MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Trigonometry Honors 2016 -2017 Course Code: 121130003

Division of Academics - Department of Mathematics Page 1 of 7 First Nine Weeks

Topic I: Right Triangle Trigonometry

FLORIDA STATE STANDARDS & MATHEMATICAL PRACTICES (MP)

ESSENTIAL CONTENT OBJECTIVES

MAFS.912.F-TF.1.1 - Understand radian measure of an

angle as the length of the arc on the unit circle subtended by the angle; Convert between degrees and radians. (MP.6)

MAFS.912.F-TF.1.2 - 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 (MP.2, MP.3. MP.6)

MAFS.912.F-TF.1.3 - Use special triangles to determine

geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π-x, π+x, and 2π-x in terms of their values for x, where x is any real number. (MP.6)

MAFS.912.G-SRT.3.7 - Explain and use the relationship

between the sine and cosine of complementary angles. (MP.2, MP.3, MP.6)

MAFS.912.G-SRT.3.8 – Use trigonometric ratios and the

Pythagorean Theorem to solve right triangles in applied problems. (MP.1, MP.4, MP.5)

A. Angles and Radian Measure 1. Angles 2. Measuring Angles Using Degrees and

Radians 3. Relationship Between Degrees and Radians 4. Angles in Standard Position 5. Coterminal Angles

B. Right Triangle Trigonometry 1. Six Trigonometric Functions 2. Function values for Some Special Angles

(π/3, π/4, π/6) 3. Fundamental Identities 4. Trigonometric Functions and Complements

C. Trigonometric Functions of Any Angle (Unit Circle) 1. Trigonometric Functions of any angle 2. Signs of the Trigonometric Functions 3. Reference Angles 4. Evaluating Trigonometric Functions using

Reference Angles

D. Trigonometric Functions of Real Numbers 1. Trigonometric Functions of Real Numbers 2. Domain and Range of Sine and Cosine

Functions 3. Even and Odd Functions 4. Periodic Functions

E. Real World Applications

I can:

Recognize and use the vocabulary of angles

Use degree measure

Use radian measure

Convert between degrees and radians

Draw angles in standard position

Find coterminal angles

Use right triangles to evaluate trigonometric functions

Find function values for 30º (π/6), 45º (π/4), 60º (π/3)

Recognize and use fundamental identities

Use equal cofunctions of complements

Evaluate trigonometric functions with a calculator

Use right triangle trigonometry to solve applied problems

Use the definition of trigonometric functions of any angle

Use the signs of the trigonometric functions

Find reference angles

Use reference angels to evaluate trigonometric functions

Use a unit circle to define trigonometric functions of real numbers

Recognize the domain and range of sine and cosine functions

Use even and odd trigonometric functions

Use periodic properties

Pacing Date(s) Traditional 23 days 08/22/16 - 09/23/16

Block 11 days 08/22/16 - 09/23/16

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Trigonometry Honors 2016 -2017 Course Code: 121130003

Division of Academics - Department of Mathematics Page 2 of 7 First Nine Weeks

INSTRUCTIONAL TOOLS

Core Text Book: Prentice Hall, Blitzer Algebra and Trigonometry 4e

Standard Suggested Lessons Teacher Notes

MAFS.912.F-TF.1.1 MAFS.912.F-TF.1.2 MAFS.912.F-TF.1.3 MAFS.912.G-SRT.3.7

MAFS.912.G-SRT.3.8★

5.1, 5.2, 5.3, 5.4

Topic I Assessment: Right Triangle Trigonometry

Notes:

The order in which the standards and suggested lessons are listed is not necessary the order of instruction. Please review each section during your instructional planning and supplement or modify components as needed to best differentiate instruction.

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:

Initial Side, Terminal side, Standard Position, Positive/Negative Angles, Coterminal Angles, Radian Measure, Sine, Cosine, Tangent, Secant, Cosecant, Cotangent, Unit Circle

Instructional Strategies: Note taking, Cooperative Learning, Differentiated remediation, Problem Creation, Chapter Project

SPED: Provide an Advanced Organizer: Differentiated remediation and practice, Online Teacher/Student resource center.

Students may believe that all trigonometric functions have a range of 1 to -1. Students need to see examples of how coefficients can change the range and the look of the graphs.

