Curriculum and Instruction Office of Mathematics

Curriculum and Instruction – Office of Mathematics Advanced Algebra & Trigonometry 2nd Nine Weeks

Introduction

In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is committed to these goals, as further described in our strategic plan, Destination2025. By 2025,

 80% of our students will graduate from high school college or career ready  90% of students will graduate on time  100% of our students who graduate college or career ready will enroll in a post-secondary opportunity

In order to achieve these ambitious goals, we must collectively work to provide our students with high-quality, College and Career Ready standards-aligned instruction. Acknowledging the need to develop competence in literacy and language as the foundation for all learning, Shelby County Schools developed the Comprehensive Literacy Improvement Plan (CLIP). The CLIP ensures a quality balanced literacy approach to instruction that results in high levels of literacy learning for all students across content areas. Destination 2025 and the CLIP establish common goals and expectations for student learning across schools. CLIP connections are evident throughout the mathematics curriculum maps.

The Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and Career Ready Standards are rooted in the knowledge and skills students need to succeed in post- secondary study or careers. While the academic standards establish desired learning outcomes, the curriculum provides instructional planning designed to help students reach these outcomes. Educators will use this guide and the standards as a roadmap for curriculum and instruction. The sequence of learning is strategically positioned so that necessary foundational skills are spiraled in order to facilitate student mastery of the standards.

These standards emphasize thinking, problem-solving and creativity through next generation assessments that go beyond multiple-choice tests to increase college and career readiness among Tennessee students. In addition, assessment blueprints (http://www.tn.gov/education/article/tnready-blueprints ) have been designed to show educators a summary of what will be assessed in each grade, including the approximate number of items that will address each standard. Blueprints also detail which standards will be assessed on Part I of TNReady and which will be assessed on Part II. Our collective goal is to ensure our students graduate ready proficiencies” with longstanding importance in for college and career. The Standards for Mathematical mathematics education. The first of these are the NCTM Practice describe varieties of expertise that mathematics process standards of problem solving, reasoning and proof, educators at all levels should seek to develop in their communication, representation and connections. students. These practices rest on important “processes and carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual The second are the strands of mathematical proficiency inclination to see mathematics and sensible, useful and specified in the National Research Council’s report Adding worthwhile, coupled with a belief in diligence and one’s It Up: adaptive reasoning, strategic competence, conceptual own efficacy). Throughout the year, students should understanding (comprehension of mathematical concepts, continue to develop proficiency with the eight Standards operations and relations) procedural fluency (skill in for Mathematical Practice. Curriculum and Instruction – Office of Mathematics

How to Use the Mathematic Curriculum Maps

This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that ultimately our students can reach Destination 2025. To reach our collective student achievement goals, we know that teachers must change their instructional practice in alignment with the three College and Career Ready shifts in instruction for Mathematics. We should see these shifts in all classrooms:

The TNCore Mathematics Standards The Tennessee Mathematics Standards: Teachers can access the Tennessee State standards, which https://www.tn.gov/education/article/mathematics- are featured throughout this curriculum map and standards represent college and career ready learning at reach respective grade level. Mathematical Shifts Focus The standards are focused on fewer topics so students can http://achievethecore.org/shifts-mathematics learn more

Coherence Topics within a grade are connected to support focus, and http://achievethecore.org/shifts-mathematics learning is built on understandings from previous grades

Rigor The standards set expectations for a balanced approach to http://achievethecore.org/shifts-mathematics pursuing conceptual understanding, procedural fluency, and application and modeling 1) Focus 2) Coherence 3) Rigor

Throughout this curriculum map, you will see resources as well as links to tasks that will support you in ensuring that students are able to reach the demands of the standards in your classroom. In addition to the resources embedded in the map, there are some high-leverage resources around each of the three shifts that teachers should consistently access:

Shelby County Schools2015/2016 Revised 9/23/15 3 of 10 Curriculum Maps:

