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TRENTON PUBLIC SCHOOLS Department of Curriculum and Instruction 108 NORTH CLINTON AVENUE TRENTON, NEW JERSEY 08609 Algebra II CURRICULUM GUIDE AND INSTRUCTIONAL ALIGNMENT August 2013-Revised June 2014 1 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards Algebra II Units at Glance (From NJDOE Model Curriculum - each unit is designed to take approximately 30 days.) Overview Building on the understanding of linear, quadratic and exponential functions from Algebra I, this course will extend function concepts to include polynomial, rational, and radical functions. The standards in this course continue the work of modeling situations and solving equations. Unit 1 standards will focus on the similarities of arithmetic with rational numbers and the arithmetic with rational expressions. The work in unit 2 will extend student’s algebra knowledge of linear and exponential functions to include polynomial, rational, radical, and absolute value functions. The standards included in unit 3 builds on the students’ previous knowledge of functions, trigonometric ratios and circles in geometry to extend trigonometry to model periodic phenomena. The work of unit 4 will explore the effects of transformations on graphs of functions and will include identifying an appropriate model for a given situation. The standards require development of models more complex than those of previous courses. The standards in Unit 5 will relate the visual displays and summary statistics learned in prior courses to different types of data and to probability distributions. Samples, surveys, experiments and simulations will be used as methods to collect data. 2 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards Unit 1: Polynomials. Cluster Prerequisites Perform arithmetic Operations with complex numbers. Standard N.RN.1, 2, 3 Extend the properties of exponents to rational numbers Use properties of rational and irrational numbers N.CN.1 A.REI. 2 N.CN.2 Create linear equations and inequalities in one variable and use them to solve problems. Justify each step in the process and the solution A.REI.4 Use complex Solve quadratic equations in one N.CN.7 numbers in variable. N.CN.9 polynomial identities A.APR.7 and Perform addition, subtraction and equations. multiplication with polynomials and relate it to arithmetic operations with integers 3 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content Description Know there is a complex number i such that i2 = −1, and every complex number has the form a + bi with a and b real. Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Solve quadratic equations with real coefficients that have complex solutions. (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. A.C. = Additional Content ★=Modeling standards Solve quadratic equations in one variable. Interpret the structure of expressions. A.SSE.3 Manipulate expressions using A.REI.4 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 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 A.SSE.1 A.SSE.2 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 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). F.LE.2 Construct linear and exponential Write expressions in functions, including arithmetic and A.SSE.4 geometric sequences, given a graph, a equivalent forms to description of a relationship, or two solve problems input-output pairs (include reading these from a table). 4 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content complex solutions and write them as a ± bi for real numbers a and b. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.★ A.C. = Additional Content ★=Modeling standards Understand the relationship between zeros and factors of polynomials A.APR.1 . Perform addition, subtraction and A.APR.2 multiplication with polynomials and relate it to arithmetic operations with A.APR.3 integers Use polynomial identities to solve problems. 8.G.7 Apply Pythagorean theorem to determine unknown side lengths in right triangles. A.APR.4 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). 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. Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2 can be used to generate Pythagorean triples. Unit 2: Expressions and Equations (1). Extend the Properties of Exponents to rational exponents. 5 M8.EE.1 Apply the properties of integer N.RN.1 exponents to simplify and write equivalent numerical expressions M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5. S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards M 8.EE.2 Evaluate square roots and N.RN.2 cubic roots of small perfect squares and cubes respectively and use square and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p where p is a positive rational number. Rewrite rational expressions 6 A.SSE.1 Interpret parts of A.APR.6 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 A.SSE.3 Manipulate 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 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards Understand solving equations as a process of reasoning and explain the reasoning A.CED.4 Solve linear equations and A.REI.1 inequalities in one variable (including literal equations). Justify each step in the process and solution. A.CED.4 Understand solving Solve linear equations and A.REI.2 equations as a process of reasoning and inequalities in one variable explain the reasoning. (including literal equations). 