80% of Our Students Will Graduate from High School College Or Career Ready s8

Curriculum and Instruction – Office of Mathematics 4th Quarter Bridge Math

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

Shelby County Schools 2015/2016 3-9-16 1 of 10 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 for college and career. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation and connections.

The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations) procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics and sensible, useful and worthwhile, coupled with a belief in diligence and one’s own efficacy). Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.

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

Shelby County Schools 2015/2016 3-9-16 2 of 10 Curriculum and Instruction – Office of Mathematics 4th Quarter Bridge Math

instructional practice in alignment with the three College and Career Ready shifts in instruction for Mathematics. We should see these shifts in all classrooms:

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:

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

Curriculum Maps: Shelby County Schools 2015/2016 3-9-16 3 of 10  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 Tennessee Bridge Math & Pearson/Prentice Hall Algebra I, Algebra II & Glencoe Geometry 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/Glencoe 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.

Shelby County Schools 2015/2016 3-9-16 4 of 10 Curriculum and Instruction – Office of Mathematics 4th Quarter Bridge Math

TN State Standards Essential Understandings Content & Tasks Literacy Connections Unit 9 – Right Triangles McGraw Hill TN Bridge Math Chapters 10 & 14 McGraw Hill Glencoe Geometry Chapter 8 Pearson Algebra 2, Chapter 13 (Allow 3 weeks for instruction, review, and assessment) Making Connections 7. Apply special right-triangle 10-2 The Pythagorean Theorem M-NG Numbers & Graphic properties and the Pythagorean 8-2 The Pythagorean Theorem and Its Converse Mathematics Theorem to solve congruent, similar Video Lesson: Use Pythagorean theorem shape, and contextual problems. to find the length of the hypotenuse Video Lesson: Use the Pythagorean theorem to find the length of a leg Video Lesson: Converse of the Pythagorean theorem

Making Connections 7. Apply special right-triangle 10-3 Special Right Triangles Writing in Math M-NG Numbers & Graphic properties and the Pythagorean 8-3 Special Right Triangles Video Lesson: 45-45-90-triangles List the special right triangles. Why Mathematics Theorem to solve congruent, Video Lesson 45-45-90 triangles 2 is it important to memorize them? similar shape, and contextual Video Lesson: intro-to-30-60-90-triangles problems. Video Lesson: 30-60-90-triangle- example-problem Video Lesson: area-of-a-regular-hexagon Making Connections 3. Relate the basic definitions of 14-1 Basic Trigonometric Ratios Writing in Math Shelby County Schools 2015/2016 3-9-16 5 of 10 TN State Standards Essential Understandings Content & Tasks Literacy Connections M-SG Symbolic & Graphic the trigonometric ratios to the 8-4 Trigonometry Give a mnemonic device for the Mathematics right triangle. Video Lesson: basic-trigonometry basic trigonometric ratios. Video Lesson: example--using-soh-cah- toa Making Connections 3. Relate the basic definitions of 14-2 Solve Right Triangles M-SG Symbolic & Graphic the trigonometric ratios to the 8-4 Trigonometry Mathematics right triangle. Video Lesson: example--trig-to-solve- the-sides-and-angles-of-a-right-triangle

Making Connections 4. Identify the graphs of basic 14-3 Graph the Sine Function M-SG Symbolic & Graphic trigonometric functions and 13-4 The Sine Function Mathematics shifts of those graphs. Making Connections 4. Identify the graphs of basic 14-4 Experiment with the Sine Function M-SG Symbolic & Graphic trigonometric functions and 13-4 The Sine Function Mathematics shifts of those graphs.

