Orange Board of Education ___________________ Web viewOrange Board of Education Algebra I (Subject and Grade) ... interpret P(1+r) ... Create linear expressions and equations in one

Orange Board of Education Algebra I Curriculum Guide

Unit I:

Topic: Relationships Between Quantities and Reasoning with Equations

Skills:* Interpret parts of an expression and equation (linear and non-

linear), such as terms, factors, and coefficients* Interpret complicated expressions by viewing one or more of parts

as a single entity. For example, interpret P(1+r)ⁿ as the product of P and a factor not depending on P.

* Apply ratio table to solve problems* Apply Factor Product relationships to solve problems* Create linear expressions and equations in one variable* Use distance formula to solve problems* Understand properties of equality* Solve multi-step equations and justify each step in the process and

the solution by using properties of equality* Rearrange formulas to highlight a quantity of interest, use the same

reasoning in solving equation (including solve literal equations)* Solve literal equations* Interpret formulas into meaningful parts* Use properties such as the commutative/distributive properties to

understand formulas of equivalent forms* Create equations, inequalities, and system of linear

equations/inequalities in two or more variables to represent relationships between quantities

* Graph equations/inequalities, system of equations on coordinate axes with labels and scales.

* Use graph to find the solutions of system of linear equations* Solve system of linear equations graphically

Projected # of days:28 days

Orange Board of Education Algebra I (Subject and Grade)

Unit 2:

Topic: Linear Relationships Skills:* Graph equations, inequalities , and systems of inequalities in two variables.* Explain the meaning of solution on the graph for an equation, inequalities, and system of inequalities.* Form equivalent equations.* Convert linear equation from slope-intercept from to standardform.* Solve system of linear equation algebraically.* Find approximate solutions of linear equations by table of value* Use technology to graph and approximate the solution.* Explain and interpret the definition of function including domain and range and how they are related.* Use function notation in a context and evaluate functions for inputs and their corresponding outputs.* Graph functions by hand and with technology.* Use functions to describe linear relationships between two quantities.* Identify, describe, and compare domain and other key features of a function in one or multiple representations.*Define appropriate domain for a function* Compare properties of two or more functions each represented in a different way (algebraically, graphically, numerically in tables, or by descriptions)* Identify arithmetic and geometric sequence.* Create a function for a geometric sequence whose domain is a subset of the integers.

Projected # of days :25 days


Cycle 3:

Topic: expressions and Equations Skills* Create a linear equation for a set of data on a table* Create a linear equation for the situation given* Interpret parts of the equation in terms of a context given* Create a linear inequality for a situation given* Interpret parts of the inequality in terms of the context given* Form exponential growth/decay function* Identify exponential growth/decay factor and growth/decay rate* Interpret parts of the exponential function in terms of the context* Identify different types of polynomial* Perform addition, subtraction and multiplication with polynomial* Factor polynomial and use Zero property to solve equations* Identify quadratic functions from tables, graphs, or equations* Graph quadratic functions* Identify vertex, y-intercept, x-intercept on a quadratic graph* Create quadratic equations by using vertex form* Solve quadratic equations by using factoring, completing the square* Use discriminant formula to decide how many real solution a quadratic equation has.* Use quadratic formula to solve quadratic equations

Projected # of days 27 days


Cycle 4:

Topic: Quadratic Functions and Modeling Skills* Identify zero of polynomials* Apply the concept of zero of polynomial to sketch the graph* Create equivalent quadratic equation in standard from, vertex

form, or factor form* Sketch a quadratic function graph showing key features (including

intercepts, minimums/maximums, domain, range)* Use graphing calculator to graph a quadratic function and

approximate intercepts, minimums/maximums from the graph* Compare properties of two functions each represented in a

different way (algebraically, graphically, numerically in tables, or by verbal descriptions)

* Calculate (over a specified period if presented symbolically or as a table) or estimate (if presented graphically) and interpret the average rate of change of a function.

* Using graphs and tables to compare linear, quadratic, and exponential models

* Create a function (linear, exponential, or quadratic) to model a real-live problem.

* Identify rational and irrational numbers in a real number system* Use the properties of rational and irrational numbers to explain

why the sum or product of two rational/irrational numbers is a rational/irrational number.

