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CITY OF BURLINGTON PUBLIC SCHOOL DISTRICT CURRICULUM Revision Date: August 2016

Submitted by: Kaitlyn Rauchut

CCR Math 9

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Table of Contents

Topic Page Overview 3

Common Core Standards for High School Mathematics 5

Course Proficiencies 11

21st Century Skills and Themes 13

Scope and Sequence 14

Standards Overview: Student Learning Objectives, Activities, and Resources

Unit 1 33

Unit 2 37

Unit 3 41

Unit 4 44

Unit 5 49

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COURSE OVERVIEW

Algebra I is associated with high school content standards within four conceptual categories: Number & Quantity, Algebra, Functions, and Statistics & Probability. Each conceptual category contains domains of related clusters of standards. CCR 9 is designed to provide students with tools to help them master topics found in Algebra I. This course will address topics in Operations and Linear Equations, Inequalities, Linear Functions and Data. The scope and sequence is designed in conjunction with the Common Core State Standards providing a consistent and clear understanding of what students are expected to learn. The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully prepared for the future, our communities will be best positioned to compete successfully in the global economy. The curriculum guide has been generated to not only help students achieve the Common Core State Standards, but to ensure that students will be prepared for college and career opportunities following high school graduation. Many of the concepts presented in Algebra I are progressions of the concepts that were started in grades 6 through 8; the content presented in this course is intended to extend and deepen the previous understandings. Unit 1 begins with setting the stage for work with expressions and equations through understanding quantities and the relationships between them. The work in unit 2 will build on the grade 8 concepts for linear and exponential relationships. Success in unit 2 will lay the groundwork for later units where the students will extend this knowledge to quadratic and exponential functions. The standards included in unit 3 blend the conceptual understandings of expressions and equations with procedural fluency and problem solving. The students will not encounter solutions of quadratic equations that are complex. The standards presented in unit 4 involve functions and extending the concepts of integer exponents to concepts of rational exponents. The understandings will be applied to other types of equations in future courses. Unit 5 will build on previous work with descriptive statistics. Linear models will be used to assess how a model fits data. . Primary Resource(s) Textbook Title: Algebra 1 Common Core Publisher: Pearson Education, Inc. Copyright: 2012 Supplemental/Other Common Core Coach Algebra 1, 1st Edition- Triumph Learning

National Council of Teachers of Mathematics http://www.nctm.org/standards/content.aspx?id=3874

SAT – College Board http://sat.collegeboard.com/practice/sat-subject-test-preparation/mathematics-level-1

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Purplemath--www.purplemath.com/modules/ Shmoop.com Prealgebra-www.shmoop.com/pre-algebra Algebra2goTM Beginning Algebra- www.saddleback.edu/faculty/lperez/algebra2go/begalgebra/ HippoCampus- www.hippocampus.org Algebra lessons—Interactive Mathematics- www.intmath.com Virtual Nerd- virtualnerd.com MathTV.com- www.mathtv.com Khan Academy- www.khanacademy.org Dynamic Algebra Explorations- math.kendallhunt.com/x19172.html This curriculum will also employ devices as developed by City of Burlington School District Mathematics Committee. The problem solving model UMAR is shown below and will be used to enable students to maximize the Common Core Mathematics Practices.

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Common Core Standards for High School Mathematics

Mathematics – High School Number & Quantity The Real Number System (N-RN) B. Use properties of rational and irrational numbers. N-RN.B.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. Quantities (N-Q) A. Reason quantitatively and use units to solve problems. N-Q.A.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. N-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. PARCC: In Algebra I, this standard will be assessed by ensuring that some modeling tasks (involving Algebra I content or securely held content from grades 6-8) require the student to create a quantity of interest in the situation being described. N-Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Mathematics – High School Algebra Seeing Structure in Expressions (A-SSE) A. Interpret the structure of expressions. A-SSE.A.1 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. PARCC: Tasks limited to numerical and polynomial expressions in one variable. Recognize 532-472 as a difference of squares and see an opportunity to rewrite it in the easier-to -evaluate form (53+47)(53-47). See an opportunity to rewrite a2+9a+14 as (a+7)(a+2). B. Write expressions in equivalent forms to solve problems. A-SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

a. Factor quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the max and min value of the function it defines.

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c. Use the properties of exponents to transform expressions for exponential functions.

PARCC: Tasks are limited to exponential expressions with integer exponents. Tasks have a real-world context. As described in the standard, there is an interplay between the mathematical structure of the expression and the structure of the situation such that choosing and producing an equivalent form of the expression reveals something about the situation. Arithmetic with Polynomials and Rational Expressions (A-APR) A. Perform arithmetic operations on polynomials. 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. B. Understand the relationship between zeros and factors of polynomials. A-APR.B.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. PARCC: Tasks are limited to quadratic and cubic polynomials in which linear and quadratic factors are available. Creating Equations (A-CED) A. Create equations that describe numbers or relationships. A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple radical and exponential functions. PARCC: Tasks are limited to linear, quadratic, or exponential equations with integer exponents. 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-CED.A.3 Represent 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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 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. Reasoning with Equations and Inequalities (A-REI) A. Understand solving equations as a process of reasoning and explain the reasoning. 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. PARCC: Tasks are limited to quadratic equations. B. Solve equations and inequalities in one variable. A-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. A-REI.B.4 Solve quadratic equations in one variable.

a. 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.

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b. Solve quadratic equations by inspection (e.g., for x2=49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a + bi, a - bi for real numbers a and b.

PARCC: Tasks do not require students to write solutions for quadratic equations that have roots with non-zero imaginary parts. However, tasks can require the student to recognize cases in which a quadratic equation has no real solutions.

C. Solve systems of equations. 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. 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. PARCC: Tasks have a real-world context. Tasks have hallmarks of modeling as a mathematical practice (less defined tasks, more of the modeling cycle, etc.). D. Represent and solve equations and inequalities graphically. 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). 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. PARCC: Tasks that assess conceptual understanding of the indicated concept may involve any of the function types mentioned in the standard except exponential and logarithmic functions. Finding the solutions approximately is limited to cases where f(x) and g(x) are polynomial functions. 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 Mathematics - High School Functions Interpreting Functions (F-IF) A. Understand the concept of a function and use function notation. 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. 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. PARCC: This standard is part of the Major work in Algebra I and will be assessed accordingly. B. Interpret functions that arise in applications in terms of the context. 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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity PARCC: Tasks have a real-world context. Tasks are limited to linear functions, quadratic functions, square root functions, cube root functions, piece-wise defined functions (including step functions and absolute value functions) and exponential functions with domains in the integers.

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F-IF.B.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. 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. PARCC: Tasks have a real-world context. Tasks are limited to linear functions, quadratic functions, square root functions, cube root functions, piece-wise defined functions (including step functions and absolute value functions) and exponential functions with domains in the integers. C. Analyze functions using different representations. F-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. F-IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. 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. F-IF.C.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. PARCC: Tasks are limited to linear functions, quadratic functions, square root, cube root, piecewise defined (including step functions and absolute value functions), and exponential functions with domains in the integers. Building Functions (F-BF) A. Build a function that models a relationship between two quantities. F-BF.A.1 Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context. PARCC: Tasks have a real-world context. Tasks are limited to linear, quadratic and exponential functions with domains in the integers. B. Build new functions from existing functions. F-BF.B.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. PARCC: Identifying the effect on the graph of replacing f(x) by f(x) +k, kf(x), and f(x+k) for specific values of k (both positive and negative) is limited to linear and quadratic functions. Experimenting with cases and illustrating an explanation of the effects on the graph using technology is limited to linear functions, quadratic functions, square root functions, cube root functions, piecewise-defined functions (including step functions and absolute value functions), and exponential functions with domains in the integers. Tasks do not involve recognizing even and odd functions. Linear, Quadratic, and Exponential Models (F- lve problems. F-LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.

a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

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c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. F-LE.A.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). PARCC: Tasks are limited to constructing linear and exponential functions in simple context (not multi-step). F-LE.A.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. B. Interpret expressions for functions in terms of the situation they model. F-LE.B.5 Interpret the parameters in a linear or exponential function in terms of a context. PARCC: Tasks have a real-world context. Exponential functions are limited to those with domains in the integers. High School - Statistics & Probability Interpreting categorical and quantitative data (S-ID) A. Summarize, represent, and interpret data on a single count or measurement variable. S-ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). S-ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (inter-quartile range, standard deviation) of two or more different data sets. S-ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). B. Summarize, represent, and interpret data on two categorical and quantitative variables. 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.

a. 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.

PARCC: Tasks have real world context. Exponential functions are limited to those with domains in the integers. b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a linear function for a scatter plot that suggests a linear association.

C. Interpret linear models. 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.

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Fluency Recommendations The PARCC Model Content Frameworks recommend the following fluencies for Algebra I students: A/G Algebra I students become fluent in solving characteristic problems involving the analytic geometry of lines, such as writing down the equation of a line given a point and a slope. Such fluency can support them in solving less routine mathematical problems involving linearity, as well as in modeling linear phenomena (including modeling using systems of linear inequalities in two variables). A-APR.A.1 Fluency in adding, subtracting, and multiplying polynomials supports students throughout their work in algebra, as well as in their symbolic work with functions. Manipulation can be more mindful when it is fluent. A-SSE.A.1b Fluency in transforming expressions and chunking (seeing parts of an expression as a single object) is essential in factoring, completing the square, and other mindful algebraic calculations. Standards for Mathematical Practice The Standards for Mathematical Practice form an important part of the Algebra I course, as well: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

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COURSE PROFICIENCIES In accordance with district policy as mandated by the New Jersey Administrative Code and the Common Core State Standards for Mathematics, the following are proficiencies required for the successful completion of the above named course. The student will be able to: The student will: 1. Determine if sets of rational and irrational numbers are closed under operations. 2. Determine whether a given relation is a function, and if so, represent it using function notation. 3. Solve linear equations with all real numbers. 4. Solve linear equations using multiple transformations and correct errors in a given solution to a linear equation 5. Rearrange linear formulas to highlight a quantity of interest. 6. Model real life problems using linear equations. 7. Use rates, ratios and proportions to model and solve real life problems. 8. Graph linear equations using a table. 9. Graph vertical and horizontal lines and recognize their equations. 10. Find the intercepts of a line and use the intercepts to graph the line. 11. Find the slopes of lines and use slopes of given lines to determine whether lines are parallel, perpendicular, intersecting, or coincident. 12. Graph a linear equation that is written in slope intercept form. 13. Determine the equation of a line given the slope and y-intercept. 14. Determine the equation of a line given the slope and a point. 15. Determine the equation of a line given two points on the line. 16. Use a linear model to predict real life outcomes. 17. Solve a system of linear equations by graphing. 18. Solve a system of linear equations by substitution. 19. Solve a system of linear equations by linear combination. 20. Determine the best method to solve a system of linear equations. 21. Determine the number of solutions to a system of linear equations. 22. Solve real life problems by writing a system of equations and interpret the solutions. 23. Graph a linear inequality in two variables. 24. Solve systems of linear inequalities.

