Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

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 aligned instruction. 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 readiness is rooted in the knowledge and skills students need to succeed in post-secondary study or careers. The TN State Standards represent three fundamental shifts in mathematics instruction: focus, coherence and rigor.

Shelby County Schools 2016/2017Revised 2/6/17

1 of 19

Focus

The Standards call for a greater focus in mathematics. Rather than racing to cover topics in a mile-wide, inch-deep curriculum, the Standards require us to significantly narrow and deepen the way time and energy is spent in the math classroom. We focus deeply on the major work of each grade so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom. For geometry, the major clusters, account for 65% of time spent on instruction.Supporting Content - information that supports the understanding and implementation of the major work of the grade.Additional Content - content that does not explicitly connect to the major work of the grade yet it is required for proficiency.

Coherence

Thinking across grades:The TN Standards are designed around coherent progressions from grade to grade. Learning is carefully connected across grades so that students can build new understanding on to foundations built in previous years. Each standard is not a new event, but an extension of previous learning. Linking to major topics:Instead of allowing additional or supporting topics to detract from the focus of the grade, these concepts serve the grade level focus. For example, instead of data displays as an end in themselves, they are an opportunity to do grade-level word problems.

Rigor

Conceptual understanding: The TN Standards call for conceptual understanding of key concepts. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures. Procedural skill and fluency: The Standards call for speed and accuracy in calculation. While high school standards for math do not list high school fluencies, there are fluency standards for algebra 1, geometry, and algebra 2..Application: The Standards call for students to use math flexibly for applications in problem-solving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content.

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

The Standards for Mathematical Practice describe varieties of expertise, habits of minds and productive dispositions that mathematics educators at all levels should seek to develop in their students. These practices rest on important National Council of Teachers of Mathematics (NCTM) “processes and proficiencies” with longstanding

importance in mathematics education. Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.

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 practice so that it is in alignment with the three mathematics instructional shifts.

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 the content standards and mathematical practice standards that teachers should consistently access:

Shelby County Schools 2016/2017Revised 2/6/17

2 of 19

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

The TN Mathematics StandardsThe Tennessee Mathematics Standards:https://www.tn.gov/education/article/mathematics-standards

Teachers can access the Tennessee State standards, which are featured throughout this curriculum map and represent college and career ready learning at reach respective grade level.

Standards for Mathematical PracticeMathematical Practice Standardshttps://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view

Teachers can access the Mathematical Practice Standards, which are featured throughout this curriculum map. This link contains more a more detailed explanation of each practice along with implications for instructions.

Purpose of the Mathematics Curriculum Maps

This curriculum framework or map is meant to help teachers and their support providers (e.g., coaches, leaders) on their path to effective, college and career ready (CCR) aligned instruction and our pursuit of Destination 2025. It is a resource for organizing instruction around the TN State Standards, which define what to teach and what students need to learn at each grade level. The framework is designed to reinforce the grade/course-specific standards and content—the major work of the grade (scope)—and provides a suggested sequencing and pacing and time frames, aligned resources—including sample questions, tasks and other planning tools. Our hope is that by curating and organizing a variety of standards-aligned resources, teachers will be able to spend less time wondering what to teach and searching for quality materials (though they may both select from and/or supplement those included here) and have more time to plan, teach, assess, and reflect with colleagues to continuously improve practice and best meet the needs of their students.

The map is meant to support effective planning and instruction to rigorous standards; it is not meant to replace teacher planning or prescribe pacing or instructional practice. In fact, our goal is not to merely “cover the curriculum,” but rather to “uncover” it by developing students’ deep understanding of the content and mastery of the standards. Teachers who are knowledgeable about and intentionally align the learning target (standards and objectives), topic, task, and needs (and assessment) of the learners are best-positioned to make decisions about how to support student learning toward such mastery. Teachers are therefore expected--with the support of their colleagues, coaches, leaders, and other support providers--to exercise their professional judgment aligned to our shared vision of effective instruction, the Teacher Effectiveness Measure (TEM) and related best practices. However, while the framework allows for flexibility and encourages each teacher/teacher team to make it their own, our expectations for student learning are non-negotiable. We must ensure all of our children have access to rigor—high-quality teaching and learning to grade-level specific standards, including purposeful support of literacy and language learning across the content areas.