* Use properties of exponent operation to solve problems* Convert expressions between radicals and rational exponents* Translation functions (f(x) + k, kf(x), f(kx), and f(x+k)) on a graph.



Unit 5:


Topic:Functions and Descriptive Statistics

Skills* Create linear and exponential functions (growth/decay and arithmetic and geometric sequences) from graphs and tables.* Describe the relationship between two quantities with an explicit formula, and how quantities increase linearly and exponentially over equal intervals.* Create a scatter plot to represent and describe data for two variables.* Create a function (emphasize linear and exponential models) to fit a scatter plot data, and use the function to solve problems.* Use a graphing calculator to create a scatter plot and interpret the slope, intercept and correlation coefficient of a linear model.* Distinguish between correlation and causation in a data context* Summary and interpret categorical data for two categories in a two- way frequency table.* Analyze the trends in the data and recognize associations from a two-way frequency table.* Create a histogram for the data given.* Use center tendency to compare and interpret the shape, center, and spread in the content from a histogram.* Create side-by-side box of whisker plots and compare the shape, center and spread in the content for the plots.* Analyze the effects of outliers for the data given* Analyze the distribution of the data from a box plot and a histogram.*Calculate the standard deviation of a data set.*Use standard deviation of a data set to fit it to a normal distribution.* Use normal distribution model to estimate population percentages* Use calculators, spreadsheets, and tables to estimate areas under the normal curve.



Unit 1 : Relationships Between Quantities and Reasoning with Equations

Goal(s)(NJCCCS and CCSS):HSN.Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.HSN.Q.2: Define appropriate quantities for the purpose of descriptive modeling.HSN.Q.3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.HSA.SSE.A1a:Interpret parts of an expression, such as terms, factors, and coefficients. 1b:Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as he product of P and a factor not depending on P.HSA.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.HSA.CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.HSA.CED.3:Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.HSA.CED.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.HSA.REI.3:Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Essential Questions:1. How do mathematical ideas interconnect and build on one another to produce a coherent whole?2. How can we use mathematical models to describe physical relationships?3. How can we use physical models to clarify mathematical relationships?


Skills/Knowledge/Understandings:Understanding:*concept of expressions, equations, and inequalities*the properties of equalitySkills: SWBAT*use ratio table to solve real life problems*interpret the meaning of each part of an expression, an equations, and an inequalities.*create expressions, equations, inequalities and system of equations/inequalities to model real life situations*solve multi-step equations (including literal equations) and justify each step of procedure by using properties of equality.*graph equations, inequalities on a coordinate graph*represent a relationship between two quantities by using graph, table, or algebraic symbols.* solve system of linear equations/inequalities by using graphObjectives:1. Given formulas, equations, and inequalities, students can interpret the meaning of each part of formula, equations, and inequalities with at

least 85% accuracy.2. Given real life situations, students can model the context by using tables, graphs, or algebraic equations/inequalities and solve the problems with at least 85% accuracy.3. Given equations (multi-step, and literal equations), students can solve them, reasoning each-step of procedure by using properties of equality, and justify if the solutions are viable or non-viable proficiently with at least 85% accuracy.Assessments:Formative: * daily do now * daily exit ticket *class work *class discussion * homework *bi-weekly department wide assessment *Diagnostic assessmentSummative:* CCSS Model curriculum unit assessments

Authentic: Phone Plan Project

Literacy Connections:*All students will write in clear, concise, organized language that varies in content and form for different audiences and purpose.*All students will pose questions in mathematics, sequence events in a situation given, and develop recording skills in class activities.*All students will construct charts and graphs to illustrate or determine the impact of details in real life problems.*All students will interpret the numbers on each term of an equation into meaningful context in a real life situation.