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25. Sketch the graph of a quadratic function. 26. Solve a system with one or more quadratic functions. 27. Solve quadratic equations by taking square root. 28. Solve quadratic equations by using the quadratic formula. 29. Solve quadratic equations by graphing. 30. Solve quadratic equations by completing the square. 31. Graph the square root and cube root functions and determine and analyze their key characteristics. 32. Multiply and divide exponential expressions. 33. Simplify and evaluate expressions with positive, negative, and zero exponent. 34. Graph and model exponential functions. 35. Analyze a table, numerical pattern, graph, equation, or context to determine whether a linear, exponential, or quadratic relationship could be represented. 36. Recognize linear and exponential functions as arithmetic and geometric sequences and construct their formulas. 37. Combine and classify polynomials. 38. Determine the product of polynomials. 39. Perform all basic operations on polynomials. 40. Solve polynomial equations in factored form using the zero product property. 41. Factor polynomials in the form ax^2+bx+c a=1 completely and use the factors to solve equations (use special patterns where appropriate). 42. Factor polynomials in the form ax^2+bx+c a is not equal to 1 completely and use the factors to solve equations. 43. Factor polynomials using GCF or special patterns. 44. Solve quadratic equations by completing the square. 45. Solve and graph linear inequalities in one variable. 46. Solve and graph compound inequalities. 47. solve absolute value equations. 48. Graph the absolute value of a linear function and determine and analyze its key characteristics. 49. Graph and write piecewise functions. 50. Compare measures of central tendency. 51. Represent and analyze data with plots on the real number line 52. Understand the difference between causation and correlation.

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Integration of 21st century themes and skills in this curriculum include:

Lessons, where appropriate, incorporate multiple perspectives to infuse cultural and global awareness.

Learning incorporates skills focusing on financial, economic, business, and entrepreneurial literacy.

Lessons integrate a focus on civic literacy so that student can better understand the rights and obligations of citizenship.

Learning advocates for health literacy as a critical component of a healthy lifestyle and the ability to make good health-related decisions.

Students explore areas that support environmental literacy, including society’s impact on the environment and what can be done to support environmental solutions.

Lessons, activities, and assessments require creativity and innovation on the part of the students. They are required to create projects and products as examples of mastery in each unit.

Critical thinking and problem solving skills are a core component of learning and assessment throughout this curriculum. Students are required, in each unit, to advance their learning through all levels of Bloom’s Taxonomy to address the evaluation, synthesis, and creation of products using learning at the highest levels. Problem-solving is a recurring theme in the curriculum as students must seek ways to creatively apply the concepts to solve problems rather than simply remember the material.

Communication and collaboration is crucial for student success as learners. Throughout this curriculum, students must be able to communicate deep understanding through open ended responses (both orally and in writing). In addition, students are often required to work collaboratively with their peers, which promotes the ability to succeed in the area of social cooperative work, increases communication skills, and promotes leadership and responsibility.

Students must be information literate, i.e. they must be able to find and use information effectively, in order to succeed in class as learning activities require independent research of relevant information outside of the provided textbook and/or resources.

Learning and assessment activities support the push to make students media literate, as they are often required to analyze, evaluate, and create messages in a wide variety of media modes, genres, and formats.

In order to succeed in this course, students must be able to use technology as a tool in order to research, organize, evaluate, and communicate information.

Activities in the curriculum help develop life and career skills in all students by promoting flexibility and adaptability, requiring initiative and self-direction in the learning process, supporting social and cross-cultural skills in both content and teamwork efforts, and measuring productivity and accountability through independent and group assignment completion.

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Scope and Sequence

Unit Title and Description

Common Core Standard(s)

Domain & Standard

Pacing (must equal 165

days for full-year or 83 days for

half-year course)

Benchmarking & Assessments

Suggested Interdisciplinary Activities

Example for Each Subject Area

Unit 1: Number Sense, Concepts, and

Applications: Relationships Between

Quantities and Reasoning with Equations

Unit 1 Description: This unit begins with setting the stage for work with expressions and equations through understanding quantities and the relationships between them. In this unit students analyze and explain precisely the process of solving an equation. Through repeated reasoning, students develop fluency in writing, interpreting, and translating between various forms of linear equations and inequalities and make conjectures about the form that a linear equation might take in a solution to a problem. They reason abstractly and quantitatively by choosing and interpreting units in the context of creating equations in two variables to represent relationships between quantities. They master the solution of linear equations and apply related solution techniques and the properties of exponents to the creation and solution of simple exponential equations. They learn the terminology specific to polynomials and understand that polynomials form a system analogous to the integers. Essential Questions

What techniques are used for solving linear equations systematically?

What real-life situations can be solved by writing and graphing linear

N.Q.1: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. N.Q.2: Define appropriate quantities for the purpose of descriptive modeling. N.Q.3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. A.SSE.1: Interpret expressions that represent a quantity in terms of its context.

a. Interpret parts of an expression, such as terms, factors, and coefficients.

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

A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear functions. A.CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A.CED.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For

30 Days NJ DOE Model Curriculum Unit Assessment (PDF | Word) NJ DOE Model Curriculum Unit Scoring Guide (PDF | Word) Mid-Module Assessment Task Algebra I Module 1: End-of-Module Assessment Study Island Benchmark Common Core Coach Book Performance Based Tasks PARCC Released Items

Career Education Mathematical Modeling: All the printing presses at a print shop were scheduled to make copies of a novel and a cookbook. They were to print the same number of copies of each book, but the novel had twice as many pages as the cookbook. All of the printing presses worked for the first day on the larger book, turning out novels. Then, on day two, the presses were split into two equally sized groups. The first group continued printing copies of the novel and finished printing all the copies by the evening of the second day. The second group worked on the cookbook but did not finish by evening. One printing press, working for two additional full days, finished printing the remaining copies of the cookbooks. If all printing presses printed pages (for both the novel and cookbook) at the same constant rate, how many printing presses are there at the print shop? Health/PE Write a single or compound inequality for the scenario. Unsafe body temperatures are those lower than 96℉ or

above 104℉. English Language Arts & Literacy Consider the following scenario. For each, specify the

variable and say, “𝑊 is the width of the rectangle,” for

example, and write a compound inequality that represents the scenario given. Draw its solution set on a number line. Students are to present a persuasive speech in English class. The guidelines state that the

speech must be at least minutes but not exceed 12

minutes. In Lewis Carroll’s Through the Looking Glass, Tweedledum says, “The sum of your weight and twice mine is 361 pounds.” Tweedledee replies, “The sum of

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equations?

How can patterns, relations, and functions be used as tools to best describe and help explain real-life situations?

How are functions and their graphs related?

How can technology be used to investigate properties of linear functions and their graphs?

What techniques can be used to solve linear equations?

How can we determine whether an equation or a graph is a function?

How can we translate verbal models into algebraic models to represent and solve real-life situations?

How can change be best represented mathematically?

How can we use mathematical language to describe change?

How can we use mathematical models to describe change or change over time?

How are patterns of change related to the behavior of functions?

What techniques can be used to graph linear equations?

How can we determine whether an equation or a graph is a function?

Enduring Understanding(s)

Graphs and equations are alternative (and often equivalent) ways for depicting and analyzing patterns of change.

Functional relationships can be expressed in real contexts, graphs, algebraic equations, tables, and words; each representation of a given function is simply a different way of expressing the same idea.

The value of a particular representation depends on its purpose.

example, rearrange Ohm’s law V = IR to highlight resistance R. A.REI.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A.REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Major Supporting Additional (identified by PARCC Model Content Frameworks Selected Opportunities for Connections to Mathematical Practices 1. Make sense of problems and

persevere in solving them. *

2. Reason abstractly and

quantitatively.

SLO 4 Create abstract algebraic models of real-world problems then transform them.

3. Construct viable arguments and

critique the reasoning of others.

4. Model with mathematics. *

5. Use appropriate tools strategically.

6. Attend to precision.

SLO 6 Use precise language when giving descriptions.

7. Look for and make use of structure.

8. Look for and express regularity in

repeated reasoning.

SLO 3 Write general formulas after working with specific examples.

*MP.1 and MP.4 are overarching practices relevant to Algebra 1. (PARCC Model

your weight and twice mine is 362 pounds.” Find both of their weights. Math

For each question below, provide an explanation or an

example to support your claim.

a. Is it possible to have a system of equations that

has no solution?

b. Is it possible to have a system of equations that

has more than one solution?

c. Is it possible to have a system of inequalities

that has no solution?

Science Mercury is one of only two elements that are liquid at room temperature. Mercury is non-liquid for temperatures less than −38.0℉ or greater than 673.8℉. Write a compound inequality for the temperatures at which mercury is nonliquid. Alexus is modeling the growth of bacteria for an

experiment in science. She assumes that there are 𝐵𝐵 bacteria in a Petri dish at 12:00 noon. In reality, each bacterium in the Petri dish subdivides into two new bacteria approximately every 20 minutes. However, for the purposes of the model, Alexus assumes that each bacterium subdivides into two new bacteria exactly every 20 minutes. Create a table that shows the total number of bacteria in the Petri dish at 1/3 hour intervals for 2 hours starting with time 0 to represent 12:00 noon. Write an equation that describes

the relationship between total number of bacteria 𝑇𝑇 and time ℎ in hours, assuming there are 𝐵𝐵 bacteria in the

Petri dish at ℎ = 0. History/Social Studies A poll shows that a candidate is projected to receive 57% of the votes. If the margin for error is plus or minus

3%, write a compound inequality for the percentage of votes the candidate can expect to get.

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Proportionality involves a relationship in which the ratio of two quantities remains constant as the corresponding values of the quantities change.

Graphs and equations are alternative (and often equivalent) ways for depicting and analyzing patterns of change.

The value of a particular representation depends on its purpose.

