I can solve linear inequalities and write my solution as an inequality, graph on a number line and write in interval notation.

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1 Curriculum Map: Algebra II Course: Algebra II Sub-topic: Uncategorized Grade(s): 9 to 12 Unit: Unit 1 - Linear Function Timeline: Week 1 to 4 The purpose of this module is to establish a community of mathematical thinkers. Tto launch the important mathematical processes, proficiencies, and practices that will support the growth and independence of our students as mathematical thinkers in a learning community. Students will review Algebraic Concepts by completing individual and collaborative assignments so that they can apply these concepts to the higher level concepts of Algebra II. Enduring Understandings:What will students understand (about what big ideas) as a result "Students will understand Some mathematical relationships are always true; these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities. I can solve linear equations. Essential Questions:What arguable, recurring, and thoughtprovoking How are Algebraic Concepts important to solving problems presented to you? Why problem solve (or why think mathematically)? I can solve linear inequalities and write my solution as an inequality, graph on a number line and write in interval notation. I can solve compound inequalities and write my solution as an inequality, graph on a number line and write in interval notation. I can solve absolute value equations. I can solve absolute value inequalities. I can solve literal equations for a specific variable. A I can determine the slope between two points and of a given graph. I can determine the equation of a line (including vertical & horizontal lines and parallel & perpendicular lines). CC.2.1.HS.F.1 (Advanced) Apply and extend the properties of exponents to solve problems with rational exponents. CC.2.1.HS.F.3 (Advanced) Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays. CC.2.1.HS.F.4 (Advanced) Use units as a way to understand problems and to guide the solution of multi-step problems. CC.2.1.HS.F.5 (Advanced) Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. CC.2.2.HS.C.1 (Advanced) Use the concept and notation of functions to interpret and apply them in terms of their context. CC.2.2.HS.C.2 (Advanced) Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 (Advanced) Write functions or sequences that model relationships between two quantities. CC.2.2.HS.D.7 (Advanced) Create and graph equations or inequalities to describe numbers or relationships. NATIONAL: US Common Core State Standards (2010) MA.MP.1 (Advanced) Make sense of problems and persevere in solving them. MA.MP.2 (Advanced) Reason abstractly and quantitatively. MA.MP.3 (Advanced) Construct viable arguments and critique the reasoning of others. MA.MP.4 (Advanced) Model with mathematics. MA.MP.5 (Advanced) Use appropriate tools strategically. MA.MP.6 (Advanced) Attend to precision. MA.MP.7 (Advanced) Look for and make use of structure. MA.MP.8 (Advanced) Look for and express regularity in repeated reasoning. Page 1 of 19

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3 Unit: Unit 2 - Quadratic Functions (Length of time varies according to level) Timeline: 9 Weeks The purpose of this unit is to learn how to solve, graph, and apply quadratic patterns to real life applications. Transformations will be introduced in this unit and reinforced with the other families of functions. Characteristics of graphs, such as domain, range, increasing interval and decreasing interval will be explored and will be reinforced in each of the other families of functions. The quadratic function unit lays the foundations necessary for polynomial functions, radical functions, exponential functions, logarithmic functions, and rational functions. The relationship between the algebraic zeros/roots/solutions/x intercepts and graphical representations will be analyzed and determined. Enduring Understandings:What will students understand (about Essential Questions:What arguable, recurring, and thoughtprovoking what big ideas) as a result "Students will understand...relations and functions are mathematical relationships that can be How can we extend arithmetic properties and processes to algebraic represented and analyzed using words, tables, graphs, and equations. expressions and processes in order to solve problems?...data can be modeled with mathematical functions that approximate How can we determine if a real-world situation should be represented the data well and help us make predictions based on the data. as a quadratic function? When given a real-world situation, how do you choose an appropriate model to represent it? I can find the characteristics (domain, range, increasing, decreasing) of quadratic functions. A , A I can determine the inverse of quadratic functions. A I can graph absolute value functions and determine the characteristics of the function. I can graph piecewise functions including a linear function and an absolute value function and determine the characteristics of the function. A I can graph quadratics from vertex form and specify the characteristics. A , A , A I can graph quadratics from standard form and specify the characteristics. A , A I can convert between vertex form and standard form. A , A I can solve applications of quadratics. A I can factor the greatest common factor, the British Method (including difference of two squares & perfect square trinomials) & by grouping. I can solve quadratics by factoring. I can add, subtract, multiply, and divide complex numbers. A , A , A , A I can simplify radicals, including negative radicands. A I can solve quadratics by taking the square roots. A I can solve quadratics by completing the square. A I can solve quadratics by the quadratic formula. A I can determine the number and type of solutions by using the discriminant. I can graph piecewise functions consisting of a linear function and a quadratic function. I can graph piecewise functions consisting of an absolute value function and a quadratic function. CC.2.1.HS.F.6 (Advanced) Extend the knowledge of arithmetic operations and apply to complex numbers. CC.2.1.HS.F.7 (Advanced) Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems. CC.2.2.HS.C.1 (Advanced) Use the concept and notation of functions to interpret and apply them in terms of their context. Page 3 of 19

