ࡱ> (*#$%&'w bjbj >ee    4 hf>" (((()))eeeeeee$hXk f))))) f(("f,,,)((e,)e,,j^c(-*}`2e8f0hf`Jk*kdcckd)),))))) f fY+)))hf))))k))))))))) :  TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUMContent Area: Mathematics Course Title: Algebra IGrade Level: High School Writing, Evaluating and Graphing of Linear Equations and Function Notation  6 weeks Writing, Evaluating and Graphing of Linear Inequalities, and Absolute Value Equations/Inequalities  6 weeks Systems of Equations and Inequalities  4 weeks Properties of Exponents, Exponential Functions, and Scientific Notation  3 weeks Polynomials: Factor and Operations  5 weeks Radical Expressions and Equations  3 weeksDate Created:July 25, 2012Board Approved on: TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUMContent Area: MathematicsCourse Title: Algebra IGrade Level: High School Quadratics: Solving and Graphing  6 weeks Data Analysis  1 week       Date Created:July 25, 2012Board Approved on: TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUM Unit Overview Content Area: Mathematics Grade: High SchoolUnit: Linear Equations: Writing, Evaluating and Graphing/ Function NotationDomain: Creating Equations/Reasoning with Equations & Inequalities/ Interpreting Functions/ Building FunctionsUnit Summary: This unit focuses on manipulating expressions, writing, solving, and graphing linear equations. Expressions and equations will be solved algebraically. Functions will be used in a variety of ways to describe real world relationships and patterns.Primary interdisciplinary connections: Infused within the unit are connections to the 2009 NJCCCS for Mathematics, Language Arts Literacy and Technology.21st century themes: The unit will integrate the 21st Century Life and Career standards 9.1 strands A-D. These strands include: Critical thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership, and cross cultural understanding and interpersonal communication. Learning TargetsContent StandardsNumber Common Core Standard for MasteryA.REI.3Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.A.CED.1Create equations and inequalities in one variable and use them to solve problems. A.CED.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.NumberCommon Core Standard for IntroductionA.CED.4Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. A.REI.1Explain 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.A.CED.3Represent 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. A.REI.10Understand 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).F.IF.1Understand 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.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.F.IF.5Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.F.BF.1Write a function that describes a relationship between two quantities.Unit Essential Questions How do you translate real-life situations into equations? How do you solve equations using algebra and other strategies? How can linear equations be used to model real world data? How can linear graphing be used to predict outcomes? How can we model real world situations using function notation? Unit Enduring Understandings Students will understand that Equation solving is working backward and undoing operations. Function notation provides instructions to be applied to mathematical expressions. Input and output values in a table can be translated to a graph as the x and y coordinates. Unit Objectives Students will know Expressions are simplified by various means Equations can be solved using the properties of equality. Slope is a constant change The solution of a two variable equation can be represented as a linear graph. Functional notation is a way to name a function that is defined by a graph. Unit Objectives Students will be able to Write algebraic expressions using variables. Simplify expressions using order of operations, the distributive property, and combining like terms. Translate expressions and statements into algebraic expressions and equations. Evaluate variable expressions. Check solutions of equations and inequalities. Use a process including properties of equality and justification to solve equations. Solve literal equations for a given variable. Plot points & name coordinates of points on the coordinate plane. Calculate slope of a line using the Slope Formula. Identify the slope of a line from its graph. Write the equation of a line given its graph or two points on the line. Write an equation in slope intercept form, point-slope form, and standard form. Represent the solution of a two-variable equation as a linear graph. Use the graphing calculator to graph equations. Identify the domain and range of a function. Find the value of the range given the domain values. Write Real World scenarios with independent and dependant variables using function notation. Graph an equation presented in function notation.  TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUM Evidence of LearningFormative AssessmentsObservation Homework Class participation Whiteboards/communicatorsDO-NOW Notebook Writing prompts Summative Assessments Quiz Test Projects Quarterly Tests Performance Based AssessmentModifications (ELLs, Special Education, Gifted and Talented) Teacher tutoring Peer tutoring Cooperative learning groups Modified assignments Differentiated instruction Native language texts and native language to English dictionary Follow all IEP modifications/504 plan Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources: For further clarification refer to NJ Class Standard Introductions at HYPERLINK "http://www.njcccs.org"www.njcccs.org. Graphing Calculator Microsoft Excel/PowerPoint Teacher-made tests, worksheets, warm-ups, and quizzes Glencoe/ McGrawhill Algebra I Textbook  HYPERLINK "http://www.connectEd.mcgraw-hill.com" www.connectEd.mcgraw-hill.com  HYPERLINK "http://www.nlvm.com" www.nlvm.com  HYPERLINK "http://www.ixl.com" www.ixl.com  HYPERLINK "http://teachers.henr.co.k12.va.us/math/hcpsalgebra1" http://teachers.henr.co.k12.va.us/math/hcpsalgebra1  HYPERLINK "http://www.purplemath.com" www.purplemath.com  HYPERLINK "http://www.Kutasoftware.com" www.Kutasoftware.com  HYPERLINK "http://www.Khanacademy.com" www.Khanacademy.com  HYPERLINK "http://www.mathworksheetsite.com" www.mathworksheetsite.com  HYPERLINK "http://www.brightstorm.com" www.brightstorm.com  HYPERLINK "http://www.funbrain.com" www.funbrain.com  HYPERLINK "http://www.coolmath.com" www.coolmath.com  HYPERLINK "http://www.Edhelper.com" www.Edhelper.com  HYPERLINK "http://www.ehow.com" www.ehow.com  HYPERLINK "http://www.phschools.com" www.phschools.com Teacher Notes:  TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUM Unit Overview Content Area: Mathematics Grade: High SchoolUnit: Inequalities Writing/Graphing and Evaluating/Absolute Value Equations & InequalitiesDomain: Reasoning with Equations & Inequalities/Creating EquationsUnit Summary: This unit focuses on manipulating expressions and inequalities, writing, solving, and graphing linear equations and inequalities. Expressions, equations, and inequalities will be solved algebraically. Skills learned from linear equations will be applied to both inequality and absolute value graphs.Primary interdisciplinary connections: Infused within the unit are connections to the 2009 NJCCCS for Mathematics, Language Arts Literacy and Technology.21st century themes: The unit will integrate the 21st Century Life and Career standards 9.1 strands A-D. These strands include: Critical thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership, and cross cultural understanding and interpersonal communication. Learning TargetsContent Standards Number Common Core Standard for MasteryA.REI.12Graph 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.A.REI.1Explain 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.NumberCommon Core Standard for IntroductionA.CED.3Represent 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. A.REI.11Explain 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 equations f(x) = g(x); find solutions approximately: using technology to graph functions, make table of values or find successive approximations.Unit Essential Questions How do you translate real-life situations into inequalities? How do you solve inequalities using algebra and other strategies? How can we model real world situations using absolute value? Unit Enduring Understandings Students will understand that The rules for solving equations can be applied when solving inequalities and absolute value equations. Solving inequalities is similar to solving equations, working backward and undoing operations, the exception being when multiplying or dividing by a negative number. The solution to an inequality is a set, not just a single solution. There is a connection between the graphs of both absolute value and linear equations. Absolute value is the distance from zero. Unit Objectives Students will know How to graph a wide variety of inequalities and absolute value equations. How to recognize the differences in a graph of an inequality and absolute value equations. How to use graphing skills to sketch inequalities and absolute value equations. How to solve inequalities and absolute value equations. Unit Objectives Students will be able to Translate expressions and statements into algebraic expressions, equations and inequalities Evaluate absolute-value expressions and inequalities. Check solutions of equations and inequalities. Use a process including properties of equality and justification to solve equations and inequalities. Use the sign-change rule for multiplying or dividing both sides of a one variable inequality by a negative number. Solve absolute value equations that contain 0, 1 or 2 solutions. Solve absolute value inequality is an and or an or compound inequality.  TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUM Evidence of LearningFormative AssessmentsObservation Homework Class participation Whiteboards/communicatorsDO-NOW Notebook Writing prompts Summative Assessments Quiz Test Projects Quarterly Tests Performance Based AssessmentModifications (ELLs, Special Education, Gifted and Talented) Teacher tutoring Peer tutoring Cooperative learning groups Modified assignments Differentiated instruction Native language texts and native language to English dictionary Follow all IEP modifications/504 plan Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources: For further clarification refer to NJ Class Standard Introductions at HYPERLINK "http://www.njcccs.org"www.njcccs.org. Graphing Calculator Microsoft Excel/PowerPoint Teacher-made tests, worksheets, warm-ups, and quizzes Glencoe/ McGrawhill Algebra I Textbook  HYPERLINK "http://www.connectEd.mcgraw-hill.com" www.connectEd.mcgraw-hill.com  HYPERLINK "http://www.nlvm.com" www.nlvm.com  HYPERLINK "http://www.ixl.com" www.ixl.com  HYPERLINK "http://teachers.henr.co.k12.va.us/math/hcpsalgebra1" http://teachers.henr.co.k12.va.us/math/hcpsalgebra1  HYPERLINK "http://www.purplemath.com" www.purplemath.com  HYPERLINK "http://www.Kutasoftware.com" www.Kutasoftware.com  HYPERLINK "http://www.Khanacademy.com" www.Khanacademy.com  HYPERLINK "http://www.mathworksheetsite.com" www.mathworksheetsite.com  HYPERLINK "http://www.brightstorm.com" www.brightstorm.com  HYPERLINK "http://www.funbrain.com" www.funbrain.com  HYPERLINK "http://www.coolmath.com" www.coolmath.com  HYPERLINK "http://www.Edhelper.com" www.Edhelper.com  HYPERLINK "http://www.ehow.com" www.ehow.com  HYPERLINK "http://www.phschools.com" www.phschools.com Teacher Notes:  TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUM Unit OverviewContent Area: Mathematics Grade: High SchoolUnit: Systems of Equations and InequalitiesDomain: Reasoning with Equations and Inequalities/Creating EquationsUnit Summary: This unit focuses on solving systems of equations and inequalities using the graphing, substitution, and elimination methods. Students will solve systems with 0, 1, and infinitely many solutions. Primary interdisciplinary connections: Infused within the unit are connections to the 2010 NJCCCS for Mathematics, Language Arts Literacy and Technology.21st century themes: The unit will integrate the 21st Century Life and Career standards 9.1 strands A-D. These strands include: Critical thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership, and cross cultural understanding and interpersonal communication. Learning TargetsContent Standards NumberCommon Core Standard for MasteryA.REI.5Prove 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.6Solve systems of linear equations exactly and approximately (e.g. with graphs), focusing on pairs of linear equations in two variables.A.REI.12Graph 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.A.CED.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. NumberCommon Core Standard for IntroductionA.REI.11Explain 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 equations f(x) = g(x); find solutions approximately: using technology to graph functions, make table of values or find successive approximations.A.CED.3Represent 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.Unit Essential Questions How are systems of equations solved using graphing, substitution, and elimination? When is it appropriate to use each method? What are the three types of solutions to a system? What does the intersecting region of a system of inequalities represent? How can real world situations be solved using a system of equations?Unit Enduring Understandings Students will understand that The intersection of two lines provides a solution to the system. Solving systems by graphing has its limitations. Multiplying an entire equation by a non-zero constant does not change the value of the equation/inequality. A solution to a system of equations has significance in the real world.Unit Objectives Students will know There are various methods to solve systems of equations and inequalities. When to employ a particular method to solve the systems of equations. Unit Objectives Student will be able to . Solve systems using substitution. Solve systems using elimination. Solve systems using graphing. Solve systems of linear inequalities. Use systems to find the solutions to real world situations. TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUM Evidence of LearningFormative AssessmentsObservation Homework Class participation Whiteboards/communicatorsDO-NOW Notebook Writing prompts Summative Assessments Quiz Test Projects Quarterly Tests Performance Based AssessmentModifications (ELLs, Special Education, Gifted and Talented) Teacher tutoring Peer tutoring Cooperative learning groups Modified assignments Differentiated instruction Native language texts and native language to English dictionary Follow all IEP modifications/504 plan Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources: For further clarification refer to NJ Class Standard Introductions at HYPERLINK "http://www.njcccs.org"www.njcccs.org. Graphing Calculator Microsoft Excel/PowerPoint Teacher-made tests, worksheets, warm-ups, and quizzes Glencoe/ McGrawhill Algebra I Textbook  HYPERLINK "http://www.connectEd.mcgraw-hill.com" www.connectEd.mcgraw-hill.com  HYPERLINK "http://www.nlvm.com" www.nlvm.com  HYPERLINK "http://www.ixl.com" www.ixl.com  HYPERLINK "http://teachers.henr.co.k12.va.us/math/hcpsalgebra1" http://teachers.henr.co.k12.va.us/math/hcpsalgebra1  