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. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Justify each step in the process and solution. Solve systems of equations A.REI.3 A.REI.6 Solve linear equations and inequalities in one variable (including literal equations). Justify each step in the process and solution A.CED.2 Create equations in two or more variables to A.REI.7 represent relationships between quantities; graph equations on coordinate axes with labels and scales 7 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3. S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards Write expressions in equivalent forms to solve problems N.RN.2 Rewrite expressions involving radicals and A.SSE.3 rational exponents using the properties of exponents. F.IF.1 Interpret functions that F.IF.2 arise in applications in Explain terms of a context. F.IF.4 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. F.IF.2 Use function Analyze functions using notation, evaluates functions F.IF.8 different for inputs in their domains, representations. and interprets statements that use function notation in terms of a context. 8 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 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%. 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.★ 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. S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards Translate between the geometric description and the equation for a conic section F.IF.7 Graph functions by hand (in G.PE.2 simple cases) and with technology (in complex cases) to describe linear relationships between two quantities and identify, describe, and compare domain and other key features in one or multiple representations Derive the equation of a parabola given a focus and directrix. Unit 3: Expressions and Equations (2). A.REI.5 Represent and solve equations and A.REI.6 inequalities graphically. A.REI.7 Build a function that models a relationship between two quantities F.BF.1 Interpret Expressions for functions in terms of the situation they model 8.F.1 Build new functions from F.IF.1 F.IF.2 existing functions. F.IF.7 9 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.★ F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.★ F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context. F.BF.4 Find inverse functions. a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = 2 x3 or f(x) = (x+1)/(x-1) for x ≠1. M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards Extend the domain of trigonometric functions using the unit circle. F.TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. F.TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. F.TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.★ F.TF.8 Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin (θ), cos (θ), or tan (θ), given sin (θ), cos (θ), or tan (θ), and the quadrant of the angle. F.TF.1 Model periodic phenomena with trigonometric functions. 8.G.6 Prove and apply 8.G.7 trigonometric identities. Interpret functions that arise in applications in terms of a context. nalyze functions using different representations. S.ID.7 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. 7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ e. Graph trigonometric functions, showing period, midline, and amplitude N.Q.2 Define appropriate quantities for the purpose of descriptive modeling. A.REI.4 Reason quantitatively and use units to solve problems 10 F.IF. 4 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards Unit 4: Modeling with Functions F.IF.4 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.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.* b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. Build new functions from existing functions. 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. Construct and compare linear, quadratic, and exponential models and solve problems. F.LE.4 Understand and evaluate random processes underlying statistical experiments. S.IC.1 Interpret functions that arise in applications in terms of a context. Analyze functions using different representations. F.IF.7 A.REI.4 F.IF.3 Build a function that models a relationship between two quantities. F.IF.7 11 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 For exponential models, express as a logarithm the solution to a bct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. Understand statistics as a process for making inferences about population parameters based on a random sample from that population. S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards S.ic.1 S.IC.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? S.IC.3 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. S.ic.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each S.IC.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. s.ic.3 s.ic.3 S.IC.