ALGEBRA 100 HONORS GRADE: 8

ALGEBRA 100 HONORS GRADE: 8 Prerequisite: Pre Algebra, Grade 7 or Pre Algebra Honors, Grade 7; teacher recommendation Credits: 5 ABSTRACT This full year course prepares students for more rigorous study in higher honors mathematics courses by providing the necessary foundations of algebraic concepts and skills. In order to accomplish this, emphasis will be placed on the following: developing number sense and an ability to represent numbers in a variety of forms; understanding, selecting and applying various methods of performing numerical operations; understanding the symbolism of algebra, using exponents, solving linear equations and inequalities; applying absolute value; factoring expressions; exploring real numbers; understanding the basic concepts of coordinate geometry, developing spatial sense and an ability to use geometric properties and relationships; identifying quadratic functions; introducing basic trigonometric functions; developing the understanding of patterns, relationships and functions to analyze real world situations; using statistical analysis and probability to describe data; model situations and support appropriate inferences and arguments; applying the concepts of discrete mathematics to model and explore a variety of practical situations; using a variety of estimation strategies and recognizing situations in which estimation is appropriate. Students will use all available technology to enhance mathematical knowledge and application. Technology usage is recommended through the use of graphing calculators and computers. They will analyze relationships among variables and quantities and use these relationships to solve real-world problems, ranging from everyday applications to the

sciences. They will develop reasoning ability and will become self-reliant, independent mathematical thinkers willing to take part in decision-making and risk-taking in order to arrive at reasonable conclusions. They will be able to pose and solve mathematical problems found in all disciplines. UNIT: 1: Tools of Algebra September 2: Solving Equations & Inequalities October-November 24 days 3: Solving & Applying Proportions November ESTABLISHED GOALS: (NJ CCCS and/or CCS) STAGE 1: DESIRED RESULTS What will students understand as a result of the unit? What are the BIG ideas? Math CCSS EE.8.7, SP.8.1 A-REI.1 Math CCSS EE.8.7 A-CED.1, A-REI.3 Math CCSS EE.8.5 A-SSE.1 Technology CCCS 8.1, 8.2 Technology CCCS 8.1, 8.2 Technology CCCS 8.1, 8.2 ENDURING UNDERSTANDINGS: (Students will Understand that...) 21st Century Life and Careers CCCS 9.1, 9.2, 9.3 will use variables to transform English phrases into mathematical expressions. will extend your ability to calculate with whole numbers, decimals, and factions to include integers. will use the order of operations and the distributive property to simplify expressions. will show the relationship between two sets of real-world data, using a scatter plot. 2 21st Century Life and Careers CCCS 9.1, 9.2, 9.3 will solve equations, including equations with variables on both sides, using properties of equality. will develop the ability to solve problems by defining variables, relating them to one another, and writing an equation. will use measures of central tendency to describe a set of data. will learn how to graph inequalities. will solve inequalities, noting the differences from the methods used 21st Century Life and Careers CCCS 9.1, 9.2, 9.3 will find ratios and rates to model real-world situations. will use proportions to measure objects indirectly. will solve problems that involve discounts, taxes, and interest.

ESSENTIAL QUESTIONS: (What provocative questions will foster inquiry, understanding, and transfer of learning?) 1: Tools of Algebra September Why do you sometimes need variables when writing equations to represent real-world situations? Why are the rules for the order of operations necessary? How can you express an integer as a rational number? How would you explain the process for graphing a point on a coordinate plane to another student? 2: Solving Equations & Inequalities October-November 24 days for solving equations. will write and solve compound inequalities by interpreting phrases that use and or or. When solving equations, what type of operations must you use to get the variable alone on one side of the equal sign? How can you clear an equation of fractions or decimals? How is solving an equation with 2 variable terms on the same side of the equal sign different than solving an equation with variable terms on both sides of the equal sign? What are the two ways to help set up a distance problem? When should the mean be used to describe data and when should the median be used? What is the main difference between solving inequalities using multiplication and division and solving equations using multiplication and division? 3: Solving & Applying Proportions November How can you use proportions to find a distance that is difficult to measure? What are two ways to write percent problems? What are the differences between theoretical probability and experimental probability? How does finding the probability of independent events differ from finding the probability of dependent events? 3