Additional Instructional SupportShelby County Schools adopted our current math textbooks for grades 9-12 in 2010-2011. The textbook adoption process at that time followed the requirements set forth by the Tennessee Department of Education and took into consideration all texts approved by the TDOE as appropriate. We now have new standards;

Shelby County Schools 2016/2017Revised 2/6/17

3 of 19

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

therefore, the textbook(s) have been vetted using the Instructional Materials Evaluation Tool (IMET). This tool was developed in partnership with Achieve, the Council of Chief State Officers (CCSSO) and the Council of Great City Schools. The review revealed some gaps in the content, scope, sequencing, and rigor (including the balance of conceptual knowledge development and application of these concepts), of our current materials. The additional materials purposefully address the identified gaps in alignment to meet the expectations of the CCR standards and related instructional shifts while still incorporating the current materials to which schools have access. Materials selected for inclusion in the Curriculum Maps, both those from the textbooks and external/supplemental resources (e.g., engageny), have been evaluated by district staff to ensure that they meet the IMET criteria.

How to Use the Mathematics Curriculum Maps

OverviewAn overview is provided for each quarter. The information given is intended to aid teachers, coaches and administrators develop an understanding of the content the students will learn in the quarter, how the content addresses prior knowledge and future learning, and may provide some non-summative assessment items.

Tennessee State StandardsThe TN State Standards are located in the left column. Each content standard is identified as the following: Major Work, Supporting Content or Additional Content.; a key can be found at the bottom of the map. The major work of the grade should comprise 65-85% of your instructional time. Supporting Content are standards that supports student’s learning of the major work. Therefore, you will see supporting and additional standards taught in conjunction with major work. It is the teacher’s responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.

ContentTeachers are expected to carefully craft weekly and daily learning objectives/ based on their knowledge of TEM Teach 1. In addition, teachers should include related best practices based upon the TN State Standards, related shifts, and knowledge of students from a variety of sources (e.g., student work samples, MAP, etc.). Support for the development of these lesson objectives can be found under the column titled ‘Content’. The enduring understandings will help clarify the “big picture” of the standard. The essential questions break that picture down into smaller questions and the objectives provide specific outcomes for that standard(s). Best practices tell us that clearly communicating and making objectives measureable leads to greater student mastery.

Instructional Support and ResourcesDistrict and web-based resources have been provided in the Instructional Resources column. Throughout the map you will find instructional/performance tasks and additional resources that align with the standards in that module. The additional resources provided are supplementary and should be used as needed for content support and differentiation.

Shelby County Schools 2016/2017Revised 2/6/17

4 of 19

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

Topics Addressed in Quarter Properties of Angles and Segments in Circles Arc Length, Sector Area, and Equations of Circles Use Coordinates to Prove Simple Geometric Theorems Algebraically Volume of Solids Visualizing Solids Trigonometry with All Triangles

OverviewDuring the fourth quarter students continue their study of circles. They explore and apply the properties of angles and segments in circles including the intersection of two secants, two tangents, two chords or a secant and a tangent. Then they find and apply arc length and area of sectors and write equations of circles and graph them in the coordinate plane. Students use coordinates to prove simple geometric theorems algebraically and then students explain volume formulas and use them to solve problems in prisms, pyramids, cylinders, cones and spheres. Students learn how to construct regular hexagons, squares, and triangles in circles. At this point, students have covered most of the content & standards needed prior to the TNReady End of Course Exam. Since there are 3 to 4 weeks of class after the EOC exam, students will examine some additional content/standards. Students will then spend some time reviewing and extending their understanding of surface area of solids. The year will conclude by studying law of sines and cosines to find missing sides in any triangle, not just right triangles.