Interdisciplinary Connections:NJ World Class Standards: (21st-Century Life and Careers)9.2 Personal Financial Literacy: All students will develop skills and strategies that promote personal and financial responsibility related to financial planning, savings, investment, and charitable giving in the global economy. 9.2.12.A.6 Analyze and critique various sources of income and available resource.NJ World Class Standards: (Science)5.2: Physical Science: All students will understand that physical science principles, including fundamental ideas about matter, energy, and motion, are powerful conceptual tools for making sense of phenomena in physical, living, and Earth systems science. 5.2.8.E.1: Calculate the speed of an object when given distance and time. 5.2.12.E.1: Compare the calculated and ,measured speed, average speed, and acceleration of an object in motion, and account for differences that may exist between calculated and measured values.NJCCCS (Language Art Literacy) 3.1.12.E.1: Assess, and apply reading strategies that are effective for a variety of texts (e.g., previewing, generating questions, visualizing, monitoring, summarizing, evaluating). 3.1.12.E.3.: Analyze the ways in which a text’s organizational structure supports or confounds its meaning or purpose.Technology Integration:1. Smart Board, Smart Response2. TI-84 plus calculator3. Carnegie learning Tutorial https://2013.carnegielearning.com/2013.05.39/auth/login2013.html?1550Nav=%257c&NodeID=517Key Vocabulary:*dependency, *dependent variable, *independent variable, *coefficient, *linear equation, *non-linear equation, *properties of equality*literal equation, *inequalities, *x-intercept, *y-intercept, *solution, *system of linear equations, *exponential equation, *unit rate*distributive property, *commutative property, *like terms, *point of intersection,Useful Sites:PMI https://njctl.org/what-is-psi-pmi/theisland https://hs.studyisland.com/?1550Nav=I&NodeID=413Yourteacher www.mathhelp.com/algebra-1-tutoring.phpKHANACADEMY https://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/systems-word-problems/v/algebraic-word-problem#1Algebra-class.com www.algebra-class.com/algebra-made-easy.htmlIXL www.ixl.com/math/algebra-1CCSS Math Resource ccssmath.ore


Primary Documents:

Text Crosswalk: (Carnegie Common Core Algebra I)Lesson 1.1 (p 4 - 16)Lesson 2.1 - 2.6 (p 74 - 148)Lesson 3.1- 3.3 (p 167 -194)Lesson 4.1 (p 214 - 221)Lesson 4.3 (p 236 - 242)Lesson 5.1 - 5.2 (p 296 - 308)

*Differentiation: www.marzanoresearch.com/free_resources/itembank.aspx


Unit 2: Linear RelationshipsGoal(s)(NJCCCS and CCSS):HSA.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.HSA.REI.6:Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.HSA.REI.10:Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).HSA.REI.11:Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.HSA.REI.12:Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.HSF.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).HSF.IF.2:Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.HSF.IF. 3:Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1 .HSF.BF.2:Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.HSF.IF.5:Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.HSF.IF.7:Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. 7a:Graph linear and quadratic functions and show intercepts, maxima, and minima.HSF.IF.9:Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the


Essential Questions:1. How can we decide when to use an exact answer and when to use an estimate?2. How can patterns, relations, and functions be used as tools to best describe and help explain real-life situations?3. How are patterns of change related to the behavior of functions?Skills/Knowledge/Understandings:Understanding:*the concept of the solution of linear inequalities*the concept and definition of a function*the concept of the domain and range of a functionSkills:SWBAT* graph equations and system of inequalities* explain the meaning of solution* create equivalent equations* convert linear equations into different form* solve system of linear equation algebraically* identify function and relationship* use function notation to represent the relationship between two quantities* decide appropriate domain of a function to model a real life situation* compare functions which are in different representation* write functions to represent arithmetic and geometric sequences

Objectives:*Given a real-life situation, students can create equations or system of inequalities, solve them graphically and algebraically, and explain the meaning of solution in the context with at least 85% accuracy.*Given a real-life situation, students can create a function in function notation, and define a reasonable domain with at least 85% accuracy.*Given two or more functions each represented in a different way, students can compare the properties of each function proficiently.Assessments:Formative: * daily do now * daily exit ticket *class work *class discussion * homework *bi-weekly department wide assessment *Diagnostic assessmentSummative:* CCSS Model curriculum unit assessments

Authentic: The Big Race Exhibition (Algebra, Representations)