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant S.IC.6 Evaluate reports based on data S.CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,”“not”). Unit 5: Probability and Statistics Understand independence and nditional probability and use them to interpret data. 12 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards s.cp.1 S.CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent s.cp.1 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. S.CP.3 s.cp.1 s.cp.1 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. S.CP.4 S.CP.5 . Use the rules of probability to compute probabilities of compound events in a uniform probability model 13 S.CP.6 S.cp.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model. Apply the S.CP.7 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards Grade level: HS Unit #1 UNIT NAME: Polynomials District-Approved Text: Pearson Stage 1 – Desired Results Enduring Understandings/Goals: Operations and properties of the real number system can be extended to situations involving complex numbers Expressions can be written in multiple ways using the rules of algebra. Essential Questions: How does knowledge of real numbers help when working with complex numbers? Why structure expressions in different ways? 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. Standard: Student Learning Suggested Suggested Objectives Instructional Resources Strategies N.CN.1 Know there is a 1) Use properties of Pearson 4-8 Use complex number i such that i2 operations to add, subtract, Algebra pp. 248-255 = −1, and every complex and multiply complex tiles to number has the form a + bi numbers. create with a and b real. A.C.* examples of 14 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards N.CN.2 Use the relation i2 = – 1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. A.C 15 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content polynomial s. Use different colored chalk/mark ers for each of the terms. Create a column for the 4 parts of FOIL. Use FOIL method (First, Outers, Inners, Last) to reinforce the commutati ve, associative , and distributive properties. Algebra tiles to solve multi-step equations. A.C. = Additional Content ★=Modeling standards N.CN.7 Solve quadratic equations with real coefficients that have complex solutions. A.C* 2) Solve quadratic equations with real coefficients that have complex solutions. A.REI.4.b Solve quadratic equations in one variable. 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. S.C. N.CN.9 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Product of P and a factor not 16 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 3) Show that the Fundamental Theorem of Algebra is true for quadratic polynomials. + S.C. = Supporting Content Provide students with a variety of parabolas and then sort into 3 piles. (Those that model a real solution; those that model with 2 real solutions, and those that model no real solution. Scatterplot to gain insight into possible relationship s between two variables. Have students work in pairs or groups to Pearson 5-5,56 pp. 312-324 Pearson 5-6 pp. 319-324 A.C. = Additional Content ★=Modeling standards depending on P. 17 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content create a jingle, poem, or rap that describes the patterns found. Construct videos about expanding powers of binomials and polynomial s. A.C. = Additional Content ★=Modeling standards A.APR.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). M.C. A.SSE.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments. M.C. A.SSE.2 Use the structure of 18 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 4) Restructure by performing arithmetic operations on polynomial and rational expressions. 5) Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.★ 6) Use an appropriate S.C. = Supporting Content Make connections between arithmetic of integers and arithmetic of polynomials Use the distributive property • Perform arithmetic operations on polynomials Factor polynomials. Offer multiple real world examples such as calculating mortgage payments Use real word Pearson 5-4 Pearson CB 95, 9-5 Pearson 4-4, 5- A.C. = Additional Content ★=Modeling standards 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). M.C. factoring technique to factor expressions completely including expressions with complex numbers 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. M.C. A.APR.4 Prove Polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2 can be used to generate Pythagorean triples. A.C. 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). M.C. 19 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 7) Explain the relationship between zeros and factors of polynomials and use zeros to construct a rough graph of the function defined by the polynomial. S.C. = Supporting Content context examples. Extend beyond simplifying expressions Factor by grouping Have students create their own expressions that meets specific criteria and verbalize how they can be written and re-written in different forms Pair or group students to share their expressions and re-write one another’s expressions 2) Create experiences with long division of polynomials 3, 6-1, 6-2, 6-3, 8-4 Pearson 4-5, 52, 5-6, CB 5-7 Pearson CB 5-5 Pearson 4-4, 53, 6-1, 6-2, 6-3, 8-4 3) Graph A.C. = Additional Content ★=Modeling standards polynomial functions in factor form 