1: Tools of Algebra September 2: Solving Equations & Inequalities October-November 24 days 3: Solving & Applying Proportions November STAGE 2: ASSESSMENT EVIDENCE What evidence will be collected to determine whether or not the understandings have been developed, the knowledge and skills attained, and the state standards met? [Anchor the work in performance tasks that involve application, supplemented as needed by prompted work, quizzes, observations, etc.] PERFORMANCE TASKS: (Through what authentic performance tasks will students demonstrate the desired understandings?) (By what criteria will performances of understanding be judged?) OTHER EVIDENCE: (Through what other evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals) will students demonstrate achievement of the desired results?) (How will students self-assess their learning?) Assessments of each learning activity Mathematical Practices: 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. Teacher observations Peer evaluations Rubrics Bulletin Boards of exemplars Tests Quizzes Peer and self evaluations Presentations Daily notes 4 Mathematical Practices: 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. Teacher observations Peer evaluations Rubrics Bulletin Boards of exemplars Tests Quizzes Peer and self evaluations Presentations Daily notes Mathematical Practices: 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. Teacher observations Peer evaluations Rubrics Bulletin Boards of exemplars Tests Quizzes Peer and self evaluations Presentations Daily notes

RESOURCES: 1: Tools of Algebra September 2: Solving Equations & Inequalities October-November 24 days 3: Solving & Applying Proportions November Homework Homework Homework Notebooks/binder Agenda NJ ASK Mathematics Reference Sheet, Grade 8 http://www.phschool.com Manipulatives NJ ASK preparation problems www.funbrain.com Notebooks/binder Agenda NJ ASK Mathematics Reference Sheet, Grade 8 http://www.phschool.com Manipulatives NJ ASK preparation problems www.funbrain.com Notebooks/binder Agenda NJ ASK Mathematics Reference Sheet, Grade 8 http://www.phschool.com Manipulatives NJ ASK preparation problems www.funbrain.com STAGE 3: LEARNING PLAN What learning experiences and instruction will enable students to achieve the desired results? Utilize the WHERETO* acronym to consider key design elements. SKILLS AND TOPICS: (What specific activities will students do and what skills will students know as a result of the unit?) Lessons EE.8.7. Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Solve linear equations with rational number coefficients, including 5 EE.8.7. Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Solve linear equations with rational number coefficients, including equations whose solutions require EE.8.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. A-SSE.1. Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret complicated expressions by

1: Tools of Algebra September 2: Solving Equations & Inequalities October-November 24 days 3: Solving & Applying Proportions November equations whose solutions require expanding expressions using the distributive property and collecting like terms. SP.8.1. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. 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. 8.1 All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problems individually and collaboratively to create and communicate knowledge. 8.2 All students will develop an expanding expressions using the distributive property and collecting like terms. 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-REI.3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 8.1 All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problems individually and collaboratively to create and communicate knowledge. 8.2 All students will develop an understanding of the nature and impact of technology, engineering, technological design and the designed world as they relate to the individual, 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. 8.1 All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problems individually and collaboratively to create and communicate knowledge. 8.2 All students will develop an understanding of the nature and impact of technology, engineering, technological design and the designed world as they relate to the individual, global society, and the environment. 9.1: All students will demonstrate creative, critical thinking, collaboration and problem solving skills to function successfully as global citizens and workers in diverse ethnic and organizational cultures. 9.2: All students will develop skills and strategies that promote personal and financial responsibility related to financial planning, savings, investment, 6

CROSS-CURRICULAR / DIFFERENTIATION: 1: Tools of Algebra September understanding of the nature and impact of technology, engineering, technological design and the designed world as they relate to the individual, global society, and the environment. 9.1: All students will demonstrate creative, critical thinking, collaboration and problem solving skills to function successfully as global citizens and workers in diverse ethnic and organizational cultures. 9.2: All students will develop skills and strategies that promote personal and financial responsibility related to financial planning, savings, investment, and charitable giving in the global economy. 9.3: All students will apply knowledge about and engage in the process of career awareness, exploration, and preparation in order to navigate the globally competitive work environment of the information age. Centers Tiered Lessons Open-Ended Responses 7 2: Solving Equations & Inequalities October-November 24 days global society, and the environment. 9.1: All students will demonstrate creative, critical thinking, collaboration and problem solving skills to function successfully as global citizens and workers in diverse ethnic and organizational cultures. 9.2: All students will develop skills and strategies that promote personal and financial responsibility related to financial planning, savings, investment, and charitable giving in the global economy. 9.3: All students will apply knowledge about and engage in the process of career awareness, exploration, and preparation in order to navigate the globally competitive work environment of the information age. Centers Tiered Lessons Open-Ended Responses 3: Solving & Applying Proportions November and charitable giving in the global economy. 9.3: All students will apply knowledge about and engage in the process of career awareness, exploration, and preparation in order to navigate the globally competitive work environment of the information age. Centers Tiered Lessons Open-Ended Responses