Literacy Connections:*All students will write in clear, concise, organized language that varies in content and form for different audiences and purpose.*All students will construct charts and graphs to illustrate or determine the impact of details in a real life problems.*All students will use comparing and contrasting skills to articulate the feature of different functions.Interdisciplinary Connections:NJCCCS (Language Arts Literacy) 3.1.12.A.1 Interpret and use common textual features (e.g., paragraphs, topic, sentence, index, glossary, table of contents) and graphic features (e.g., charts, maps, diagrams) to comprehend information. 3.1.12.E.1: Assess, and apply reading strategies that are effective for a variety of texts (e.g., previewing, generating questions, visualizing, monitoring, summarizing, evaluating). 3.1.12.E.3.: Analyze the ways in which a text’s organizational structure supports or confounds its meaning or purpose.Technology Integration:Technology Integration:1. Smart Board, Smart Response2. TI-84 plus calculator3. Carnegie learning Tutorial https://2013.carnegielearning.com/2013.05.39/auth/login2013.html?1550Nav=%257c&NodeID=517Key Vocabulary:*function, *domain, *range, *function notation, *arithmetic sequence, *geometric sequence, *slope, *real number, *integer, *elimination,*substitution, *ordered pair, *infinite solution, *solution set, *boundary,*maximum, *minimum,*recursive function. *equivalent equations,* Absolute value rateUseful Sites:PMI https://njctl.org/what-is-psi-pmi/theisland https://hs.studyisland.com/?1550Nav=I&NodeID=413Yourteacher www.mathhelp.com/algebra-1-tutoring.phpKHANACADEMY https://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/systems-word-problems/v/algebraic-word-problem#1Algebra-class.com www.algebra-class.com/algebra-made-easy.htmlIXL www.ixl.com/math/algebra-1CCSS Math Resource ccssmath.orePrimary Documents:


Text Crosswalk: (Carnegie Common Core Algebra I)Lesson 1.2 - 1.4 (p 32 - 61) Lesson 6.2 - 6.3 (p 384 - 397)Lesson 2.1 - 2.2 (p79 - 100) Lesson 7.1 - 7.4 (412 - 446)Lesson 2.6 (p138 - 148) Lesson 15.1 - 15.2 (p 878 - 894)Lesson 4.3 (p235 - 250)Lesson 4.5 (p 276 - 285)Lesson 5.1 -5.2 (p 295 - 309)



Unit 3: Expressions and EquationsGoal(s)(NJCCCS and CCSS):HSA.SSE.1: Interpret expressions that represent a quantity in terms of its context 1a:Interpret parts of an expression, such as terms, factors, and coefficients. 1b: 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.HSA.SSE.2:Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).HSA.SSE.3:Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. 3a:Factor a quadratic expression to reveal the zeros of the function it defines. 3b:Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines 3c:Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.HSA.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.HSA.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.HSA.CED.2:Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.HSA.CED.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.HSA.REI.4:Solve quadratic equations in one variable. 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. 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.


Essential Questions:1. What makes an algebraic algorithm both effective and efficient?2. How do mathematical representations reflect the needs of society across cultures?3. How can we use mathematical model to describe non-linear change in real life situation?Skills/Knowledge/Understandings:Understanding:*the difference between linear and non-linear functions*the definition of different types of polynomials* the meaning of “zero” of a polynomial* zero product property* what is a quadratic function* the meaning of vertex, intercepts on a quadratic graph*what is the discriminant formula for a quadratic equationSkills: SWBAT* create linear equations from a table, graph, and a situation given* apply linear inequality to model a real-life situation* apply exponential function to model the situation given* operate polynomials in addition, subtraction, and multiplication* create and graph quadratic equation* interpret vertex, intercepts of a quadratic graph in terms of context* decide number of solution of a quadratic function by using discriminant formula* solve quadratic function by using quadratic formula

Objectives:* Given a table, graph, or a situation, students will apply a linear or non-linear mathematical model to represent the data or situation, and use variety of methods to solve the problems with at least 85% accuracy.* Given a couple set of polynomial, students will operate them in addition, subtraction, and multiplication and display the combined polynomial in standard form with at least 85% accuracy.* Given expresses, students will manipulate expression using factoring, completing the square and properties of exponents to produce equivalent forms that highlight particular properties such as zeros of the maximum or minimum of the function.


