About the Standards

Interdisciplinary Connections

L.11-12.6. Acquire and use accurate general academic and domain-specific words and phrases, sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.

8.1.12.DA.5: Create data visualizations from large data sets to summarize, communicate, and support different interpretations of real-world phenomena.  

Integration of Technology

9.4.12.TL.1: Assess digital tools based on features such as accessibility options, capacities, and utility for accomplishing a specified task (e.g., W.11-12.6.).

9.4.12.TL.2: Generate data using formula-based calculations in a spreadsheet and draw conclusions about the data

9.4.12.TL.3: Analyze the effectiveness of the process and quality of collaborative environments. • 9.4.12.TL.4: Collaborate in online learning communities or social networks or virtual worlds to analyze and propose a resolution to a real-world problem (e.g., 7.1.AL.IPERS.6).

21st Century Skills

9.4.12.CI.1: Demonstrate the ability to reflect, analyze, and use creative skills and ideas (e.g., 1.1.12prof.CR3a).

9.4.12.CI.2: Identify career pathways that highlight personal talents, skills, and abilities (e.g., 1.4.12prof.CR2b, 2.2.12.LF.8).

9.4.12.CI.3: Investigate new challenges and opportunities for personal growth, advancement, and transition (e.g., 2.1.12.PGD.1).

9.4.12.CT.1: Identify problem-solving strategies used in the development of an innovative product or practice (e.g., 1.1.12acc.C1b, 2.2.12.PF.3).

9.4.12.CT.2: Explain the potential benefits of collaborating to enhance critical thinking and problem solving (e.g., 1.3E.12profCR3.a).

9.4.12.CT.3: Enlist input from a variety of stakeholders (e.g., community members, experts in the field) to design a service learning activity that addresses a local or global issue (e.g., environmental justice).

9.4.12.CT.4: Participate in online strategy and planning sessions for course-based, school-based, or other project and determine the strategies that contribute to effective outcomes.

9.4.12.DC.1: Explain the beneficial and harmful effects that intellectual property laws can have on the creation and sharing of content (e.g., 6.1.12.CivicsPR.16.a).

9.4.12.DC.2: Compare and contrast international differences in copyright laws and ethics.

9.4.12.DC.3: Evaluate the social and economic implications of privacy in the context of safety, law, or ethics (e.g.,  6.3.12.HistoryCA.1).

9.4.12.DC.4: Explain the privacy concerns related to the collection of data (e.g., cookies) and generation of data through automated processes that may not be evident to users (e.g., 8.1.12.NI.3).

9.4.12.DC.5: Debate laws and regulations that impact the development and use of software.

9.4.12.DC.6: Select information to post online that positively impacts personal image and future college and career opportunities.

9.4.12.DC.7: Evaluate the influence of digital communities on the nature, content and responsibilities of careers, and other aspects of society (e.g., 6.1.12.CivicsPD.16.a).

9.4.12.DC.8: Explain how increased network connectivity and computing capabilities of everyday objects allow for innovative technological approaches to climate protection.

9.4.12.GCA.1: Collaborate with individuals to analyze a variety of potential solutions to climate change effects and determine why some solutions (e.g., political. economic, cultural) may work better than others (e.g., SL.11-12.1., HS-ETS1-1, HS-ETS1-2, HS-ETS1-4, 6.3.12.GeoGI.1, 7.1.IH.IPERS.6, 7.1.IL.IPERS.7, 8.2.12.ETW.3).

9.4.12.IML.1: Compare search browsers and recognize features that allow for filtering of information. • 9.4.12.IML.2: Evaluate digital sources for timeliness, accuracy, perspective, credibility of the source, and relevance of information, in media, data, or other resources (e.g., NJSLSA.W8, Social Studies Practice: Gathering and Evaluating Sources.

9.4.12.IML.3: Analyze data using tools and models to make valid and reliable claims, or to determine optimal design solutions (e.g., S-ID.B.6a., 8.1.12.DA.5, 7.1.IH.IPRET.8)

9.4.12.IML.4: Assess and critique the appropriateness and impact of existing data visualizations for an intended audience (e.g., S-ID.B.6b, HS-LS2-4).

