polynomials and Factoring Quadratic Functions and Equations S.ID.6c, S.ID.7, S.ID.8, S.ID.9 6.1 Solving Systems by Graphing A.REI.6 6.2 Solving Systems by Substitution A.REI.6 6.3 Solving Systems Using Elimination A.REI.5, A.REI.6 6.4 Applications of Linear systems 3 weeks N.Q.2, N.Q.3, A.CED.3, A.REI.6 6.5 Linear Inequalities A.CED.3, A.REI.12 6.6 Systems of Linear Inqualities A.REI.12 Chapters 1-6 1 weeks all 7.2-7.3 Multiplication properties of exponents N.RN.1 7.5 Exponential Functions N.RN.2 7.4 Division properties of exponents N.RN.1 7.1 Zero and negative exponents Prepares for N.RN.1 and N.RN.2 7.2 Scientific Notation 5 weeks N.RN.1 A.SSE.1, A.CED.2, A.REI.11, 7.6 Exponential Functions F.IF.4, F.IF.5, F.IF.7, F.IF.7e, F.IF.9, F.LE.2 A.SSE.1, A.SSE.1.a, A.SSE.1.b, 7.7 Exponential Growth and decay A.SSE.3.c, A.CED.2, A.REI.11, F.IF.4, F.IF.7, F.IF.8, F.IF.8b, F.BF.1, F.BF.3, F.LE.1.c, F.LE.5 8.1 Adding and Subtracting Polynomials A.APR.1 8.2 Multiplying and Factoring A.APR.1 8.3 Multiplying Binomials A.APR.1 8.4 Multiplying special cases 5 weeks A.APR.1 8.5 Factoring x 2 + bx + c A.SSE.1.a 8.6 Factoring ax 2 + bx + c A.SSE.1.a, A.SSE.1.b 8.7 Factoring special cases A.SSE.1, A.SSE.1.a, A.SSE.1.b, A.SSE.2 9.1 Quadratic graphs and properties A.SSE.1, A.CED.2, F.IF.4, F.IF.5, F.IF.7a, F.IF.7b, F.BF.3 A.SSE.1, A.CED.2, F.IF.4, 9.2 Quadratic Functions F.IF.7, F.IF.7a, F.IF.9, F.BF.1, F.BF.3 N.Q.2, A.CED.1, A.CED.4, 9.3 Solving Quadratic Equations A.APR.3, A.REI.4, A.REI.4.b 4 weeks A.SSE.3, A.SSE.3.a, A.CED.1, 9.4 Factoring to Solve Quad Equations A.REI.4, A.REI.4.b, F.IF.8, F.IF.8.a N.Q.3, A.SSE.1, A.SSE.1.a, 9.5 Completing the Square A.SSE.1.b, A.SSE.3, A.CED.1, A.REI.1, A.REI.4, A.REI.4.a, A.REI.4.b, F.IF.8.a
Radial Expressions and Equations Data Analysis and Probability Final review and Exam week 9.6 The Quadratic Formula and N.Q.3, A.SSE.1, A.CED.1, Discriminant A.REI.4, A.REI.4.a, A.REI.4.b 9.7 Linear, Quadratic and Exponential F.IF.4, F.BF.1.b, F.LE.1.a, Models F.LE.2, F.TF.5 10.2 simplifying Radicals Prepares for A.REI.2 1 weeks 10.5 Graphs of square and cube roots A.CED.2, F.IF.7b 12.2 Frequency and Histograms N.Q.1, S.ID.1 12.3 Means of Central Tendency N.Q.2, S.ID.2, S.ID.3 2 weeks 12.4 Box and Whisker Plots N.Q.1, S.ID.1, S.ID.2 12.5 Samples and Surveys S.IC.3 Chapters 7,8,9, 10, 12 1 weeks all
Course Title: Algebra 1 Grade Level: 9 th Overarching What is the Real Number System? 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? 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 quadratics and, polynomials. 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, proportions, 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. 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. 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.
Foundations for Algebra Can numbers be classified by their characteristics? How can numbers be represented on the number line? How can the definition of a square root be used to find the exact square roots of some non-negative numbers? How can the square roots of other non-negative numbers be approximated? How are properties related to algebra? How can collecting and analyzing data help you make decisions or predictions? Whole number, integer, rational, irrational, real, radical/square root, measures of central tendency (mean, median, mode). Students will be able to: Classify real numbers To identify properties of real numbers Identify perfect square numbers. Estimate non-perfect square root values. Calculate measures of central tendency of a set of data. MA.9-12.N.RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. MA.9-12.A.SSE.1 - Interpret expressions that represent a quantity in terms of its context MA.9-12.A.CED.1 - Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. MA.9-12.S-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. Show uses for Venn diagrams of properties of real numbers. 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 estimate non-perfect square roots to the hundredths place without the use of a calculator. Work in groups and have students use a Venn diagram to show the examples of real numbers Allow students to create their own word bank using real numbers
Solving 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? 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.N.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.A.SSE.1 - Interpret expressions that represent a quantity in terms of its context 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-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.A-CED.1 - Create equations and inequalities in one variable and use them to solve problems. MA.9-12.A-CED.4 - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Use websites on Smart Board to play equation games. Refer to Algebra Supplemental Binder for various worksheets. Have students create tutorial videos using Jing. Algebra tiles. Give students specific criteria to create their own equation.
Have students create tutorial videos using Jing. Write a short news article that includes numbers and a range around the n umbers to introduce absolute value equations.