A variety of families of functions can be used to model and solve real world situations.

Content Frameworks) Technical Subjects Profit of a Company: Assessment Variation activity by Illustrative Mathematics World Languages

A store plans to export Brazilian coffee for $10 per lb. and Columbian coffee for $14 per lb. If the store

decides to make a 150-lb. blend of the two and sell it for $11 per lb., how much of each type of coffee should be used?

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Scope and Sequence

Unit Title and Description

Common Core Standard(s)

Domain & Standard

Pacing (must equal 165 days for full-year

or 83 days for half-year course)

Benchmarking & Assessments

Suggested Interdisciplinary Activities

Example for Each Subject Area

Unit 2: Linear Relationships Unit 2 Description: Unit 2 will build on the grade 8 concepts for linear and exponential relationships. Success in This unit will lay the groundwork for later units where the students will extend this knowledge to quadratic and exponential functions. In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module, students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally; translate between representations; and understand the limitations of various representations. Essential Questions:

What techniques can be used to solve and graph a system of linear equations or inequalities in one or two variables?

How can we model and solve real-life situations using a system of linear equations or inequalities?

How can functional relationships be used to express real contexts, graphs, algebraic equations, tables and words?

How is each representation of a function a different way of expressing the

A.REI.5: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. A.REI.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. A.REI.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). A.REI.11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. A.REI.12: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

32 Days

NJ DOE Model Curriculum Unit Assessment (PDF | Word) NJ DOE Model Curriculum Unit Scoring Guide (PDF | Word) Study Island Benchmark Common Core Coach Book Performance Based Tasks PARCC Released Items

Career Education Lou opens a bank account. The deal he makes with his mother is that if he doubles the amount that was in the account at the beginning of each month by the end of the month, she will add an additional $5 to the account at the end of the month. d. Let 𝐴(𝑛) represent the amount in the account at the

beginning of the 𝑛th month. Assume that he does, in fact, double the amount every month. Write a recursive formula for the amount of money in his account at the beginning of the (𝑛 + 1)th month. e. What is the least amount he could start with in order to have $300 by the beginning of the third month? After graduating from college, Jane has two job offers to consider. Job A is compensated at $100,000 a year but with no hope of ever having an increase in pay. Jane knows a few of her peers are getting that kind of an offer right out of college. Job B is for a social media start-up, which guarantees a mere $10,000 a year. The founder is sure the concept of the company will be the next big thing in social networking and promises a pay increase of 25% at the beginning of each new year. f. Which job will have a greater annual salary at the beginning of the fifth year? By approximately how much? g. Which job will have a greater annual salary at the beginning of the tenth year? By approximately how much? h. Which job will have a greater annual salary at the beginning of the twentieth year? By approximately how much? i. If you were in Jane’s shoes, which job would you take? Health/PE

Consider Akelia’s sequence of jumping jacks , , 11,

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same idea?

How are functions and their graphs related?

How can systems of equations be used to solve real-life situations? Enduring Understandings:

Systems of linear equations or inequalities can be used to model and solve real world situations.

Systems of equations and inequalities can be solved with a variety of different methods.

The solutions to a system of linear inequalities can be represented by an intersection of two half planes. .

A.CED.3: Represent 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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. F.IF.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F.IF.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. F.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. F.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. F.IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear functions

14, 17, …. j. If you believed in patterns, what might you say is the next number in the sequence? k. Write a formula for Akelia’s sequence. l. Explain how each part of the formula relates to the sequence. According to the International Basketball Association (FIBA), a basketball must be inflated to a pressure such that when it is dropped from a height of 1,800 mm, it

rebounds to a height of 1,300 mm. Maddie decides to test the rebound-ability of her new basketball. She assumes that the ratio of each rebound height to the

previous rebound height remains the same at 1300

1800. Let

𝑓(𝑛) be the height of the basketball after 𝑛 bounces. Complete the chart below to reflect the heights Maddie expects to measure.

𝒏 𝒇(𝒏)

0 1,800

1

2

3

4

English Language Arts & Literacy Students will work in groups of three and will be able to write the equation of the line for each interval from a graph that they produce on the ranger. They will write a story to coincide with their graph. They will then swap with another group who will have to reproduce the graph from the story and find the equations of the line. Math Suppose the graph of 𝑓 is given. Write an equation for

each of the following graphs after the graph of 𝑓 has been transformed as described. Note that the transformations are not cumulative.

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. F.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. Major Supporting Additional (identified by PARCC Model Content Frameworks) Selected Opportunities for Connection to Mathematical Practices 1. Make sense of problems and persevere in solving them. * 2. Reason abstractly and quantitatively. SLO 4 Determine the relationship between domain and range of a function and explain the connection to the inputs and outputs. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. * 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. SLO 5 Describing the regularity in the way terms cancel can lead to a general formula for a geometric sequence. *MP.1 and MP.4 are overarching practices relevant to Algebra 1. (PARCC Model Content Frameworks)

m. Translate units upward.

n. Translate units downward.

o. Translate units right.

p. Translate units left.

q. Reflect about the 𝑥-axis.

r. Reflect about the 𝑦-axis.

s. Stretch vertically by a factor of .

t. Shrink vertically by a factor of 1

3.

u. Shrink horizontally by a factor of 1

3.

v. Stretch horizontally by a factor of .

Science There was no snow on the ground when it started falling at midnight at a constant rate of 1.5 inches per hour. At

4:00 a.m., it starting falling at a constant rate of inches

per hour, and then from 7:00 a.m. to 9:00 a.m., snow

was falling at a constant rate of inches per hour. It

stopped snowing at 9:00 a.m. (Note: This problem models snow falling by a constant rate during each time period. In reality, the snowfall rate might be very close to constant but is unlikely to be perfectly uniform throughout any given time period.) w. Write a piecewise linear function that models the depth of snow as a function of time since midnight. x. Create a graph of the function.

y. When was the depth of the snow on the ground

inches? z. How deep was the snow at 9:00 a.m.? A river has an initial minnow population of 40,000 that is

growing at 5% per year. Due to environmental conditions, the amount of algae that minnows use for food is decreasing, supporting 1,000 fewer minnows each year. Currently, there is enough algae to support 50,000 minnows. Is the minnow population increasing linearly or exponentially? Is the amount of algae decreasing at a linear or an exponential rate? In what year will the minnow population exceed the amount of algae available?

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History/Social Studies

2. From 2000 to 2013, the value of the U.S. dollar has been shrinking. The value of the U.S. dollar over time (𝑣(𝑡)) can be modeled by the following formula:

𝑣(𝑡) = 1.36(0.9758)𝑡, where 𝑡 is the number of years since 2000

a. How much was a dollar worth in the year 2005?

b. Graph the points (𝑡, 𝑣(𝑡)) for integer values of 0 ≤

𝑡 ≤ 14. c. Estimate the year in which the value of the dollar fell below $1.00.

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Scope and Sequence

Unit Title and Description

Common Core Standard(s)

Domain & Standard

Pacing (must equal 165 days for full-year

or 83 days for half-year course)

Benchmarking & Assessments

Suggested Interdisciplinary Activities

Example for Each Subject Area

Unit 3: Expressions and Equations Unit 3 blends the conceptual understandings of expressions and equations with procedural fluency and problem solving. The students will not encounter solutions of quadratic equations that are complex. In earlier modules, students analyze the process of solving equations and developing fluency in writing, interpreting, and translating between various forms of linear equations and linear and exponential functions. These experiences combined with modeling with data, set the stage for this unit. Here students continue to interpret expressions, create equations, rewrite equations and functions in different but equivalent forms, and graph and interpret functions, but this time using polynomial functions, and more specifically quadratic functions, as well as square root and cube root functions. Essential Questions

What techniques can be used to simply expressions with exponents?

How can we use mathematical language to describe non-linear change?

How can we model situations using exponents?

How can we use mathematical language to describe exponential change?

How can we use exponential models for real life situations?

A.SSE.1: Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P. A.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). A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. c. 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%. A.APR.1: Understand that polynomials form a system analogous to the integers,

43 days NJ DOE Model Curriculum Unit Assessment (PDF | Word) NJ DOE Model Curriculum Unit Scoring Guide (PDF | Word) Study Island Benchmark Common Core Coach Book Performance Based Tasks PARCC Released Items Open-Ended Questions Labs- Individual, Partner, Group Formative Assessments: Exit Tickets and Questioning Inquiry-Based Projects

Career Education Peter is a painter, and he wonders if he would have time to catch a paint bucket dropped from his ladder before it

hits the ground. He drops a bucket from the top of his -

foot ladder. The height, , of the bucket during its fall

can be represented by the equation, ℎ = −16𝑡2 + 9, where the height is measured in feet from the ground, and the time since the bucket was dropped, 𝑡, is measured in seconds. After how many seconds does the bucket hit the ground? Do you think he could catch the bucket before it hits the ground? Health/PE Mischief is a toy poodle that competes with her trainer in the agility course. Within the course, Mischief must leap through a hoop. Mischief’s jump can be modeled by the

equation ℎ = −16𝑡2 + 12𝑡, where is the height of the

leap in feet and 𝑡 is the time since the leap, in seconds. At what values of 𝑡 does Mischief start and end the jump? English Language Arts & Literacy Can you graph a quadratic function if you don’t know the vertex? Can you graph a quadratic function if you only know the 𝑥-intercepts? Have students explain in their math journal. Math Science A physics teacher put a ball at the top of a ramp and let it roll down toward the floor. The class determined that the height of the ball could be represented by the

equation ℎ = −16𝑡2 + 4, where the height, , is

measured in feet from the ground and time, 𝑡, is measured in seconds.

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How can we use algebraic representation to analyze patterns?

Why are number and algebraic patterns important as rules?

How can we add, subtract, and multiply polynomials?

What techniques can be used to factor polynomials and solve polynomial equations?

What are the similarities and differences between linear, quadratic, and exponential functions?

Enduring Understandings

Graphs and equations are alternative (and often equivalent) ways for depicting and analyzing patterns of non-linear change.

Mathematical models can be used to describe physical relationships; these relationships may be linear, quadratic, or exponential.