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. M.C. Suggested Performance Tasks: Exemplars Extended projects Math Webquests Writing in Math/Journal 20 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 Pearson 4-5, 52, 5-6, CB 5-7 Stage 2 – Assessment Evidence Other Evidence: Classwork Exit Slips Homework Individual and group tests Open-ended questions Portfolio Quizzes S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards Stage 3 – Learning Plan Lesson Format 7-10 min: Do Now/Journaling/Pretest (whole class) Journaling Pretest Activate students’ prior knowledge Can be a review of info Pose EQ or provide relevant question / inquiry Quick multiple choice format related to EU Not to be counted as a test grade Share-out with several students Review correct answers 10-15 min: Homework Review (whole class) 15-20 min: Mini Lesson/Content Presentation /Guided Practice (whole class) Content Presentation Guided Practice Note taking of solutions to sample problems. Clarify instructions for assignments and projects Video or multi-media presentation Teach specific skills (i.e. which problem solving skill is appropriate, how to use rubrics) 30 min: Independent Practice (small group/independent) Anchor Activity: major assignment that Center Activities: variety of activities related to unit everyone is responsible for completing allowing some flexibility and choice for students to complete Word Wall activities, technology center with math web quests, math centers 2 min: Transition back to seats for whole class 10 min: Closure/Assessment/Evaluation Exit slip Assign homework 21 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards Grade level: HS UNIT NAME: Operations and Algebraic Thinking District-Approved Text: Pearson Unit #2 Stage 1 – Desired Results Enduring Understandings/Goals: Algebraic expressions symbolize numerical relationships and can be manipulated in the same way as numbers. There is often an optimal method of manipulating equations and equalities. Essential Questions: How can the properties of the real number system be useful when working with polynomials and rational expressions? In what ways can the problem be solved and why should one method be chosen over another? 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. Standard: Student Learning Suggested Instructional Strategies Suggested Objectives Resources N.RN.1 Explain how the 1. Use properties of integer Pearson definition of the meaning exponents to explain and Algebra Review p.225 of rational exponents convert between Concept Byte p.360 follows from extending the expressions involving Section 6-4 properties of integer radicals and rational exponents to those values, exponents, using correct allowing for a notation for notation. For example, radicals in terms of we define 51/3 to be the rational exponents. For cube root of 5 because example, we define 51/3 to be the cube root of 5 22 we want (51/3)3 = 5(1/3)3 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5. M.C. to hold, so (51/3)3 must equal 5. N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. M.C. A.APR.6 Rewrite simple 2. Rewrite simple rational rational expressions in expressions in different different forms; write forms using inspection, a(x)/b(x) in the form q(x) long division, or, for the + r(x)/b(x), where a(x), more complicated b(x), q(x), and r(x) are examples, a computer polynomials with the algebra system. degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. S C. A.REI.1 Explain each step 3. Solve simple rational and in solving a simple radical equations in one equation as following from variable, explain the the equality of numbers reasoning, and give asserted at the previous examples showing how step, starting from the extraneous solutions may assumption that the arise. original equation has a solution. Construct a 23 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 Write rational expressions in different forms Begin with simple, one step equations and require students to write out a justification for each step used to solve the equations Ensure that students are proficient with solving simple rational and radical equations that have no extraneous solutions before moving on to equations S.C. = Supporting Content A.C. = Additional Content Pearson 5-4, 8-6 Pearson 6-5, 8-6 ★=Modeling standards viable argument to justify a solution method. M.C. A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. M.C. 3. Solve simple rational and radical equations in one variable, explain the reasoning, and give examples showing how extraneous solutions may arise. A.REI.6 Solve systems of linear equations exactly 24 4. Solve systems of linear M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content that result in quadratics and possible solutions that need to be eliminated Provide visual examples of radical and rational equations with technology so that students can see the solutions as the intersections of two functions and further understand how extraneous solutions do not fit the model Pearson Begin with simple, one step equations and require students to 6-5, 8-6 write out a justification for each step used to solve the equations Ensure that students are proficient with solving simple rational and radical equations that have no