9.4.12.IML.5: Evaluate, synthesize, and apply information on climate change from various sources appropriately (e.g., 2.1.12.CHSS.6, S.IC.B.4, S.IC.B.6, 8.1.12.DA.1, 6.1.12.GeoHE.14.a, 7.1.AL.PRSNT.2). 

9.4.12.IML.6: Use various types of media to produce and store information on climate change for different purposes and audiences with sensitivity to cultural, gender, and age diversity (e.g., NJSLSA.SL5).

9.4.12.IML.7: Develop an argument to support a claim regarding a current workplace or societal/ethical issue such as climate change (e.g., NJSLSA.W1, 7.1.AL.PRSNT.4).

9.4.12.IML.8: Evaluate media sources for point of view, bias, and motivations (e.g., NJSLSA.R6,  7.1.AL.IPRET.6).

9.4.12.IML.9: Analyze the decisions creators make to reveal explicit and implicit messages within information and media (e.g., 1.5.12acc.C2a, 7.1.IL.IPRET.4).

Career Education

 9.2.12.CAP.1: Analyze unemployment rates for workers with different levels of education and how the economic, social, and political conditions of a time period are affected by a recession. • 9.2.12.CAP.2: Develop college and career readiness skills by participating in opportunities such as structured learning experiences, apprenticeships, and dual enrollment programs. 

9.2.12.CAP.3: Investigate how continuing education contributes to one's career and personal growth. 

9.2.12.CAP.4: Evaluate different careers and develop various plans (e.g., costs of public, private, training schools) and timetables for achieving them, including educational/training requirements, costs, loans, and debt repayment. 

9.2.12.CAP.5: Assess and modify a personal plan to support current interests and postsecondary plans. 

9.2.12.CAP.6: Identify transferable skills in career choices and design alternative career plans based on those skills. 

 9.2.12.CAP.7: Use online resources to examine licensing, certification, and credentialing requirements at the local, state, and national levels to maintain compliance with industry requirements in areas of career interest. 

9.2.12.CAP.8: Determine job entrance criteria (e.g., education credentials, math/writing/reading comprehension tests, drug tests) used by employers in various industry sectors. 

9.2.12.CAP.9: Locate information on working papers, what is required to obtain them, and who must sign them. 

9.2.12.CAP.10: Identify strategies for reducing overall costs of postsecondary education (e.g., tuition assistance, loans, grants, scholarships, and student loans).

9.2.12.CAP.11: Demonstrate an understanding of Free Application for Federal Student Aid (FAFSA) requirements to apply for postsecondary education.

9.2.12.CAP.12: Explain how compulsory government programs (e.g., Social Security, Medicare) provide insurance against some loss of income and benefits to eligible recipients. 

9.2.12.CAP.13: Analyze how the economic, social, and political conditions of a time period can affect the labor market.

9.2.12.CAP.14: Analyze and critique various sources of income and available resources (e.g., financial assets, property, and transfer payments) and how they may substitute for earned income.

9.2.12.CAP.15: Demonstrate how exemptions, deductions, and deferred income (e.g., retirement or medical) can reduce taxable income. 

9.2.12.CAP.16: Explain why taxes are withheld from income and the relationship of federal, state, and local taxes (e.g., property, income, excise, and sales) and how the money collected is used by local, county, state, and federal governments. 

9.2.12.CAP.17: Analyze the impact of the collective bargaining process on benefits, income, and fair labor practice. 

9.2.12.CAP.18: Differentiate between taxable and nontaxable income from various forms of employment (e.g., cash business, tips, tax filing and withholding). 

9.2.12.CAP.19: Explain the purpose of payroll deductions and why fees for various benefits (e.g., medical benefits) are taken out of pay, including the cost of employee benefits to employers and self-employment income. • 9.2.12.CAP.20: Analyze a Federal and State Income Tax Return.

9.2.12.CAP.21: Explain low-cost and low-risk ways to start a business. 

9.2.12.CAP.22: Compare risk and reward potential and use the comparison to decide whether starting a business is feasible. 

9.2.12.CAP.23: Identify different ways to obtain capital for starting a business.