Real world situations, involving exponential relationships, can be solved using multiple representations.

namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A.CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A.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. A.REI.4: Solve quadratic equations in one variable. a. 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. b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. Major Content Supporting Content (Identified by PARCC Model Content Frameworks). Selected Opportunities for Connection to Mathematical Practices

a. What do you notice about the structure of the quadratic expression in this problem?

b. In the equation, explain what the represents.

c. Explain how you would use the equation to determine the time it takes the ball to reach the floor. d. Now consider the two solutions for 𝑡. Which one is reasonable? Does the final answer make sense based on this context? Explain. History/Social Studies Below are some examples of curves found in architecture around the world. Some of these might be represented by graphs of quadratic functions. What are the key features these curves have in common with a graph of a quadratic function? St. Louis Arch, Bellos Falls Arch Bridge, Arch of Constantin, and Roman Aqueduc. The photographs of architectural features above MIGHT be closely represented by graphs of quadratic functions. Answer the following questions based on the locations. a. How would you describe the overall shape of a graph of a quadratic function? b. What is similar or different about the overall shape of the above curves? Technical Subjects Many business contexts can be modeled with quadratic functions. This is because the expressions representing the price (price per item), the cost (cost per item), and the quantity (number of items sold) are typically linear. The product of any two of those linear expressions will produce a quadratic expression that can be used as a model for the business context. The variables used in business applications are not as traditionally accepted as variables that are used in physics applications, but there are some obvious reasons to use 𝑐 for cost, 𝑝 for

price, and 𝑞 for quantity (all lowercase letters). For total production cost, we often use 𝐶 for the variable, 𝑅 for

total revenue, and 𝑃 for total profit (all uppercase letters). You have seen these formulas in previous lessons, but we will review them here since we use them in the next two lessons.

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1. Make sense of problems and persevere in solving them. *

2. Reason abstractly and quantitatively. SLO 1 Analyze expressions by examining their parts in context.

3. Construct viable arguments and critique the reasoning of others. SLO 6 Examine the steps in the derivation of the quadratic formula to determine if they are logical and ask questions to improve the clarify.

4. Model with mathematics. *

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure. SLO 2 Look for structural similarities when writing equivalent expressions.

8. Look for and express regularity in repeated reasoning. *MP.1 and MP.4 are overarching practices relevant to Algebra 1. (PARCC Model Content Frameworks)

Business Application Vocabulary UNIT PRICE (PRICE PER UNIT): The price per item a business sets to sell its product, sometimes represented as a linear expression. QUANTITY: The number of items sold, sometimes represented as a linear expression. REVENUE: The total income based on sales (but without considering the cost of doing business). UNIT COST (COST PER UNIT) OR PRODUCTION COST: The cost of producing one item, sometimes represented as a linear expression. PROFIT: The amount of money a business makes on the sale of its product. Profit is determined by taking the total revenue (the quantity sold multiplied by the price per unit) and subtracting the total cost to produce the items (the quantity sold multiplied by the production cost per unit): Profit = Total Revenue −Total Production Cost. The following business formulas will be used in this lesson: Total Production Costs

= (cost per unit)(quantity of items sold)

Total Revenue = (price per unit)(quantity of items sold) Profit = Total Revenue − Total Production Costs

Now answer the questions related to the following business problem: A theater decided to sell special event tickets at $10 per ticket to benefit a local charity. The theater can seat up to 1,000 people, and the manager of the theater expects

to be able to sell all 1,000 seats for the event. To maximize the revenue for this event, a research company volunteered to do a survey to find out whether the price of the ticket could be increased without losing revenue. The results showed that for each $1 increase

in ticket price, 20 fewer tickets would be sold. a. Let 𝑥 represent the number of $1.00 price-per-ticket increases. Write an expression to represent the expected price for each ticket. World Languages The table below represents the value of Andrew’s international stock portfolio, where 𝑉 represents the

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value of the portfolio in hundreds of dollars and 𝑡 is the time in months since he started investing. Answer the questions that follow based on the table of values.

𝒕 (months) 𝑽(𝒕) (hundreds of

dollars)

2 325

4 385

6 405

8 385

10 325

12 225

14 85

16 −95

18 −315

a. What kind of function could model the data in this table? How can you support your conclusion? b. Assuming this data is in fact quadratic, how much did Andrew invest in his stock initially? Explain how you arrived at this answer. c. What is the maximum value of his stock, and how long did it take to reach the maximum value? d. If the pattern continues to follow the quadratic trend shown above, do you advise Andrew to sell or keep his stock portfolio? Explain why.

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Scope and Sequence

Unit Title and Description Common Core

Standard(s) Domain & Standard

Pacing (must equal 165

days for full-year or 83 days for

half-year course)

Benchmarking & Assessments

Suggested Interdisciplinary Activities

Example for Each Subject Area

Unit 4: Functions and Modeling Unit 4 presents standards that involve functions and extending the concepts of integer exponents to concepts of rational exponents. The understandings will be applied to other types of equations in future courses. In this unit, students synthesize what they have learned during the year about functions to select the correct function type in a series of modeling problems. Students no longer have the benefit of a module or lesson title that includes function type to guide them in their choices. Skills and knowledge from the previous modules will support the requirements of this module, including writing, rewriting, comparing, and graphing functions and interpretation of the parameters of an equation.. Essential Questions:

What techniques can we use to solve and graph quadratic equations?

How can we model and solve real-life situations using quadratic equations?

How can we use mathematical language to describe non-linear change?

How can we model situations using quadratics? Enduring Understandings

Graphs and equations are alternative (and often equivalent) ways for depicting and analyzing patterns of non-linear change.

Mathematical models can be used

A.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. N.RN.3: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a non-zero rational number and an irrational number is irrational. F.IF.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity F.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. F.IF.6: Calculate and interpret the

35 Days

NJ DOE Model Curriculum Unit Assessment (PDF | Word) NJ DOE Model Curriculum Unit Scoring Guide (PDF | Word) Study Island Benchmark Common Core Coach Book Performance Based Tasks PARCC Released Items Individual Projects Partner Assessments Labs- Groups Formative Assessments Journal Writing

Career Education Margie got $1,000 from her grandmother to start her college fund. She is opening a new savings account and finds out that her bank offers a 2% annual interest rate, compounded monthly. What type of function would best represent the amount of money in Margie’s account? Justify your answer mathematically. Health/PE

NYC Sports Gym had 425 members in 2011. Based on statistics, the total number of memberships increases by 2% annually. e. What type of function models the total number of memberships in this situation? f. If the trend continues, what function represents the total number of memberships in 𝑛 years? How did you know? Justify your reasoning. Spencer and McKenna are on a long-distance bicycle ride. Spencer leaves one hour before McKenna. The graph below shows each rider’s distance in miles from his or her house as a function of time since McKenna left on her bicycle to catch up with Spencer. (Note: Parts (e), (f), and (g) are challenge problems.) g. Which function represents Spencer’s distance? Which function represents McKenna’s distance? Explain your reasoning. h. Estimate when McKenna catches up to Spencer. How far have they traveled at that point in time? i. One rider is speeding up as time passes and the other one is slowing down. Which one is which, and how can you tell from the graphs? j. According to the graphs, what type of function would best model each rider’s distance? k. Create a function to model each rider’s distance as a function of the time since McKenna started riding her bicycle. Use the data points labeled on the graph to create a precise model for each rider’s distance.

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to describe physical relationships; these relationships are often non-linear.

Real world situations, involving quadratic relationships, can be solved using multiple representations.

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 F.IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. F.IF.8a: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. 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. F.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. F.BF.1: Write a function that describes a

relationship between two quantities. ★

a. Determine an explicit expression, a recursive process, or steps for calculation from a context. F.BF.3: Identify the effect on the graph of

l. What is the meaning of the 𝑥- and 𝑦-intercepts of each rider in the context of this problem?

English Language Arts & Literacy Research linear, quadratic, and exponential functions using the Internet. For each of the three types of functions, provide an example of a problem/situation you found on the Internet where that function was used to model the situation or answer the problem. Include the actual function used in the example and web page where you found the example. Journal about the features of the model and what defines them. Science City workers recorded the number of squirrels in a park over a period of time. At the first count, there were 15

pairs of male and female squirrels (30 squirrels total).

After months, the city workers recorded a total of 60

squirrels, and after a year, there were 120. m. What type of function can best model the population of squirrels recorded over a period of time, assuming the same growth rate and that no squirrel dies? n. Write a function that represents the population of squirrels recorded over 𝑥 number of years. Explain how you determined your function. A population of insects is known to triple in size every month. At the beginning of a scientific research project, there were 200 insects.

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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. F.LE.1: Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals; and that exponential functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative another. F.LE.2:Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). F.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. F.LE.5: Interpret the parameters in a linear or exponential function in terms of a context. Major Content Supporting Content Additional Content (Identified by PARCC Model Content Frameworks).

o. What type of function models the population of the insects after 𝑡 years? p. Write a function that models the population growth of the insects after 𝑡 years. Derek throws a baseball upward from an initial height

of 3 ft. The baseball hits the ground after seconds.

a. What was the initial velocity of the baseball?

b. What is the function that models the height, (in

feet), of the baseball over a period of time 𝑡 (in seconds)? c. At what time did the baseball reach its maximum height? What was the maximum height of the baseball? History/Social Studies Noam and Athena had an argument about whether it would take longer to get from NYC to Boston and back by car or by train. To settle their differences, they made separate, nonstop round trips from NYC to Boston. On the trip, at the end of each hour, both recorded the number of miles they had traveled from their starting points in NYC. The tables below show their travel times, in hours, and the distances from their starting points, in miles. The first table shows Noam’s travel time and distance from the starting point, and the second represents Athena’s. Use both data sets to justify your answers to the questions below.

Time in Hours

Noam’s Distance

Time in Hours

Athena’s Distance

𝟎 𝟎 0 0

𝟏 𝟓𝟓 1 81

𝟐 𝟏𝟏𝟎 2 144

𝟑 𝟏𝟔𝟓 3 189

𝟒 𝟐𝟐𝟎 4 216

𝟓 𝟏𝟔𝟓 5 225

𝟔 𝟏𝟏𝟎 6 216

𝟕 𝟓𝟓 7 189

𝟖 𝟎 8 144

9 81

10 0

a. Who do you think is driving, and who is riding the train? Explain your answer in the context of the

Page 28 of 53

problem. b. According to the data, how far apart are Boston and New York City? Explain mathematically. c. How long did it take each of them to make the round trip? d. According to their collected data, which method of travel was faster? Technical Subjects

3. Consider the following sequence: 8, 17, 32, 53, 80, 113, …

a. What pattern do you see, and what does that pattern mean for the analytical representation of the function? b. Using your art skills, create a symbolic representation of the sequence? World Languages

Arnold wants to be able to count to 100 in Spanish. His teacher puts him on a workout regimen designed to improve his counting strength. The following chart shows how many numbers Arnold can state after each month of training. How many months will it take Arnold to achieve his goal if this pattern continues?