extraneous solutions before moving on to equations that result in quadratics and possible solutions that need to be eliminated. Provide visual examples of radical and rational equations with technology so that students can see the solutions as the intersections of two functions and further understand how extraneous solutions do not fit the model. Pearson A.C. = Additional Content ★=Modeling standards equations and simple systems consisting of a linear and a quadratic equation in two variables, algebraically and graphically. A.REI.7 Solve a simple 4. Solve systems of linear system consisting of a equations and simple linear equation and a systems consisting of a quadratic equation in two linear and a quadratic variables algebraically and equation in two variables, graphically. For example, algebraically and find the points of graphically. intersection between the line y = –3x and the circle x2 + y2 = 3. A.C. A.SSE.3 Choose and 5. Write equivalent produce an equivalent expressions for form of an expression to exponential functions reveal and explain using the properties of properties of the quantity exponents. represented by the expression.★ 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%. M.C. 3-1, 3-2, 3-3, 4-9 and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. A.C. 25 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content Pearson 3-1, 3-2, 3-3, 4-9 Pearson 1-1 A.C. = Additional Content ★=Modeling standards FIF.4 For a function that 6. Interpret key features of models a relationship graphs and tables in between two quantities, terms of the quantities, interpret key features of and sketch graphs graphs and tables in terms showing key features of the quantities, and given a verbal description sketch graphs showing of the relationship. Key key features given a features include: verbal description of the intercepts; intervals relationship. Key features where the function is include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★ M.C. increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. ★ FIF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. S.C. 7. Rewrite a function in different but equivalent forms to identify and explain different properties of the function. G.PE.2 Derive the equation of a parabola, given a focus and directrix. A.C. 8. Derive the equation of a parabola given a focus and directrix. 26 Pearson 2-3, 2-5, 4-1, 4-2, 4-3, 5-1, 5-8, Concept Byte p.459, 13.1, 13.4, 13.5 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content Use the process of factoring and completing the square in a quadratic function to show zeros, extreme value, and symmetry of the graph and interpret this in terms of a context. Use the properties of exponents to interpret expressions for exponential functions Pearson 2-4, 4-2, 59, 6-8, 7-2, 7-3, CB 7.5 Pearson 10-2, 10-6 Parabolas A.C. = Additional Content ★=Modeling standards Suggested Performance Tasks: Exemplars Extended projects Math Webquests Writing in Math/Journal Stage 2 – Assessment Evidence Other Evidence: Classwork Exit Slips Homework Individual and group tests Open-ended questions Portfolio Quizzes Stage 3 – Learning Plan Lesson Format 7-10 min: Do Now/Journaling/Pretest (whole class) Journaling Pretest Activate students’ prior knowledge Can be a review of info Pose EQ or provide relevant question / inquiry Quick multiple choice format related to EU Not to be counted as a test grade Share-out with several students Review correct answers 10-15 min: Homework Review (whole class) 15-20 min: Mini Lesson/Content Presentation /Guided Practice (whole class) Content Presentation Guided Practice Note taking of solutions to sample problems. Clarify instructions for assignments and projects Video or multi-media presentation Teach specific skills (i.e. which problem solving skill is appropriate, how to use rubrics) 30 min: Independent Practice (small group/independent) Anchor Activity: major assignment that Center Activities: variety of activities related to unit everyone is responsible for completing allowing some flexibility and choice for students to complete Word Wall activities, technology center with math web quests, math centers 2 min: Transition back to seats for whole class 27 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards 10 min: Closure/Assessment/Evaluation Exit slip Assign homework UNIT NAME: Expressions and Equations(2) Grade level: HS District-Approved Text: Pearson Unit #3 Stage 1 – Desired Results Enduring Understandings/Goals: Equations, verbal descriptions, graphs and table provide insights into the relationships between quantities Essential Questions: How can the relationship between quantities best be represented? 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. Standard: Student Learning Suggested Instructional Suggested Objectives Strategies Resources 28 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards A.REI.11 Explain why the xcoordinates 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.★ M.C. F.BF.2 Write arithmetic and geometric sequences both recursively and 29 Pearson 3-1, 5-3, 7-5, 1)Find approximate solutions for the intersections of functions and explain why the xcoordinates 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) involving linear, polynomial, rational, absolute value, and exponential functions. 2) Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 Concept Byte 7-6 p.484, 8-6 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards with an explicit formula, use them to model situations, and translate between the two forms. ★ M.C. F.BF.4 Find inverse functions. a)Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, situations, and translate between the two forms.★ Pearson 6-7, 7-3 3)Determine the inverse function for a simple function that has an inverse and write an expression for it. f(x) =2 x3 or f(x) = (x+1)/(x–1) for x A.C. F.IF.4 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. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. e. Graph exponential 30 4)Graph functions expressed symbolically and show key features of the graph (including intercepts, intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity) by hand in simple cases and using technology for more complicated M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 Use a set of given characteristics to sketch the graph of a function Examine a table of related quantities and identify features in the table , such as intervals on which the interval increases, decreases , or exhibits periodic behavior S.C. = Supporting Content Pearson 2-3, 2-5, 4-1, 4-2, 4-3, 51, 5-8, CB 7-3, 13-1, 134, 13-5 2-3, 2-4, CB 2-4, 2-6, 27, 4-1, 4-2, 5-1, 5-2, 5-8, 6-8, 7-2, CB 8-2, 8-3 CB 2-4, 2-7, 2-8, 6-8 5-1, 5-2, 5-9 CB 8-2 7-1, 7-2, 7-3, CB 7-5, 134, 13-5, 13-6, 13-7, 13-8 A.C. = Additional Content ★=Modeling standards and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. S.C. N.Q.2 Define appropriate quantities for the purpose of descriptive modeling. S.C. F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context. A.C. F.TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. A.C. F.TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian 31 cases. 5)Interpret the parameters in a linear or exponential function in terms of a context. 6) Uses the radian measure of an angle to find the length of the arc in the unit circle subtended by the angle and find the measure of the angle given the length of the arc. 7)Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers (interpreted as radian measures of angles traversed counterclockwise around the unit circle) and use M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content Pearson 13-3 Pearson 13-4, 13-5, 13-6 A.C. = Additional Content ★=Modeling standards measures of angles traversed counterclockwise around the unit circle. A.C. F.TF.8 Prove the Pythagorean identity sin 2 (θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. A.C. F.TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.★ A.C. the Pythagorean identity (sin θ )2 + (cos θ )2 = 1 to find sin θ , cos θ , or tan θ , given sin θ , cos θ , or tan θ , and the quadrant of the angle. 7)Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers (interpreted as radian measures of angles traversed counterclockwise around the unit circle) and use the Pythagorean identity (sin θ )2 + (cos θ )2 = 1 to find sin θ , cos θ , or tan θ , given sin θ , cos θ , or tan θ , and the quadrant of the angle. 8)Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. ★ Suggested Performance Tasks: Exemplars Extended projects Math Webquests Writing in Math/Journal 32 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 Pearson 14-1 Pearson 13-4, 13-5, 13-6, 13-7 Stage 2 – Assessment Evidence Other Evidence: Classwork Exit Slips Homework Individual and group tests Open-ended questions S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards Portfolio Quizzes Stage 3 – Learning Plan Lesson Format 7-10 min: Do Now/Journaling/Pretest (whole class) Journaling Pretest Activate students’ prior knowledge Can be a review of info Pose EQ or provide relevant question / inquiry Quick multiple choice format related to EU Not to be counted as a test grade Share-out with several students Review correct answers 10-15 min: Homework Review (whole class) 15-20 min: Mini Lesson/Content Presentation /Guided Practice (whole class) Content Presentation Guided Practice Note taking of solutions to sample problems. Clarify instructions for assignments and projects Video or multi-media presentation Teach specific skills (i.e. which problem solving skill is appropriate, how to use rubrics) 30 min: Independent Practice (small group/independent) Anchor Activity: major assignment that Center Activities: variety of activities related to unit everyone is responsible for completing allowing some flexibility and choice for students to complete Word Wall activities, technology center with math web quests, math centers 2 min: Transition back to seats for whole class 10 min: Closure/Assessment/Evaluation Exit slip Assign homework 33 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards UNIT NAME: Modeling with Functions Grade level: HS District-Approved Text: Pearson Unit #4 Stage 1 – Desired Results Enduring Understandings/Goals: Trigonometric functions are useful for modeling periodic phenomena Essential Questions: When does a function best model a situation? 