(What cross-curricular (e.g. writing, literacy, math, science, history, 21 st century life and careers, technology) learning activities are included in this unit that will help achieve the desired results?) (What type of differentiated instruction will be used for ELL, SP.ED. and G&T students?) 1: Tools of Algebra September Differentiation: Special Education: Modifications as dictated in the student's IEP Collaboration with resource teacher and parent Positive reinforcement. Modify lesson as needed according to ability. English Language Learners: Use cooperative grouping Provide written and oral instructions. Encourage support from native language speakers who are more proficient in English. Extended time for completing assessments. Gifted and Talented: Advanced Problem Solving Above grade level math placement option for qualified students, including Geometry Honors Higher order, critical and creative thinking skills. Cluster grouping Flexible skill grouping within a class or across grade level for rigor. 8 2: Solving Equations & Inequalities October-November 24 days Differentiation: Special Education: Modifications as dictated in the student's IEP Collaboration with resource teacher and parent Positive reinforcement. Modify lesson as needed according to ability. English Language Learners: Use cooperative grouping Provide written and oral instructions. Encourage support from native language speakers who are more proficient in English. Extended time for completing assessments. Gifted and Talented: Advanced Problem Solving Above grade level math placement option for qualified students, including Geometry Honors Higher order, critical and creative thinking skills. Cluster grouping Flexible skill grouping within a class or across grade level for rigor. 3: Solving & Applying Proportions November Differentiation: Special Education: Modifications as dictated in the student's IEP Collaboration with resource teacher and parent Positive reinforcement. Modify lesson as needed according to ability. English Language Learners: Use cooperative grouping Provide written and oral instructions. Encourage support from native language speakers who are more proficient in English. Extended time for completing assessments. Gifted and Talented: Advanced Problem Solving Above grade level math placement option for qualified students, including Geometry Honors Higher order, critical and creative thinking skills. Cluster grouping Flexible skill grouping within a class or across grade level for rigor. Teacher-selected instructional

1: Tools of Algebra September 2: Solving Equations & Inequalities October-November 24 days 3: Solving & Applying Proportions November Teacher-selected instructional strategies that are focused to provide challenge, engagement, and growth opportunities. Multi-disciplinary unit and/or project. Applied and integrated skills for the 21 st Century learner. Teacher-selected instructional strategies that are focused to provide challenge, engagement, and growth opportunities. Multi-disciplinary unit and/or project. Applied and integrated skills for the 21 st Century learner. strategies that are focused to provide challenge, engagement, and growth opportunities. Multi-disciplinary unit and/or project. Applied and integrated skills for the 21 st Century learner. *WHERETO W = Help the students know WHERE the unit is going and WHAT is expected. Help the teacher know WHERE the students are coming from (prior knowledge, interests). H = HOOK all students and HOLD their interest. E = EQUIP students, help them EXPERIENCE the key ideas and EXPLORE the issue. R = Provide opportunities to RETHINK and REVISE their understandings and work. E = Allow students to EVALUATE their work and its implications. T = TAILORED to the different needs, interests, and abilities of learners. O = ORGANIZE to maximize initial and sustained engagement as well as effective learning. UNIT: 4: Graphs & November-December 5: Linear Equations & Their Graphs December-January 13 days 6: Systems of Equations & Inequalities January-February 12 days 9