Month Pull-Up Count

1 2

2 5

3 10

4 17

5 26

6 37

…

Page 29 of 53

Scope and Sequence

Unit Title and Description Common Core

Standard(s) Domain & Standard

Pacing (must equal 165

days for full-year or 83 days for

half-year course)

Benchmarking & Assessments

Suggested Interdisciplinary Activities

Example for Each Subject Area

Unit 5: Descriptive Statistics Unit 5 will build on previous work with descriptive statistics. Linear models will be used to assess how a model fits the data. In this units, students reconnect with and

deepen their understanding of statistics and

probability concepts first introduced in Grades

6, 7, and 8. Students develop a set of tools for

understanding and interpreting variability in

data, and begin to make more informed

decisions from data. They work with data

distributions of various shapes, centers, and

spreads. Students build on their experience with

bivariate quantitative data from Grade 8. This

module sets the stage for more extensive work

with sampling and inference in later grades.

Essential Questions:

How do you compare measures of

central tendency and dispersion?

How do you find the relative

frequency in a two-way table?

How do you make and interpret stem-

and-leaf plots and histograms?

How to you make and interpret a box-

and whisker plot?

Enduring Understandings

Dot plots, histograms and box plots

are different ways to analyze data.

Data displays often reveal patterns

and trends that may not be obvious.

S.ID.1: Represent data with plots on the real number line (dot plots, histograms, and box plots). S.ID.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. S.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). S.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. S.ID.6a: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. S.ID.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. S.ID.8: Compute (using technology) and interpret the correlation coefficient of a linear fit.

25 Days

NJ DOE Model Curriculum Unit Assessment (PDF | Word) NJ DOE Model Curriculum Unit Scoring Guide (PDF | Word) Mid-Module Assessment Task Algebra I Module 1: End-of-Module Assessment Study Island Benchmark Common Core Coach Book Performance Based Tasks PARCC Released Items

Career Education

Consider the following scenario. Transportation officials collect data on flight delays (the number of minutes a flight takes off after its scheduled time). Consider the dot plot of the delay times in minutes for 60 BigAir flights during December 2015:

4. How many flights left more than 60 minutes late? 5. Why is this data distribution considered skewed? 6. Is the tail of this data distribution to the right or to the left? How would you describe several of the delay times in the tail? 7. Draw a box plot over the dot plot of the flights for December. 8. What is the interquartile range, or IQR, of this data set?

The mean of the 60 flight delays is approximately 42

minutes. Do you think that 42 minutes is typical of the

number of minutes a BigAir flight was delayed? Why or why not? Health/PE

All the members of a high school softball team were asked how many hours they studied in a typical week. The results are shown in the histogram below.

Page 30 of 53

S.ID.9: Distinguish between correlation and causation. Major Content Supporting Content Additional Content (Identified by PARCC Model Content Frameworks). Selected Opportunities for Connection to Mathematical Practices 1. Make sense of problems and persevere in solving them. * 2. Reason abstractly and quantitatively. SLO 5 Examine several related events to determine if the relationship is correlation or causation. Ex. Watching TV and getting a low score on a test. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. * 5. Use appropriate tools strategically. SLO 5 Compute the correlation coefficient for a linear model using technology. 6. Attend to precision. SLO 3 Create data displays and give oral or written descriptions, in context, using explicit language. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. *MP.1 and MP.4 are overarching practices relevant to Algebra 1. (PARCC Model Content Frameworks)

a. We can see from the histogram that four students

studied around hours per week. How many students

studied around 15 hours per week? b. How many students were there in total? c. Suppose that the four students represented by the

histogram bar centered at had all studied exactly hours,

the five students represented by the next histogram bar had all studied exactly 10 hours, and so on. If you were to add up the study times for all of the students, what result would you get? d. What is the mean study time for these students? e. What would you consider to be a typical deviation from the mean for this data set? English Language Arts & Literacy Science

Jenna has bought a new hybrid car. Each week for a period of seven weeks, she has noted the fuel efficiency (in miles per gallon) of her car. The results are shown below.

45 44 43 44 45 44 43 Calculate the standard deviation of these results to the nearest hundredth. Be sure to show your work. History/Social Studies

The following histogram represents the age distribution of the population of the United States in 2010.

Page 31 of 53

What do you think this graph is telling us about the population of the United States? Why might we want to study the data represented by this graph? Technical Subjects

Consider the following scenario. The company that created a popular video game “Leaders” plans to release a significant upgrade of the game. Users earn or lose points for making decisions as the leader of an imaginary country. In most cases, repeated playing of the game improves a user’s ability to make decisions. The company will launch an online advertising campaign, but at the moment, they are not sure how to focus the advertising. Your goal is to help the company decide how the advertising campaign should be focused. Five videos have been proposed for the following target audiences: Video 1: Target females with beginning level scores Video 2: Target males with advanced level scores Video 3: Target all users with middle range level scores Video 4: Target males with beginning level scores Video 5: Target females with advanced level scores Why might the company be interested in developing different videos based on user score? World Languages

Students at a local high school are involved in a special project that involves communicating with people in Kenya. Consider a box plot of the ages of 200 randomly selected people from Kenya.

Page 32 of 53

A data distribution may contain extreme data (specific data values that are unusually large or unusually small relative to the median and the interquartile range). A box plot can be used to display extreme data values that are identified as outliers. Each “*” in the box plot represents the ages of four people from this sample. Based on the sample, these four ages were considered outliers. Estimate the values of the four ages represented by an *. An outlier is defined to be any data value that is more than 1.5 × (𝐼𝑄𝑅) away from the nearest quartile. What is the median age of the sample of ages from Kenya? What are the approximate values of Q1 and Q3? What is the approximate IQR of this sample?

Page 33 of 53

Unit 1 Standards Overview

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs Students

(SE, ELL, 504, G&T)

N.Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

Solve multi-step problems that can be represented algebraically with accurate and appropriately defined units, scales, and models (such as graphs, tables, and data displays). Interpret terms, factors, coefficients, and expressions (including complex linear and exponential expressions) in terms of context. Solve linear equations and inequalities in one variable (including literal equations). Justify each step in the process and solution. Create linear equations and inequalities in one variable and use them to solve problems. Justify

Pearson SuccessNet On-Line Teacher’s Edition Pearson Online Resources and Materials Study Island Web-Based Math Resources http://www.artofproblemsolving.com/liz/Alcumus/index.php Various leveled texts available via hard copy and on line. CSI Algebra eBook CSI Pre-Algebra eBook CC Stations Alg.1 Access to below level resources can be found in other texts used in the department (Algebra 1 Foundations) http://www.phsuccessnet.com http://collegeboard.org

Guided Instruction of content using: Small Group Targeted Instruction- Leveled by Reading Level Interactive Notebook Student Responses to concept Open-ended Questions Activity Labs Guided problem solving Math Puzzles Task Cards Scavenger Hunts Standardized test items Lesson 1

Ability to use prior knowledge of properties of integer exponents to build understanding of rational exponents and radicals. Knowledge of the connection between radical and exponential notation. Ability to translate between radical and exponential notation. Ability to perform operations on both rational and irrational numbers. Ability to make connections between symbolic representations and proper mathematics vocabulary for linear, quadratic and exponential expressions.

Formative: Journals/logs KWL chart At the bell activities Question and answer Individual white boards/Promethean Board ActiVotes Homework Quizzes Constructed response/open-ended problem solving Performance tasks Exit slips Summative: Performance based assessments Quizzes Tests Constructed response/open-ended problem solving Performance tasks Project NJ DOE Model Curriculum Assessment

http://www.khanacademy.org/ Thinkfinity website: http://www.thinkfinity.org/home IXL Website: http://www.IXL.com/math/ United Streaming: http://streaming.discoveryeducation.com/index.cfm http://edhelper.com/place_value.html http://illuminations.nctm.org http://insidemathematics.org www.teachingchannel.org www.Learnzillion.com http://illustrativem

Special Education Accommodations Web-based Math Resources Teacher generated/differentiated instruction activities Small group instruction Adapted assignments Additional time Alternative Assessments Chunking of content, assignment and/or assessments One-on-one re-teaching Volunteer/peer tutoring Accommodations based on IEP and/or need ELL Accommodations Use of Manipulatives Simplified language in word problems Visuals Flashcards Multiple-meaning words Bilingual dictionary/picture dictionary Math Support, Learning Support, or ELL Teachers as appropriate and based on need Gifted Modifications

N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.

N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

A.SSE.1 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.

A.CED.1 Create equations and inequalities in one variable and use them to solve

Page 34 of 53

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs Students

(SE, ELL, 504, G&T)

problems. Include equations arising from linear functions.

each step in the process and the solution. Create linear equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 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.

http://prc.parcconline.org http://asvabtestbank.com http://khanacademy.com http://engageny.org http://ixl.com Vocabulary: real numbers natural numbers whole numbers integers rational numbers irrational numbers simplify evaluate distributive property like terms absolute value inverse operations equation inequality domain function percent of change ratio proportion square root multiplication property power of a power distributive property over multiplication

Develop and/or apply number theory concepts to find common factors and multiples. Lesson 2 Model and solve

real‐world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations. Lesson 4 Apply concepts of radicals and integer exponents to generate equivalent expressions. Lesson 5 Distinguish between rational and irrational numbers using their properties. Lesson 6 Estimate irrational numbers by comparing them to rational numbers.

Ability to identify parts of an expression such as terms, factors, coefficients, etc. for linear, quadratic and exponential expressions. Ability to interpret and apply rules for order of operations for linear, quadratic and exponential expressions. Ability to use properties of mathematics to alter the structure of an expression. Ability to select and then use an appropriate factoring technique. Ability to connect the factors, zeros and x-intercepts of a graph. Ability to use the Zero-Product Property to solve

athematics.org/standards/k8 http://wiki.warren.kyschools.us/groups/wcpscommoncorestandards/ www.teachingchannel.org http://www.learnzillion.com Study Island, other resources below: Operations with Real Numbers and Expressions Pearson Algebra I: Units 1, 2, 3, 4, 8, 9, 10, 11, 12 Thinking Maps Graphing calculator Google Forms Exit Tickets

Pace Activities at Which They Learn Deeper levels of understanding and abstraction are possible for most mathematical topics, so differentiation becomes important. Varied Topics Meeting Student Interest Pre-Assessments Students Create assessments that allow for differences in understanding, creativity, and accomplishment. Use supplemental materials that provide more enriched opportunities. Use multiple resources. Use inquiry-based, discovery learning approaches that emphasize open-ended problems with multiple solutions or multiple paths to solutions. Allow students to design their own ways to find the answers to complex questions. Gifted students may discover more than you thought was possible. Use lots of higher-level questions in justification and discussion of problems. Ask "why" and

A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A.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.

