MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Division of Academics - Department of Mathematics Page 1 of 12 Topic II First Nine Weeks - Revised 09/19/2017 Post Hurricane Irma

ALGEBRA 2 HONORS Course Code: 120034001

Topic II: Quadratic Functions, Equations, and Relations

MATHEMATICS FLORIDA STATE STANDARDS (MAFS) & MATHEMATICAL PRACTICES (MP)

ESSENTIAL CONTENT OBJECTIVES

MAFS.912.N-CN.3.7: Solve quadratic equations with real coefficients that have complex solutions. (MP.1, MP.7)

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)

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 – and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. (MP.2, MP.7, MP.8)

MAFS.912.N-CN.1.1: 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 (MP.2, MP.6)

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 Ohm’s law V = IR to highlight resistance R. (MP.1, MP.2, MP.4,

MP.5)

A. Quadratic Equations a. Solving Quadratic

Equations by Taking Square Roots.

b. Complex Numbers c. Finding Complex

Solutions of Quadratic Equations

I can:

Rewrite a quadratic equation in vertex form by completing the square.

Solve a quadratic equation by choosing an appropriate method (i.e., completing the square, the quadratic formula, or factoring).

Complete an algebraic proof to explain steps for solving a simple equation.

Construct a viable argument to justify a solution method.

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.

Identify zeros, extreme values, and symmetry of a quadratic function written symbolically.

Add, subtract, and multiply complex numbers and use 𝑖2 = −1 to write the answer as a complex number.

Solve multi-variable formulas or literal equations for a specific variable.

Pacing Date(s) Traditional 18 09/26/17 – 10/20/17

Block 9 09/26/17 – 10/20/17

Topics I & II Assessment Window 10/13/17 – 10/20/17

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Division of Academics - Department of Mathematics Page 2 of 12 Topic II First Nine Weeks - Revised 09/19/2017 Post Hurricane Irma

ALGEBRA 2 HONORS Course Code: 120034001

MATHEMATICS FLORIDA STATE STANDARDS (MAFS) & MATHEMATICAL PRACTICES (MP)

ESSENTIAL CONTENT OBJECTIVES

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)

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)

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)

B. Quadratic Relations and Systems of Equations,

a. Parabolas b. Solving Linear Systems in

Three Variables

I can:

Write the equation of a parabola when given the focus and directrix.

Find a solution or an approximate solution for 𝑓(𝑥) = 𝑔(𝑥) using a graph.

Find a solution or an approximate solution for 𝑓(𝑥) = 𝑔(𝑥) using a table of values.

Find a solution or an approximate solution for 𝑓(𝑥) = 𝑔(𝑥) using successive approximations that gives the solution

to a given place value.

Demonstrate why the intersection of two functions is a solution to 𝑓(𝑥) = 𝑔(𝑥).

Identify the quantities in a real-world situation that should be represented by distinct variables.

Write constraints for a real-world context using equations, inequalities, a system of equations, or a system of inequalities.

Write a system of equations given a real-world situation.

Graph a system of equations that represents a real-world context using appropriate axis labels and scale.

Solve systems of linear equations.

Write a system of equations for a modeling context that is best represented by a system of equations.

Write a system of inequalities for a modeling context that is best represented by a system of inequalities.

Interpret the solution of a real-world context as viable or not viable.

Solve a simple system of a linear equation and a quadratic equation in two variables algebraically.

Solve a simple system of a linear equation and a quadratic equation in two variables graphically.

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Division of Academics - Department of Mathematics Page 3 of 12 Topic II First Nine Weeks - Revised 09/19/2017 Post Hurricane Irma

ALGEBRA 2 HONORS Course Code: 120034001

RECOMMENDED INSTRUCTIONAL DESIGN AND PLANNING CONTINUUM

Before During After

Prior to the lesson:

Outline content standard(s).

Determine learning targets.

Anticipate student understanding and misconceptions.

Determine prerequisite skills.

Plan for learning experiences that target Rigor o Conceptual Understanding o Procedural Fluency o Application

Determine the task students will demonstrate to reach the desired learning targets.

Plan instructional delivery methods that will maximize initial engagement and sustain it throughout the lesson.