4 CC.2.2.HS.C.2 (Advanced) Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 (Advanced) Write functions or sequences that model relationships between two quantities. CC.2.2.HS.C.4 (Advanced) Interpret the effects transformations have on functions and find the inverses of functions. CC.2.2.HS.C.6 (Advanced) Interpret functions in terms of the situations they model. CC.2.2.HS.D.2 (Advanced) Write expressions in equivalent forms to solve problems. CC.2.2.HS.D.4 (Advanced) Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs. CC.2.2.HS.D.5 (Advanced) Use polynomial identities to solve problems. CC.2.2.HS.D.7 (Advanced) Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.8 (Advanced) Apply inverse operations to solve equations or formulas for a given variable. CC.2.2.HS.D.9 (Advanced) Use reasoning to solve equations and justify the solution method. CC.2.3.HS.A.10 (Advanced) Translate between the geometric description and the equation for a conic section. Page 4 of 19

5 Unit: Unit 3 - Polynomial Functions Timeline: 4 Weeks The purpose of this unit is to build upon the knowledge of families of functions from the quadratic unit with polynomial functions by writing equations of polynomials, graphing polynomials and solving polynomials. Multiple representatives (graphing, equations, and tables/charts) will be utilized. This unit expands on students' understanding and skills related to functions, equations, and graphs. Students will understand polynomial functions by doing both group and individual activities so that they will be able to manipulate and interpret data. Enduring Understandings:What will students understand (about what big ideas) as a result "Students will understand...data can be modeled with mathematical functions that approximate the data well and help us make predictions based on the data....families of functions exhibit properties and behaviors that can be recognized across representations....functions can be transformed, combined, and composed to create new functions in mathematical and real world situations....mathematical functions are relationships that assign each member of one set (domain) to a unique member of another set (range), and the relationship is recognizable across representations....patterns exhibit relationships that can be extended, described, and generalized. Essential Questions:What arguable, recurring, and thoughtprovoking How can we extend arithmetic properties and processes to polynomial expressions and processes in order to solve problems? How can we determine if a real-world situation should be represented as a polynomial function? How do we demonstrate the benefits of multiple methods of representing polynomial functions (tables, graphs, equations, and contextual situations)? How are solutions of polynomial functions related to their graphs? How can polynomial functions be represented by equivalent forms? For a polynomial function, how are factors, zeros, and x-intercepts related?...relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations. I can classify and perform operations with polynomials. I can describe end behavior of a polynomial graph.(a ) I can find the zeros of a polynomial from its factored form (Factor Theorem). (just sets of parentheses) (A ) I can write a polynomial function from its zeros. I can understand and apply the term multiplicity. (A ) I can sketch the graph of a polynomial function using end behavior. (A ) I can solve polynomials by factoring. (A ) I can factor the sum or Difference of cubes. I can solve polynomials by graphing. I can divide polynomials by using long division. I can divide polynomials using synthetic division. I can use the Remainder Theorem to evaluate a polynomial function.(a ) I can determine the factors of a polynomial by using synthetic division. I can solve equations using the Rational Root Theorem. (A & A ) I can fit data to linear, quadratic, cubic, or quartic models.(a & A ) CC.2.2.HS.C.1 (Advanced) Use the concept and notation of functions to interpret and apply them in terms of their context. CC.2.2.HS.C.2 (Advanced) Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 (Advanced) Write functions or sequences that model relationships between two quantities. CC.2.2.HS.C.4 (Advanced) Interpret the effects transformations have on functions and find the inverses of functions. CC.2.2.HS.D.3 (Advanced) Extend the knowledge of arithmetic operations and apply to polynomials. CC.2.2.HS.D.4 (Advanced) Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs. CC.2.2.HS.D.5 (Advanced) Use polynomial identities to solve problems. CC.2.2.HS.D.7 (Advanced) Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.8 (Advanced) Apply inverse operations to solve equations or formulas for a given variable. CC.2.2.HS.D.9 (Advanced) Use reasoning to solve equations and justify the solution method. Page 5 of 19

