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MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide ALGEBRA 2 HONORS Course Code: 120034001 Pacing Traditional 18 Block 9 Topic V Assessment Window Topic V: Quadratic Functions, Equations, and Relations MATHEMATICS FLORIDA STATE STANDARDS (MAFS) & MATHEMATICAL PRACTICES (MP) MAFS.912.N-CN.3.7: Solve quadratic equations with real coefficients that have complex solutions. (MP.1, MP.7) Also assesses: MAFS.912.A-REI.2.4: Solve quadratic equations in one variable. (MP.2, MP.7, MP.8) MAFS.912.A-REI.1.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. (MP.1, MP.2, MP.3, MP.7) *NO CALCULATOR* MAFS.912. F-IF.3.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. (MP.2, MP.7) MAFS.912.N-CN.1.2: Use the relation β and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. (MP.2, MP.7, MP.8) *NO CALCULATOR* Also assesses: MAFS.912.N-CN.1.1: Know there is a complex number, π, such that π 2 = β1, and every complex number has the form π + ππ with a and b real (MP.2, MP.6) *NO CALCULATOR* MAFS.912.A-CED.1.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohmβs law V = IR to highlight resistance R. (MP.1, MP.2, MP.4, MP.5) (Assessed with A-CED.1.1) MAFS.912.G-GPE.1.2: Derive the equation of a parabola given a focus and directrix. (MP.2, MP.3, MP.7, MP.8) MAFS.912.A-REI.4.11: 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. (MP.2, MP.4, MP.5, MP.6) Division of Academics - Department of Mathematics Topic V Second Nine Weeks Date(s) 11/10/16 β 12/09/16 11/10/16 β 12/09/16 12/05/16 β 12/09/16 ESSENTIAL CONTENT OBJECTIVES (from Item Specifications) A. Quadratic Equations 1. Solving Quadratic Equations by Taking Square Roots. 2. Solving Equations by Completing the Square (A1-22.2) 3. Complex Numbers 4. Finding Complex Solutions of Quadratic Equations I can: ο· Rewrite a quadratic equation in vertex form by completing the square. ο· Solve a quadratic equation by choosing an appropriate method (i.e., completing the square, the quadratic formula, or factoring). ο· Complete an algebraic proof to explain steps for solving a simple equation. ο· Construct a viable argument to justify a solution method. ο· Calculate and interpret the average rate of change of a continuous function that is represented algebraically, in a table of values, on a graph, or as a set of data with a real-world context. ο· Identify zeros, extreme values, and symmetry of a quadratic function written symbolically. ο· Add, subtract, and multiply complex numbers and use π 2 = β1 to write the answer as a complex number. ο· Solve multi-variable formulas or literal equations for a specific variable. ο· Write the equation of a parabola when given the focus and directrix. ο· Find a solution or an approximate solution for π(π₯) = π(π₯) using a graph. ο· Find a solution or an approximate solution for π(π₯) = π(π₯) using a table of values. ο· Find a solution or an approximate solution for π(π₯) = π(π₯) using successive approximations that gives the solution to a given place value. ο· Demonstrate why the intersection of two functions is a solution to π(π₯) = π(π₯). B. Quadratic Relations and Systems of Equations 1. Parabolas 2. Solving Linear Systems in Three Variables Page 1 of 18 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide ALGEBRA 2 HONORS MATHEMATICS FLORIDA STATE STANDARDS (MAFS) & MATHEMATICAL PRACTICES (MP) MAFS.912.A-CED.1.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (MP.1, MP.2, MP.4, MP.5) Also assesses: MAFS.912.A-CED.1.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different food. (MP.1, MP.2, MP.4, MP.5) MAFS.912.A-REI.3.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. (MP.2, MP.4, MP.5, MP.6, MP.7, MP.8) MAFS.912.A-REI.3.