Year at a Glance Document

Content Standard Type of Rigor Foundational Standards Sample Assessment ItemsG-GPE.B.4 Conceptual Understanding A-REI.B.4 Illustrative: G-GPE.B.4 TasksG-MG.A.1 Conceptual Understanding & Application 8.G.A.1, 2,3, 4,5 Illustrative: G-MG.A.1 TasksG-MG.A.3 Application 8.G.A.5; 8.G.B.7 Illustrative: G-MG.A.3 TasksG-CO.D.12 Procedural skill & fluency, Conceptual

Understanding & Application8.G.A. 2,3, 4,5 Illustrative: G-CO.D.12 Tasks

Shelby County Schools 2016/2017Revised 2/6/17

5 of 19

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

G-CO.D.13 Procedural skill & fluency, Conceptual Understanding & Application

8.G.A.2,3, 4,5 Illustrative: G-CO.D.13 Tasks

TNReady High School Assessment Blueprints

Geometry Practice Test (you must login to your EdTools account)

Fluency The high school standards do not set explicit expectations for fluency, but fluency is important in high school mathematics. Fluency in algebra can help students get past the need to manage computational and algebraic manipulation details so that they can observe structure and patterns in problems. Such fluency can also allow for smooth progress toward readiness for further study/careers in science, technology, engineering, and mathematics (STEM) fields. These fluencies are highlighted to stress the need to provide sufficient supports and opportunities for practice to help students gain fluency. Fluency is not meant to come at the expense of conceptual understanding. Rather, it should be an outcome resulting from a progression of learning and thoughtful practice. It is important to provide the conceptual building blocks that develop understanding along with skill toward developing fluency.

The fluency recommendations for geometry listed below should be incorporated throughout your instruction over the course of the school year. G-SRT.B.5 Fluency with the triangle congruence and similarity criteria G-GPE.B.4,5,7 Fluency with the use of coordinates G-CO.D.12 Fluency with the use of construction tools

References: http://www.tn.gov/education/article/mathematics-standards http://www.corestandards.org/ http://www.nctm.org/ http://achievethecore.org/

Shelby County Schools 2016/2017Revised 2/6/17

6 of 19

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESProperties of Angles and Segments in Circles

(Allow approximately 1 week for instruction, review, and assessment)Domain: G-C Circles Cluster: Understand and apply theorems about circles G-C.A.2 Identify and describe

relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

G-C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

Domain: G-CO Congruence Cluster: Make geometric constructions G-CO.D.12 Make formal geometric

constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

Enduring Understanding(s)All circles are similar and that relationships exist between angles formed by radii, chords, secants and tangents.

Essential Question(s)How can the properties of circles, polygons, lines and angles be useful when solving geometric problems?

Objective(s):Students will Identify and describe relationships among

tangents and radii; Identify and describe relationships among

circumscribed angles and central angles; Construct a tangent line from a point.

Use the following lesson(s) first to introduce concepts/build conceptual understanding.engage ny Geometry Module 5, Topic C, Lesson 11: Properties of Tangents

Use the textbook resources to address procedural skill and fluency.Lesson 10.5 Tangents pp.718-725Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.

Task(s)Tangent Lines and the Radius of a Circle TaskGSE Analytic Geometry Unit 3: Circles and Volume (select from the tasks)

VocabularyTangent, point of tangency, common tangent

Writing in Math/DiscussionHow many tangents can be drawn from a point outside a circle, from a point on a circle, and from a point inside a circle? Explain your reasoning.

Domain: G-CO Congruence Cluster: Make geometric constructions G-CO.D.12 Make formal geometric

Enduring Understanding(s)All circles are similar and that relationships exist between angles formed by radii, chords, secants

Use the textbook resources to address procedural skill and fluency.Extend Lesson 10-5 Geometry Lab: Inscribed

Writing in Math/DiscussionWhy is the term “incenter” a good term for the intersection of the three angle bisectors?

Shelby County Schools 2016/2017Revised 2/6/17

7 of 19

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

Domain: G-CO Congruence Cluster: Make geometric constructions G-CO.D.13 Construct an equilateral

triangle, a square, and a regular hexagon inscribed in a circle

Domain: G-C Circles Cluster: Understand and apply theorems about circles G-C.A.3 Construct the inscribed and

circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

and tangents.

Essential Question(s)How can the properties of circles, polygons, lines and angles be useful when solving geometric problems?