Unit 10 – Probability and Statistics McGraw Hill TN Bridge Math Multiple Chapters McGraw Hill Glencoe Geometry Pearson Algebra 1 Pearson Algebra 2 (Allow 4 weeks for instruction, review, and assessment) Making Connections 1. Understand and use basic 9-1 Review Percents and Probability Writing in Math M-ND Numeric & Diagnostic 11-2 Probability counting techniques in contextual Compare and contrast percents and Mathematics settings. probability. What do they have in common? What are the differences in them? Applications: Ways of Looking at the 2. Solve problems involving percent 9-2 Percent of Increase and Decrease World of increase or decrease, for example 2-10 Change Expressed as a Percent A-AN – Applications with Numbers mark-ups and mark-downs. Video Lesson: solving-percent-problems Making Connections 4. Find the probability of simple 9-3 Problem Solving Skills: Simulations W-NM Numeric Mathematics events, disjoint events, compound 11-2 Probability events, and independent events, Simulation - Go to p 104 of Documents and independent events in various setting using a variety of counting techniques. Making Connections 4. Find the probability of simple 9-4 Compound Events W-NM Numeric Mathematics events, disjoint events, compound 11-4 Probability of Multiple Events Shelby County Schools 2015/2016 3-9-16 6 of 10 Curriculum and Instruction – Office of Mathematics 4th Quarter Bridge Math

TN State Standards Essential Understandings Content & Tasks Literacy Connections events, and independent events, Video Lesson: compound-probability and independent events in various setting using a variety of counting techniques. Making Connections W-NM4. Find the probability of simple 9-5 Independent and Dependent Events W-NM Numeric Mathematics events, disjoint events, compound 11-4 Probability of Multiple Events M-ND Numeric & Diagrammatic events, and independent events, and Video Lesson: introduction-to- Mathematics independent events in various setting dependent-probability using a variety of counting techniques. M-ND2. Use counting techniques to calculate probabilities for conditional and independent events. Making Connections 1. Understand and use basic 9-6 Permutations and Combinations Writing in Math M-ND Numeric & Diagrammatic 11-1 Permutations and Combinations counting techniques in contextual Define “permutation” and Mathematics settings. Khan Academy Permutations and Combinations videos “combination.” Give some tips on how to know when to use a permutation or combination. Making Connections 4. Compare measures of central 2-9 Display Data Discussion M-ND Numeric & Graphic Video Lesson: histograms tendency and spread for a single Have students to bring a sample of Mathematics data set along with its graph and summary statistics. data represented by a table. Working in pairs, have them discuss their tables and determine whether a different type of display might have been more effective and why. Applications: Ways of Looking at the 1. Solve problems involving 10-5 Problem Solving Skills: Circle World constructing and interpreting pie Graphs Skills Handbook p799, Circle Graphs A-AN – Applications with Data charts. Video Lesson: Circle graphs Making Connections 1. Given a variety of appropriate 6-3 Write Equations for Lines M-ND Symbolic & Graphic information, determine the equation 5-3 Slope Intercept Form Mathematics of a line. 5-4 Point-Slope Form Video Lessons: Slope intercept Shelby County Schools 2015/2016 3-9-16 7 of 10 TN State Standards Essential Understandings Content & Tasks Literacy Connections

Making Connections 5. Compare data using graphs and 9-7 Scatter Plots and Box-and-Whisker Writing in Math M-NG Numeric & Graphic Plots summary statistics, and measures Is it possible for the mean of a set of Mathematics of central tendency and spread. 5-7 Scatter Plots and Trend Lines 12-4 Box-and-Whisker Plots data to fall outside the box part of a box-and-whisker plot? Explain. Making Connections 5. Compare data using graphs and Graphing Technology Lab: Scatter Plots M-NG Numeric & Graphic summary statistics, and measures Video Lessons: Using the TI-84 to find Mathematics of central tendency and spread. regression lines and scatter plots