Content Area: Mathematics

Course Title:   Algebra I

Grade level: 9-11

Unit 1: Modeling with Linear Equations and Inequalities

September - October

Unit 2: Modeling with Linear Functions, Linear Systems, & Exponential Functions  

November-January

Unit 3: Quadratic Equations, Functions & Polynomials

February- April

Unit 4: Modeling with Statistics

May-June

Date Created:

Board Approved On:

Lower Cape May Regional School District  (Insert Subject/Content Area) Curriculum

Unit 1 Overview

Content Area:  Mathematics

Unit Title:  Modeling with Linear Equations and Inequalities 

Target Course/Grade Level: 9, 10, 11

Unit Summary:

    In unit 1 we will:

· Perform arithmetic operations on polynomials  

· Understand the relationship between zeros and factors

· Interpret the structure of expressions

· Solve equations and inequalities in one variable

· Create equations that describe numbers or relationships

· Interpret functions that arise in applications in terms of the context

· Represent and solve equations and inequalities graphically

· Build a function that models a relationship between two quantities

· Construct & compare linear, quadratic, & exponential models

· Build new functions from existing functions

· Analyze functions using different representation

- Use properties of rational and irrational numbers 

Learning Targets

CPI #

Cumulative Progress Indicators (CPI) for Unit

  A.REI.B.3 

             Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

  A.REI.A.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.

  A.CED.A.4 

              Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.  

        Interpret expressions that represent a quantity in terms of its context.

  A.CED.A.1 

              Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear functions and quadratic functions, and simple rational and exponential functions.

 A.REI.A.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.

 A.CED.A.2 

              Create equations in two or more variables to represent relationships between quantities; Graph equations on coordinate axes with labels and scales.

 A.REI.D.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). [Focus on linear equations.]

 S.ID.C.7 

             Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

 S.ID.C.8 

            Compute (using technology) and interpret the correlation coefficient of a linear fit.  

 S.ID.C.9 

           . Distinguish between correlation and causation.

 A.REI.D.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.* [Focus on linear equations.]

Unit Enduring Questions:

●       How do you solve linear inequalities and equations in one variable?

 ●       What are the different parts of an expression?    ●       What is a scatter plot and what can it be used to determine?

 ●       How do you solve systems of equations?

Unit Enduring Understandings: 

• Solve linear equations and inequalities in one variable (including literal equations); justify each step in the process.
• Interpret terms, factors, coefficients, and other parts of expressions in terms of a context .
• Equations and inequalities describe relationships.
• Equations can represent real-world and mathematical problems.
• Equations represent quantitative relationships
• Scatter plots represent the relationship between two variables.
• Scatter plots can be used to determine the nature of the association between the variables.
• Linear models may be developed by fitting a linear function to approximately linear data.
• The correlation coefficient represents the strength of a linear association.
• y = f(x), y=g(x) represent a system of equations
• Systems of equations can be solved graphically  

Unit Objectives: Students will know…. 

• Literal equations can be rearranged using the properties of equality.
• how to interpret terms, factors, coefficients, and other parts of expressions in terms of a context . 
• how to create linear equations and inequalities in one variable and use them in contextual situations to solve problems.  Justify each step in the process and the solution.
• How to create linear equations in two variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
• How to represent data on a scatter plot, describe how the variables are related and use technology to fit a function to data.
• How to interpret the slope, intercept, and correlation coefficient of a data set of a linear model; distinguish between correlation and causation.
• Explain why the solutions of the equation f(x) = g(x) are the x-coordinates of the points where the graphs of the linear equations y=f(x) and y=g(x) intersect
• Find approximate solutions of f(x) = g(x), where f(x) and g(x) are linear functions, by making a table of values, using technology to graph and finding successive approximations.

Unit Objectives: Students will be able to…...