A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Page 35 of 53

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs Students

(SE, ELL, 504, G&T)

and division (power of a product / power of a quotient) division property exponent zero exponent negative exponent undefined values monomial binomial trinomial quadratic function polynomial roots or zeros of quadratic functions

Lesson 7 Apply and extend the properties of exponents to solve problems with rational exponents. Lesson 8: Apply properties of rational and irrational numbers to solve real‐world or mathematical problems. Lesson 9: Interpret the structure of expressions to represent a quantity in terms of its context. Lesson 10: Write expressions in equivalent forms to solve problems. Lesson 11: Extend the knowledge of arithmetic operations and apply to polynomials.

quadratic equations Ability to recognize key features of a quadratic model given in vertex form. Ability to connect experience with properties of exponents to more complex expressions by writing expressions in different forms. Ability to show that when polynomials are added, subtracted or multiplied that the result is another polynomial. Ability to identify the mathematic property (addition property of equality, distributive property, etc.) used at each step in the solution process as a means of justifying

"what if" questions. Provide units, activities, or problems that extend beyond the normal curriculum. Offer challenging mathematical recreations such as puzzles and games. 504 Accommodations Extra time to complete assigned work Simplify complex directions Break long assignments into smaller parts Provide auditory directions, cues, and clues Use tactile and manipulative aides in teaching Provide simultaneous visual, auditory, and kinesthetic experiences Provide cognitive behavioral feedback: positive feedback for attention to task (frequency based on what student can currently do) short-term reinforcers (e.g. happy face, check mark, star, in-class rewards) and long-term (e.g. accumulate points for rewards at home) Permit use of calculator Provide graph paper to

Page 36 of 53

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs Students

(SE, ELL, 504, G&T)

Lesson 12: Use polynomial identities to solve problems. Lesson 13: Extend the knowledge of rational functions to rewrite in equivalent forms. Lesson 14: Use reasoning to solve equations and justify the solution method.

a step. Ability to simplify/reduce a rational algebraic expression.

space numbers Model correct computational procedure Encourage self-talk Provide enlarged print problems and work area Encourage turning lined paper sideways to maintain column alignment

Page 37 of 53

Unit 2 Standards Overview

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs

Students (SE, ELL, 504, G&T)

A.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Solve systems of linear equations in two variables graphically and algebraically. Include solutions that have been found by replacing one equation by the sum of that equation and a multiple of the other. Find approximate solutions of linear equations by making a table of values, using technology to graph and successive approximations. Graph equations, inequalities, and systems of inequalities in two variables and explain that the solution to an equation is all points along the curve, the solution to a system of linear functions is the point of intersection, and the solution to a system of

Pearson SuccessNet On-Line Teacher’s Edition Pearson Online Resources and Materials Study Island Web-Based Math Resources Pearson SuccessNet On-Line Teacher’s Edition Pearson Online Resources and Materials Study Island Web-Based Math Resources http://www.artofproblemsolving.com/liz/Alcumus/index.php Various leveled texts available via hard copy and on line. CSI Algebra eBook CSI Pre-Algebra eBook

Guided Instruction of content using: Small Group Targeted Instruction- Leveled by Reading Level Interactive Notebook Student Responses to concept Open-ended Questions Activity Labs Guided problem solving Math Puzzles Task Cards Scavenger Hunts Standardized test items Lesson 1: Analyze and solve linear equations and

Ability to choose appropriate units of measure to represent context of the problem. Ability to convert units of measure using dimensional analysis. Ability to select and use units of measure to accurately model a given real world scenario. Knowledge of and ability to apply rules of significant digits. Ability to use precision of initial measurements to determine the level of precision with which answers can be reported. Ability to solve linear equations. Ability to set up and solve proportions. Ability to determine if a relation is a

Formative: Journals KWL chart Questioning Whiteboard Activities Daily Checks Homework Quizzes Constructed Response Performance tasks Exit slips Room Wrap Around Jig Saw Graphic Organizers Summative: NJ DOE Model Curriculum Assessment Performance Based Assessments Quizzes Lesson Tests Open-Ended Responses Group and Individual Projects

Study Island http://www.khanacademy.org Thinkfinity website: http://www.thinkfinity.org/home IXL Website: http://www.IXL.com/math/ United Streaming: http://streaming.discoveryeducation.com/index.cfm http://edhelper.com/place_value.html http://illuminations.nctm.org http://insidemathematics.org www.teachingchannel.org http://illustrative

Special Education Accommodations Web-based Math Resources Teacher generated/differentiated instruction activities Small group instruction Adapted assignments Additional time Alternative Assessments Chunking of content, assignment and/or assessments One-on-one re-teaching Volunteer/peer tutoring Accommodations based on IEP and/or need ELL Accommodations Use of Manipulatives Simplified language in word problems Visuals Flashcards Multiple-meaning words Bilingual dictionary/picture dictionary Math Support, Learning Support, or

A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

A.REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Page 38 of 53

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs

Students (SE, ELL, 504, G&T)

A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

inequalities is the intersection of the corresponding half-planes; describe constraints with linear equations and inequalities and systems of equations and/or inequalities to determine if solutions are viable or non-viable. Write a function for a geometric sequence defined recursively, whose domain is a subset of the integers. Explain and interpret the definition of functions including domain and range and how they are related; correctly use function notation in a context and evaluate functions for inputs and their corresponding outputs. Graph functions by hand (in simple cases) and with technology (in complex cases) to

CC Stations Alg.1 Access to below level resources can be found in other texts used in the department (Algebra 1 Foundations) http://www.phsuccessnet.com http://collegeboard.org http://prc.parcconline.org http://asvabtestbank.com http://khanacademy.com http://engageny.org http://ixl.com Vocabulary: independent variable dependent variable function solving equations literal equations inverse operations domain range origin y-intercept x-intercept axis rate of change systems of equations

pairs of simultaneous linear equations. Lesson 2: Define, evaluate, and compare functions. Lesson 3: Use concepts of functions to model relationships between quantities. Lesson 4: Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays. Lesson 5: Use units as a way to understand problems and to guide the solution of

multi‐step problems. Lesson 6: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Lesson 7: Write functions or sequences that model relationships

function. Ability to identify the domain and range of a function from multiple representations. Ability to use functional notation. Knowledge of and ability to apply the vertical line test. Ability to write arithmetic sequences and the relationship as an example of linear functions. Ability to relate the concept of domain to each function studied. Ability to translate from algebraic representations to graphic or numeric representations and identify key features using the various representations. Ability to describe the restrictions on the domain of all functions based on

mathematics.org/standards/k8 http://wiki.warren.kyschools.us/groups/wcpscommoncorestandards / http://www.learnzillion.com

ELL Teachers as appropriate and based on need Gifted Modifications Pace Activities at Which They Learn Deeper levels of understanding and abstraction are possible for most mathematical topics, so differentiation becomes important. Varied Topics Meeting Student Interest Pre-Assessments Students Create assessments that allow for differences in understanding, creativity, and accomplishment. Use supplemental materials that provide more enriched opportunities. Use multiple resources. Use inquiry-based, discovery learning approaches that emphasize open-ended problems with multiple solutions or multiple paths to solutions. Allow students to design

A.CED.3 Represent 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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x

is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

F.IF.2 Use function notation, evaluate functions for inputs in their domains, and

Page 39 of 53

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs

Students (SE, ELL, 504, G&T)

interpret statements that use function notation in terms of a context.

describe linear relationships between two quantities and identify, describe, and compare domain and other key features in one or multiple representations. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

elimination method for solving systems of equations substitution method for solving systems of equations graphing method for solving systems of equations

between two quantities. Lesson 8: Create and graph equations or inequalities to describe numbers or relationships. Lesson 9: Apply inverse operations to solve equations or formulas for a given variable. Lesson 10: Use reasoning to solve equations and justify the solution method. Lesson 11: Represent, solve, and interpret equations and inequalities.

real world context. Ability to graph linear functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Ability to write a function that describes a relationship between two quantities.

their own ways to find the answers to complex questions. Gifted students may discover more than you thought was possible. Use lots of higher-level questions in justification and discussion of problems. Ask "why" and "what if" questions. Provide units, activities, or problems that extend beyond the normal curriculum. Offer challenging mathematical recreations such as puzzles and games. 504 Accommodations Extra time to complete assigned work Simplify complex directions Break long assignments into smaller parts Provide auditory directions, cues, and clues Use tactile and manipulative aides in teaching Provide simultaneous

F.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.

F.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.

F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear functions.

F.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

Page 40 of 53

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs

Students (SE, ELL, 504, G&T)

an algebraic expression for another, say which has the larger maximum.

visual, auditory, and kinesthetic experiences Provide cognitive behavioral feedback: positive feedback for attention to task (frequency based on what student can currently do) short-term reinforcers (e.g. happy face, check mark, star, in-class rewards) and long-term (e.g. accumulate points for rewards at home) Permit use of calculator Provide graph paper to space numbers Model correct computational procedure

Page 41 of 53

Unit 3 Standards Overview

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs Students (SE, ELL,

504, G&T)

A.SSE.1 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.