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7 Unit: Unit 4 - Radical Functions The purpose of this unit is to build upon the knowledge of families of functions with radical functions by writing equations of radicals, graphing radicals, and solving radicals. Multiple representatives (graphing, equations, and tables/charts) will be utilized. This unit expands on students' understanding and skills related to functions, equations, and graphs. Students will understand radical functions by doing both group and individual activities so that they will be able to manipulate and interpret data. Enduring Understandings:What will students understand (about what big ideas) as a result "Students will understand...corresponding to every power, there is a root. For example, just as there are squares (second powers), there are square roots. Just as there are cubes (third powers), there are cube roots, and so on....if the nth root of a and the nth root of b are real numbers, then the product of the nth root of a and the nth root of b equals the nth root of ab....you can combine like radicals using properties of real numbers....you can write a radical expression in an equivalent form using a fractional (rational) exponent instead of a radical sign....solving a square root equation may require that you square each side of the equation. This can introduce extraneous solutions....you can add, subtract, multiply, and divide functions based on how you perform these operations for real numbers. One difference, however is that you must consider the domain of each function....the inverse of a function may or may not be a function....a square root function is the inverse of a quadratic function that has a restricted domain. I can find and simplify square and cube roots with variables. I can find and simplify 4th and 5th roots with variables. I can multiply radical expressions (including conjugates). I can add and subtract radical expressions. I can divide radical expressions (rationalize the denominator). I can divide radical expressions (multiply by the conjugate). I can review rules of exponents. I can simplify expressions with rational exponents. I can simplify expressions with rational exponents. I can solve square root and other radical equations. I can add, subtract, multiply, and divide functions. I can find the composite of two functions. I can find the Domain of a function without looking at the graph. I can find the inverse of a relation or a function. I can graph square root and other radical functions. Essential Questions:What arguable, recurring, and thoughtprovoking To simplify the nth root of an expression, what must be true about the expression? When you square each side of an equation, is the resulting equation equivalent to the original? How are a function and its inverse function related? CC.2.1.HS.F.1 (Advanced) Apply and extend the properties of exponents to solve problems with rational exponents. CC.2.2.HS.C.1 (Advanced) Use the concept and notation of functions to interpret and apply them in terms of their context. CC.2.2.HS.C.2 (Advanced) Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 (Advanced) Write functions or sequences that model relationships between two quantities. CC.2.2.HS.C.4 (Advanced) Interpret the effects transformations have on functions and find the inverses of functions. CC.2.2.HS.D.2 (Advanced) Write expressions in equivalent forms to solve problems. CC.2.2.HS.D.7 (Advanced) Create and graph equations or inequalities to describe numbers or relationships. Page 7 of 19

8 CC.2.2.HS.D.8 (Advanced) Apply inverse operations to solve equations or formulas for a given variable. CC.2.2.HS.D.9 (Advanced) Use reasoning to solve equations and justify the solution method. Page 8 of 19