HYPERLINK "http://www.purplemath.com" www.purplemath.com  HYPERLINK "http://www.Kutasoftware.com" www.Kutasoftware.com  HYPERLINK "http://www.Khanacademy.com" www.Khanacademy.com  HYPERLINK "http://www.mathworksheetsite.com" www.mathworksheetsite.com  HYPERLINK "http://www.brightstorm.com" www.brightstorm.com  HYPERLINK "http://www.funbrain.com" www.funbrain.com  HYPERLINK "http://www.coolmath.com" www.coolmath.com  HYPERLINK "http://www.Edhelper.com" www.Edhelper.com  HYPERLINK "http://www.ehow.com" www.ehow.com  HYPERLINK "http://www.phschools.com" www.phschools.com Teacher Notes:  TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUM Unit OverviewContent Area: Mathematics Grade: High SchoolUnit: Properties of Exponents, Exponential Functions, Scientific NotationDomain: Exponents and Exponential Functions/ The Real Number System/ Seeing Structure in Expressions/ Linear Exponential Models/ Interpreting Functions/ Building Functions/ Reasoning with Equations and InequalitiesUnit Summary: This unit focuses on simplifying expressions involving exponents and scientific notation. Real world problems will be modeled with exponential growth and decay equations and proportional applications.Primary interdisciplinary connections: Infused within the unit are connections to the 2009 NJCCCS for Mathematics, Language Arts Literacy and Technology.21st century themes: The unit will integrate the 21st Century Life and Career standards 9.1 strands A-D. These strands include: Critical thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership, and cross cultural understanding and interpersonal communication. Learning TargetsContent Standards NumberCommon Core Standard for MasteryN.RN.1Explain 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. N.RN.2Rewrite expressions involving radical and rational exponents using the properties of exponents.A.SSE.2Use the structure of an expression to identify ways to rewrite it.F.LE.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.F.IF.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.F.IF.7.eGraph exponential and logarithmic functions, showing intercepts and end behavior, and explain different properties of the function. F.IF.8Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.F.IF.8.bUse the properties of exponents to interpret expressions for exponential functions. NumberCommon Core Standard for IntroductionF.BF.2Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.F.BF.3Identify the effect on the graph of replacing 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. A.REI.11Explain 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, exponential, and logarithmic functions. Unit Essential Questions How do we compare the differences between linear and exponential growth? How can we apply the concept of exponential growth/decay to real world problems? How are geometric sequences related to exponential functions/ When do quantities have a nonlinear relationship? Unit Enduring Understandings Students will understand that There can still be a relationship between two numbers even if there is no linear pattern. Predictions can be made using exponential growth and decay models. Scientific notation can be used to represent extremely large or extremely small numbers. Expressions involving exponents may be simplified by applying the laws of exponents.Unit Objectives Students will know How to simplify exponents using the laws of exponents. Scientific notation is primarily used to write very small or very large numbers. How to recognize a growth or decay exponential equation or graph. How to relate geometric sequences to exponential functions.Unit Objectives Students will be able to Multiply and divide monomials using the properties of exponents. Evaluate and rewrite expressions involving rational exponents. Find products and quotients of numbers expressed in scientific notation. Graph exponential functions. Solve problems involving exponential growth or decay. Identify and generate geometric sequences. Write exponential equations that model real-world growth and decay data   TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUM Evidence of LearningFormative AssessmentsObservation Homework Class participation Whiteboards/communicatorsDO-NOW Notebook Writing prompts Summative Assessments Quiz Test Projects Quarterly Tests Performance Based AssessmentModifications (ELLs, Special Education, Gifted and Talented) Teacher tutoring Peer tutoring Cooperative learning groups Modified assignments Differentiated instruction Native language texts and native language to English dictionary Follow all IEP modifications/504 plan Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources: For further clarification refer to NJ Class Standard Introductions at HYPERLINK "http://www.njcccs.org"www.njcccs.org. Graphing Calculator Microsoft Excel/PowerPoint Teacher-made tests, worksheets, warm-ups, and quizzes Glencoe/ McGrawhill Algebra I Textbook  HYPERLINK "http://www.connectEd.mcgraw-hill.com" www.connectEd.mcgraw-hill.com  HYPERLINK "http://www.nlvm.com" www.nlvm.com  HYPERLINK "http://www.ixl.com" www.ixl.com  HYPERLINK "http://teachers.henr.co.k12.va.us/math/hcpsalgebra1" http://teachers.henr.co.k12.va.us/math/hcpsalgebra1  HYPERLINK "http://www.purplemath.com" www.purplemath.com  HYPERLINK "http://www.Kutasoftware.com" www.Kutasoftware.com  HYPERLINK "http://www.Khanacademy.com" www.Khanacademy.com  HYPERLINK "http://www.mathworksheetsite.com" www.mathworksheetsite.com  HYPERLINK "http://www.brightstorm.com" www.brightstorm.com  HYPERLINK "http://www.funbrain.com" www.funbrain.com  HYPERLINK "http://www.coolmath.com" www.coolmath.com  HYPERLINK "http://www.Edhelper.com" www.Edhelper.com  HYPERLINK "http://www.ehow.com" www.ehow.com  HYPERLINK "http://www.phschools.com" www.phschools.com Teacher Notes:  TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUM Unit OverviewContent Area: Mathematics Grade: High SchoolUnit: Polynomials: Factor and OperationsDomain: Arithmetic with Polynomials and Rational Expressions/ Seeing Structure in ExpressionsUnit Summary: In this unit, students will begin working with polynomials. After naming polynomials they will perform the basic operations such as adding, subtracting, and multiplying two or more polynomials. Students will also factor polynomials.Primary interdisciplinary connections: Infused within the unit are connections to the 2009 NJCCCS for Mathematics, Language Arts Literacy and Technology.21st century themes: The unit will integrate the 21st Century Life and Career standards 9.1 strands A-D. These strands include: Critical thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership, and cross cultural understanding and interpersonal communication. Learning TargetsContent Standards NumberCommon Core Standard for MasteryA.APR.1Understand 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.A.SSE.1Interpret expressions that represent a quantity in terms of its context.A.SSE.1.aInterpret parts of an expression, such as terms, factors, and coefficients.A.SSE.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.A.SSE.3.aFactor a quadratic expression to reveal the zeros of the function it defines.NumberCommon Core Standard for IntroductionA.SSE.1.bInterpret complicated expressions by viewing one or more of their parts as a single entity. A.SSE.2Use the structure of an expression to identify ways to rewrite it. Unit Essential Questions How would we perform the basic mathematical operations on polynomials and polynomial equations? How could a polynomial be expressed as the product of two or more factors? When can a polynomial be factored? What terms are used to describe the zeros of a polynomial? How can polynomial equations be used to solve real world problems?Unit Enduring Understandings Students will understand that Polynomials can be added and subtracted by combining like terms. Polynomials can be classified by their degree and the number of terms. Polynomials can be multiplied using a variety of methods. Polynomials can be factored.Unit Objectives Students will know How to determine a degree of a polynomial. How to manipulate polynomials. How to reverse a polynomial into factors. Unit Objectives Students will be able to Identify a polynomial function and determine its degree Add, subtract and multiply polynomials. Factor polynomials completely. Factor a greatest common factor from a polynomial. Factor a trinomial as the product of two binomials. Write polynomials in standard form.  TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUM Evidence of LearningFormative AssessmentsObservation Homework Class participation Whiteboards/communicatorsDO-NOW Notebook Writing prompts Summative Assessments Quiz Test Projects Quarterly Tests Performance Based AssessmentModifications (ELLs, Special Education, Gifted and Talented) Teacher tutoring Peer tutoring Cooperative learning groups Modified assignments Differentiated instruction Native language texts and native language to English dictionary Follow all IEP modifications/504 plan Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources: For further clarification refer to NJ Class Standard Introductions at HYPERLINK "http://www.njcccs.org"www.njcccs.org. Graphing Calculator Microsoft Excel/PowerPoint Teacher-made tests, worksheets, warm-ups, and quizzes Glencoe/ McGrawhill Algebra I Textbook  HYPERLINK "http://www.connectEd.mcgraw-hill.com" www.connectEd.mcgraw-hill.com  HYPERLINK "http://www.nlvm.com" www.nlvm.com  HYPERLINK "http://www.ixl.com" www.ixl.com  HYPERLINK "http://teachers.henr.co.k12.va.us/math/hcpsalgebra1" http://teachers.henr.co.k12.va.us/math/hcpsalgebra1  HYPERLINK "http://www.purplemath.com" www.purplemath.com  HYPERLINK "http://www.Kutasoftware.com" www.Kutasoftware.com  HYPERLINK "http://www.Khanacademy.com" www.Khanacademy.com  HYPERLINK "http://www.mathworksheetsite.com" www.mathworksheetsite.com  HYPERLINK "http://www.brightstorm.com" www.brightstorm.com  HYPERLINK "http://www.funbrain.com" www.funbrain.com  HYPERLINK "http://www.coolmath.com" www.coolmath.com  HYPERLINK "http://www.Edhelper.com" www.Edhelper.com  HYPERLINK "http://www.ehow.com" www.ehow.com  HYPERLINK "http://www.phschools.com" www.phschools.com