Objective(s):Students will Construct an equilateral triangle, a square,

and a regular hexagon inscribed in a circle. Construct the inscribed and circumscribed

circles of a triangle

and Circumscribed Circles, p. 726

Use geometry software or graphing calculator such as TI-Nspire or the Cabri Jr. APP on the TI-84 to investigate. A regular compass and straight edge can also be used.

ACT Practice(sample problems to prepare for the ACT)

Glencoe, pp.692-693 & pp.774-775

Explain your reasoning.

Domain: G-C Circles Cluster: Understand and apply theorems about circles G-C.A.2 Identify and describe

relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Enduring Understanding(s)All circles are similar and that relationships exist between angles formed by radii, chords, secants and tangents.

Essential Question(s) How can the properties of circles, polygons,

lines and angles be useful when solving geometric problems?

Objective(s):Students will Find measures of angles formed by lines

intersecting on or inside a circle and describe the relationships;

Find measures of angles formed by lines intersecting outside the circle and describe the relationships.

Use the following lesson(s) first to introduce concepts/build conceptual understanding.engage ny Geometry Module 5, Topic C, Lesson 16: Similar Triangles in Circle-Secant (or Circle-Secant-Tangent) Diagrams

Use the textbook resources to address procedural skill and fluency.Lesson 10-6 Secants, Tangents, and Angle Measures, pp. 727-735Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.

Task(s)Chords, Secants, and Tangents Tasks, pp. 56

VocabularySecant

Ticket Out the DoorSelect examples and ask students to name the segments in the figure as they leave.

Shelby County Schools 2016/2017Revised 2/6/17

8 of 19

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

& 69GSE Analytic Geometry Unit 3: Circles and Volume (select from the tasks)

Domain: G-C Circles Cluster: Understand and apply theorems about circles G-C.A.2 Identify and describe

relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Enduring Understanding(s)All circles are similar and that relationships exist between angles formed by radii, chords, secants and tangents.

Essential Question(s)How can the properties of circles, polygons, lines and angles be useful when solving geometric problems?

Objective(s):Students will Find measures of segments that intersect in

the interior of a circle and describe the relationships;

Find measures of segments that intersect in the exterior of a circle and describe the relationships.

Use the textbook resources to address procedural skill and fluency.Lesson 10-7 Special Segments in Circles, pp. 736-742

VocabularyChord segment, secant, external secant segment, tangent segment

Writing in Math/DiscussionDescribe the relationship among segments in a circle when two secants intersect inside a circle.

Ask students to describe how the lesson on secants, tangents, and angles (10-6) helped them better understand the lesson on special segments in a circle.

Domain: G-C Circles Cluster: Understand and apply theorems about circles G-C.A.2 Identify and describe

relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Enduring Understanding(s)All circles are similar and that relationships exist between angles formed by radii, chords, secants and tangents.

Essential Question(s) How can the properties of circles, polygons,

lines and angles be useful when solving geometric problems?

Objective(s):Students will

Use the textbook resources to address procedural skill and fluency.Lesson 10-6 Secants, Tangents, and Angle Measures, pp. 727-735Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.

Task(s)Chords, Secants, and Tangents Tasks, pp. 56 & 69

Writing in Math/DiscussionExplain how to find the measure of an angle formed by a secant and a tangent that intersect outside a circle.

Shelby County Schools 2016/2017Revised 2/6/17

9 of 19

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

Find measures of angles formed by lines intersecting on or inside a circle and describe the relationships;

Find measures of angles formed by lines intersecting outside the circle and describe the relationships.

GSE Analytic Geometry Unit 3: Circles and Volume (select from the tasks)

Arc Length, Sector Area, and Equations of Circles (Allow approximately 1.5 weeks for instruction, review, and assessment)

Domain: G-C Circles Cluster: Understand and apply theorems about circles G-C.A.2 Identify and describe

relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Domain: G-C Circles Cluster: Find arc lengths and areas of sectors of circles G-C.B.5 Derive using similarity the fact

that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Enduring Understanding(s)The properties of polygons, lines, and angles can be used to understand circles; the properties of circles can be used to solve problems involving polygons, lines and angles.