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. (MP.2, MP.4, MP.5, MP.6, MP.7, MP.8) Division of Academics - Department of Mathematics Topic V Second Nine Weeks Course Code: 120034001 ESSENTIAL CONTENT OBJECTIVES (from Item Specifications) I can: ο· Identify the quantities in a real-world situation that should be represented by distinct variables. ο· Write constraints for a real-world context using equations, inequalities, a system of equations, or a system of inequalities. ο· Write a system of equations given a real-world situation. ο· Graph a system of equations that represents a real-world context using appropriate axis labels and scale. ο· Solve systems of linear equations. ο· Write a system of equations for a modeling context that is best represented by a system of equations. ο· Write a system of inequalities for a modeling context that is best represented by a system of inequalities. ο· Interpret the solution of a real-world context as viable or not viable. ο· Solve a simple system of a linear equation and a quadratic equation in two variables algebraically. ο· Solve a simple system of a linear equation and a quadratic equation in two variables graphically. Page 2 of 18 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide ALGEBRA 2 HONORS Course Code: 120034001 INSTRUCTIONAL TOOLS Pacing Core Text Book: Houghton Mifflin Harcourt β Algebra 2 Algebra 2 Honors Course Description Algebra 2 Item Specifications Date(s) 11/10/16 β 12/09/16 11/10/16 β 12/09/16 12/05/16 β 12/09/16 Traditional 18 Block 9 Topic V Assessment Window Algebra 2 Honors β H.M.H. Resources Unit Resources Unit Tests β A, B, and C Performance Assessment Module Resources Module Test B Common Core Assessment Readiness Advanced Learners β Challenge Worksheets Additional Unit Resources Math in Careers Video Assessment Readiness (Mixed Review) Lesson Resources Lessons β Work text/Interactive Student Edition Practice and Problem Solving: A/B Advanced Learners - Practice and Problem Solving: C Success for English Learners PMT Preferences: Auto-assign for intervention and enrichment: YES Test and Quizzes Auto-assign Homework for intervention and enrichment: NO STANDARDS MAFS.912.A-CED.1.2β MAFS.912.A-CED.1.3β MAFS.912.A-CED.1.4β MAFS.912.A-REI.1.1 MAFS.912.A-REI.2.4 MAFS.912.A-REI.3.6 MAFS.912.A-REI.3.7 MAFS.912.F-IF.3.8 MAFS.912.G-GPE.1.2 MAFS.912.N-CN.1.1 MAFS.912.N-CN.1.2 MAFS.912.N-CN.3.7 PMT Preferences: Auto-assign for intervention and enrichment: YES Auto-assign for intervention and enrichment: NO Standard-Based Intervention Auto-assign for intervention and enrichment: YES Course Intervention Daily Intervention MODULES TEACHER NOTES Algebra 2 Honors Block Schedule β Suggested Pace Module 3 Module 4 Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 3.1 A1-22.2 3.2 3.3 4.2 4.3 4.4 Review Topic 5 Test MAFS.912.A-REI.4.11β Topic V Assessment: Quadratic Functions, Equations, and Relations Division of Academics - Department of Mathematics Topic V Second Nine Weeks Page 3 of 18 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide ALGEBRA 2 HONORS Course Code: 120034001 INSTRUCTIONAL TOOLS Reporting Category: Algebra and Modeling % of Test 36% Average % Correct 2015 29% Average % Correct 2016 20% Reporting Category: Functions and Modeling % of Test 36% Average % Correct 2015 24% Average % Correct 2016 23% Reporting Category: Statistics, Probability, and the Number System % of Test 28% Average % Correct 2015 17% Average % Correct 2016 27% MODELING CYCLE (β ) The basic modeling cycle involves: 1. Identifying variables in the situation and selecting those that represent essential features. 2. Formulating a model by creating and selecting geometric, graphical, tabular, algebraic, or statistical representations that describe relationships between the variables. 3. Analyzing and performing operations on these relationships to draw conclusions. 4. Interpreting the results of the mathematics in terms of the original situation. 5. Validating the conclusions by comparing them with the situation, and then either improving the model or, if it is acceptable. 6. Reporting on the conclusions and the reasoning behind them. Choices, assumptions, and approximations are present throughout this cycle. http://www.cpalms.org/Standards/mafs_modeling_standards.aspx Vocabulary: Directrix, focus of a parabola, linear equations in the three variables, matrix, ordered triple, complex number, imaginary unit, pure imaginary number. Algebra 2 Honors REPORTING CATEGORY: ALGEBRA AND MODELING PRACTICE ITEMS 1. 2. 