 Locate the TDOE Standards in the left column. Analyze the language of the standards and match each standard to a learning target in the second column.  Consult your McGraw-Hill Algebra and Trigonometry 2nd edition by John W. Coburn or Pearson Algebra and Trigonometry 4th edition by Robert Blitzer Teachers’ Edition (TE) and other cited references to map out your week(s) of instruction.  Plan your weekly and daily objectives, using the standards' explanations provided in the second column. Best practices tell us that making objectives measureable increases student mastery.  Carefully review the web-based resources provided in the 'Content and Tasks' column and use them as you introduce or assess a particular standard or set of standards.  Review the CLIP Connections found in the right column. Make plans to address the content vocabulary, utilizing the suggested literacy strategies, in your instruction.  Examine the other standards and skills you will need to address in order to ensure mastery of the indicated standard.  Using your McGraw-Hill or Pearson TE and other resources cited in the curriculum map, plan your week using the SCS lesson plan template. Remember to include differentiated activities for small-group instruction and math stations.

4 Curriculum and Instruction – Office of Mathematics

2nd Nine Weeks Advanced Algebra & Trigonometry TN State Standards Essential Understandings Content & Tasks CLIP Connections Equations and Inequalities (3 weeks) F-BF – Building Functions 5. Find inverse functions (including 4.1 One-to-One Inverse Functions McGraw-Hill (Coburn) Build new functions from existing exponential and logarithmic)see (Coburn) Chapter Connections sections a-d on map functions. 2.7 Inverse Functions (Blitzer) Real-world Connections 6. Explain why the graph of a E x pon e nt i a l Gr o wth P ro j ec t: R a bbi t s, Exercises – Applications function and its inverse are R a bbi t s, and More R a bbi t s reflections of one another over the Extending the line y=x. Concept F-IF – Interpreting Functions 2. Identify or analyze the 4.2 Exponential Functions (Coburn) Analyze functions using different distinguishing properties of 4.1 Exponential Functions (Blitzer) representations. exponential, polynomial, logarithmic, trigonometric, and rational functions from tables, graphs, and equations. N-NE – Number Expressions 2. Understand the inverse 4.3 Logarithms and Logarithmic Compare and contrast relationship between exponents and Represent, interpret, compare, and Functions (Coburn) exponential functions and logarithms and use this relationship simplify number expressions. 4.2 Logarithmic Functions (Blitzer) logarithmic functions. to solve problems involving logarithms and exponents. E x a mp l e s of Prop e rties of L o g a rithm s N-NE – Number Expressions 1. Use the laws of exponents and 4.4 Properties of Logarithms: logarithms to expand or collect Solving Exponential and terms in expressions; simplify Logarithmic Equations (Coburn) Represent, interpret, compare, and expressions or modify them in order simplify number expressions. 4.3 Properties of Logarithms to analyze them or compare them. (Blitzer) 3. Classify real numbers and order 4.4 Exponential and Logarithmic real numbers that include Equations (Blitzer) transcendental expressions, E x a mp l e s of So l ving L o g a rithmic including roots and fractions of pi E q u a t i ons and e.