• solve linear equations with coefficients represented by letters in one variable  
• use the properties of equality to justify steps in solving linear equations
• solve linear inequalities in one variable.
• rearrange linear formulas and literal equations, isolating a specific variable.
• identify different parts of an expression, including terms, factors and constants.
• explain the meaning of parts of an expression in context.
• identify and describe relationships between quantities in word problems.
• create linear equations in one variable.
• create linear inequalities in one variable.
• use equations and inequalities to solve real world problems.
• explain each step in the solution process.
• identify and describe relationships between quantities in word problems.
• create linear equations in one variable.
• create linear inequalities in one variable.
• use equations and inequalities to solve real world problems.
• explain each step in the solution process.
• create linear equations in two variables, including those from a context.
• select appropriate scales for constructing a graph.
• interpret the origin in graphs.
• graph equations on coordinate axes, including labels and scales.
• identify and describe the solutions in the graph of an equation.
• distinguish linear models representing approximately linear data from linear. equations representing “perfectly” linear relationships.
• create a scatter plot and sketch a line of best fit.
• fit a linear function to data using technology.  
• solve problems using prediction equations.
• interpret the slope and the intercepts of the linear model in context.
• determine the correlation coefficient for the linear model using technology.
• determine the direction and strength of the linear

association between two variables.

● 

 explain the relationship between the xcoordinate of a point of intersection and the solution to the equation f(x) = g(x) for linear equations y = f(x) and y = g(x).

● 

find approximate solutions to the system by making a table of values, graphing, and finding successive approximations

Lower Cape May Regional School District  (Insert Subject/Content Area) Curriculum

Unit 2 Overview

Content Area:  Mathematics

Unit Title:  Modeling with Linear Functions, Linear Systems, & Exponential Functions  

Target Course/Grade Level: 9

Unit Summary:

In unit 2:

    . Solve linear systems of equations

· Create equations that describe numbers or relationships

· Interpret the structure of expressions

· Represent and solve equations and inequalities graphically

· Construct & compare linear & exponential models

· Interpret expressions for functions in terms of the situation

· Build a function that models a relationship between two quantities

· Understand the concept of a function and use function notation

· Interpret functions that arise in applications in terms of the context

· Analyze functions using different representations 

Learning Targets

CPI #

Cumulative Progress Indicators (CPI) for Unit

  A.CED.A.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.  

  A.REI.D.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.

  A.CED.A.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

  F.IF.A.1 

              Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

  F.IF.A.2 

       Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.  

  F.IF.A.3 

       Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.  

 A.SSE.A.1 

  Interpret expressions that represent a quantity in terms of its context

A.SSE.A.1a: Interpret parts of an expression, such as terms, factors, and coefficients.

A.SSE.A.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity.  

 F.IF.B.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.

 F.IF.B.5 

       Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

A.REI.C.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.

 F.IF.B.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

m a graph

Unit Enduring Questions:

• How do you solve a systems of equations algebraically 
• What is domain and range? 
• Are sequences functions?
• What is the rate of change of a nonlinear function?

Unit Enduring Understandings:

• Systems of equations can be solved exactly (algebraically) and approximately (graphically). 
• F(x) is an element in the range and x is an element in the domain 
• Sequences are functions, sometimes defined and represented recursively.

Sequences are functions whose domain is a subset of integers. 

• ·  Rate of change of non-linear functions varies.

Unit Objectives: Students will know….

• how to solve multi step contextual problems by identifying variables, writing equations, and solving systems of linear equations in two variables algebraically and graphically.  
• how to graph linear inequalities and systems of linear inequalities in two variables and explain that the solution to the system
• how to Explain the definition of a function, including the relationship between the domain and range.  Use function notation, evaluate functions and interpret statements in context
• how to Write linear and exponential functions given a graph, table of values, or written description; construct arithmetic and geometric sequences.
• How to write explicit expressions, recursive processes and steps for calculation from a context that describes a linear or exponential relationship between two quantities.
• How to sketch graphs of linear and exponential functions expressed symbolically or from a verbal description. Show key features and interpret parameters in context.
• properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
• Calculate and interpret the average rate of change of a function presented symbolically or as a table; estimate the rate of change from a graph.

Unit Objectives: Students will be able to…...

• identify and define variables representing essential features for the model.
• model real world situations by creating a system of linear equations.
• solve systems of linear equations using the elimination or substitution method.
• solve systems of linear equations by graphing.
• interpret the solution(s) in context.
• model real world situations by creating a system of linear inequalities given a context.
• interpret the solution(s) in context.
• use the definition of a function to determine whether a relationship is a function.
• use function notation once a relation is determined to be a function.
• evaluate functions for given inputs in the domain.
• explain statements involving function notation in the context of the problem
• create arithmetic and geometric sequences from verbal descriptions
• create arithmetic sequences from linear functions.
• create geometric sequences from exponential functions
• identify recursively defined sequences as functions.
• create linear and exponential functions given a graph, a description of a relationship, or a table of values.
• given a context, write an explicit expressions, a recursive process or steps for calculation for linear and exponential relationships
• interpret parts of linear and exponential functions in context
• given a verbal description of a relationship, sketch linear and exponential functions.
• identify intercepts and intervals where the function is positive/negative.
• interpret parameters in context.
• determine the practical domain of a function.
• compare key features of two linear functions represented in different ways.
• compare key features of two exponential functions represented in different ways.