1 ππ‘ 2 The formula π = represents the distance π that a freefalling object will fall near a planet or the moon in a given time π‘. In the formula, π represents the acceleration due to 2 gravity. a) Solve the formula for π‘. b) A freeβfalling object near the moon drops 20.5. For how many second does the object is falling? Use π = 1.6π/π 2. The following equation represents a particle moving linearly, in three dimensions: π = Scientist 1:π£ = β2π β 2π0 β ππ‘ 2 and scientist 2: = π π‘ β ππ‘ 2 2 β π0 π‘ ππ‘ 2 2 + π£π‘ + π0 . Two scientists solve the equation for π£ and their equations are as follows: . How did each scientist come up with the equation? Show the steps. Division of Academics - Department of Mathematics Topic V Second Nine Weeks Page 4 of 18 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide ALGEBRA 2 HONORS Course Code: 120034001 INSTRUCTIONAL TOOLS REPORTING CATEGORY: ALGEBRA AND MODELING PRACTICE ITEMS Solve the following quadratic equations. Explain each step. a) 2π₯ 2 β 7π₯ β 4 = 0 b) 4π₯ 2 + 12π₯ + 9 = 0 c) π₯ 2 + 6π₯ + 2 = 0 4. The steps used to simplify an expression are shown. Identify the missing property that justifies each step. Steps Justification 3. 5π + 4(6 + 3π) 5π + 24 + 12π 24 + 5π + 12π 24 + (5π + 12π) 24 + 17π 5. 6. 7. 8. 9. Given Expression Substitution Property Which of the following quadratic equations has no real solutions? A. π₯ 2 + 3π₯ β 5 = 0 B. 4π₯ 2 + 4π₯ + 1 = 0 C. 2π₯ 2 β 4π₯ + 3 = 0 D. π₯ 2 β 6π₯ β 2 = 0 Consider the quadratic equation 3π₯ 2 β 9π₯ + 20 = 13. a) What method should be used to most easily solve the equation over the set of complex numbers? Explain your reasoning. b) Solve the equation using the method from part a). Show your work, and write the solutions using the imaginary unit π as necessary. Which points are on the parabola with focus (0.4) and directrix π¦ = β4? ο° (8, β4) ο° (0, β4) ο° (0, 4) ο° (4, 1) ο° (9, 12) ο° (12, 9) 1 Which focus and directrix correspond to a parabola described by y= π₯ 2 ? 16 A. Focus (0, β4) and directrix π¦ = β4 B. Focus (0, 4) and directrix π¦ = 4 C. Focus (0, β4) and directrix π¦ = 4 D. Focus (0, 4) and directrix π¦ = β4 Which point is always on a parabola with focus πΉ(0, π) and directrix π¦ = βπ? A. (0, 0) B. (0, π) C. (π, 0) D. (π, π) Division of Academics - Department of Mathematics Topic V Second Nine Weeks Page 5 of 18 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide ALGEBRA 2 HONORS Course Code: 120034001 INSTRUCTIONAL TOOLS REPORTING CATEGORY: ALGEBRA AND MODELING PRACTICE ITEMS 10. Solve the following quadratic equations. Explain each step. d) 2π₯ 2 β 7π₯ β 4 = 0 e) 4π₯ 2 + 12π₯ + 9 = 0 f) π₯ 2 + 6π₯ + 2 = 0 11. The steps used to simplify an expression are shown. Identify the missing property that justifies each step. Steps Justification 5π + 4(6 + 3π) Given Expression 5π + 24 + 12π 24 + 5π + 12π 24 + (5π + 12π) 24 + 17π Substitution Property 12. Which of the following quadratic equations has no real solutions? A. π₯ 2 + 3π₯ β 5 = 0 B. 4π₯ 2 + 4π₯ + 1 = 0 C. 2π₯ 2 β 4π₯ + 3 = 0 D. π₯ 2 β 6π₯ β 2 = 0 13. Consider the quadratic equation 3π₯ 2 β 9π₯ + 20 = 13. c) What method should be used to most easily solve the equation over the set of complex numbers? Explain your reasoning. d) Solve the equation using the method from part a). Show your work, and write the solutions using the imaginary unit π as necessary. 14. Which points are on the parabola with focus (0.4) and directrix π¦ = β4? ο° (8, β4) ο° (0, β4) ο° (0, 4) ο° (4, 1) ο° (9, 12) ο° (12, 9) 1 15. Which focus and directrix correspond to a parabola described by y= π₯ 2 ? 16 A. Focus (0, β4) and directrix π¦ = β4 B. Focus (0, 4) and directrix π¦ = 4 C. Focus (0, β4) and directrix π¦ = 4 D. Focus (0, 4) and directrix π¦ = β4 16. Which point is always on a parabola with focus πΉ(0, π) and directrix π¦ = βπ? A. (0, 0) B. (0, π) C. (π, 0) D. (π, π) Division of Academics - Department of Mathematics Topic V Second Nine Weeks Page 6 of 18 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide ALGEBRA 2 HONORS Course Code: 120034001 INSTRUCTIONAL TOOLS REPORTING CATEGORY: ALGEBRA AND MODELING PRACTICE ITEMS 17. Which is one of the appropriate steps in finding the solutions for π₯ 2 + 8π₯ β 9 = 0 when solved by completing the square? A. (π₯ + 4)2 = 25 B. (π₯ + 8)2 = 9 C. (π₯ + 4)2 = 9 D. (π₯ + 9)(π₯ β 1) = 0 18. For the scenario below, use the model β = β16π‘ 2 + π£0 π‘ + β0 , where β = height (in feet), β0 = initial height (in feet), π£0 = initial velocity (in feet per second), and t = time (in seconds). A cheerleading squad performs a stunt called a βbasket tossβ where a team member is thrown into the air and is caught moments later. During one performance, a cheerleader is thrown upward, leaving her teammatesβ hands 6 feet above the ground with an initial vertical velocity of 15 feet per second. When the girl falls back, the team catches her at a height of 5 feet. How long was the cheerleader in the air? 1 A. second 16 9 B. 1 second 16 C. 1 second D. 2 seconds 2 19. If a + 2i is a root of the quadratic equation 2x + 6x + c = 0, find the values of the real numbers a and c . 