Interpret parts of expressions in terms of context including those that represent square and cube roots; use the structure of an expression to identify ways to rewrite it. Rewrite expressions using factoring, completing the square and properties of exponents to produce equivalent forms that highlight particular properties such as the zeros or the maximum or minimum value of the function. Perform addition, subtraction and multiplication with polynomials and relate it to arithmetic operations with integers. Create equations and inequalities in one variable and use them to solve

Pearson SuccessNet On-Line Teacher’s Edition Pearson Online Resources and Materials Study Island Web-Based Math Resources Pearson SuccessNet On-Line Teacher’s Edition Pearson Online Resources and Materials Study Island Web-Based Math Resources http://www.artofproblemsolving.com/liz/Alcumus/index.php Various leveled texts available via hard copy and on line. CSI Algebra eBook CSI Pre-Algebra eBook

Guided Instruction of content using: Small Group Targeted Instruction- Leveled by Reading Level Interactive Notebook Student Responses to concept Open-ended Questions Activity Labs Guided problem solving Math Puzzles Task Cards Scavenger Hunts Standardized test items Lesson 1: Choose a level of accuracy appropriate

Ability to create equations in one variable and use them to solve problems. Ability to find solutions of systems of linear equations in real world situations. Ability to determine unknown parameters needed to create an equation that accurately models a given situation. Ability to represent constraints by equations and by systems of equations and interpret solutions as viable or non-viable options in a modeling

Formative: Journals KWL chart Questioning Whiteboard Activities Daily Checks Homework Quizzes Constructed Response Performance tasks Exit slips Room Wrap Around Jig Saw Graphic Organizers Summative: NJ DOE Model Curriculum Assessment Performance Based Assessments Quizzes Lesson Tests Open-Ended Responses Group and Individual Projects

Study Island http://www.khanacademy.org/ Thinkfinity website: http://www.thinkfinity.org/ IXL Website: http://www.IXL.com/math/ United Streaming: http://streaming.discoveryeducation.com/index.cfm http://edhelper.com/place_value.html http://illuminations.nctm.org http://insidemathematics.org www.teachingchannel.org http://illustrativ

Special Education Accommodations Web-based Math Resources Teacher generated/differentiated instruction activities Small group instruction Adapted assignments Additional time Alternative Assessments Chunking of content, assignment and/or assessments One-on-one re-teaching Volunteer/peer tutoring Accommodations based on IEP and/or need ELL Accommodations Use of Manipulatives Simplified language in word problems Visuals Flashcards Multiple-meaning words Bilingual dictionary/picture dictionary Math Support, Learning Support, or ELL Teachers as appropriate and based on need Gifted Modifications Pace Activities at Which They Learn Deeper levels of

A.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).

A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

Page 42 of 53

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs Students (SE, ELL,

504, G&T)

c. 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%.

problems. Include equations arising from linear and quadratic functions, simple rational and exponential functions and highlighting a quantity of interest in a formula. Create linear and quadratic equations that represent a relationship between two or more variables. Graph equations on the coordinate axes with labels and scale. Solve quadratic equations in one variable using a variety of methods [including inspection (e.g. x2 = 81), factoring, completing the square, and the quadratic formula]. Derive the quadratic formula by completing the square and recognize when there are no real solutions

CC Stations Alg.1 Access to below level resources can be found in other texts used in the department (Algebra 1 Foundations) http://www.phsuccessnet.com http://collegeboard.org http://prc.parcconline.org http://asvabtestbank.com http://khanacademy.com http://engageny.org http://ixl.com Vocabulary: independent variable dependent variable function domain range origin y-intercept x-intercept axis systems of inequalities solving systems of inequalities

to limitations on measurement when reporting quantities. Lesson 2: Create and graph equations or inequalities to describe numbers or relationships. Lesson 3: Use reasoning to solve equations and justify the solution method. Lesson 4: Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

context. Ability to distinguish between a mathematical solution and a contextual solution. Ability to recognize/create equivalent forms of literal equations. Ability to solve absolute value equations and inequalities.

emathematics.org/standards/k8 http://wiki.warren.kyschools.us/groups/wcpscommoncorestandards/ http://www.learnzillion.com

understanding and abstraction are possible for most mathematical topics, so differentiation becomes important. Varied Topics Meeting Student Interest Pre-Assessments Students Create assessments that allow for differences in understanding, creativity, and accomplishment. Use supplemental materials that provide more enriched opportunities. Use multiple resources. Use inquiry-based, discovery learning approaches that emphasize open-ended problems with multiple solutions or multiple paths to solutions. Allow students to design their own ways to find the answers to complex questions. Gifted students may discover more than you thought was possible. Use lots of higher-level questions in justification and discussion of problems. Ask "why" and "what if" questions. Provide units, activities, or problems that extend beyond the normal curriculum. Offer challenging mathematical recreations such as puzzles and games. 504 Accommodations

A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A.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

Page 43 of 53

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs Students (SE, ELL,

504, G&T)

to highlight resistance R. absolute value absolute value inequalities

Extra time to complete assigned work Simplify complex directions Break long assignments into smaller parts Provide auditory directions, cues, and clues Use tactile and manipulative aides in teaching Provide simultaneous visual, auditory, and kinesthetic experiences Provide cognitive behavioral feedback: positive feedback for attention to task (frequency based on what student can currently do) short-term reinforcers (e.g. happy face, check mark, star, in-class rewards) and long-term (e.g. accumulate points for rewards at home) Permit use of calculator Provide graph paper to space numbers Model correct computational procedure Encourage self-talk Provide enlarged print problems and work area Encourage turning lined paper sideways to maintain column alignment

A.REI.4 Solve quadratic equations in one variable. a. 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. b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Page 44 of 53

Unit 4 Standards Overview

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs

Students (SE, ELL, 504, G&T)

A.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.

Interpret parts of expressions in terms of context including those that represent square and cube roots; use the structure of an expression to identify ways to rewrite it. Rewrite expressions using factoring, completing the square and properties of exponents to produce equivalent forms that highlight particular properties such as the zeros or the maximum or minimum value of the function. Perform addition, subtraction and multiplication with polynomials and relate it to arithmetic operations with integers. Create equations and inequalities in one variable and use them to solve problems. Include

Pearson SuccessNet On-Line Teacher’s Edition Pearson Online Resources and Materials Study Island Web-Based Math Resources Pearson SuccessNet On-Line Teacher’s Edition Pearson Online Resources and Materials Study Island Web-Based Math Resources http://www.artofproblemsolving.com/liz/Alcumus/index.php Various leveled texts available via hard copy and on line. CSI Algebra eBook CSI Pre-Algebra eBook

Guided Instruction of content using: Small Group Targeted Instruction- Leveled by Reading Level Interactive Notebook Student Responses to concept Open-ended Questions Activity Labs Guided problem solving Math Puzzles Task Cards Scavenger Hunts Standardized test items Lesson 1: Understand the connections between

Ability to determine if a relation is a function. Ability to analyze data for the existence of a pattern and represent the pattern algebraically and/or graphically. Ability to determine whether a relation is a function, given a set of points or a graph. Ability to identify the domain and range of a function from multiple representations. Ability to use of function notation. Knowledge of and ability to apply the vertical line test. Ability to make connections between context and algebraic representations which use function

Formative: Journals KWL chart Questioning Whiteboard Activities Daily Checks Homework Quizzes Constructed Response Performance tasks Exit slips Room Wrap Around Jig Saw Graphic Organizers Summative: NJ DOE Model Curriculum Assessment Performance Based Assessments Quizzes Lesson Tests Open-Ended Responses Group and Individual Projects

Study Island http://www.khanacademy.org / Thinkfinity website: http://www.thinkfinity.org/home IXL Website: http://www.IXL.com/math/ United Streaming: http://streaming.discoveryeducation.com/index.cfm http://edhelper.com/place_value.html http://illuminations.nctm.org http://insidemathematics.org www.teachingchannel.org http://illustrative

Special Education Accommodations Web-based Math Resources Teacher generated/differentiated instruction activities Small group instruction Adapted assignments Additional time Alternative Assessments Chunking of content, assignment and/or assessments One-on-one re-teaching Volunteer/peer tutoring Accommodations based on IEP and/or need ELL Accommodations Use of Manipulatives Simplified language in word problems Visuals Flashcards Multiple-meaning words Bilingual dictionary/picture dictionary Math Support, Learning Support, or ELL Teachers as appropriate and based on need

N.RN.3

Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a non-zero rational number and an irrational number is irrational.

F.IF.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior;

and periodicity. ★

F.IF.5

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

Page 45 of 53

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs

Students (SE, ELL, 504, G&T)

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. ★

equations arising from linear and quadratic functions, simple rational and exponential functions and highlighting a quantity of interest in a formula. Create linear and quadratic equations that represent a relationship between two or more variables. Graph equations on the coordinate axes with labels and scale. 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 (e.g. x2 = 81), factoring, completing the square, and the quadratic formula].

CC Stations Alg.1 Access to below level resources can be found in other texts used in the department (Algebra 1 Foundations) http://www.phsuccessnet.com http://collegeboard.org http://prc.parcconline.org http://asvabtestbank.com http://khanacademy.com http://engageny.org http://ixl.com Vocabulary: linear equation arithmetic sequence common difference geometric sequence common ratio term continuous data discrete data relation function function notation vertical line test

proportional relationships, lines, and linear equations. Lesson 2: Define, evaluate, and compare functions. Lesson 3: Use concepts of functions to model relationships between quantities. Lesson 4: Use the concept and notation of functions to interpret and apply them in terms of their context. Lesson 5: Graph and analyze functions and use their properties to make connections between the different representations. Lesson 6: Write functions or sequences that model relationships between two quantities. Lesson 7: Interpret the effects

notation to write arithmetic and geometric sequences. Emphasize arithmetic and geometric sequences as examples of linear and exponential functions. Ability to translate from algebraic representations to graphic or numeric representations and identify key features using the various representations. Ability to relate the concept of domain to each function studied. Ability to describe the restrictions on the domain of all functions based on real world context. Knowledge that the rate of change of a function can be positive, negative or zero.

mathematics.org/standards/k8 http://wiki.warren.kyschools.us/groups/wcpscommoncorestandards/ http://www.learnzillion.com

Gifted Modifications Pace Activities at Which They Learn Deeper levels of understanding and abstraction are possible for most mathematical topics, so differentiation becomes important. Varied Topics Meeting Student Interest Pre-Assessments Students Create assessments that allow for differences in understanding, creativity, and accomplishment. Use supplemental materials that provide more enriched opportunities. Use multiple resources. Use inquiry-based, discovery learning approaches that emphasize open-ended problems with multiple solutions or multiple paths to solutions. Allow students to design their own ways to find the answers to complex questions. Gifted students may discover more than you

F.IF.6

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change

from a graph. ★

F.IF.7

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more

complicated cases. ★

a. Graph linear and quadratic functions and show intercepts, maxima, and minima.

b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

F.IF.8a

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of

Page 46 of 53

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs

Students (SE, ELL, 504, G&T)

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.

domain range translation linear function graph quadratic function graph absolute value function graph exponential growth exponential function graph square root function graph rational function graph

transformations have on functions and find the inverses of functions. Lesson 8: Interpret functions in terms of the situations they model. Lesson 9: Summarize, represent, and interpret data on two categorical and quantitative variables. Lesson 10: Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays. Lesson 12: Use units as a way to understand problems and to guide the

solution of multi‐step problems.