Assessments:Formative: * daily do now * daily exit ticket *class work *class discussion * homework *bi-weekly department wide assessment *Diagnostic assessmentSummative:* CCSS Model curriculum unit assessments

Authentic: Project: Two ways tripling a tree’s height in four years

Literacy Connections:*All students will write in clear, concise, organized language that varies in content and form for different audiences and purpose.*All students will construct charts and graphs to illustrate or determine the impact of details in a real life problems.*All students will use comparing and contrasting skills to articulate the feature of different functions.*All students will examine story for patterns and then predict or hypothesize the theme, climax and conclusion.Interdisciplinary Connections:NJ World Class Standards: (21st-Century Life and Careers)Money management involves setting financial goals. 9.2.12.B.1: Prioritize financial decisions by systematically considering alternatives and possible consequence. 9.2.12.B.2: Compare strategies for saving and investing and the factors that influence how much should be saved or invested to meet financial goals. 9.2.12 B.9.: Chart and evaluate the growth of mid- and long-term investments.NJ World Class Standards: (Science)5.2: Physical Science: All students will understand that physical science principles, including fundamental ideas about matter, energy, and motion, are powerful conceptual tools for making sense of phenomena in physical, living, and Earth systems science. 5.2.12.E.4: Measure and describe the relationship between the force acting on an object and the resulting acceleration.NJCCCS (Language Arts Literacy) 3.1.12.A.2: Identify interrelationships between and among ideas and concepts within a text, such as cause-and-effect relationships. 3.1.12.E.1: Assess, and apply reading strategies that are effective for a variety of texts (e.g., previewing, generating questions, visualizing, monitoring, summarizing, evaluating). 3.1.12.E.3.: Analyze the ways in which a text’s organizational structure supports or confounds its meaning or purpose.Technology Integration:Technology Integration:1. Smart Board, Smart Response2. TI-84 plus calculator3. Carnegie learning Tutorial https://2013.carnegielearning.com/2013.05.39/auth/login2013.html?1550Nav=%257c&NodeID=517


Key Vocabulary:*exponential growth, *growth factor, *growth rate, * exponential decay, *decay factor, *decay rate, * polynomial, *monomial, *degree of monomial, * binomial, *trinomial, *quadratic, *cubic, * FOIL pattern, *area model, *zero-product property, “factored form, “perfect square,*radicand, *quadratic equation, *leading coefficient, *parabola, *vertex, *axis of symmetry, *roots of a quadratic equation, *discriminant,Useful Sites:PMI https://njctl.org/what-is-psi-pmi/theisland https://hs.studyisland.com/?1550Nav=I&NodeID=413Yourteacher www.mathhelp.com/algebra-1-tutoring.phpKHANACADEMY https://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/systems-word-problems/v/algebraic-word-problem#1Algebra-class.com www.algebra-class.com/algebra-made-easy.htmlIXL www.ixl.com/math/algebra-1CCSS Math Resource ccssmath.orePrimary Documents:

Text Crosswalk:Lesson 5.5 - 5.6 (p337 - 354)Lesson 11.1 - 11.4 (p 618 - 652)Lesson 12.1 - 12.7 (p703 - 778)Lesson 13.1 - 13.2 (p 789 - 812)Lesson 14.4 ( p 859 - 868)Lesson 15.1 (p 914 - 920)



Unit 4:Quadratic Functions and ModelingGoal(s)(NJCCCS and CCSS):HSA.APR.3:Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.HSN.RN.1:Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.HSN.RN.2:Rewrite expressions involving radicals and rational exponents using the properties of exponents.HSN.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.HSF.IF.4:For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicityHSF.IF.5:Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the functionHSF.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.HSF.IF.7:Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases 7a:Graph linear and quadratic functions and show intercepts, maxima, and minima. 7b:Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.HSF.IF.8:Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 8a:Use 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.HSF.IF.9:Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.