20. For each of the following, determine if the statement is true or false. If false, explain your reasoning. STATEMENTS TRUE FALSE There is a parabola with focus of (2, 3), directrix π¦ = 1, and vertex (0, 0). ο° ο° The parabola with focus of (0, ¼) and directrix y = -¼ has no x-intercepts. ο° ο° (π₯ + 4)2 = 29π¦ β 4.5) has focus at (β4, 5) and directrix π¦ = 4 ο° ο° 21. Which ordered pair is in the solution set of the system of equations shown below? π¦ 2 β π₯ 2 + 32 = 0 3π¦ β π₯ = 0 A. (2, 6) B. (3, 1) C. (β1, β3) D. (β6, β2) 22. The directrix of the parabola 12(π¦ + 3) = (π₯ β 4)2 has the equation π¦ = β6. Find the coordinates of the focus of the parabola. 23. Solve the system 6π₯ β 2π¦ β 4π§ = β8 3π₯ β 5π¦ + 5π§ = β14 π₯ + π¦ β 5π§ = 6 Division of Academics - Department of Mathematics Topic V Second Nine Weeks Page 7 of 18 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide ALGEBRA 2 HONORS Course Code: 120034001 INSTRUCTIONAL TOOLS REPORTING CATEGORY: STATISTICS, Probability, AND THE NUMBER SYSTEM PRACTICE ITEMS 24. Which one of the following is in the simplest form of A. B. C. D. -48 ? β4πβ3 4ββ3 β4β3 4πβ3 25. What does the imaginary number π represent? A. β1 B. β1 C. ββ1 D. -ββ1 26. Simplify each expression and tell whether it represents a real number or a non-real number. a) β144 β β64 b) β144 + ββ64 27. Let π, π, and π be any real numbers. Find the product ππ(π + ππ). Which of the following sums, differences, and products can be simplified to 6 β 3π? ο° (9 β 5π) + (3 β 2π) ο° (4 + 2π) + (2 β 5π) ο° (9 β 5π) β (3 β 2π) ο° (4 + 2π) β (2 β 5π) ο° 3π(β1 + 2π) ο° 3π(β1 β 2π) 28. Consider the following expressions i8 - i2 i 7 - i5 i6 - i 4i 4 - 2i 3 6i 4 - 2i2 a) b) Which of these expressions can be expressed as in the form a + 0i? Which of these expressions can be expressed as an imaginary number 0 + bi? Division of Academics - Department of Mathematics Topic V Second Nine Weeks Page 8 of 18 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide ALGEBRA 2 HONORS Course Code: 120034001 INSTRUCTIONAL TOOLS REPORTING CATEGORY: STATISTICS, Probability, AND THE NUMBER SYSTEM PRACTICE ITEMS 29. For which of the following operations will the complex numbers (4 β 3π) and (1 + 2π) produce a real solution? Find the solution. A. Addition B. Subtraction C. Multiplication D. Division 30. Given π is the imaginary unit, (2 β π¦π)2 in simplest form is A. π¦ 2 β 4yi + 4 B. βπ¦ 2 β 4yi + 4 C. π¦ 2 + 4 D. βπ¦ 2 + 4 STEM Lessons - Model Eliciting Activity STEM Lessons N/A CPALMS Perspectives Videos Professional/Enthusiasts Gear Heads and Gear Ratios Hurricane Dennis & Failed Math Models Solving Systems of Equations, Oceans & Climate Determining Strengths of Shark Models based on Scatterplots and Regression Expert Problem Solving with Project Constraints Using Mathematics to Optimize Wing Design Division of Academics - Department of Mathematics Topic V Second Nine Weeks Page 9 of 18 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide ALGEBRA 2 HONORS Course Code: 120034001 MATHEMATICS FLORIDA STANDARDS MATHEMATICAL PRACTICES DESCRIPTION MAFS.K12.MP.1 Make sense of problems and persevere in solving them. MAFS.K12.MP.2 Reason abstractly and quantitatively. MAFS.K12.MP.3 Construct viable arguments and critique the reasoning of others. MAFS.K12.MP.4 Model with mathematics. Mathematically proficient students will be able to: Explain the meaning of a problem and looking for entry points to its solution. Analyze givens, constraints, relationships, and goals. Make conjectures about the form and meaning of the solution and plan a solution pathway. Consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. Monitor and evaluate their progress and change course if necessary. Explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. ο· Check answers to problems using a different method, and continually ask, βDoes this make sense?