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? 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.N.Q.2 - Define appropriate quantities for the purpose of descriptive modeling 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-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.A-CED.1 - Create equations and inequalities in one variable and use them to solve problems. Use websites on Smart Board to play inequality games. Refer to Algebra Supplemental Binder for various worksheets. Have students create tutorial videos using Jing. Modeling using inequalities. Have students create a chart showing what words mean less than and greater than. Give students specific criteria to create and graph their own inequality. Have students create tutorial videos using Jing.
An Introduction to 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? 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.N.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.N.Q.2 - Define appropriate quantities for the purpose of descriptive modeling. MA.9-12.A.SSE.1 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r) n as the product of P and a factor not depending on P. MA.9-12.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). 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.F-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.F-IF.7.a - Graph linear and quadratic functions and show intercepts,
maxima, and minima. MA.9-12.F-BF.1 - Write a function that describes a relationship between two quantities. MA.9-12.F-BF-1a - Determine an explicit expression, a recursive process, or steps for calculation from a context. MA.9-12.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. MA.9-12.F-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). 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). 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.
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? 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. Direct Variation. 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 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.N.Q.2 - Define appropriate quantities for the purpose of descriptive modeling. MA.9-12.A-CED.1 - - Create equations and inequalities in one variable and use them to solve problems. 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.A-CED.4 - - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. MA.9-12.A.SSE.1 - Interpret expressions that represent a quantity in terms of its context MA.9-12.A.SSE.2 - Use the structure of an expression to identify ways to rewrite it. For example, see x 4 y 4 as (x 2 ) 2 (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 y 2 )(x 2 + y 2 ). 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.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.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.F-IF.7.a - Graph linear and quadratic functions and show intercepts, maxima, and minima. MA.9-12.F.BF.1- Write a function that describes a relationship between two quantities. MA.9-12.F.BF.1a- Determine an explicit expression, a recursive process, or steps for calculation from a context. MA.9-12.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 MA.9-12.F.LE.1.b - Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. MA.9-12.F.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.F.LE.4 - For exponential models, express as a logarithm the solution to a b ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. 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.6.a - Fit a function to the data; use functions fitted to data to solve problems in the context of the data. MA.9-12.S-ID.6.b - Informally assess the fit of a function by plotting and analyzing residuals. MA.9-12.S-ID.6.c - Fit a linear function for a scatter plot that suggests a linear association. 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. 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. Use the motion sensor and CBR 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.
Systems of Equations & 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? System of equations, elimination method, substitution method, graphing method, solution to a system, no solution, infinitely many solutions. 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.9-12.N.Q.2 Define appropriate quantities for the purpose of descriptive modeling. MA.9-12.N.Q.3 - Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. 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.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.9-12.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.9-12.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.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. MA.9-12.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. 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 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. Allow students that are struggling to work on their algebraic skills by giving reinforcement problems for homework. YouTube video instruction. 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? 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. Recognize that exponential functions show growth or decay. 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. MA.9-12.N-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.N-RN.2 - Rewrite expressions involving radicals and rational exponents using
the properties of exponents. MA.9-12A.-SSE.1 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r) n as the product of P and a factor not depending on P. MA.9-12.A-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.A-SSE.3.c - Use the properties of exponents to transform expressions for exponential functions. MA.9-12.F.BF.1- Write a function that describes a relationship between two quantities. MA.9-12.F.BF.1a- Determine an explicit expression, a recursive process, or steps for calculation from a context. MA.9-12.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. MA.9-12.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 MA.9-12.F-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). Have students create tutorial videos using Jing. Reference the Discovering Algebra textbook for some good ideas for real-world problems. Have students find expressions for area and perimeter of polygons whose sides are expressions rather than numbers. Look for fun activities on the web to differentiate lesson. (i.e. Number Balls ) Polynomials and Factoring 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? 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.A-SSE.1.a - Interpret parts of an expression, such as terms, factors, and coefficients. 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. MA.9-12.A-REI.4 - Solve quadratic equations in one variable. MA.9-12.A-REI.4.b - Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. 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. 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. Quadratic Functions and Equations 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? 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. Solve a quadratic equation by completing the square. Solve a quadratic equation using the quadratic formula. 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.A-REI.4 - Solve quadratic equations in one variable.
MA.9-12.A-REI.4.b - Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. 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.F-IF.7.a - Graph linear and quadratic functions and show intercepts, maxima, and minima. 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) Pair students up; have one student develop the criteria for the parabola and have the other student graph it. Data Analysis and Probability What is the difference between theoretical probability and experimental probability? When is it appropriate to use a permutation? Combination? How is probability related to real-world events? Probability, theoretical probability, experimental probability, independent, dependent, combination, permutation, event, outcome, counting principle Students will be able to: Calculate theoretical and experimental probabilities. Calculate independent and dependent events. Apply the counting principle. Use permutations and combinations appropriately to count outcomes. MA.9-12.S-CP.1 - [Standard] - Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not"). MA.9-12.S-CP.2 - [Standard] - Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. MA.9-12.S-CP.9 - [Standard] - Use permutations and combinations to compute probabilities of compound events and solve problems. MA.9-12.S-MD.5 - [Standard] - Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. MA.9-12.S-MD.6 - [Standard] - Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). MA.9-12.S-MD.7 - [Standard] - Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a
game). Use the interactive dice and spinners on the Smart Board to calculate probabilities. Have students conduct an experiment to generate data for experimental probabilities. Find a menu on the web and have them draw a tree diagram of appetizers, entrée and dessert. Select students in the class, and have the class figure out how many different ways they can be arranged in line. Select the same group of students from the class, but this time have the class figure out how many different groups of three can be made from the whole group. Pretend the classroom is a carnival and have students create their own carnival games. Students must accurately state the probability of successfully completing the game.