9 Unit: Unit 5 - Exponential and Logarithmic Fuctions The purpose of this unit is to build upon the knowledge of families of functions with exponential and logarithmic functions by writing equations of exponential functions and logarithmic functions, graphing exponential and logarithmic functions, and solving exponential and logarithmic equations. Multiple representatives (graphing, equations, and tables/charts) will be utilized. This unit expands on students' understanding and skills related to functions, equations, and graphs. Students will understand exponential and logarithmic functions by doing both group and individual activities so that they will be able to manipulate and interpret data. Enduring Understandings:What will students understand (about what big ideas) as a result "Students will understand...you can represent represent repeated multiplication with a function in the form of y = ab x where b is a positive number other than 1....logarithms and exponents have corresponding properties....the exponential function y = b x is one-to-one, so its inverse x = b y is a function. To express "y as a function of x" for the inverse, write y = log b x....you can use logarithms to solve exponential equations. You can use exponents to solve logarithmic equations....the functions y = e x and y = ln x are inverse functions. Just as before, this means that if a = e b, then b = ln a, and vice versa....the factor a in y = ab x can stretch or compress, and possibly reflect the graph of the parent function y = b x....the exponential function y = b x can stretch or compress, and possibly reflect the graph of the parent function y = b x. I can model exponential growth and decay. I can solve simple exponential equations. I can explore the properties of functions of the form y = abx. I can graph exponential functions that have base e. I can find half life and compound interest. I can write and evaluate logarithmic expressions. I can graph logarithmic functions. I can use the properties of logarithms. I can solve exponential equations I can solve logarithmic equations. I can evaluate and simplify natural logarithmic expressions. I can solve equations using natural logarithms. Essential Questions:What arguable, recurring, and thoughtprovoking How do you model a quantity that changes regularly over time by the same percentage? How are exponents and logarithms related? How are exponential functions and logarithmic functions related? CC.2.2.HS.C.1 (Advanced) Use the concept and notation of functions to interpret and apply them in terms of their context. CC.2.2.HS.C.2 (Advanced) Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 (Advanced) Write functions or sequences that model relationships between two quantities. CC.2.2.HS.C.4 (Advanced) Interpret the effects transformations have on functions and find the inverses of functions. CC.2.2.HS.C.5 (Advanced) Construct and compare linear, quadratic, and exponential models to solve problems. CC.2.2.HS.C.6 (Advanced) Interpret functions in terms of the situations they model. CC.2.2.HS.D.2 (Advanced) Write expressions in equivalent forms to solve problems. CC.2.2.HS.D.7 (Advanced) Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.8 (Advanced) Apply inverse operations to solve equations or formulas for a given variable. CC.2.2.HS.D.9 (Advanced) Use reasoning to solve equations and justify the solution method. Page 9 of 19

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11 Unit: Unit 6 - Rational Functions The purpose of this unit is to build upon the knowledge of families of functions with rational functions by writing equations of rational functions, graphing rational functions, and solving rational equations. Multiple representatives (graphing, equations, and tables/charts) will be utilized. This unit expands on students' understanding and skills related to functions, equations, and graphs. Students will understand rational functions by doing both group and individual activities so that they will be able to manipulate and interpret data. Enduring Understandings:What will students understand (about what big ideas) as a result "Students will understand...in a direct variation, two positive quantities either increase together or decrease together. In an inverse variation, as one quantity increases the other decreases....transformations of the parent reciprocal function include stretches, compressions (or shrinks), reflections, and horizontal and vertical translations....a rational function is a ratio of polynomial functions. If a rational function is in simplified form and the polynomial in the denominator is not constant, the graph of the rational function features asymptotic behavior. It looks quite different from the graphs of either of its polynomial components....you can use much of what you know about multiplying and dividing fractions to multiply and divide rational expressions....to operate with rational expressions, you can use much of what you know about operating with fractions. To add or subtract rational expressions, you first find a common denominator-preferably the least common multiple (LCM) of the denominators. Essential Questions:What arguable, recurring, and thoughtprovoking Are two quantities inversely proportional if an increase in one corresponds to a decrease in the other? What kinds of asymptotes are possible for a rational function? Are a rational expression and its simplified form equivalent?...to solve an equation containing rational expressions, first multiply each side by the least common denominator of the rational expressions. Doing this, however, can introduce extraneous solutions. I can recognize and use inverse variation. I can recognize and use joint variation. I can determine the horizontal and vertical asymptotes of reciprocal and rational functions. I can determine the holes of reciprocal and rational functions. I can graph rational functions by evaluating the function. I can graph rational functions using translations and transformations. I can determine the characteristics (domain, range, increasing, decreasing, asymptotes) of rational functions. I can determine restrictions of rational expressions. I can simplify rational expressions. I can multiply rational expressions. I can divide rational expressions. I can add rational expressions. I can subtract rational expressions. I can solve rational equations. (Cross Multiplying, Clearing the Denominator by multiplying by the LCM, Combining Rational Expressions) I can determine extraneous solutions. CC.2.2.HS.C.1 (Advanced) Use the concept and notation of functions to interpret and apply them in terms of their context. CC.2.2.HS.C.2 (Advanced) Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 (Advanced) Write functions or sequences that model relationships between two quantities. CC.2.2.HS.C.4 (Advanced) Interpret the effects transformations have on functions and find the inverses of functions. CC.2.2.HS.C.6 (Advanced) Interpret functions in terms of the situations they model. Page 11 of 19