β ο· Identify correspondences between different approaches. ο· ο· ο· ο· ο· ο· ο· ο· ο· ο· ο· Mathematically proficient students will be able to: Make sense of quantities and their relationships in problem situations. Decontextualizeβto abstract a given situation and represent it symbolically. Contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols Create a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them. Know and be flexible using different properties of operations and objects. Mathematically proficient students will be able to: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Make conjectures and build a logical progression of statements to explore the truth of their conjectures. Analyze situations by breaking them into cases, and can recognize and use counterexamples. Justify their conclusions, communicate them to others, and respond to the arguments of others. Reason inductively about data, making plausible arguments that take into account the context from which the data arose. Compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, andβif there is a flaw in an argumentβexplain what it is. ο· Determine domains to which an argument applies. ο· ο· ο· ο· ο· ο· ο· ο· ο· ο· ο· ο· Mathematically proficient students will be able to: Apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. Use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Apply what they know and feel comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. Identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. Analyze relationships mathematically to draw conclusions. Interpret mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Division of Academics - Department of Mathematics Topic V Second Nine Weeks Page 10 of 18 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide ALGEBRA 2 HONORS Course Code: 120034001 MATHEMATICS FLORIDA STANDARDS MATHEMATICAL PRACTICES DESCRIPTION MAFS.K12.MP.5 Use appropriate tools strategically. MAFS.K12.MP.6 Attend to precision. MAFS.K12.MP.7 Look for and make use of structure. MAFS.K12.MP.8 Look for and express regularity in repeated reasoning. Mathematically proficient students will be able to: ο· Consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. ο· Make sound decisions about when each of the tools appropriate for their grade or course might be helpful, recognizing both the insight to be gained and their ο· ο· ο· ο· limitations. Example: High school students analyze graphs of functions and solutions using a graphing calculator. Detect possible errors by strategically using estimation and other mathematical knowledge. Know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. Use technological tools to explore and deepen their understanding of concepts ο· ο· ο· ο· ο· Mathematically proficient students will be able to: Communicate precisely to others. Use clear definitions in discussion with others and in their own reasoning. State the meaning of the symbols they choose, including using the equal sign consistently and appropriately. Be careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. Calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. Mathematically proficient students will be able to: ο· Discern a pattern or structure. Example: In the expression x2 + 9x + 14, students can see the 14 as 2 × 7 and the 9 as 2 + 7. ο· Recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. Step back for an overview and shift perspective. ο· See complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. Example: They can see 5 β 3(x β y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. Mathematically proficient students will be able to: ο· Notice if calculations are repeated, and look both for general methods and for shortcuts. Example: Noticing the regularity in the way terms cancel when expanding (x1)(x+1),(x-1)(x2+x+1),and(x-1)(x3 +x2+x+1)might lead them to the general formula for the sum of a geometric series. ο· Maintain oversight of the process, while attending to the details as they work to solve a problem. ο· Continually evaluate the reasonableness of their intermediate results. Division of Academics - Department of Mathematics Topic V Second Nine Weeks Page 11 of 18 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide ALGEBRA 2 HONORS Course Code: 120034001 Domain: CREATING EQUATIONS STANDARD CODE STANDARD DESCRIPTION Cluster 1: Create equations that describe numbers or relationships Create two or more to represent