ESTABLISHED GOALS: (NJ CCCS and/or CCS) ENDURING UNDERSTANDINGS: (Students will Understand that they will...) 4: Graphs & November-December 5: Linear Equations & Their Graphs December-January 13 days STAGE 1: DESIRED RESULTS What will students understand as a result of the unit? What are the BIG ideas? Math CCSS F.8.1, F.8.2 F-IF.1, F-IF.2, F.BF.2, F-LE.2 Technology CCCS 8.1, 8.2 21st Century Life and Careers CCCS 9.1, 9.2, 9.3 move from the specific case of equations in one variable to the study of functions in two variables. learn about the function rules, and model data using equations, tables, and graphs. learn how to use inductive reasoning for recognizing number patterns called sequences Math CCSS EE.8.6, F.8.3, F.8.4, F.8.5, SP.8.2 A-REI.10, F-IF.5, F-IF.6, F-IF.7a, F-BF.3, F-LE.5 Technology CCCS 8.1, 8.2 21st Century Life and Careers CCCS 9.1, 9.2, 9.3 learn how to write linear equations and recognize their different forms. by working with rate of change, interpret the slope in real-world situations. determine whether the graphs of two linear equations are parallel or perpendicular. 6: Systems of Equations & Inequalities January-February 12 days Math CCSS EE.8.8 A-CED.2, A-REI.5, A-REI.6, A-REI.11 A-REI.12 Technology CCCS 8.1, 8.2 21st Century Life and Careers CCCS 9.1, 9.2, 9.3 extend your ability to solve equations to include solving a system of two equations with two variables. learn methods of solving a linear system and how to determine which method is best for a given situation. graph the solution to a system of linear inequalities. 10

ESSENTIAL QUESTIONS: (What provocative questions will foster inquiry, understanding, and transfer of learning?) 4: Graphs & November-December What are the key differences between relations and functions? What are the advantages and disadvantages of representing functions using rules, tables and graphs? 5: Linear Equations & Their Graphs December-January 13 days What are the two ways to find the slope of a line? How does changing the value of the slope affect the graph of the line? How does changing the value of the y-intercept affect the graph of the line? How do you find the x- and y- intercepts of a linear equation? What is the difference between a trend line and a line of best fit? 6: Systems of Equations & Inequalities January-February 12 days Why is it sometimes easier to solve equations using substitution rather than graphing? When is it best to solve a linear system by elimination and by using substitution? Compare graphing linear inequalities with graphing linear equations. STAGE 2: ASSESSMENT EVIDENCE What evidence will be collected to determine whether or not the understandings have been developed, the knowledge and skills attained, and the state standards met? [Anchor the work in performance tasks that involve application, supplemented as needed by prompted work, quizzes, observations, etc.] PERFORMANCE TASKS: (Through what authentic performance tasks will students demonstrate the desired understandings?) (By what criteria will performances of understanding be judged?) Assessments of each learning activity Mathematical Practices: 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 11 Mathematical Practices: 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. Mathematical Practices: 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.

OTHER EVIDENCE: (Through what other evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals) will students demonstrate achievement of the desired results?) (How will students self-assess their learning?) 4: Graphs & November-December repeated reasoning. Teacher observations Peer evaluations Rubrics Bulletin Boards of exemplars Tests Quizzes Peer and self evaluations Presentations Daily notes Homework 5: Linear Equations & Their Graphs December-January 13 days Teacher observations Peer evaluations Rubrics Bulletin Boards of exemplars Tests Quizzes Peer and self evaluations Presentations Daily notes Homework 6: Systems of Equations & Inequalities January-February 12 days Teacher observations Peer evaluations Rubrics Bulletin Boards of exemplars Tests Quizzes Peer and self evaluations Presentations Daily notes Homework RESOURCES: Notebooks/binder Agenda NJ ASK Mathematics Reference Sheet, Grade 8 http://www.phschool.com Manipulatives NJ ASK preparation problems www.funbrain.com Notebooks/binder Agenda NJ ASK Mathematics Reference Sheet, Grade 8 http://www.phschool.com Manipulatives NJ ASK preparation problems www.funbrain.com Notebooks/binder Agenda NJ ASK Mathematics Reference Sheet, Grade 8 http://www.phschool.com Manipulatives NJ ASK preparation problems www.funbrain.com STAGE 3: LEARNING PLAN What learning experiences and instruction will enable students to achieve the desired results? Utilize the WHERETO* acronym to consider key design elements. SKILLS AND TOPICS: (What specific activities will students do and what skills will students know as F.8.1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an 12 EE.8.6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the EE.8.8. Analyze and solve pairs of simultaneous linear equations. Understand that solutions to a system of two linear equations in two