HSF.BF.1:Write a function that describes a relationship between two quantities. 1a: Determine an explicit expression, a recursive process, or steps for calculation from a context.HSF.BF.3:Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x),f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.HSF.LE.3:Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.HSF.LE.5:Interpret the parameters in a linear or exponential function in terms of a context.Essential Questions:1. How can we best represent and verify geometric/algebraic relationships?2. How do geometric relationships help to solve problems and/or make sense of phenomena?3. How can change be best represented mathematically?4. How can we model situation using exponents and quadratics?Skills/Knowledge/Understandings:Understandings:* the different forms of a quadratic equation (standard form, vertex form, and factor form) are equivalent* the meaning of average rate of change* the real number system* rational numbers and irrational numbers* properties of rational and irrational numbers* radicals and rational exponents* parent functionSkills: SWBAT* use zero of polynomials to sketch the graph.* convert quadratic equations into different forms* estimate the intercepts, minimums or maximum of a quadratic function by using graphing calculators* compare functions which display in different representation.* calculate average rate of change* interpret average rate of change in terms of context* write a number in radical or rational exponent* identify the graph after a parent function translated in a specific rule.


Objectives:* Using zero of polynomials, students will sketch a polynomial or a quadratic equation to show key features of the equations with at least 85% accuracy.* Given linear or non-linear function which represented in different ways, students will compare and analyze each function and list at least two key features of the functions.* Give a parent function and a rule of translation, student will identify or create the image graph on a coordinate graph with at least 85% accuracy.

Assessments:Formative: * daily do now * daily exit ticket *class work *class discussion * homework *bi-weekly department wide assessment *Diagnostic assessmentSummative:* CCSS Model curriculum unit assessments

Authentic: Project: * Modeling the World * Water Balloon ContestLiteracy Connections:*All students will write in clear, concise, organized language that varies in content and form for different audiences and purpose.*All students will construct charts and graphs to illustrate or determine the impact of details in a real life problems.*All students will use comparing and contrasting skills to articulate the feature of different functions.*All students will examine story for patterns and then predict or hypothesize the theme, climax and conclusion.Interdisciplinary Connections:NJ World Class Standards: (Science)5.2: Physical Science: All students will understand that physical science principles, including fundamental ideas about matter, energy, and motion, are powerful conceptual tools for making sense of phenomena in physical, living, and Earth systems science. 5.2.12.E.4: Measure and describe the relationship between the force acting on an object and the resulting acceleration.NJCCCS (Language Art Literacy) 3.1.12.E.1: Assess, and apply reading strategies that are effective for a variety of texts (e.g., previewing, generating questions, visualizing, monitoring, summarizing, evaluating). 3.1.12.E.3.: Analyze the ways in which a text’s organizational structure supports or confounds its meaning or purpose.


Technology Integration:1. Smart Board, Smart Response2. TI-84 plus calculator3. Classroom computer learning station4. Carnegie learning Tutorial https://2013.carnegielearning.com/2013.05.39/auth/login2013.html?1550Nav=%257c&NodeID=517Key Vocabulary:

* zero of function, *root, * number system, * rational number, *irrational number, * real number, *real solution, *maximum value,* *minimum value, *leading coefficient, * rate of change, *vertex form, * standard form of quadratic equation, * translation, *reflection,* transformation, *parent function, *zero exponent, * negative exponent, * reciprocal, *product of power, * power of product, *power of

power property, *growth factor, *growth rate, *decay rate, *decay factor, * radical expression, * radical, * simplest form of a radical expression, * product property of radicals, * quotient property of radicals,

Useful Sites:PMI https://njctl.org/what-is-psi-pmi/theisland https://hs.studyisland.com/?1550Nav=I&NodeID=413Yourteacher www.mathhelp.com/algebra-1-tutoring.phpKHANACADEMY https://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/systems-word-problems/v/algebraic-word-problem#1Algebra-class.com www.algebra-class.com/algebra-made-easy.htmlIXL www.ixl.com/math/algebra-1CCSS Math Resource ccssmath.orePrimary Documents:

Text Crosswalk:Lesson 4.2 (p 224 - 234)Lesson 4.4 (p 252 - 274)Lesson 5.5 (p 337 - 346)Lesson 11.6 (p 662 - 637)Lesson 12. 5 - 12.7 (p 751 - 778)



Unit 5: Functions and Descriptive StatisticsGoal(s)(NJCCCS and CCSS):HSS.ID.1:Represent data with plots on the real number line (dot plots, histograms, and box plots).HSS.ID.2:Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.HSS.ID.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).HSS.ID.4:Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.HSS.ID.5:Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.HSS.ID.6:Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. 6a:Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. 6b:Informally assess the fit of a function by plotting and analyzing residuals. 6c:Fit a linear function for a scatter plot that suggests a linear association.HSS.ID.7:Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.HSS.ID.8:Compute (using technology) and interpret the correlation coefficient of a linear fit.HSS.ID.9:Distinguish between correlation and causation.HSF.LE.1:Distinguish between situations that can be modeled with linear functions and with exponential functions. 1a:Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. 1b:Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. 1c:Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.HSF.LE.2:Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).HSF.LE.3:Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.