relationships between quantities; graph equations on coordinate axes with labels and Understand solving equations as a process of equations reasoning in and explain thevariables reasoning scales. Context Complexity: Level 2: Basic Applications of Skills and Concepts MAFS.912.A-CED.1.2 Assessed Level 2 writes or chooses a system of linear equations with integral coefficients for a real-world context or writes a single equation for a real-world context that has at least three variables with integral coefficients Level 3 Level 4 Level 5 writes or chooses a system of two equations writes a system of three equations for employs the modeling cycle when with rational coefficients, where one equation a real-world context. writing equations that have at least can be a simple quadratic equation for a realtwo variables. world context; writes a single equation that has at least three variables with rational coefficients for a real-world context; identifies the meaning of the variables Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Context Complexity: Level 3: Strategic Thinking MAFS.912.A-CED.1.3 (Assessed with MAFS.912.ACED.1.2) Level 2 Level 3 Level 4 identifies variables; writes constraints models constraints using a combination of explain why a solution is viable or as a system of linear inequalities or equations, inequalities, systems of equations, nonviable for a real-world context linear equations for a real-world context systems of inequalities for a real-world context; interprets solutions as viable or nonviable based on the context Level 5 employs the modeling cycle when writing constraints Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohmβs law V = IR to highlight resistance R. MAFS.912.A-CED.1.4 (Assessed with MAFS.912.ACED.1.1) Context Complexity: Level 1: Recall Level 2 Level 3 solves a literal linear equation in a real- solves a literal equation that requires three world context that requires two procedural steps. procedural steps Division of Academics - Department of Mathematics Topic V Second Nine Weeks Level 4 solves a literal equation that requires four or five procedural steps. Level 5 solves a literal equation that requires six procedural steps. Page 12 of 18 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide ALGEBRA 2 HONORS Course Code: 120034001 Domain: ALGEBRA: REASONING WITH EQUATIONS & INEQUALITIES STANDARD CODE STANDARD DESCRIPTION Cluster 1: Understand solving equations as a process of reasoning and explain the reasoning Understand solving equations as a process of reasoning and explain the reasoning 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. Understand solving equations as a process of reasoning and explain the reasoning Context Complexity: Level 3: Strategic Thinking & Complex Reasoning MAFS.912.A-REI.1.1 Assessed Level 2 chooses the correct justifications for the steps in solving a simple quadratic equation, where a = 1, containing integer coefficients Level 3 Level 4 chooses the correct justifications for the justifies the steps in solving a quadratic steps in solving a quadratic equation, equation with complex solutions where a does not equal 1, containing rational coefficients Level 5 constructs a viable argument to justify the steps in solving radical, rational, and exponential equations (with bases 2, 10, or e) Cluster 2: Solve equations and inequalities in one variable Solve quadratic equations in one variable. Context Complexity: Level 2: Basic Application of Skills & Concepts MAFS.912.A-REI.2.4 (Assessed with MAFS.912.NCN.3.7) Level 2 Level 3 solves quadratic equations of the form ax2 solves quadratic equations of the form + bx + c = d with integral coefficients ax2 + bx + c = d with integral coefficients, where b/a is an integer Level 4 solves quadratic equations of the form ax2 + bx + c = d with rational coefficients Level 5 [intentionally left blank] Cluster 3: Solve systems of equations Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Context Complexity: Level 1: Recall MAFS.912.A-REI.3.6 (Assessed with MAFS.912.ACED.1.2) Level 2 explains whether a system of equations has one, infinitely many, or no solutions; solves a system of equations by graphing or substitution (manipulation of equations may be required) or elimination in the form of ax+ by = c and dx + ey = f, where multiplication is required for both