Essential Question(s)How can the properties of circles, polygons, lines and angles be useful when solving geometric problems?

Objective(s):Students will Derive and apply the formula for arc

length; Derive the fact that the length of the arc

intercepted by an angle is proportional to the radius;

Define and apply radian measure. Explore the relationship between inscribed

angles and central angles and their intercepted arcs.

Use the following lesson(s) first to introduce concepts/build conceptual understanding.engage ny Geometry Module 5, Topic A, Lesson 4; Experiments with Inscribed Angles

Use the textbook resources to address procedural skill and fluency.Lesson 10-2 – Measuring Angles and Arcs, pp. 692-700Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.

Task(s)Circles and Spheres TasksCircles and their Relationships among Central Angles, Arcs and Chords Task , p.15 Investigating Angle Relationships in Circles Tasks, p. 46 & p.52

VocabularyCentral angle, arc, minor arc, major arc, semicircle, congruent arcs, adjacent arcs, arc length

Writing in Math/DiscussionDescribe the three different types of arcs in a circle and the method for finding the measure of each one.

Domain: G-C Circles Cluster: Find arc lengths and areas of sectors

Enduring Understanding(s)The properties of polygons, lines, and angles

Use the following lesson(s) first to introduce concepts/build conceptual understanding.

VocabularySector of a circle, segment of a circle

Shelby County Schools 2016/2017Revised 2/6/17

10 of 19

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

of circles G-C.B.5 Derive using similarity the fact

that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

can be used to understand circles; the properties of circles can be used to solve problems involving polygons, lines and angles.

Essential Question(s)How can the properties of circles, polygons, lines and angles be useful when solving geometric problems?

Objective(s):Students will Derive a formula for the area of a

sector of a circle; Find the area of circles and sectors of

circles.

engageny Geometry Module 3, Topic A, Lesson 4

Use the textbook resources to address procedural skill and fluency.Lesson 11-3 – Areas of Circles, pp.782 - 788Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.

Task(s)Arc Length and Area of Sector Tasks, p. 82 & p.91Grain Storage TaskGSE Analytic Geometry Unit 3: Circles and Volume (select from the tasks)

ACT Practice(sample problems to prepare for the ACT)

Glencoe, pp.774-775

Writing in Math/DiscussionIf the radius of a circle doubles, will the measure of a sector of that circle double? Will it double if the arc measure of that sector doubles?

Ticket Out the DoorHave students describe how to find the area of a circle, given its circumference.

Domain: G-GPE Expressing Geometric Properties with EquationsCluster: Translate between the geometric description and the equation for a conic section G-GPE.A.1 Derive the equation of a

circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Domain: G-GPE Expressing Geometric Properties with EquationsCluster: Use coordinates to prove simple

Enduring Understanding(s)The properties of polygons, lines, and angles can be used to understand circles; the properties of circles can be used to solve problems involving polygons, lines and angles

Essential Question(s)How can the properties of circles, polygons, lines and angles be useful when solving geometric problems?

Objective(s):Students will

Use the textbook resources to address procedural skill and fluency.Lesson 10-8 – Equations of Circles and Graphing Technology Lab 10.8 (using TI-Nspire), pp.743 - 749

Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each Standard

VocabularyCompound locus

Writing in Math/DiscussionDescribe how the equation for a circle changes if the circle is translated a units to the right and b units down.

Shelby County Schools 2016/2017Revised 2/6/17

11 of 19

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

geometric theorems algebraically G-GPE.B.4 Use coordinates to prove

simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin and containing the point (0, 2).

Derive the equation of a circle given the center and the radius.

Complete the square to find the center and radius of a circle by an equation.

(Designed as a resource tool to assist teachers in deepening their understanding of what each standard means in terms of what students must know and be able to do.It outlines only a sample of instructional strategies and examples. Links to conceptual categories and specific standards in the document can be accessed from page 5 Mathematics Standards for High School.)