Ability to identify the rate of change from multiple representations. Determine an explicit expression, a recursive process, or steps for calculations from a context. Ability to focus on vertical translations of graphs of linear and exponential functions. Relate the vertical translation of a linear function to its y-intercept. Ability to compare the graphs of linear functions, quadratic functions, absolute value functions, square root functions, and exponential functions and identify main components and equations for each. Knowledge of the characteristics of categorical data. Ability to recognize types of relationships

thought was possible. Use lots of higher-level questions in justification and discussion of problems. Ask "why" and "what if" questions. Provide units, activities, or problems that extend beyond the normal curriculum. Offer challenging mathematical recreations such as puzzles and games. 504 Accommodations Extra time to complete assigned work Simplify complex directions Break long assignments into smaller parts Provide auditory directions, cues, and clues Use tactile and manipulative aides in teaching Provide simultaneous visual, auditory, and kinesthetic experiences Provide cognitive behavioral feedback: positive feedback for attention to task (frequency based on what student can

F.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.

F.BF.1 Write a function that describes a relationship

between two quantities. ★

a. Determine an explicit expression, a recursive process, or steps for calculation from a context.

F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their

Page 47 of 53

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs

Students (SE, ELL, 504, G&T)

graphs and algebraic expressions for them.

that lend themselves to linear and exponential models. Ability to create and use regression models to represent a contextual situation.

currently do) short-term reinforcers (e.g. happy face, check mark, star, in-class rewards) and long-term (e.g. accumulate points for rewards at home) Permit use of calculator Provide graph paper to space numbers Model correct computational procedure Encourage self-talk Provide enlarged print problems and work area Encourage turning lined paper sideways to maintain column alignment

F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.

a. Prove that linear functions grow by equal differences over equal intervals;

and that exponential functions grow by equal factors over equal intervals.

b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative another.

F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly,

Page 48 of 53

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs

Students (SE, ELL, 504, G&T)

quadratically, or (more generally) as a polynomial function.

F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

Page 49 of 53

Unit 5 Standards Overview

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs

Students (SE, ELL, 504, G&T)

S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).

Represent data on the real number line (i.e. dot plots, histograms, and box plots) and use statistics, appropriate to the shape of the data distribution, to interpret and compare center and spread in the context of the data (account for effects of outliers) Summarize and interpret categorical data for two categories in two-way frequency tables; recognize associations and trends in the data. Represent and describe data for two variables on a scatter plot, fit a function to the data, analyze residuals (in order to informally assess fit), and use the function to solve problems. Uses a given function or choose a function suggested by the context.

Pearson SuccessNet On-Line Teacher’s Edition Pearson Online Resources and Materials Study Island Web-Based Math Resources Pearson SuccessNet On-Line Teacher’s Edition Pearson Online Resources and Materials Study Island Web-Based Math Resources http://www.artofproblemsolving.com/liz/Alcumus/index.php Various leveled texts available via hard copy and on line. CSI Algebra eBook CSI Pre-Algebra eBook

Guided Instruction of content using: Small Group Targeted Instruction- Leveled by Reading Level Interactive Notebook Student Responses to concept Open-ended Questions Activity Labs Guided problem solving Math Puzzles Task Cards Scavenger Hunts Standardized test items Lesson 1: Analyze and/or interpret bivariate data displayed in

Ability to identify, describe, and/or use constant rates of change. Knowledge that the rate of change of a function can be positive, negative, zero, or none. Ability to identify the rate of change from multiple representations. Ability to identify the domain and range of a function from multiple representations. Ability to translate from algebraic representations to graphic or numeric representations and identify key features using the various representations. Ability to identify or write a linear equation when given various parts of a linear equation, table

Formative: Journals KWL chart Questioning Whiteboard Activities Daily Checks Homework Quizzes Constructed Response Performance tasks Exit slips Room Wrap Around Jig Saw Graphic Organizers Summative: NJ DOE Model Curriculum Assessment Performance Based Assessments Quizzes Lesson Tests Open-Ended Responses Group and Individual Projects

Study Island http://www.khanacademy.org/ Thinkfinity website: http://www.thinkfinity.org/home IXL Website: http://www.IXL.com/math/ United Streaming: http://streaming.discoveryeducation.com/index.cfm http://edhelper.com/place_value.html http://illuminations.nctm.org http://insidemathematics.org www.teachingchannel.org http://illustrativemathematics.org/standards/k8

Special Education Accommodations Web-based Math Resources Teacher generated/differentiated instruction activities Small group instruction Adapted assignments Additional time Alternative Assessments Chunking of content, assignment and/or assessments One-on-one re-teaching Volunteer/peer tutoring Accommodations based on IEP and/or need ELL Accommodations Use of Manipulatives Simplified language in word problems Visuals Flashcards Multiple-meaning words Bilingual dictionary/picture

S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

S.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).

S.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.

S.ID.6a Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

a. Fit a function to the data; use functions fitted to data to solve problems in the

Page 50 of 53

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs

Students (SE, ELL, 504, G&T)

context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models.

Emphasize linear and exponential models. Interpret the slope and intercept of a linear model in the context of the data; compute (using technology) and interpret the correlation coefficient of a linear fit. Distinguish between correlation and causation.

CC Stations Alg.1 Access to below level resources can be found in other texts used in the department (Algebra 1 Foundations) http://www.phsuccessnet.com http://collegeboard.org http://prc.parcconline.org http://asvabtestbank.com http://khanacademy.com http://engageny.org http://ixl.com Vocabulary: linear equation rate of change slope y-intercept x-intercept domain range origin slope-intercept form standard form point-slope form outliers

multiple representations. Lesson 2: Use concepts of functions to model relationships between quantities. Lesson 3: Use the concept and notation of functions to interpret and apply them in terms of their context. Lesson 4: Graph and analyze functions and use their properties to make connections between the different representations. Lesson 5: Write functions or sequences that model relationships between two quantities. Lesson 6: Construct and compare linear, quadratic, and exponential models to solve problems. Lesson 7:

or graph. Ability to determine the slope and/or y-intercept represented by a linear equation or graph. Ability to describe the restrictions on the domain of all functions based on real world context. Ability to focus on vertical translations of graphs of linear functions. Relate the vertical translation of a linear function to its y-intercept. Knowledge of the characteristics of categorical data. Ability to translate from linear algebraic representations to graphic or numeric representations and identify key features using the various representations. Ability to recognize types of relationships that lend themselves to linear models.

http://wiki.warren.kyschools.us/groups/wcpscommoncorestandards/ http://www.learnzillion.com

dictionary Math Support, Learning Support, or ELL Teachers as appropriate and based on need Gifted Modifications Pace Activities at Which They Learn Deeper levels of understanding and abstraction are possible for most mathematical topics, so differentiation becomes important. Varied Topics Meeting Student Interest Pre-Assessments Students Create assessments that allow for differences in understanding, creativity, and accomplishment. Use supplemental materials that provide more enriched opportunities. Use multiple resources. Use inquiry-based, discovery learning approaches that emphasize open-

S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.

S.ID.9 Distinguish between correlation and causation.

Page 51 of 53

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs

Students (SE, ELL, 504, G&T)

quartile interquartile range measure of central tendency dependent events independent events box and whisker plots stem and leaf plots favorable outcome scatter plot line of best fit

Interpret functions in terms of the situations they model. Lesson 8: Summarize, represent, and interpret data on a single count or measurement variable. Lesson 9: Summarize, represent, and interpret data on two categorical and quantitative variables. Lesson 10: Analyze linear models to make interpretations based on the data. Lesson 11: Summarize, represent, and interpret data on a single count or measurement variable. Lesson 12: Analyze linear models to make interpretations based

Ability to create and use regression models to represent a contextual situation. Knowledge of the characteristics of categorical data. Ability to read and use a two-way frequency table. Ability to read a segmented bar graph. Ability to recognize types of relationships that lend themselves to linear and exponential models. Ability to create and use regression models to represent a contextual situation. Ability to create a graphic display of residuals. Ability to recognize patterns in residual plots. Ability to calculate error margins

ended problems with multiple solutions or multiple paths to solutions. Allow students to design their own ways to find the answers to complex questions. Gifted students may discover more than you thought was possible. Use lots of higher-level questions in justification and discussion of problems. Ask "why" and "what if" questions. Provide units, activities, or problems that extend beyond the normal curriculum. Offer challenging mathematical recreations such as puzzles and games. 504 Accommodations Extra time to complete assigned work Simplify complex directions Break long assignments into smaller parts Provide auditory

Page 52 of 53

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs

Students (SE, ELL, 504, G&T)

on the data. Lesson 13: Recognize and evaluate random processes underlying statistical experiments. Lesson 14: Make inferences and justify conclusions based on sample surveys, experiments, and observational studies. Lesson 15: Apply the rules of probability to compute probabilities of compound events in a uniform probability model.

(residuals) with a calculator. Ability to recognize a linear relationship displayed in a scatter plot. Ability to determine an equation for the line of best fit for a set of data points. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Knowledge of the range of values and the interpretation of those values for correlation coefficients (-1 ≤ r ≤ 1). Ability to compute and analyze the correlation coefficient for the purpose of communicating the goodness of fit of a linear model for a given data set. Ability to provide examples of two

directions, cues, and clues Use tactile and manipulative aides in teaching Provide simultaneous visual, auditory, and kinesthetic experiences Provide cognitive behavioral feedback: positive feedback for attention to task (frequency based on what student can currently do) short-term reinforcers (e.g. happy face, check mark, star, in-class rewards) and long-term (e.g. accumulate points for rewards at home) Permit use of calculator Provide graph paper to space numbers Model correct computational procedure Encourage self-talk Provide enlarged print problems and work area Encourage turning lined paper sideways to maintain column alignment

Page 53 of 53

Algebra 1 Standards

Domain & Standard

Standard Statement Student Learning Objectives (SLO)

Leveled Materials and Media/School Library Resources

Suggested Instructional

Activities

Suggested Student Output

Assessments: Portfolios,

Evaluations, & Rubrics

Multimedia Integration

Accommodation of Special Needs

Students (SE, ELL, 504, G&T)

variables that have a strong correlation but one does not cause the other. Ability to find probabilities for compound