equations Division of Academics - Department of Mathematics Topic V Second Nine Weeks Level 3 Level 4 solves a system that consists of linear [intentionally left blank] equations in two variables with rational coefficients by graphing, substitution, or elimination; interprets solutions in a real- world context or mathematical context Level 5 [intentionally left blank] Page 13 of 18 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide ALGEBRA 2 HONORS Course Code: 120034001 Domain: ALGEBRA: REASONING WITH EQUATIONS & INEQUALITIES STANDARD CODE STANDARD DESCRIPTION Cluster 3: Solve systems of equations 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 = β3x and the circle x² + y² = 3. Context Complexity: Level 2: Basic Application of Skills & Concepts Level 2 MAFS.912.A-REI.3.7 (Assessed with MAFS.912.ACED.1.2) Level 3 solves a simple system consisting of a solves a simple system consisting of a linear equation and a quadratic equation in linear equation, where the slope and two variables, when given a graph the y- intercept are integers and a univariate quadratic with integral coefficients by graphing; solves a simple system, consisting of a linear equation of the form y = kx and a circle centered at (0, 0) by graphing and algebraically; solves a simple system consisting of a linear equation of the form y = kx and a univariate quadratic algebraically Level 4 solves a simple system consisting of a linear equation, where the slope and the y- intercept are rational numbers and a univariate quadratic with rational coefficients by graphing; solves a simple system, consisting of a linear equation and a circle by graphing and algebraically; solves a simple system consisting of a linear equation of the form Ax + By = C, where A, B, and C are integers and a bivariate quadratic algebraically Level 5 solves a simple system consisting of a linear equation and a bivariate quadratic algebraically and graphically Cluster 4: Represent and solve equations and inequalities graphically 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 Context Complexity: Level 2: Basic Application of Skills & Concepts MAFS.912.A-REI.4.11 Assessed Level 2 determines an integral solution or approximate solution using successive approximations for f(x) = g(x) given a graph or table of linear, quadratic, or exponential functions Division of Academics - Department of Mathematics Topic V Second Nine Weeks Level 3 determines a solution or an approximate solution for f(x) = g(x) using a graph, table of values, or successive approximations, where f(x) and g(x) are an exponential with a rational exponent, polynomial degree greater than two, rational, absolute value, and logarithmic Level 4 completes an explanation on how to find a solution for f(x) = g(x) Level 5 employs the modeling cycle when validating that the intersection of two functions is a solution to f(x) = g(x) Page 14 of 18 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide ALGEBRA 2 HONORS Course Code: 120034001 Domain: FUNCTIONS: INTERPRETING FUNCTIONS STANDARD CODE STANDARD DESCRIPTION Cluster 3: Analyze functions using different representations Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Understand solving equations as a process of reasoning and explain the reasoning b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = ,y= ,y= ,y= , and classify them as representing exponential growth or decay Context Complexity: Level 2: Basic Applications of Skills and Concepts MAFS.912.F-IF.3.8 Assessed Level 2 factors difference of two squares with a degree of 2, and trinomials with a degree of 2 whose leading coefficent has up to 4 factors and interprets the zeros; completes the square when the leading coefficent is 1; interprets the extreme values. Level 3 Level 4 interprets key features of quadratics by interprets symmetry of a quadratic factoring or completing the square. function written symbolically for a realworld context. Level 5 [intentionally left blank] Domain: GEOMETRY: EXPRESSING GEOMETRIC PROPERTIES WITH EQUATIONS STANDARD CODE STANDARD DESCRIPTION Cluster 1: Translate between the geometric description and the equation for a conic section Derive equation of explain a parabola given a focus and directrix. Understand solving equations as a process of the reasoning and the reasoning Context Complexity: Level 2: Basic