Task(s)Equations of Circles Lesson GSE Analytic Geometry Unit 3: Circles and Volume (select from the tasks)

Use coordinates to prove simple geometric theorems algebraically(Allow approximately 1 week for instruction, review, and assessment)

Domain: G-GPE Expressing Geometric Properties with EquationsCluster: Use coordinates to prove simple geometric theorems algebraically G-GPE.B.4 Use coordinates to prove

simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin and containing the point (0, 2).

Domain: G-GPE Expressing Geometric Properties with EquationsCluster: Use coordinates to prove simple geometric theorems algebraicallyG-GPE.B.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio

Enduring Understanding(s)Geometric definitions, properties and theorems allow one to describe, model, and analyze situations in the real world.

Essential Question(s)How is coordinate algebra used when writing geometric proofs?

Objective(s):Students willFind midpoints of segments and points that divide segments into 3, 4, or more proportional, equal parts.

Use the following lesson(s) first to introduce concepts/build conceptual understanding.engage ny Geometry, Module 4, Topic D Lesson 12: Dividing Segments Proportionately

Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.

Task(s)Scaling a Triangle in the Coordinate Plane Partitioning Segments in the Coordinate Plane

Use the interactive resources to address procedural skill and fluency.Dividing Line Segments Expressing Geometric Properties with Equations HSG-GPE.B.6

Volume of Solids (Allow approximately 1.5 week for instruction, review, and assessment)t)

Shelby County Schools 2016/2017Revised 2/6/17

12 of 19

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESDomain: G-GMD Geometric Measurement and DimensionCluster: Explain volume formulas and use them to solve problems G-GMD.A.1 Give an informal

argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

G-GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. ★

Enduring Understanding(s)Two- and three-dimensional objects with or without curved surfaces can be described, classified, and analyzed by their attributes.

Essential Question(s) In what ways do we use cones, cylinders,

spheres, right rectangular prisms, triangular prisms in real-life?

How do I find the surface area and volume of a three dimensional figure?

Objective(s):Students will Find volumes of prisms and cylinders

in the context of the real world.

Use the following lesson(s) first to introduce concepts/build conceptual understanding.engage ny Geometry, Module 3, Topic B Lesson 5: Three-Dimensional SpaceLesson 6: General Prisms and Cylinders and Their Cross-Sections

Use the textbook resources to address procedural skill and fluency.Lesson 12.4 pp. 847-854Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.

Task(s)How much money is that? (prism)Centerpiece (cylinder)

Writing in Math/DiscussionWrite a helpful response to the following questions posted on an Internet garden forum.“I am new to gardening. The nursery will deliver a truckload of soil, which they say is 4 yards. I know that a yard is 3 feet, but what is a yard of soil? How do I know what to order?”

Domain: G-GMD Geometric Measurement and DimensionCluster: Explain volume formulas and use them to solve problems G-GMD.A.1 Give an informal

argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

G-GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. ★

Enduring Understanding(s)Geometric definitions, properties and theorems allow one to describe, model, and analyze situations in the real world.

Essential Question(s) In what ways do we use cones, cylinders,

spheres, right rectangular prisms, triangular prisms in real-life?

How do I find the surface area and volume of a three dimensional figure?

Objective(s):Students will

Use the following lesson(s) first to introduce concepts/build conceptual understanding. engage ny Geometry, Module 3, Topic B Lesson 8: Definition and Properties of Volume Lesson 9: Scaling Principle for Volumes Lesson 10: The Volume of Prisms and Cylinders and Cavalieri’s Principle

Use the textbook resources to address procedural skill and fluency.Lesson 12.5 pp. 857-863Use the following resources to deepen students' conceptual understanding of mathematical content and develop their

Writing in Math/DiscussionCompare and contrast finding volumes of pyramids and cones with finding volumes of prisms and cylinders.

Shelby County Schools 2016/2017Revised 2/6/17

13 of 19

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

Understand the precise language that describes the properties of volume.

Find volumes of pyramids and cones in the context of the real world.

ability to apply that knowledge to non-routine problems.

Task(s)Doctors Appointment (cone) Great Egyptian Pyramids (pyramid)

Domain: G-GMD Geometric Measurement and DimensionCluster: Explain volume formulas and use them to solve problems G-GMD.A.1 Give an informal

argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

G-GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. ★

Enduring Understanding(s)Geometric definitions, properties and theorems allow one to describe, model, and analyze situations in the real world.