Shelby County Schools2015/2016 Revised 9/23/15 5 of 10 2nd Nine Weeks Advanced Algebra & Trigonometry TN State Standards Essential Understandings Content & Tasks CLIP Connections S-MD - Model with Data 1. Create scatter plots, analyze MWTI – Modeling with Technology I Model data using regression patterns and describe relationships (pp283-292) (Coburn) equations for bivariate data (linear, polynomial, MWTII – Modeling with Technology II trigonometric or exponential) to (pp491-502) (Coburn) model real-world phenomena and to 4.5 Exponential Growth and Decay; make predictions. Modeling Data (Blitzer) 2. Determine a regression equation 4.5 Applications From Business, to model a set of bivariate data. Finance and Science (Coburn) McGraw-Hill (Coburn) Justify why this equation best first (optional) Chapter Connections the data. Real-world Connections 3. Use a regression equation modeling bivariate data to make Exercises – Applications predictions. Identify possibly Extending the considerations regarding the Concept accuracy of predictions when interpolating or extrapolating. Exponential & Logarithmic Functions (3 weeks) G-AT- Applied Trigonometry G-AT-3. Derive and apply the 5.1 Angles Measures, Special List the special triangles given. Use trigonometry to solve problems. formulas for the area of a sector of a Triangles, Special Angles (Coburn) Why are they important to circle (Coburn). memorize? F-TF – Trigonometric Functions 5.1 Angles and Radian Measure G-AT-4. Calculate the arc length of a (Blitzer) Compare and contrast degree Extend the domain of trigonometric circle subtended by a central angle. measure and radian measure. functions using the unit circle. F-TF1.Convert from radians to degrees and from degrees to radians. G-AT- Applied Trigonometry 1. Use the definitions of the basic 5.2 The Trigonometry of Right Give a mnemonic device for the trigonometric ratios of sides in a right Use trigonometry to solve problems. Triangles (Coburn) trigonometric functions. triangle to solve problems about 5.2 Right Triangle Trigonometry lengths of sides and measures of (Blitzer) angles. Review of Special Right Triangles P y t h a g o r ea n T r ip l e s: F-IF – Interpreting Functions 2. Identify or analyze the 5.3 Trigonometric and The McGraw-Hill (Coburn) Analyze functions using different distinguishing properties of … Coordinate Plane (Coburn) Chapter Connections representations. trigonometric…functions from 5.3 Trigonometric Functions of Any 6 Curriculum and Instruction – Office of Mathematics

2nd Nine Weeks Advanced Algebra & Trigonometry TN State Standards Essential Understandings Content & Tasks CLIP Connections tables graphs, and equations. Angle (Blitzer) Real-world Connections Trig-reference Exercises – Applications Extending the Concept F-TF – Trigonometric Functions 2. Use special triangles to 5.4 Unit Circles and the Extend the domain of trigonometric determine geometrically the values Trigonometry of Real Numbers functions using the unit circle. of sine, cosine, tangent, for π/3, π/4, (Coburn) and π/6, and use the unit circle to 5.4 Trigonometric Functions of Real express the values of sine, cosine, Numbers; Periodic Functions and tangent for π-x, π+x, and 2π-x (Blitzer) in terms of their values for x, where Cir c le T r i g R e fer e n c e : x is any real number. 3. Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. G-GT – Graphing Trigonometric 1. Interpret transformations of 5.5 Graphs of Sine and Cosine; McGraw-Hill (Coburn) Functions trigonometric functions. Cosecant and Secant (Coburn) Chapter Connections Model periodic phenomena with 2. Match a trigonometric equation 5.6 Graphs of Tangent and Real-world Connections trigonometric functions. Cotangent (Coburn) with its graph. Exercises – Applications 5.7 Transformations and Extending the 3. Determine the difference made Applications of Trigonometry Graphs Concept by choice of units for angle (Coburn) measurement when graphing a trigonometric function. 5.5 Graphs of Sine and Cosine Functions (Blitzer) 4. Graph the sine, cosine, and 5.6 Graphs of Other Trigonometric tangent functions and identify Functions (Blitzer) characteristics such as period, amplitude, phase shift, and 5.8 Applications of Trigonometric asymptotes. Functions (Blitzer)

Shelby County Schools2015/2016 Revised 9/23/15 7 of 10 2nd Nine Weeks Advanced Algebra & Trigonometry TN State Standards Essential Understandings Content & Tasks CLIP Connections Intro to Graphs