● 

calculate the rate of change from a table of values or from a function presented symbolically

● 

 estimate the rate of change from a graph.

Lower Cape May Regional School District  (Insert Subject/Content Area) Curriculum

Unit 3 Overview

Content Area:  Mathematics

Unit Title:  Quadratic Equations, Functions & Polynomials 

Target Course/Grade Level:  9

Unit Summary:

      ·  Perform arithmetic operations on polynomials

· Understand the relationship between zeros and factors

· Interpret the structure of expressions

· Solve equations and inequalities in one variable

· Create equations that describe numbers or relationships

· Interpret functions that arise in applications in terms of the context

· Represent and solve equations and inequalities graphically

· Build a function that models a relationship between two quantities

· Construct & compare linear, quadratic, & exponential models

· Build new functions from existing functions

· Analyze functions using different representations

        -         Use properties of rational and irrational numbers

Learning Targets

CPI #

Cumulative Progress Indicators (CPI) for Unit

  A.APR.A.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.

  A.SSE.A.2 

              Use the structure of an expression to identify ways to rewrite it.

  A.REI.B.4 

 Solve quadratic equations in one variable.

A.REI.B.4a. Use 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. Derive the quadratic formula from this form.

A.REI.B.4b. 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

  A.CED.A.1 

       Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear functions and quadratic functions, and simple rational and exponential functions.  

  F.IF.B.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.  

  F.IF.B.5 

              Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

 F.IF.B.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.                  

 A.REI.D.11 

       Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*

A.APR.C.4

Prove polynomial identities and use

them to describe numerical relationships.

A.REI.C.6

Solve systems of linear equations

exactly and approximately (e.g., with graphs),

focusing on pairs of linear equations in two

variables.

Unit Enduring Questions:

 ●       What are polynomials?

 ●       How do you solve a quadratic equation?

• How do you add, subtract, and multiply polynomials?
• What are the steps for transforming a quadratic equation into vertex form?

Unit Enduring Understandings:

• Polynomials form a system analogous to the integers.  
• Polynomials are closed under the operations of addition, subtraction, and multiplication.  
• Multiple methods for solving quadratic equations
• Transforming a quadratic equation into the form (x - p)2 = q yields an equation having the same solutions

Unit Objectives:

Students will know……..

• Add, subtract, and multiply polynomials, relating these to arithmetic operations with integers.  Factor to produce equivalent forms of quadratic expressions in one variable.
• Derive the quadratic formula by completing the square and recognize when there are no real solutions.  
• Solve quadratic equations in one variable using a variety of methods (including inspection, taking square roots, factoring, completing the square, and the quadratic formula) and write complex solutions in a ± bi form
• Create quadratic equations in one variable and use them to solve problems
• Interpret key features of quadratic functions from graphs and tables.   Given a verbal description of the relationship, sketch the graph of a quadratic function, showing key features and relating the domain of the function to its graph.
• Find approximate solutions of f(x) = g(x), where f(x) is a linear function and g(x) is a quadratic function by making a table of values, using technology to graph and finding successive approximations.  

Unit Objectives:

Students will be able to…...

●       add and subtract polynomials.  

• multiply polynomials.  
• recognize numerical expressions as a difference of squares and rewrite the expression as the product of sums/differences.  
• recognize polynomial expressions in one variable as a difference of squares and rewrite the expression as the product of sums/differences.  

●    use the method of completing the square to transform a quadratic equation in x into an equation of the form (x - p)2 = q.  