Essential Questions:1. How can the collection, organization, interpretation, and display of data be used to answer questions?2. How can we compare and contrast data?3. How can the representation of data influence decision?Skills/Knowledge/Understandings:Understanding:* the usage of a two-way frequency table* the difference of negative correlation, positive correlation, and no correlation in graphs* the difference between correlation and causation* the meaning of normal distribution* the concept of standard deviationSkills:* compare functions over equal intervals* create a scatter plot for the data given* find the line of best fit* use the line of best fit to predict data* Distinguish correlation and causation* find the correlation coefficient* use two-way frequency table to analyze data* create histogram and box-and-whisker plot (including side-by-side box plot)* analyze the effect of outlier in a set of data* use the normal distribution to predict or analyze data* find the standard deviation of the set of data givenObjectives:*Given a set of data of two quantities, students will create a scatter plot and find the mathematical model to represent the data, and use the model to analyze the relationship (correlation ) and trend of the data and predict the possible data not on the given.* Given a set of data, students will represent data on a histogram, or box plot and compare the interpret differences in shape, center, and spread in the context of the data.* Given a set of data, students will use the standard deviation of the data to fit it to a normal distribution and estimate population percentages.


Assessments:Formative: * daily do now * daily exit ticket *class work *class discussion * homework *bi-weekly department wide assessment *Diagnostic assessmentSummative:* CCSS Model curriculum unit assessments, Final Examination, Post test

Authentic:

Literacy Connections:* All students will validate or persuade, use data or details to determine and support a particular position.* All students will confer with others to generate new knowledge or to confirm a position on a topic.* All students will write in clear, concise, organized language that varies in context and form for different audiences and purpose.Interdisciplinary Connections:NJ World Class Standards: (Technology)8.1 Educational Technology: All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problems individually and collaboratively and to create and communicate knowledge. 8.1.12. A. : Construct a spreadsheet, enter data, and use mathematical or logical functions to manipulate data, generate charts and graphs, and interpret the results.NJCCCS (Language Art Literacy) 3.1.12.E.1: Assess, and apply reading strategies that are effective for a variety of texts (e.g., previewing, generating questions, visualizing, monitoring, summarizing, evaluating). 3.1.12.E.3.: Analyze the ways in which a text’s organizational structure supports or confounds its meaning or purpose.Technology Integration:1. Smart Board, Smart Response2. TI-84 plus calculator3. Classroom computer learning station4. Carnegie learning Tutorial https://2013.carnegielearning.com/2013.05.39/auth/login2013.html?1550Nav=%257c&NodeID=517Key Vocabulary:arithmetic sequence, geometric sequence, interval, scatter plot, residuals, line of best fit, correlation, causation, correlation coefficient,frequency table, two-way frequency table, trend of data, histogram, box-and-whisker plot, side-by-side box plot, median, mean, mode, lower quartile, upper quartile, minimum, maximum, inter quartile range, outlier, standard deviation, normal distribution, bell distribution


Useful Sites:PMI https://njctl.org/what-is-psi-pmi/theisland https://hs.studyisland.com/?1550Nav=I&NodeID=413Yourteacher www.mathhelp.com/algebra-1-tutoring.phpKHANACADEMY https://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/systems-word-problems/v/algebraic-word-problem#1Algebra-class.com www.algebra-class.com/algebra-made-easy.htmlIXL www.ixl.com/math/algebra-1CCSS Math Resource ccssmath.orePrimary Documents:

Text Crosswalk:Lesson 8.1 - 8.5 (p 456 - 511)Lesson 9.1 - 9.3 (p 524 - 551)Lesson 9.6 (p 564 - 567)Lesson 10.1 - 10.4 (p 580 - 608)