12 CC.2.2.HS.D.2 (Advanced) Write expressions in equivalent forms to solve problems. CC.2.2.HS.D.6 (Advanced) Extend the knowledge of rational functions to rewrite in equivalent forms. CC.2.2.HS.D.7 (Advanced) Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.8 (Advanced) Apply inverse operations to solve equations or formulas for a given variable. CC.2.2.HS.D.9 (Advanced) Use reasoning to solve equations and justify the solution method. Page 12 of 19

13 Unit: Unit 7 - Modeling with Functions Timeline: 2 Weeks The purpose of this unit is to combine linear, quadratic, polynomial, radical, exponential, logarithmic, and rational functions to have students choose the most accurate model for data and situations. Real world data can be appropriately modeled with a variety of function families to help solve problem scenarios. Students will model with functions by doing both group and individual activities so that they will be able to apply the concepts of functions to real world situations. Enduring Understandings:What will students understand (about Essential Questions:What arguable, recurring, and thoughtprovoking what big ideas) as a result "Students will understand...families of functions exhibit properties and behaviors that can be How can a given function be represented? What connections can be recognized across representations. made between the various representations?...functions can be transformed, combined, and composed to create How can an equation, table, and graph be used to analyze the rate new functions in mathematical and real world situations. of change and other applicable information, related to a real-world...mathematical functions are relationships that assign each member problem and the representative function? of one set (domain) to a unique member of another set (range), and How do you explain the benefits of multiple methods of the relationship is recognizable across representations. representing exponential functions (tables, graphs, equations, and...relations and functions are mathematical relationships that can be contextual situations)? represented and analyzed using words, tables, graphs, and equations. Which function best models a given real-world scenario? What does...comparing representations across families of functions allows us to the function look like in the real world? choose an appropriate approach and make connections between How are solutions of functions related to their graphs? families of functions. How can functions be represented by equivalent forms?...modeling involves identifying and selecting features of a real-world When given a real-world situation, how do you choose an situation, representing those features symbolically, analyzing and appropriate model to represent it? reasoning about the model and the characteristics of the situation, and considering the accuracy and limitations of the model. 1. I can represent and solve equations algebraically and graphically and explain the reasoning. (CC.2.2.HS.D.7,CC.2.2.HS.D.9, CC.2.2.HS.D.10, A ,2, MP2,3,4,6) 2. I can understand, determine and interpret end behavior of functions. (CC.2.4.HS.B.3, MP4) 3. I can understand, calculate and graph asymptotes. (A , MP4,6) 4. I can analyze functions in equivalent forms and using different representations. (CC.2.2.HS.C.2, A , MP1,2,4) 5. I can understand how transformations affect the graphs of parent functions. (CC.2.2.HS.C.4,A , MP7,8) 6. I can create equations that describe numbers or relationships. (CC.2.2.HS.D.7, A , MP2,4) 7. I can interpret, compare and solve functions that arise in applications in terms of a context. (CC.2.2.HS.C.6, A , MP4,7) 8. I can construct and compare linear, quadratic, and exponential models and solve problems. (CC.2.2.HS.C.5, A , MP2,4) 9. I can create and/or solve equations (including literal, polynomial, rational, radical, exponential, and logarithmic) both algebraically and graphically. (CC.2.2.HS.D.10, A , MP2,4) 10. I can use and/or explain reasoning while solving equations, and justify the solution method. (CC.2.2.HS.D.9, MP3,6) 11. I can determine how a change in one variable relates to a change in a second variable. (CC.2.2.HS.C.4, A , MP1,2,4) 12. I can use exponents, roots, and/or absolute values to represent equivalent forms or to solve problems. (CC.2.2.HS.D.6, A ,2, MP1,4) CC.2.1.HS.F.3 (Advanced) Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays. CC.2.1.HS.F.4 (Advanced) Use units as a way to understand problems and to guide the solution of multi-step problems. CC.2.2.HS.C.1 (Advanced) Use the concept and notation of functions to interpret and apply them in terms of their context. CC.2.2.HS.C.2 (Advanced) Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 (Advanced) Write functions or sequences that model relationships between two quantities. CC.2.2.HS.C.4 (Advanced) Interpret the effects transformations have on functions and find the inverses of functions. CC.2.2.HS.C.5 (Advanced) Construct and compare linear, quadratic, and exponential models to solve problems. CC.2.2.HS.C.6 (Advanced) Interpret functions in terms of the situations they model. CC.2.2.HS.D.1 (Advanced) Interpret the structure of expressions to represent a quantity in terms of its context. Page 13 of 19