E x plor a t i on of T ra nsfo r mations of T rig G r a phs

S um m a r y of Pro p e rties o f T rig G ra phs An Introduction to Trigonometry Functions (3 weeks) G-GT – Graphing Trigonometric Apply trigonometric identities to 6.1 Fundamental Identities and Create a toolbox for all the Functions verify identities and solve equations. Families of Identities (Coburn) different trigonometric Apply trigonometric identities to Identities include: Pythagorean, 6.2 Constructing and Verifying identities. verify identities and solve equations. quotient, sum/difference, double- Identities (Coburn) angle, and half-angle. 6.1 Verifying Trigonometric Identities (Blitzer) TASK – I d e nt i t i e s and E qu a t i ons TASK – H o p ewell G eome t ry TASK – Cir c ular R ea soni n g G-GT – Graphing Trigonometric Apply trigonometric identities to 6.3 The Sum and Difference McGraw-Hill (Coburn) Functions verify identities and solve equations. Identities (Coburn) Chapter Connections Identities include: Pythagorean, Apply trigonometric identities to 6.2 Sum and Difference Identities Real-world Connections verify identities and solve equations. quotient, sum/difference, double- (Blitzer) angle, and half-angle. Exercises – Applications E x a mp l e s of Sum a nd D i f fe r e n c e Extending the F o r mu l a s Concept G-GT – Graphing Trigonometric Apply trigonometric identities to 6.4 The Double-Angle, Half-Angle Functions verify identities and solve equations. Formulas, and Product-to-Sum Apply trigonometric identities to Identities include: Pythagorean, Identities (Coburn) verify identities and solve equations. quotient, sum/difference, double- 6.3Double-Angle, Power-Reducing, angle, and half-angle. and Half-Angle Formulas (Blitzer) E x a mp l e s of D ouble a nd H a lf A n g le F o r mu l a s 8 Curriculum and Instruction – Office of Mathematics

2nd Nine Weeks Advanced Algebra & Trigonometry TN State Standards Essential Understandings Content & Tasks CLIP Connections E x a mp l e s of Produ c t t o S um and Sum to P rodu c t F-BF – Building Functions Find inverse functions. 6.5 Inverse Trigonometric Functions Build new functions from existing and their Applications (Coburn) functions. 5.7 Inverse Trigonometric Functions (Blitzer)

G-GT – Graphing Trigonometric Apply trigonometric identities to 6.6 Solving Basic Trigonometric Functions verify identities and solve equations. Equations (Coburn) Apply trigonometric identities to Identities include: Pythagorean, 6.7 General Trigonometric Equations verify identities and solve quotient, sum/difference, double- and Applications (Coburn) angle, and half-angle. equations. 6.5 Trigonometric Equations (Blitzer) E x a mp l e s of So l ving T r ig Equ a t i ons T r i g onomet r y Pr ac t ic e T e st:

RESOURCE TOOLBOX Textbook Resources Standards Videos http://glencoe.mcgraw-hill.com/sites/0003112010/ Com m on Core S tand a rds - Math e matics Brightstorm http://interactmath.com/ Com m on Core S tand a rds - Math e matics Teacher Tube A pp e ndix A The Futures Channel TN Co r e Khan Academy ht t p: / /ww w . cc ss t oolbo x . o r g / Math TV Lamar University Tutorial Common Core Lessons Tennessee's State Mathematics Standards

Shelby County Schools2015/2016 Revised 9/23/15 9 of 10 TN Advanced Algebra & Trigonometry Standards

Calculator Interactive Manipulatives Additional Sites ht t p: / /ww w .t i -m athnspir e d. c om ht t p: / /ww w .i l ov e math.o r g / i nd e x .ph p ? ht t p: / /ww w .in t e rn e t4cl a s srooms. c om / g a t e w a y _ a l g e b r ht t p: / /edu ca t i on.t i . c om / e du ca t i onpo r tal/a c t i v opt i on =c om_docm a n a .htm i t y e x c h a n g e / a c t i vi t y http://www.mathopenref.com ht t p: / /ww w .kutaso f tw a r e . c om / f ree .ht m ht t p: / /ww w . ca sioedu ca t i on. c om / e du ca tors ht t p: / / i l lu m inations.n c t m . o r g / ht t p: / /ww w .stemr e sour c e s.com/ ht t p: / / j c - s c hools.n e t / d y n a m i c / m a th / math12.ht m l http://teachers.henrico.k12.va.us/math/ito_08/ SCS Math Tasks (Advanced Algebra & Trigonometry) CLIP Glencoe Reading & Writing in the Mathematics Classroom

Graphic Organizers (9-12)