Applications: Ways of Looking at the 1. Solve problems involving 9-8 Regression and Median-Fit Lines Writing in Math World applications of linear equations. 5-7 Scatter Plots and Trend Lines Video Lessons: Using the TI-84 to find Compare and contrast the method of A-AF – Applications with Functions regression lines and scatter plots finding the best-fit line for a set of data by hand to the linear regression method studied. Unit 11 – Additional Topics McGraw Hill TN Bridge Math Multiple Chapters McGraw Hill Glencoe Geometry Pearson Algebra 1 Pearson Algebra 2 (Allow 2 weeks for instruction, review, and assessment) Ways of Looking: Revisiting Concepts 9. Use algebra and geometry to 12-8 The Distance and Midpoint Formulas W-GM Graphic Mathematics solve problems involving midpoints Concept Byte – Distance and Midpoint and distances (i.e. geometric Formulas (p605) figures). Video Lesson: Midpoint formula Video Lesson: Distance formula Making Connections 5. Recognize composite functions as 13-10 Operations on Functions Writing in Math M-SN Symbolic & Numeric Mathematics 6-6 Function Operations an application of substitution and What is the difference between “f(x)” use this understanding to write and “y”? When is it appropriate to use expressions for and evaluate “f(x)? composite functions. Applications: Ways of Looking at the 2. Solve problems involving direct 13-5 Direct Variation World and inverse variations, such as 2-2 Direct Variation A-AF – Applications with Functions frequency, interest, and pressure. Video Lesson: Direct Variation Applications: Ways of Looking at the 2. Solve problems involving direct 13-6 Inverse Variation Writing in Math World 8-1 Inverse Variation and inverse variations, such as Think of a real-life example of inverse A-AF – Applications with Functions frequency, interest, and pressure. Video Lesson: Difference between variation. Explain how you know the type Direct and Inverse Variation Shelby County Schools 2015/2016 3-9-16 8 of 10 Curriculum and Instruction – Office of Mathematics 4th Quarter Bridge Math

TN State Standards Essential Understandings Content & Tasks Literacy Connections of variation the examples represents. Making Connections SD1. Use the laws of exponents to 13-8 Exponential Functions Writing in Math M-SD Symbolic & Diagnostic Mathematics simplify and interpret expressions for 7-1 Exploring Exponential Models What types of real-life problems are M-SN Symbolic & Numeric Mathematics exponential functions, recognizing Video Lessons: Exponential Growth and positive rational exponents as indicating Decay modeled by exponential functions? roots of the base and negative exponents as indicating the reciprocal of a power. SN1. In the context of exponential models, solve equations in exponential form.

RESOURCE TOOLBOX

Textbook Resources Standards Videos Com m on Core S tand a rds - Math e matics http://www.connected.mcgraw-hill.com/ http://www.brightstorm.com Com m on Core S tand a rds - Math e matics A pp e ndix A http://www.pearsonsuccessnet.com/ Tennessee State Standards ht t p: / /ww w .te ac h e rtub e . c om/

Shelby County Schools 2015/2016 3-9-16 9 of 10 Tennessee’s Bridge Math Standards ht t p: / /ww w .the f utur e s c h a nn e l.com/ i nd e x .php TN Co r e Interactmath Shmoop - We Speak Students ht t p: / /ww w . cc ss t oolbo x . o r g / (Online Pearson textbook problems) Common Core Lessons Khan Academy-Algebra I Khan Academy – Algebra II www.learnzillion.com Khan Academy -Geometry Khan Academy –Probability & Statistics

Additional Sites Interactive Manipulatives Calculator Math nspired 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 ra .ht ht t p: / /ww w .i l ov e math.o r g / i nd e x .ph p ? m opt i on =c om_docm a n Texas Instrument Activities ht t p: / /ww w .kutaso f tw a r e . c om / f ree .ht m http://www.mathopenref.com Casio Activities ht t p: / / i l lu m inations.n c t m . o r g / SMARTboard Lessons ht t p: / /ww w .stemr e sour c e s.com/ http://www.explorelearning.com https://compasslearning.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

Literacy: Tasks Literacy Skills and Strategies for Content Area Teachers UT Dana Center (Math, p. 22) Mars Tasks Glencoe- Reading and Writing in the Math Classroom Inside Math Tasks Graphic Organizers (9-12) Math Vision Project SCS Math Tasks Graphic Organizers (dgelman) TNCore Algebra I, Algebra II & Geometry Instructional Resources Dan Meyer's Three-Act Math Tasks

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