Applications of Skills and Concepts MAFS.912.G-GPE.1.2 Assessed Level 2 [intentionally left blank] Division of Academics - Department of Mathematics Topic V Second Nine Weeks Level 3 derives the equation of a parabola given a focus and directrix, parallel to the y-axis, on the coordinate grid Level 4 derives the equation of a parabola given a focus and directrix, parallel to the y-axis with an integral value Level 5 derives the equation of a parabola given a focus and directrix Page 15 of 18 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide ALGEBRA 2 HONORS Course Code: 120034001 Domain: NUMBER & QUANTITY: THE COMPLEX NUMBER SYSTEM STANDARD CODE STANDARD DESCRIPTION Cluster 1: Perform arithmetic operations with complex numbers. Knowofthere is a complex number such that i² = β1, and every complex number has the form a + bi with a and b real Understand solving equations as a process reasoning and explain the ireasoning Context Complexity: Level 1: Recall MAFS.912.N-CN.1.1 (Assessed with MAFS.912.N-CN.1.2) Level 2 Level 3 recognizes that a negative square root is not converts simple βperfectβ squares to a real number complex number form (bi), such as the square root of -25 is 5i Level 4 assimilates that there is a complex number i such that i2 = -1, and identifies the proper a + bi form (with a and b real) Level 5 generalizes or develops a rule that explains complex numbers and their properties Use the relation i² = β1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Context Complexity: Level 2: Basic Applications of Skills and Concepts Level 2 MAFS.912.N-CN.1.2 Assessed adds, subtracts, or multiplies simple complex numbers, with up to two steps Level 3 Level 4 uses the commutative, associative, or evaluates sums or products of complex distributive properties to identify numbers for multistep problems products or sums of complex numbers, with up to three steps Level 5 generalizes rules for abstract problems, such as explaining what type of expression results, when given (a + bi)(c + di) Cluster 3: Use complex numbers in polynomial identities and equations. Solveofquadratic equations withthe realreasoning coefficients that have complex solutions. Understand solving equations as a process reasoning and explain Context Complexity: Level 1: Recall MAFS.912.N-CN.3.7 Assessed Level 2 solves quadratic equations of the form ax2 + b = c, where c- b is a negative integer Division of Academics - Department of Mathematics Topic V Second Nine Weeks Level 3 solves quadratic equations where the discriminant is a negative perfect square Level 4 solves quadratic equations (with any real coefficients) that have complex solutions Level 5 [intentionally left blank] Page 16 of 18 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide ALGEBRA 2 HONORS Course Code: 120034001 TECHNOLOGY TOOLS CPALM RESOURCES LESSON PLANS Ranking Sports Players (Quadratic Equations Practice) Where did the answers go? Oh, they're imaginary! Selling Fuel Oil at a Loss The Quadratic Quandary TUTORIAL MAFS.912.N-CN.1.2 Adding Complex Numbers How to Subtract Complex Numbers Multiplying Complex Numbers MAFS.912.A-REI.2.4 Learning How to Complete the Square Solving Quadratic Equations by Square Roots Solving Quadratic Equations Using the Quadratic Formula VIRTUAL MANIPULATIVE Fractal Tool Equation Grapher PROBLEM-SOLVING TASK Two Squares Are Equal A Linear and Quadratic System The Circle and The Line GRAPHING CALCULATOR CORRELATION TEXAS INSTRUMENT MATH ACTIVITY TITLE Solving Systems involving Quadratic Equations: Systems of Conics Quadratic Equations Graphing Quadratic Equations Investigating the Graphs of Quadratic Equations Division of Academics - Department of Mathematics Topic V Second Nine Weeks Page 17 of 18 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide ALGEBRA 2 HONORS Course Code: 120034001 GIZMOS CORRELATION GIZMO TITLE Roots of a Quadratic Points in the Complex Plane 2 Modeling the Factorization of ax +bx+c TOPIC V VIDEO TITLE DISCOVERY EDUCATION CORRELATION Quadratic Equations: Fire in the Sky Applications of Quadratic Equations Types of Numbers Solving Systems of Quadratic Equations MATH EXPLANATION TITLE The Quadratic Formula Working with Imaginary Numbers MATH OVERVIEW Solving a System of Two Conics Division of Academics - Department of Mathematics Topic V Second Nine Weeks Page 18 of 18