14 CC.2.2.HS.D.7 (Advanced) Create and graph equations or inequalities to describe numbers or relationships. Page 14 of 19

15 Unit: Unit 8 - Sequence and Series (Standards - if time allows) The purpose of this unit is to learn how to define, notate, and interpret different types of series and sequences, such as arithmetic and geometric. Enduring Understandings:What will students understand (about what big ideas) as a result "Students will understand...if the numbers in a list follow a pattern, variables may be used to relate each number in the list to its numerical position in the list....in an arithmetic sequence, the difference between any two consecutive terms is always the same number. This number can be represented by a variable....when two terms and the number of terms in a finite arithmetic sequence are known, they can be substituted for variables in a formula to find the sum of the terms....in a geometric sequence, the ratio of any term (after the first) to its preceding term is a constant value, no matter what two terms are compared A geometric sequence can be built by multipilying each term by that constant....just as with finite arithmetic series, the sum of a finite geometric series can be found using a formula. The first term, the number of terms, and the common ratio must be known. I can identify mathematical patterns found in a sequence. I can use a formula to find the nth term of a sequence. I can define, identify, and apply arithmetic sequences. I can define, identify, and apply geometric sequences. I can define arithmetic series and find their sums. I can define geometric series and find their sums. Essential Questions:What arguable, recurring, and thoughtprovoking How can you represent the terms of sequence explicitly? How can you represent them recursively? What are equivalent explicit and recursive definitions for an arithmetic sequence? How can you model a geometric sequence? How can you model its sum? CC.2.2.HS.C.1 (Advanced) Use the concept and notation of functions to interpret and apply them in terms of their context. CC.2.2.HS.C.2 (Advanced) Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 (Advanced) Write functions or sequences that model relationships between two quantities. Page 15 of 19

16 Unit: Unit 9 - Probability and Statistics The purpose of this module is to extend and deeply explore collecting, analyzing, and designing data and their implications on interpretation. Enduring Understandings:What will students understand (about what big ideas) as a result "Students will understand...multiplication can be used to quickly count the number of ways certain things can happen....the probability of an impossible event is 0 (or 0%) The probability of a certain event is 1 (or 100%). Otherwise, the probability of an event is a number between 0 and 1 (or a percent between 0% and 100%)....to find the probability of two events occurring together, you have to decide whether one event occurring affects the other event....conditional probability exists when two events are dependent....you can use probability models to analyze situations and make fair decisions....you can use binomial probabilities in situations involving two possible outcomes....you can describe and compare sets of data using various statistical measures, depending on what characteristics you want to study....standard deviation is a measure of how far the numbers in a data set deviate from the mean....you can get good statistical information about a population by studying a sample of the population....many common statistics (such as human height, weight, and blood pressure) gathered from samples in the natural world tend to have a normal distribution about their mean. I can count permutations. I can count combinations. I can find the probability of an event using theoretical, experimental, and simulation methods. I can find the probability of the event A and B. I can find the probability of the event A or B. I can find conditional probabilities. I can use tables and tree diagrams to determine conditional probabilities. I can use probabilities to make fair decisions and analyze decisions. I can calculate measures of central tendency. I can draw and interpret box-and-whisker plots. I can find the standard deviation and variance of a set of values. I can apply standard deviation and variance. I can identify sampling methods. I can recognize bias in samples and surveys. I can find binomial probabilities and to use binomial distributions. I can use a normal distribution. Essential Questions:What arguable, recurring, and thoughtprovoking What is the difference between a permutation and a combination? What is the difference between experimental and theoretical probability? How are measures of central tendency different from standard deviation? What differentiates an independent event from a dependent event and how are the probabilities of each calculated? How does the type of data influence the choice of display? How can probability and data analysis be used to make predictions? How can data be represented, summarized and interpreted? How can the probability of single and multiple events be determined and applied to populations? CC.2.1.HS.F.3 (Advanced) Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays. CC.2.1.HS.F.5 (Advanced) Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. CC.2.4.HS.B.2 (Advanced) Summarize, represent, and interpret data on two categorical and quantitative variables. Page 16 of 19