Decide how students will reflect upon, self-assess, and set goals for their future learning.

During the lesson:

Activate (or supply) prior knowledge and/or spiral back o Warm ups, Bell Ringers, Openers, etc.

Tailor lesson experiences to the different needs and ability of the learners.

Clarify vocabulary and mathematical notation.

Incorporate a variety of higher order questions to encourage and increase critical thinking skills.

Continuously check for student understanding and provide feedback.

Provide opportunities for students to develop self-assessment and to reflect about their understanding and work.

Bring closure to the lesson so that the students can articulate what they have learned.

After the lesson:

Analyze evidence of student learning to develop intervention, enrichment, and future instruction.

Discuss results of assessments with students.

Engage students in reflective processes and goal setting.

Engage in self-reflection to adapt/modify teaching strategies to improve instruction.

Pacing Date(s) Traditional 18 09/26/17 – 10/20/17

Block 9 09/26/17 – 10/20/17

Topics I & II Assessment Window 10/13/17 – 10/20/17

Algebra 2 Honors – H.M.H. Resources

Unit Resources Unit Resources

Unit Tests – A, B, and C Math in Careers Video

Performance Assessment Assessment Readiness (Mixed Review)

Module Resources

Module Test B

Common Core Assessment Readiness

Advanced Learners – Challenge Worksheets

Lesson Resources

Lessons – Work text/Interactive Student Edition

Practice and Problem Solving: A/B

Advanced Learners - Practice and Problem Solving: C

PMT Preferences: Auto-assign for intervention and enrichment: NO Auto-assign for intervention and enrichment: NO

PMT Preferences: Auto-assign for intervention and enrichment: YES Auto-assign for intervention and enrichment: NO

Auto-assign for intervention and enrichment: YES Test and Quizzes Standard-Based Intervention

Homework Course Intervention

Daily Intervention

INSTRUCTIONAL TOOLS

Core Text Book: Houghton Mifflin Harcourt – Algebra 2

Algebra 2 Honors Course Description

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Division of Academics - Department of Mathematics Page 4 of 12 Topic II First Nine Weeks - Revised 09/19/2017 Post Hurricane Irma

ALGEBRA 2 HONORS Course Code: 120034001

MODULE LESSON STANDARDS SUGGESTED PROBLEMS

BY TEACHERS FOR TEACHERS* NOTES / RESOURCES

Module 3

3.1 MAFS.912.N-CN.1.1

MAFS.912.A-REI.2.4

HOMEWORK AND PRACTICE

5, 7 - 10 Illustrative Mathematics Task(s): Complex Number Patterns

3.2 MAFS.912.N-CN.1.1

MAFS.912.N-CN.1.2

HOMEWORK AND PRACTICE

10, 13, 20, 23, 24

Illustrative Mathematics Task(s): Computations with Complex Numbers

Powers of a Complex Number

3.3 MAFS.912.N-CN.3.7

MAFS.912.A-REI.2.4

HOMEWORK AND PRACTICE

9, 13, 17, 20, 21 Illustrative Mathematics Task(s): Completing the Square

Module 4

4.2

MAFS.912.G-GPE.1.2

MAFS.912.A-CED.1.2

MAFS.912.A-CED.1.4

HOMEWORK AND PRACTICE

1, 2, 5, 7, 9, 14, 18

GeoGebra: Cone Cross Sections

NCTM Illuminations: Cutting Conics, Human Conics

Illustrative Mathematics Task(s): Defining Parabolas Geometrically

4.3 MAFS.912.A-REI.3.7

MAFS.912.A-REI.4.11

HOMEWORK AND PRACTICE

1, 3, 5, 6, 7 (Graphically)

9, 10, 14, 17, 18 (Algebraically)

Illustrative Mathematics Task(s): A Linear and Quadratic System

4.4

MAFS.912.A-REI.3.6

MAFS.912.A-REI.4.11

MAFS.912.A-CED.1.3

HOMEWORK AND PRACTICE

3, 4, 5, 11, 12, 16 Illustrative Mathematics Task(s): Pairs of Whole Numbers

*Problems were suggested by M-DCPS teachers during May Algebra 2 PD.