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. Standard: Student Learning Suggested Instructional Objectives Strategies FIF.6 Calculate and 1. Estimate, calculate Given a table of values, interpret the average and interpret the such as the height of a rate of change of a average rate of plant overtime, students function (presented change of a function estimate the rate of plant symbolically or as a presented growth table) over a specified symbolically, in a Provide students with interval. Estimate the table, or graphically many examples of rate of change from a over a specified functional relationships, graph.★ M.C. interval.★ both linear or non-linear 34 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content Suggested Resources Pearson 2-5, 4-1, 4-2, CB 4-3, 5-8 A.C. = Additional Content ★=Modeling standards FIF.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. S.C. F.BF.1. Write a function that describes a relationship between two quantities.* b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a 35 2. Analyze and compare properties of two functions when each is represented in a different form (algebraically, graphically, numerically in tables, or by verbal descriptions). Compare a graph of one quadratic function and an algebraic expression for another and say which has the larger maximum 3. Construct a function that combines standard function types using arithmetic operations to model a relationship between two quantities.★ M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content Pearson 2-4, 4-2, 5-9, 7-3 Pearson 2-2, 2-5, 4-2, 5-2, 6-6, 7-2, 8-2, 8-3 A.C. = Additional Content ★=Modeling standards decaying exponential, and relate these functions to the model. ★ M.C. FBF.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. A.C. F.LE.4 Express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using 36 4. Identify and illustrate (using technology) an explanation of the effects 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. 5. Express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 Pearson 2-6, 2-7, 4-1, 5-9, 8-2 Allow students to work with a single parent function and examine numerous parameter changes to make generalizations. Use visual approaches to identify the graphs of even and odd functions Use technology to solve exponential equations Use technology to evaluate logarithms S.C. = Supporting Content Pearson 7-5, 7-6 A.C. = Additional Content ★=Modeling standards technology. S.IC.2 Decide if a specified model is consistent with results from a given data generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0. 5. Would a result of 5 tails in a row cause you to question the model? S.C. ★ S.IC.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. M.C. ★ 37 6. Determine if the outcomes and properties of a specified model are consistent with results from a given datagenerating process using simulation. 7. Identify different methods and purposes for conducting sample surveys, experiments, and observational studies and explain how randomization relates to each. ★ M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 Use simulations to decide if a specified model is consistent with results from a given data-generating process Pearson CB 11-3 Pearson 11-8 Use sample surveys, experiments, and observational studies Explain how randomization relates to each. S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards S.IC.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. S.C. ★ S.IC.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. M.C. ★ Use simulations provide opportunities for students to clearly distinguish between a population parameter which is constant, and a sample statistic which is a variable. Use sample surveys, experiments, and observational studies Simulate random sampling Pearson 11-8 Pearson 11-8, CB 11-10a S.IC.5 Use data from 9. Use data from a a randomized randomized experiment to experiment to compare two treatments compare two and use simulations to treatments; use decide if differences simulations to decide between parameters are if differences between significant; evaluate parameters are reports based on data. ★ significant. M.C. ★ use simulations to decide if differences between parameters are significant. Pearson 11-10b S.IC.6 Evaluate reports based on experiments, and observational studies Pearson 11-6, 11-7, 11-8 38 8. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. ★ 9. Use data from a randomized experiment to M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards data. M.C. ★ compare two treatments and use simulations to decide if differences between parameters are significant; evaluate reports based on data.