Teacher Notes:  TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUM Unit OverviewContent Area: Mathematics Grade: High SchoolUnit: Radical Expressions and EquationsDomain: The Real Number System/ Reasoning with Equations and Inequalities/ Creating Equations/ Interpreting FunctionsUnit Summary: This unit focuses on simplifying radical expressions and performing basic operations on radical expressions. Students will also learn to graph radical functions and solve radical equations.Primary interdisciplinary connections: Infused within the unit are connections to the 2009 NJCCCS for Mathematics, Language Arts Literacy and Technology.21st century themes: The unit will integrate the 21st Century Life and Career standards 9.1 strands A-D. These strands include: Critical thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership, and cross cultural understanding and interpersonal communication. Learning TargetsContent Standards NumberCommon Core Standard for MasteryN.RN.2Rewrite expressions involving radicals and rational exponents using the properties of exponents.A.REI.2Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may rise.NumberCommon Core Standard for IntroductionA.CED.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.F.IF.4For 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 verbal description of the relationship. F.IF.7.bGraph square root, cube root, and piecewise-functions, including step functions and absolute value functions. Unit Essential Questions How do we know if a radical expression is in simplest form? How can radical expressions be combined? How can you use the properties of real numbers to performs operations an radical expressions? How and why should you check your solution to radical equations?Unit Enduring Understandings Students will understand that The knowledge of radicals is a basis for higher level mathematics Radical expression with like radicals can be added or subtracted. Radical expressions must be in simplest form. The graph of a square root function has unique characteristics. Unit Objectives Students will know How to perform basic operations with radical expressions. How to solve and graph basic radical equations. Unit Objectives Students will be able to Simplify radical expressions Add, subtract, and multiply radical expressions Solve radical equations Graph the parent radical function ( EMBED Equation.3 ) Find the distance between two points using the distance formula. TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUM Evidence of LearningFormative AssessmentsObservation Homework Class participation Whiteboards/communicatorsDO-NOW Notebook Writing prompts Summative Assessments Quiz Test Projects Quarterly Tests Performance Based AssessmentModifications (ELLs, Special Education, Gifted and Talented) Teacher tutoring Peer tutoring Cooperative learning groups Modified assignments Differentiated instruction Native language texts and native language to English dictionary Follow all IEP modifications/504 plan Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources: For further clarification refer to NJ Class Standard Introductions at HYPERLINK "http://www.njcccs.org"www.njcccs.org. Graphing Calculator Microsoft Excel/PowerPoint Teacher-made tests, worksheets, warm-ups, and quizzes Glencoe/ McGrawhill Algebra I Textbook  HYPERLINK "http://www.connectEd.mcgraw-hill.com" www.connectEd.mcgraw-hill.com  HYPERLINK "http://www.nlvm.com" www.nlvm.com  HYPERLINK "http://www.ixl.com" www.ixl.com  HYPERLINK "http://teachers.henr.co.k12.va.us/math/hcpsalgebra1" http://teachers.henr.co.k12.va.us/math/hcpsalgebra1  HYPERLINK "http://www.purplemath.com" www.purplemath.com  HYPERLINK "http://www.Kutasoftware.com" www.Kutasoftware.com  HYPERLINK "http://www.Khanacademy.com" www.Khanacademy.com  HYPERLINK "http://www.mathworksheetsite.com" www.mathworksheetsite.com  HYPERLINK "http://www.brightstorm.com" www.brightstorm.com  HYPERLINK "http://www.funbrain.com" www.funbrain.com  HYPERLINK "http://www.coolmath.com" www.coolmath.com  HYPERLINK "http://www.Edhelper.com" www.Edhelper.com  HYPERLINK "http://www.ehow.com" www.ehow.com  HYPERLINK "http://www.phschools.com" www.phschools.com Teacher Notes:  TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUM Unit Overview Content Area: Mathematics Grade: High SchoolUnit: Quadratics: Solving and GraphingDomain: Arithmetic with Polynomials and Rational Expressions/ Seeing Structure in Expressions/ Reasoning with Equations and Inequalities/ Interpreting FunctionsUnit Summary: This unit focuses on solving and graphing quadratic functions. The student will be able to determine the effect of 'a' of y =ax^2 to determine the direction of the graph, the vertex point and whether the vertex point is a maxim or a minimum point. This lesson is designed to help students solve quadratic equations by using the Quadratic Formula, factoring, and graphing. Students will identify the most efficient method for solving a quadratic equation and solve the quadratic equation.Primary interdisciplinary connections: Infused within the unit are connections to the 2009 NJCCCS for Mathematics, Language Arts Literacy and Technology.21st century themes: The unit will integrate the 21st Century Life and Career standards 9.1 strands A-D. These strands include: Critical thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership, and cross cultural understanding and interpersonal communication. Learning TargetsContent Standards Number Common Core Standard for MasteryA.APR.3Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.F.IF.