4: Graphs & November-December 5: Linear Equations & Their Graphs December-January 13 days 6: Systems of Equations & Inequalities January-February 12 days a result of the unit?) input and the corresponding output.1 F.8.2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. 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-BF.2. Write arithmetic and geometric equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. F.8.3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. F.8.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. F.8.5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. 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-REI.5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation 13

4: Graphs & November-December 5: Linear Equations & Their Graphs December-January 13 days 6: Systems of Equations & Inequalities January-February 12 days sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 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). 8.1 All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problems individually and collaboratively to create and communicate knowledge. 8.2 All students will develop an understanding of the nature and impact of technology, engineering, technological design and the designed world as they relate to the individual, global society, and the environment. 9.1: All students will demonstrate creative, critical thinking, collaboration and problem solving skills to function where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. SP.8.2. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. 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). 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. 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.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. 8.1 All students will use digital tools to 14

4: Graphs & November-December 5: Linear Equations & Their Graphs December-January 13 days 6: Systems of Equations & Inequalities January-February 12 days successfully as global citizens and workers in diverse ethnic and organizational cultures. 9.2: All students will develop skills and strategies that promote personal and financial responsibility related to financial planning, savings, investment, and charitable giving in the global economy. 9.3: All students will apply knowledge about and engage in the process of career awareness, exploration, and preparation in order to navigate the globally competitive work environment of the information age. 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. 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 graphs and algebraic expressions for them. F-LE.5. Interpret the parameters in a linear or exponential function in terms access, manage, evaluate, and synthesize information in order to solve problems individually and collaboratively to create and communicate knowledge. 8.2 All students will develop an understanding of the nature and impact of technology, engineering, technological design and the designed world as they relate to the individual, global society, and the environment. 9.1: All students will demonstrate creative, critical thinking, collaboration and problem solving skills to function successfully as global citizens and workers in diverse ethnic and organizational cultures. 9.2: All students will develop skills and strategies that promote personal and financial responsibility related to financial planning, savings, investment, and charitable giving in the global economy. 9.3: All students will apply knowledge about and engage in the process of career awareness, exploration, and preparation 15

4: Graphs & November-December 5: Linear Equations & Their Graphs December-January 13 days 6: Systems of Equations & Inequalities January-February 12 days of a context. 8.1 All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problems individually and collaboratively to create and communicate knowledge. in order to navigate the globally competitive work environment of the information age. 8.2 All students will develop an understanding of the nature and impact of technology, engineering, technological design and the designed world as they relate to the individual, global society, and the environment. 9.1: All students will demonstrate creative, critical thinking, collaboration and problem solving skills to function successfully as global citizens and workers in diverse ethnic and organizational cultures. 16 9.2: All students will develop skills and strategies that promote personal and financial responsibility related to financial planning, savings, investment, and charitable giving in the global economy.

4: Graphs & November-December 5: Linear Equations & Their Graphs December-January 13 days 6: Systems of Equations & Inequalities January-February 12 days CROSS-CURRICULAR: (What cross-curricular (e.g. writing, literacy, math, science, history, 21 st century life and careers, technology) learning activities are included in this unit that will help achieve the desired results?) Centers Tiered Lessons Open-Ended Responses Differentiation: Special Education: Modifications as dictated in the student's IEP Collaboration with resource teacher and parent Positive reinforcement. Modify lesson as needed according to ability. English Language Learners: Use cooperative grouping Provide written and oral instructions. Encourage support from native language speakers who are more proficient in English. Extended time for completing assessments. 17 9.3: All students will apply knowledge about and engage in the process of career awareness, exploration, and preparation in order to navigate the globally competitive work environment of the information age. Centers Tiered Lessons Open-Ended Responses Differentiation: Special Education: Modifications as dictated in the student's IEP Collaboration with resource teacher and parent Positive reinforcement. Modify lesson as needed according to ability. English Language Learners: Use cooperative grouping Provide written and oral instructions. Encourage support from native language speakers who are more proficient in English. Extended time for completing assessments. Centers Tiered Lessons Open-Ended Responses Differentiation: Special Education: Modifications as dictated in the student's IEP Collaboration with resource teacher and parent Positive reinforcement. Modify lesson as needed according to ability. English Language Learners: Use cooperative grouping Provide written and oral instructions. Encourage support from native language speakers who are more proficient in English. Extended time for completing assessments. Gifted and Talented:

4: Graphs & November-December 5: Linear Equations & Their Graphs December-January 13 days 6: Systems of Equations & Inequalities January-February 12 days Gifted and Talented: Advanced Problem Solving Above grade level math placement option for qualified students, including Geometry Honors Higher order, critical and creative thinking skills. Cluster grouping Flexible skill grouping within a class or across grade level for rigor. Teacher-selected instructional strategies that are focused to provide challenge, engagement, and growth opportunities. Multi-disciplinary unit and/or project. Applied and integrated skills for the 21 st Century learner. Gifted and Talented: Advanced Problem Solving Above grade level math placement option for qualified students, including Geometry Honors Higher order, critical and creative thinking skills. Cluster grouping Flexible skill grouping within a class or across grade level for rigor. Teacher-selected instructional strategies that are focused to provide challenge, engagement, and growth opportunities. Multi-disciplinary unit and/or project. Applied and integrated skills for the 21 st Century learner. Advanced Problem Solving Above grade level math placement option for qualified students, including Geometry Honors Higher order, critical and creative thinking skills. Cluster grouping Flexible skill grouping within a class or across grade level for rigor. Teacher-selected instructional strategies that are focused to provide challenge, engagement, and growth opportunities. Multi-disciplinary unit and/or project. Applied and integrated skills for the 21 st Century learner. 18

7: Exponents & Exponential February-March 8: Polynomials & Factoring March 15 days 9: Quadratic Equations & March-April 16 days ESTABLISHED GOALS: (NJ CCCS and/or CCS) ENDURING UNDERSTANDINGS: (Students will Understand that they will...) STAGE 1: DESIRED RESULTS What will students understand as a result of the unit? What are the BIG ideas? Math CCSS EE.8.1, EE.8.3, EE.8.4 F-IF.7e, F-IF.8b, F.BF.2, F-LE.2 Technology CCCS 8.1, 8.2 21st Century Life and Careers CCCS 9.1, 9.2, 9.3 extend their knowledge about exponents to include zero and negative exponents. learn the properties of exponents, and how exponents are used to write a geometric sequence. graph exponential functions by making a table of values. Math CCSS A-SSE.2, A-APR.1, A-APR.7 Technology CCCS 8.1, 8.2 21st Century Life and Careers CCCS 9.1, 9.2, 9.3 categorize polynomials by their degree and number of terms. learn to add, subtract, and multiply polynomials. Math CCSS NS.8.2 A-SSE.3, A-APR.3, A-REI.4, A-REI.10, F-IF.7, F.IF.8, F-LE.1 Technology CCCS 8.1, 8.2 21st Century Life and Careers CCCS 9.1, 9.2, 9.3 examine quadratic graphs and their equations. solve quadratic equations by various techniques. determine an appropriate linear, quadratic, or exponential model for real-world data. 19

7: Exponents & Exponential February-March 8: Polynomials & Factoring March 15 days 9: Quadratic Equations & March-April 16 days ESSENTIAL QUESTIONS: (What provocative questions will foster inquiry, understanding, and transfer of learning?) What is the meaning of a zero exponent? What is the meaning of a negative exponent? How is dividing powers with the same base different from multiplying powers with the same base? How is raising a quotient to a power different than raising a power to a power? How do you square a binomial? How do you determine what numbers are used in the binomial factors when factoring expressions of the type x 2 + bx + c.? What is the first thing you should look for when factoring a trinomial? How do a and c affect a quadratic graph? How many solutions does a quadratic equation have? How can you determine the number of solutions from the graph? How do you complete the square? When is the quadratic formula useful? What is the discriminant and how is it useful? How do you choose between a linear, quadratic, or exponential model for data? STAGE 2: ASSESSMENT EVIDENCE What evidence will be collected to determine whether or not the understandings have been developed, the knowledge and skills attained, and the state standards met? [Anchor the work in performance tasks that involve application, supplemented as needed by prompted work, quizzes, observations, etc.] PERFORMANCE TASKS: (Through what authentic performance tasks will students demonstrate the desired understandings?) (By what criteria will performances of understanding be judged?) Assessments of each learning activity Mathematical Practices: 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. Mathematical Practices: 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. Mathematical Practices: 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. 20