★ Stage 2 – Assessment Evidence Suggested Performance Tasks: Exemplars Extended projects Math Webquests Writing in Math/Journal 39 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 Other Evidence: Classwork Exit Slips Homework Individual and group tests Open-ended questions Portfolio Quizzes S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards Stage 3 – Learning Plan Lesson Format 7-10 min: Do Now/Journaling/Pretest (whole class) Journaling Pretest Activate students’ prior knowledge Can be a review of info Pose EQ or provide relevant question / inquiry Quick multiple choice format related to EU Not to be counted as a test grade Share-out with several students Review correct answers 10-15 min: Homework Review (whole class) 15-20 min: Mini Lesson/Content Presentation /Guided Practice (whole class) Content Presentation Guided Practice Note taking of solutions to sample problems. Clarify instructions for assignments and projects Video or multi-media presentation Teach specific skills (i.e. which problem solving skill is appropriate, how to use rubrics) 30 min: Independent Practice (small group/independent) Anchor Activity: major assignment that Center Activities: variety of activities related to unit everyone is responsible for completing allowing some flexibility and choice for students to complete Word Wall activities, technology center with math web quests, math centers 2 min: Transition back to seats for whole class 10 min: Closure/Assessment/Evaluation Exit slip Assign homework 40 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards UNIT NAME: Inference and Conclusions from Data Grade level: HS District-Approved Text: Pearson Unit #5 Stage 1 – Desired Results Enduring Understandings/Goals: Statisticians design experiments based on random sample and analyze the data to estimate the important properties of a population and make informed judgments The rule of probability can lead to more valid and reliable predictions about the likelihood of an event occurring. Essential Questions: How can a population be described when it is large? How is probability used to make informed decision about uncertain events? 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. Standard: Student Learning Suggested Instructional Suggested Objectives Strategies Resources S.CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or 41 1. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards complements of other events (“or,” “and, ”not”). A.C. S.CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. A.C. S.CP.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. A.C. S.CP.4 Construct and Interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two 42 complements of other events (“or,” “and,””not”). 2. Use two-way frequency tables to determine if events are independent and to calculate and approximate conditional probability. Pearson 11-3 2. Use two-way frequency tables to determine if events are independent and to calculate and approximate conditional probability. Pearson 11-4 2. Use two-way frequency tables to determine if events are independent and to calculate and approximate conditional probability. Pearson 11-4 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. A.C. S.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For 3. Use everyday language to explain independence and conditional probability in real-world situations. Pearson 11-3, 11-4 S.CP.6 Find the conditional probability of A 4. Find the conditional probability of A given B as Pearson 11-4 example, compare the chance of having lung cancer if you are a smoke with the chance of being a smoker if you have lung cancer. A.C. 43 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model. A.C. S.CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. A.C. 44 the fraction of B’s outcomes that also belong to A and apply the addition [P(A or B) = P(A) + P(B) – P(A and B)] rule of probability in a uniform probability model; interpret the results in terms of the model. 4. Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A and apply the addition [P(A or B) = P(A) + P(B) – P(A and B)] rule of probability in a uniform probability model; interpret the results in terms of the model. M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content Pearson 11-3 A.C. = Additional Content ★=Modeling standards Stage 2 – Assessment Evidence Suggested Performance Tasks: Other Evidence: 9. Exemplars Classwork 10. Extended projects Exit Slips 11. Math Webquests Homework 12. Writing in Math/Journal Individual and group tests Open-ended questions Portfolio Quizzes Stage 3 – Learning Plan Lesson Format 7-10 min: Do Now/Journaling/Pretest (whole class) Journaling Pretest Activate students’ prior knowledge Can be a review of info Pose EQ or provide relevant question / inquiry Quick multiple choice format related to EU Not to be counted as a test grade Share-out with several students Review correct answers 10-15 min: Homework Review (whole class) 15-20 min: Mini Lesson/Content Presentation /Guided Practice (whole class) Content Presentation Guided Practice Note taking of solutions to sample problems. Clarify instructions for assignments and projects Video or multi-media presentation Teach specific skills (i.e. which problem solving skill is appropriate, how to use rubrics) 30 min: Independent Practice (small group/independent) Anchor Activity: major assignment that Center Activities: variety of activities related to unit everyone is responsible for completing allowing some flexibility and choice for students to complete Word Wall activities, technology center with math web quests, math centers 2 min: Transition back to seats for whole class 45 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards 10 min: Closure/Assessment/Evaluation Exit slip Assign homework 46 M.C. = Major Content Algebra II Curriculum revised on June 16, 2014 S.C. = Supporting Content A.C. = Additional Content ★=Modeling standards