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.F.IF.7.aGraph linear and quadratic functions and show intercepts, maxima, and minima.A.REI.4Solve quadratic equations in one variable.F.LE.1Distinguish between situations that can be modeled with linear functions and with exponential functions.A.APR.3Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.A.SSE.3.aFactor a quadratic expression to reveal the zeros of the function if defines.NumberCommon Core Standard for IntroductionA.REI.4.aUse the method of completing the square to transform any quadratic equation in x into an equation of the form (x p)2 = q that has the same solutions.A.REI.4.bSolve quadratic equations by inspection, 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 abi for real numbers a and b.A.SSE.3.bComplete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.F.IF.8.aUse the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.Unit Essential Questions How can we model applications using quadratic functions? How can we solve quadratic equations using the quadratic formula, factoring, or the graph of the parabola? How can we choose a linear, exponential or quadratic equation to model a real world situation? What terms are used to describe the zeros of a quadratic function? What are the different ways to solve quadratic equations and when is each appropriate? What does a quadratic function look like?Unit Enduring Understandings Students will understand that A quadratic function has the form  EMBED Equation.3 , where  EMBED Equation.3  A quadratic equation can be solved by applying a variety of techniques. A quadratic equation can be solved by using a graphing calculator. The graph of a quadratic function results in a parabola. Unit Objectives Students will know The graph of a quadratic function will intersect the x-axis in zero, one or two points. Quadratic equations are solved by factoring or by applying the quadratic formula. How to graph quadratic functions. The roots are the x intercepts of a quadratic function. Unit Objectives Students will be able to Graph parabolas Find the x-intercepts of parabolas, roots and solutions. Determine the vertex. Utilize the zero-product property to solve equations. Factor and solve quadratic equations. Solve quadratic equations using the quadratic formula. To use the discriminant to determine the number and type of real solutions.  TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUM Evidence of LearningFormative AssessmentsObservation Homework Class participation Whiteboards/communicatorsDO-NOW Notebook Writing prompts Summative Assessments Quiz Test Projects Quarterly Tests Performance Based AssessmentModifications (ELLs, Special Education, Gifted and Talented) Teacher tutoring Peer tutoring Cooperative learning groups Modified assignments Differentiated instruction Native language texts and native language to English dictionary Follow all IEP modifications/504 plan Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources: For further clarification refer to NJ Class Standard Introductions at HYPERLINK "http://www.njcccs.org"www.njcccs.org. Graphing Calculator Microsoft Excel/PowerPoint Teacher-made tests, worksheets, warm-ups, and quizzes Glencoe/ McGrawhill Algebra I Textbook  HYPERLINK "http://www.connectEd.mcgraw-hill.com" www.connectEd.mcgraw-hill.com  HYPERLINK "http://www.nlvm.com" www.nlvm.com  HYPERLINK "http://www.ixl.com" www.ixl.com  HYPERLINK "http://teachers.henr.co.k12.va.us/math/hcpsalgebra1" http://teachers.henr.co.k12.va.us/math/hcpsalgebra1  HYPERLINK "http://www.purplemath.com" www.purplemath.com  HYPERLINK "http://www.Kutasoftware.com" www.Kutasoftware.com  HYPERLINK "http://www.Khanacademy.com" www.Khanacademy.com  HYPERLINK "http://www.mathworksheetsite.com" www.mathworksheetsite.com  HYPERLINK "http://www.brightstorm.com" www.brightstorm.com  HYPERLINK "http://www.funbrain.com" www.funbrain.com  HYPERLINK "http://www.coolmath.com" www.coolmath.com  HYPERLINK "http://www.Edhelper.com" www.Edhelper.com  HYPERLINK "http://www.ehow.com" www.ehow.com  HYPERLINK "http://www.phschools.com" www.phschools.com Teacher Notes:  TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUM Unit Overview Content Area: Mathematics Grade: High SchoolUnit: Probability & Data AnalysisDomain: Interpreting Categorical and Quantitative Data/ Making Inferences and Justifying Conclusions/ Conditional Probability and the Rules of ProbabilityUnit Summary: This unit will focus on determining the probability of an event. Students will analyze data in order to determine the probability of an event occurring and make predictions. The counting methods will be utilized to determine how many possible outcomes can occur. Students will recognize possible associations and trends in the data.Primary interdisciplinary connections: Infused within the unit are connections to the 2009 NJCCCS for Mathematics, Language Arts Literacy and Technology.21st century themes: The unit will integrate the 21st Century Life and Career standards 9.1 strands A-D. These strands include: Critical thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership, and cross cultural understanding and interpersonal communication. Learning TargetsContent Standards Number Common Core Standard for MasteryS.ID.3Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).S.ID.