Pacing Date(s) Traditional 23 days 08/22/16 - 09/23/16

Block 11 days 08/22/16 - 09/23/16

Topic I Assessment Window 09/16/16 - 09/23/16

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Trigonometry Honors 2016 -2017 Course Code: 121130003

Division of Academics - Department of Mathematics Page 3 of 7 First Nine Weeks

STEM Lessons - Model Eliciting Activity

STEM Lessons

N/A

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Trigonometry Honors 2016 -2017 Course Code: 121130003

Division of Academics - Department of Mathematics Page 4 of 7 First Nine Weeks

FLORIDA STATE STANDARD(S)

MATHEMATICAL PRACTICES (MP)

DESCRIPTION

MAFS.K12.MP.1 (back to top)

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 (back to top)

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 (back to top)

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 (back to top)

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

Trigonometry Honors 2016 -2017 Course Code: 121130003

Division of Academics - Department of Mathematics Page 5 of 7 First Nine Weeks

FLORIDA STATE STANDARD(S)

MATHEMATICAL PRACTICES (MP)

DESCRIPTION

MAFS.K12.MP.5 (back to top)

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

(back to top)

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

(back to top)

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 (back to top)

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

Trigonometry Honors 2016 -2017 Course Code: 121130003

Division of Academics - Department of Mathematics Page 6 of 7 First Nine Weeks

Domain: FUNCTIONS: TRIGONOMETRIC FUNCTIONS

STANDARD CODE STANDARD DESCRIPTION

Cluster 1: Extend the domain of trigonometric functions using the unit circle.

MAFS.912.F-TF.1.1

Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle; Convert between degrees and radians. Context Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-TF.1.2

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

MAFS.912.F-TF.1.3

Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit c ircle to express the values of sine, cosine, and tangent for π-x, π+x, and 2π-x in terms of their values for x, where x is any real number. Context Complexity: Level 2: Basic Application of Skills & Concepts

Geometry: SIMILARITY, RIGHT TRIANGLES, & TRIGONOMETRY

STANDARD CODE STANDARD DESCRIPTION

Cluster 1: Define trigonometric ratios and solve problems involving right triangles.

MAFS.912.G-SRT.3.7

Explain and use the relationship between the sine and cosine of complementary angles. Context Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-SRT.3.8

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Context Complexity: Level 2: Basic Application of Skills & Concepts

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Trigonometry Honors 2016 -2017 Course Code: 121130003

Division of Academics - Department of Mathematics Page 7 of 7 First Nine Weeks

TECHNOLOGY TOOLS

CPALM RESOURCES LESSON PLANS

Introduction to Trigonometry:

Pythagoras - You Clever Dog:

Discovering Trigonometric Ratios

Round and Round the Unit Circle:

Sine, Cosine, and Tangent: The Leap from Special Triangles to the Unit Circle:

Let's Get "Triggy":

VIRTUAL MANIPULATIVE

Demonstrate the Pythagorean Theorem:

Right triangle Solver:

Right Triangle Calculator:

GIZMO CORRELATION GIZMO TITLE

Unit Circle Sine Function

Cosine Function Tangent Function

GRAPHING CALCULATOR ACTIVITIES

TITLE SITES

Radian Measure http://education.ti.com/en/us/activity/detail?id=8D7D391056E44037894A9CC2CF45C078&ref=%2Fcalculators%2Fdownloads%2FUS%2FActivities%2FSearch%2FSubject%3Fs%3D5022%26sa%3D5025%26t%3D5075%26d%3D1007%26size%3D15%26page%3D3

Motorcycle Tire Balancing http://education.ti.com/en/us/activity/detail?id=05E1A95C4C4A4577957B8C97F21F11BB

The Unit Circle http://education.ti.com/en/us/activity/detail?id=873ACBF93E584712A9D24804C9E92F83&ref=%2Fcalculators%2Fdownloads%2FUS%2FActivities%2FSearch%2FSubject%3Fs%3D5022%26sa%3D5025%26t%3D5075%26d%3D1007%26size%3D15%26page%3D3

Applications of the Unit Circle http://education.ti.com/en/us/activity/detail?id=977BDF3C473842EB8C33AB93F91A4726&ref=%2Fcalculators%2Fdownloads%2FUS%2FActivities%2FSearch%2FSubject%3Fs%3D5022%26sa%3D5025%26t%3D5075%26d%3D1007