OTHER EVIDENCE: (Through what other evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals) will students demonstrate achievement of the desired results?) (How will students self-assess their learning?) 7: Exponents & Exponential February-March 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. Teacher observations Peer evaluations Rubrics Bulletin Boards of exemplars Tests Quizzes Peer and self evaluations Presentations Daily notes Homework 8: Polynomials & Factoring March 15 days 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Teacher observations Peer evaluations Rubrics Bulletin Boards of exemplars Tests Quizzes Peer and self evaluations Presentations Daily notes Homework 9: Quadratic Equations & March-April 16 days 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Teacher observations Peer evaluations Rubrics Bulletin Boards of exemplars Tests Quizzes Peer and self evaluations Presentations Daily notes Homework RESOURCES: Notebooks/binder Agenda NJ ASK Mathematics Reference Sheet, Grade 8 http://www.phschool.com Manipulatives NJ ASK preparation problems www.funbrain.com Notebooks/binder Agenda NJ ASK Mathematics Reference Sheet, Grade 8 http://www.phschool.com Manipulatives NJ ASK preparation problems www.funbrain.com Notebooks/binder Agenda NJ ASK Mathematics Reference Sheet, Grade 8 http://www.phschool.com Manipulatives NJ ASK preparation problems www.funbrain.com STAGE 3: LEARNING PLAN What learning experiences and instruction will enable students to achieve the desired results? Utilize the WHERETO* acronym to consider key design elements. 21

7: Exponents & Exponential February-March 8: Polynomials & Factoring March 15 days 9: Quadratic Equations & March-April 16 days SKILLS AND TOPICS: (What specific activities will students do and what skills will students know as a result of the unit?) EE.8.1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3 2 3 5 = 3 3 = 1/3 3 = 1/27. EE.8.3. Use numbers expressed in the form of a single digit times a wholenumber power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 10 8 and the population of the world as 7 times 10 9, and determine that the world population is more than 20 times larger. EE.8.4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. F-IF.7. Graph functions expressed A-SSE.2. Use the structure of an expression to identify ways to rewrite it. For example, see x 4 y 4 as (x 2 ) 2 (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 y 2 )(x 2 + y 2 ). 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-APR.7. (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. 8.1 All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problems individually and collaboratively to create and communicate knowledge. NS.8.2. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π 2 ). For example, by truncating the decimal expansion of 2, show that 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. 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 1.15 t can be rewritten as (1.15 1/12 ) 12t 1.012 12t to reveal the approximate 22

7: Exponents & Exponential February-March 8: Polynomials & Factoring March 15 days 9: Quadratic Equations & March-April 16 days symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. F-IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02) t, y = (0.97) t, y = (1.01) 12t, y = (1.2) t/10, and classify them as representing exponential growth or decay. F-BF.2. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model 8.2 All students will develop an understanding of the nature and impact of technology, engineering, technological design and the designed world as they relate to the individual, global society, and the environment. 9.1: All students will demonstrate creative, critical thinking, collaboration and problem solving skills to function successfully as global citizens and workers in diverse ethnic and organizational cultures. 9.2: All students will develop skills and strategies that promote personal and financial responsibility related to financial planning, savings, investment, and charitable giving in the global economy. 9.3: All students will apply knowledge about and engage in the process of career awareness, exploration, and preparation in order to navigate the globally competitive work environment of the information age. equivalent monthly interest rate if the annual rate is 15%. 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. A-REI.4. Solve quadratic equations in one variable. 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. Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. A-REI.10. Understand that the graph of an equation in two variables is the set of 23

7: Exponents & Exponential February-March 8: Polynomials & Factoring March 15 days 9: Quadratic Equations & March-April 16 days situations, and translate between the two forms. 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). 8.1 All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problems individually and collaboratively to create and communicate knowledge. 8.2 All students will develop an understanding of the nature and impact of technology, engineering, technological design and the designed world as they relate to the individual, global society, and the environment. 9.1: All students will demonstrate creative, critical thinking, collaboration and problem solving skills to function successfully as global citizens and workers in diverse ethnic and all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). 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 and cube root functions. c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. e. Graph exponential functions, showing intercepts and end behavior. F-IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different 24