STANDARDS MODULES TEACHER NOTES

MAFS.912.A-CED.1.2★

MAFS.912.A-CED.1.3★

MAFS.912.A-CED.1.4★

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.A-REI.4.11★

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

Module 3

Module 4

Algebra 2 Honors Block Schedule – Suggested Pace

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9

3.1 3.2 3.3 3.3 4.2 4.3 4.4 4.4 Test

Topics I & II Assessment: Functions AND Quadratic Functions, Equations, and Relations

POST Hurricane

Irma

Topic Resources PowerPoint Available in Learning Village

INSTRUCTIONAL TOOLS

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Division of Academics - Department of Mathematics Page 5 of 12 Topic II First Nine Weeks - Revised 09/19/2017 Post Hurricane Irma

ALGEBRA 2 HONORS Course Code: 120034001

MODELING CYCLE (★)

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.

Connections to Redesigned SAT

Passport to Advanced Math:

Create a quadratic or exponential function or equation that models a context. The equation will have rational coefficients and may require multiple steps to simplify or solve the equation.

Determine the most suitable form of an expression or equation to reveal a particular trait, given a context.

Solve a quadratic equation having rational coefficients. The equation can be presented in a wide range of forms to reward attending to algebraic structure and can require manipulation in order to solve.

Solve a system of one linear equation and one quadratic equation. The equations will have rational coefficients.

Interpret parts of nonlinear expressions in terms of their context. Students will make connections between a context and the nonlinear equation that models the context to identify or describe the real-life meaning of a constant term, a variable, or a feature of the given equation.

Understand a nonlinear relationship between two variables by making connections between their algebraic and graphical representations. The student will select a graph corresponding to a given nonlinear equation; interpret graphs in the context of solving systems of equations; select a nonlinear equation corresponding to a given graph; determine the equation of a curve given a verbal description of a graph; determine key features of the graph of a linear function from its equation; or determine the impact on a graph of a change in the defining equation.

SAT Practice

INSTRUCTIONAL TOOLS

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Division of Academics - Department of Mathematics Page 6 of 12 Topic II First Nine Weeks - Revised 09/19/2017 Post Hurricane Irma

ALGEBRA 2 HONORS Course Code: 120034001

STEM Lessons - Model Eliciting Activity

STEM Lessons

Alternative Fuel Systems (Mathematics, Science, Language Arts)

Efficient Storage (Mathematics, Science, Language Arts)

Ranking Sports Players (Quadratic Equations Practice) (Mathematics, Language Arts)

Manufacturing Designer Gear T-Shirts (Mathematics, Language Arts)

CPALMS Perspectives Videos

Professional/Enthusiasts

Quadratic Equations and Robots

Robot Mathematics: Gearing Ratio Calculations for Performance

Hurricane Dennis & Failed Math Models

Solving Systems of Equations, Oceans & Climate

Gear Heads and Gear Ratios

Determining Strengths of Shark Models based on Scatterplots and Regression

Representations of Parabolic Functions

Expert

Using Mathematics to Optimize Wing Design

Problem Solving with Project Constraints

INSTRUCTIONAL TOOLS

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Division of Academics - Department of Mathematics Page 7 of 12 Topic II First Nine Weeks - Revised 09/19/2017 Post Hurricane Irma

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.

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.

Check answers to problems using a different method, and continually ask, “Does this make sense?”

Identify correspondences between different approaches.

MAFS.K12.MP.2

Reason abstractly and quantitatively.

Mathematically proficient students will be able to:

Make sense of quantities and their relationships in problem situations.

Decontextualize—to 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.

MAFS.K12.MP.3

Construct viable arguments and critique the reasoning of

others.

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, and—if there is a flaw in an argument—explain what it is.

Determine domains to which an argument applies.

MAFS.K12.MP.4

Model with mathematics.

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.

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Division of Academics - Department of Mathematics Page 8 of 12 Topic II First Nine Weeks - Revised 09/19/2017 Post Hurricane Irma

ALGEBRA 2 HONORS Course Code: 120034001

MATHEMATICS FLORIDA STANDARDS

MATHEMATICAL PRACTICES

DESCRIPTION

MAFS.K12.MP.5

Use appropriate tools strategically.