17 CC.2.4.HS.B.3 (Advanced) Analyze linear models to make interpretations based on the data. CC.2.4.HS.B.4 (Advanced) Recognize and evaluate random processes underlying statistical experiments. CC.2.4.HS.B.5 (Advanced) Make inferences and justify conclusions based on sample surveys, experiments, and observational studies. CC.2.4.HS.B.6 (Advanced) Use the concepts of independence and conditional probability to interpret data. CC.2.4.HS.B.7 (Advanced) Apply the rules of probability to compute probabilities of compound events in a uniform probability model. Page 17 of 19

18 Unit: Unit 10 - Conics (Standards - if time allows) The purpose of the Conics unit is to familiarize students with the structure of conics and explore their real-life applications in astronomy, physics, sound waves and light. Enduring Understandings:What will students understand (about what big ideas) as a result "Students will understand...each point of a parabola is equidistant from a point called the focus and a line called the directix....in an x - y relationship, replacing x by x - h and y by y - k (with h > What is the graph of x 2 /9 + y 2 /9 = 1? 0 and k > 0) translates the graph of the relation h units to the right and k units up....an equation of a circle with center (0, 0) and radius r in the coordinate plane is x 2 + y 2 = r 2....there are four types of curves known as conic sections: parabolas, circles, ellipses, and hyperbolas. Each curve has its own distinct shape and properties....a circle is a set of points a fixed distance from one point. An ellipse "stretches" a circle and is the set of points that have a total fixed distance from two points....the shape of a hyperbola is guided by asymptotes. I can identify conic sections. I can graph conic sections. I can write and graph the equation of a parabola. I can write and graph the equation of a circle. I can find the center and radius of a circle and use them to graph the circle. I can write the equation of an ellipse. I can find the foci of an ellipse I can graph an ellipse. I can graph hyperbolas. I can find and use the foci of a hyperbola. I can write the equation of a translated conic section. I can identify a translated conic section from an equation. Essential Questions:What arguable, recurring, and thoughtprovoking What is the intersection of a cone and a plane parallel to a line along the side of a cone? What is the difference between the algebraic representations of ellipses and hyperbolas? CC.2.2.HS.C.4 (Advanced) Interpret the effects transformations have on functions and find the inverses of functions. CC.2.3.HS.A.10 (Advanced) Translate between the geometric description and the equation for a conic section. Page 18 of 19

19 Unit: Unit 11 - Matrices (Principles & Standards - if time allows) The purpose of the matrices unit is for students to see that a matrix is just a compact notation, which allows you to specify several linear equations at once without having to write them all out. Enduring Understandings:What will students understand (about what big ideas) as a result "Students will understand Essential Questions:What arguable, recurring, and thoughtprovoking...you can extend the addition and subtraction of numbers to matrices....the product of two matrices is a matrix. To find an element in the product matrix, you multiply the elements of a row from the first matrix to the corresponding elements of a column from the second matrix. Then add the products. How can you use a matrix to organize data? How can you use a matrix equation to model a real-world situation? How can a matrix represent a transformation of a geometric figure in the plane?...a vector is a mathematical object that has both magnitude and direction....the product of a matrix and its inverse matrix is the multiplicative identity matrix. Not all matrices have inverse matrices....you can solve some matrix equations AX = B by multiplying each side oft he equation by A -1, the inverse of matrix A....you can multiply a 2 x 1 matrix representing a point by a 2 x 2 matrix to rotate the point about the origin or reflect the point across a line. I can add and subtract matrices. I can solve matrix equations. I can multiply matrices using scalar and matrix multiplication. I can find the inverse of a matrix. I can solve systems of equations using matrix inverses and multiplication. I can transform geometric figures using matrix operations. I can use basic vector operations and the dot product. CC.2.2.HS.D.10 (Advanced) Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically. Page 19 of 19