• derive the quadratic formula from                (x - p)2 = q.  
• solve quadratic equations in one variable by inspection.  • solve quadratic equations in one variable by taking square roots.  
• solve quadratic equations in one variable by completing the square.  
• solve quadratic equations in one variable using the quadratic formula.
• solve quadratic equations in one variable by factoring.
• strategically select, as appropriate to the initial form of the equation, a method for solving a quadratic equation in one variable.
• write complex solutions of the quadratic formula in a ± bi form.  
• analyze the quadratic formula, recognizing the conditions leading to complex solutions (discriminant).

 ●       create quadratic equations in one variable.  • use quadratic equations to solve real world problems.  

●       interpret maximum/minimum and intercepts of quadratic functions from graphs and tables in the context of the problem.

• sketch graphs of quadratic functions given a verbal description of the relationship between the quantities.  
• identify intercepts and intervals where function is increasing/decreasing
• determine the practical domain of a function.  

• approximate the solution(x) to a system of equations consisting of a linear and a quadratic function by using technology to graph the functions, by making a table of values and/or by finding successive approximations.  

Lower Cape May Regional School District  (Insert Subject/Content Area) Curriculum

Unit 4 Overview

Content Area:  Mathematics

Unit Title:  Modeling with Statistics 

Target Course/Grade Level:  9

Unit Summary:

• Summarize, represent, and interpret data on a single count or measurement variable 
• Summarize, represent, and interpret data on two categorical and quantitative variables
• Interpret functions that arise in applications in terms of the context

Learning Targets

CPI #

Cumulative Progress Indicators (CPI) for Unit

  F.IF.B.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.

  F.IF.B.5 

       Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.  

 S.ID.B.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.

 S.ID.B.6 

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

S.ID.B.6a. Fit a function to the data (including the use of technology); use functions fitted to data to solve problems in the context of the data.  Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.  

S.ID.B.6b. Informally assess the fit of a function by plotting and analyzing residuals, including with the use of technology.  

Unit Enduring Questions:

• How do you interpret the data distribution?
• What is the definition of a standard deviation?
• What are the categorical variables?

Unit Enduring Understandings:

 ●       Appropriate use of a statistic depends on the shape of the data distribution.

 • Standard deviation  

●       Categorical variables represent types of data which may be divided into groups 

Unit Objectives:

Students will know….

• Interpret key features of functions from graphs and tables.  Given a verbal description of the relationship, sketch the graph of a function, showing key features and relating the domain of the function to its graph.  
• Summarize and interpret categorical data for two categories in two-way frequency tables; explain possible associations and trends in the data

Unit Objectives: Students will be able to…...

●       interpret maximum/minimum and intercepts of functions from graphs and tables in the context of the problem.

• sketch graphs of functions given a verbal description of the relationship between the quantities.
• identify intercepts and intervals where function is increasing/decreasing.
• determine the practical domain of a function .  

●    construct two-way frequency tables for categorical data.

• interpret joint, marginal and conditional

relative frequencies in context.

• explain possible associations between categorical data in two-way tables.  
• identify and describe trends in the data.

Lower Cape May Regional School District  (Insert Subject/Content Area) Curriculum

Evidence of Learning

Specific Formative Assessments Utilized in Daily Lessons:

• Big Ideas online assessments
• Observation
• Self-Assessment
• Exit Ticket
• Quiz
• Choral Response
• Think-Pair-Share
• Oral Questioning

Summative Assessment Utilized throughout Units:

• QBA’s
• Benchmarks:  Big Ideas Quizzes & Tests, Big Ideas online assessments

Benchmarks

• Star Math

Alternate Assessment

• Oral Exam
• Project Based Learning

Modifications for:

ELL’s-

Dictionary

Partner Work

Special Education-

Word Bank

Differentiated work

504-

Extra time

Seating close to teacher

Students at Risk of Failure-

Parent Log

Extra time to complete assignments

Gifted and Talented Students-

Cooperative Learning Groups

Modified Assignments

Differentiated Instruction

Technology:

• Students must engage in technology applications integrated throughout the curriculum.  Applicable technology utilized in this curricula are included below:
• Ti-83 Calculators
• Youtube
• Kahn Academy
• Big Ideas          

Curriculum development Resources/Instructional Materials:

List or Link Ancillary Resources and Curriculum Materials Here:

• bigideas.com
• kahnacademy.com

Board of Education Approved Text(s)

●       Big Ideas Algebra