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.S.ID.6.aFit a function to the data, use functions fitted to data to solve problems in the context of data.S.ID.6.cFit a linear function for a scatter plot that suggests a linear association.S.ID.7Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.S.CP.2(+)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.NumberCommon Core Standard for IntroductionS.IC.1(+)Understand statistics as a process for making inferences to be made about population parameters based on a random sample from that population.S.IC.6(+)Evaluate reports based on data.S.CP.3(+)Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.S.CP.8(+)Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A), and interpret the answer in terms of the model.Unit Essential Questions How can we use experimental and theoretical probabilities to predict future events? (+)How do the individual probabilities of events impact compound probability situations? (+)How does the likelihood of an event occurring depend upon its probabilitys proximity to the limits, 0 being impossible and 1 being certain? How the collection, organization, interpretation, and display of data be used to answer questions. How does the representation of data influence decisions? How to determine if a conclusion is reasonable? How do the results of a statistical investigation be used to support an argument? How can you apply to the media or political campaigns?Unit Enduring Understandings Students will understand that In order to find the total possible outcomes of multiple categories, one must apply the fundamental counting principle. There is a difference between theoretical and experimental probability. Compound probabilities involving two different circumstances, and / or, are calculated differently. The results of a statistical analysis of an investigation can be used to support or refute an argument. Data analysis and misleading statistics are parts of the world around us.Unit Objectives Students will know (+)How to calculate and apply permutations and combinations. (+)The definition of probability as the likelihood of an event occurring. (+)How to calculate the probability of an event occurring. (+)How to calculate compound probability. (+)How and when to use the fundamental counting principle. Unit Objectives Students will be able to Use the Fundamental Counting Principle to determine the total number of possible outcomes. Calculate the probability of a simple event occurring. Determine the likelihood of an event occurring based upon 0, 0.5, and 1 as bench marks. Use nPr as well as nCr to expand on the Fundamental Counting Principle with restrictions. Determine compound probability.  TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUM Evidence of LearningFormative AssessmentsObservation Homework Class participation Whiteboards/communicatorsDO-NOW Notebook Writing prompts Summative Assessments Quiz Test Projects Quarterly Tests Performance Based AssessmentModifications (ELLs, Special Education, Gifted and Talented) Teacher tutoring Peer tutoring Cooperative learning groups Modified assignments Differentiated instruction Native language texts and native language to English dictionary Follow all IEP modifications/504 plan Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources: For further clarification refer to NJ Class Standard Introductions at HYPERLINK "http://www.njcccs.org"www.njcccs.org. Graphing Calculator Microsoft Excel/PowerPoint Teacher-made tests, worksheets, warm-ups, and quizzes Glencoe/ McGrawhill Algebra I Textbook  HYPERLINK "http://www.connectEd.mcgraw-hill.com" www.connectEd.mcgraw-hill.com  HYPERLINK "http://www.nlvm.com" www.nlvm.com  HYPERLINK "http://www.ixl.com" www.ixl.com  HYPERLINK "http://teachers.henr.co.k12.va.us/math/hcpsalgebra1" http://teachers.henr.co.k12.va.us/math/hcpsalgebra1  HYPERLINK "http://www.purplemath.com" www.purplemath.com  HYPERLINK "http://www.Kutasoftware.com" www.Kutasoftware.com  HYPERLINK "http://www.Khanacademy.com" www.Khanacademy.com  HYPERLINK "http://www.mathworksheetsite.com" www.mathworksheetsite.com  HYPERLINK "http://www.brightstorm.com" www.brightstorm.com  HYPERLINK "http://www.funbrain.com" www.funbrain.com  HYPERLINK "http://www.coolmath.com" www.coolmath.com  HYPERLINK "http://www.Edhelper.com" www.Edhelper.com  HYPERLINK "http://www.ehow.com" www.ehow.com  HYPERLINK "http://www.phschools.com" 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