Mathematically proficient students will be able to:

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.

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 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

MAFS.K12.MP.6

Attend to precision.

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.

MAFS.K12.MP.7

Look for and make use of structure.

Mathematically proficient students will be able to:

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.

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.

See complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. Example: They can see 5 – 3(x – 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.

MAFS.K12.MP.8

Look for and express regularity in repeated

reasoning.

Mathematically proficient students will be able to:

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 (𝑥 − 1)(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.

Maintain oversight of the process, while attending to the details as they work to solve a problem.

Continually evaluate the reasonableness of their intermediate results.

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Division of Academics - Department of Mathematics Page 9 of 12 Topic II First Nine Weeks - Revised 09/19/2017 Post Hurricane Irma

ALGEBRA 2 HONORS Course Code: 120034001

Domain: CREATING EQUATIONS

STANDARD CODE STANDARD DESCRIPTION

Cluster 1: Create equations that describe numbers or relationships

Understand solving equations as a process of reasoning and explain the reasoning 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. Context Complexity: Level 2: Basic Applications of Skills and Concepts

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. Context Complexity: Level 3: Strategic Thinking

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 Ohm’s law V = IR to highlight resistance R. Context Complexity: Level 1: Recall

Domain: ALGEBRA: REASONING WITH EQUATIONS & INEQUALITIES

STANDARD CODE STANDARD DESCRIPTION

Cluster 2: Solve equations and inequalities in one variable

MAFS.912.A-REI.2.4

Solve quadratic equations in one variable. Context Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 3: Solve systems of equations

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. Context Complexity: Level 1: Recall

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. For example, find the points of intersection between the line y = –3x and the circle x² + y² = 3. Context Complexity: Level 2: Basic Application of Skills & Concepts

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Division of Academics - Department of Mathematics Page 10 of 12 Topic II First Nine Weeks - Revised 09/19/2017 Post Hurricane Irma

ALGEBRA 2 HONORS Course Code: 120034001

Domain: ALGEBRA: REASONING WITH EQUATIONS & INEQUALITIES

STANDARD CODE STANDARD DESCRIPTION

Cluster 4: Represent and solve equations and inequalities graphically

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 Context Complexity: Level 2: Basic Application of Skills & Concepts

Domain: GEOMATRY: GEOMETRY: EXPRESSING GEOMETRIC PROPERTIES WITH EQUATIONS

STANDARD CODE STANDARD DESCRIPTION

Cluster 1: Translate between the geometric description and the equation for a conic section

Understand solving equations as a process of reasoning and explain the reasoning

MAFS.912.G-GPE.1.2

Derive the equation of a parabola given a focus and directrix. Context Complexity: Level 2: Basic Applications of Skills and Concepts

Domain: NUMBER & QUANTITY: THE COMPLEX NUMBER SYSTEM

STANDARD CODE STANDARD DESCRIPTION

Cluster 1: Perform arithmetic operations with complex numbers.

Understand solving equations as a process of reasoning and explain the reasoning MAFS.912.N-CN.1.1

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 Context Complexity: Level 1: Recall

MAFS.912.N-CN.1.2

Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Context Complexity: Level 2: Basic Applications of Skills and Concepts

Cluster 3: Use complex numbers in polynomial identities and equations.

Understand solving equations as a process of reasoning and explain the reasoning MAFS.912.N-CN.3.7

Solve quadratic equations with real coefficients that have complex solutions. Context Complexity: Level 1: Recall

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Division of Academics - Department of Mathematics Page 11 of 12 Topic II First Nine Weeks - Revised 09/19/2017 Post Hurricane Irma

ALGEBRA 2 HONORS Course Code: 120034001

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

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

The Circle and The Line

TECHNOLOGY TOOLS

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Division of Academics - Department of Mathematics Page 12 of 12 Topic II First Nine Weeks - Revised 09/19/2017 Post Hurricane Irma

ALGEBRA 2 HONORS Course Code: 120034001

TOPIC II DISCOVERY EDUCATION CORRELATION

VIDEO TITLE

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

GIZMOS CORRELATION

GIZMO TITLE

Roots of a Quadratic

Points in the Complex Plane

Modeling the Factorization of ax2+bx+c