Essential Question(s) In what ways do we use cones, cylinders,

spheres, right rectangular prisms, triangular prisms in real-life?

How do I find the surface area and volume of a three dimensional figure?

Objective(s):Students will Understand the precise language that

describes the properties of volume. Find and use volumes of spheres to solve

problems.

Use the following lesson(s) first to introduce concepts/build conceptual understanding.engage ny Geometry, Module 3, Topic B Lesson 11: The Volume Formula of a Pyramid and ConeLesson 12: The Volume Formula of a Sphere

Use the textbook resources to address procedural skill and fluency.Lesson 12.6 pp. 873-878

Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.

Task(s)Guessing Gumballs Task

Vocabularygreat circle, pole, hemisphere

Writing in Math/DiscussionWrite a ratio comparing the volume of a sphere with radius r to the volume of a cylinder with radius r and height 2r. Then describe what the ratio means.

Visualizing Solids (Allow approximately 3 weeks for instruction, review, and assessment)

Domain: G-MG Modeling with Geometry Cluster: Apply geometric concepts in modeling situations G-MG.A.1 Use geometric shapes,

their measures, and their properties to

Enduring Understanding(s).Geometric definitions, properties and theorems allow one to describe, model, and analyze situations in the real world.

Use the following lesson(s) first to introduce concepts/build conceptual understanding.engage ny Geometry, Module 3, Topic B Lesson 7: General Pyramids and Cones and Their Cross-Sections

VocabularyIsometric view, cross sectionWriting in Math/DiscussionWhen an object on a video game is viewed from only one side, what are some ways that

Shelby County Schools 2016/2017Revised 2/6/17

14 of 19

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESdescribe objects (e.g., modeling a tree trunk or a human torso as a cylinder). ★

Domain: G-GMD Geometric Measurement and DimensionCluster: Visualize relationships between two‐ dimensional and three‐ dimensional objects G-GMD.B.4 Identify the shapes of two‐

dimensional cross‐sections of three dimensional objects, and identify three‐dimensional objects generated by rotations of two‐dimensional objects.

Essential Question(s)In what ways, can geometric figures be used to understand real-world problems?

Objective(s):Students will Investigate cross sections of three-

dimensional figures.

Use the textbook resources to address procedural skill and fluency.Lesson 12-1 – Representations of Three- Dimensional Figures, Lesson pp. 823-828

Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each Standard(Designed as a resource tool to assist teachers in deepening their understanding of what each standard means in terms of what students must know and be able to do.It outlines only a sample of instructional strategies and examples. Links to conceptual categories and specific standards in the document can be accessed from page 5 Mathematics Standards for High School.)

Task(s)Volumes of Cylinders, Cones, Pyramids, and Spheres VideosVolumes of Cylinders, Cones, Pyramids, and Spheres Task, p.98Unit on Area, Perimeter, and Volume with multiple tasks Boxing Basketballs p.5 Great Pyramid p.13 Walter and Juanita’s Water Troughs p.17 Greenhouse p.23

the object can be made to appear three-dimensional?

Domain: G-MG Modeling with Geometry Cluster: Apply geometric concepts in modeling situations G-MG.A.3 Apply geometric methods to

solve design problems (e.g., designing

Enduring Understanding(s)Geometric definitions, properties and theorems allow one to describe, model, and analyze situations in the real world.

Use the textbook resources to address procedural skill and fluency.Lesson 12-2 – Surface Area of Prisms and Cylinders, pp.830-837

VocabularyLateral face, lateral edge, base edge, altitude, height, lateral area, axis, composite solid

Writing in Math/DiscussionShelby County Schools 2016/2017

Revised 2/6/1715 of 19

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). ★

Essential Question(s) In what ways, can geometric figures be

used to understand real-world problems?

How do surface volume and area compare to each other?

Objective(s):Students will

Find the lateral area and surface area of prisms to solve problems.

Find the lateral area and surface area of cylinders to solve problems.

Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each Standard

Task(s)Cereal Box Project (Surface Area & Volume) Tasks

Compare and contrast finding the surface area of a prism and finding the surface area of a cylinder.

Domain: G-MG Modeling with Geometry Cluster: Apply geometric concepts in modeling situations G-MG.A.3 Apply geometric methods

to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). ★

Enduring Understanding(s)Geometric definitions, properties and theorems allow one to describe, model, and analyze situations in the real world.

Essential Question(s) In what ways, can geometric figures be

used to understand real-world problems? How do surface volume and area compare

to each other?

Objective(s):Students will Find the lateral area and surface area of

pyramids to solve problems. Find the lateral area and surface area of

cones to solve problems.

Use the following lesson(s) first to introduce concepts/build conceptual understanding.engage ny -Lessons 23–24: The Volume of a Right PrismLessons 25–26: Volume and Surface AreaUse the textbook resources to address procedural skill and fluency.Lesson 12-3 – Surface Area of Pyramids and Cones, pp.838-846

VocabularyRegular pyramid, slant height, right cone, oblique cone

Writing in Math/Discussionp. 845, #41 Describe how to find the surface area of a regular polygonal pyramid with an n-gon base, height h units and an apothem of a units.

Domain: G-MG Modeling with Geometry Cluster: Apply geometric concepts in modeling situations

Enduring Understanding(s)Geometric definitions, properties and theorems allow one to describe, model, and analyze situations in the real world.

Use the textbook resources to address procedural skill and fluency.Lesson 12-6 – Surface Areas of Spheres, pp.864-871

VocabularyGreat circle, pole, hemisphere

Shelby County Schools 2016/2017Revised 2/6/17

16 of 19

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

G-MG.A.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). ★

Essential Question(s) In what ways, can geometric figures be

used to understand real-world problems? How do surface volume and area compare

to each other?Objective(s):Students will Find the surface area of a sphere to solve

problems

Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each Standard

Writing in Math/DiscussionDescribe the difference between the surface area of a sphere and the volume of a sphere.

Trigonometry with All Triangles(Allow approximately 1 week for instruction, review, and assessment)t)

(Advanced Algebra & Trigonometry)Domain: A-AT.1 Applied TrigonometryCluster: Use trigonometry to solve problems G-AT.A.5 . Understand and apply the

Law of Sines (including the ambiguous case) and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

Enduring Understanding(s).Dilations, similarity, and the properties of similar triangles allow for the application of trigonometric ratios to solve real-world situations.

Essential Question(s)How can the Law of Sines and Cosines be used to solve problems involving non-right triangles?

Objective(s):Students will Derive a trigonometric formula for the area

of a triangle Prove and apply the Law of Sines; Prove and apply the Law of Cosines.

Use the following lesson(s) first to introduce concepts/build conceptual understanding.engage ny Geometry Module 2, Topic E, Lesson 30

Use the textbook resources to address procedural skill and fluency.Lesson 8-6 – The Law of Sines and Cosines

Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.

Task(s)Right Triangle Trigonometry TasksStudents explore the relationships that exist among and between sides and angles of right triangles. They build upon their previous knowledge of similar triangles and of the Pythagorean Theorem to determine the side

VocabularyLaw of Sines, Law of Cosines

Writing in Math/DiscussionDraw and label a triangle that can be solved: a. using only the Law of Sines; b. using only the Law of Cosines. Explain why each triangle cannot be solved using the other Law.

Shelby County Schools 2016/2017Revised 2/6/17

17 of 19

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESlength ratios in special right triangles and to understand the conceptual basis for the functional ratios sine, cosine, and tangent. They explore how the values of these trigonometric functions relate in complementary angles and how to use these trigonometric ratios to solve problems. Through the work with these eight tasks, students not only develop the skills and understanding needed for the study of many technical areas but also build a strong foundation for future study of trigonometric functions.

Shelby County Schools 2016/2017Revised 2/6/17

18 of 19

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics

Quarter 4 GEOMETRY

RESOURCE TOOLBOXThe Resource Toolbox provides additional support for comprehension and mastery of subject-level skills and concepts. While some of these resources are embedded in the map, the use of these categorized materials can assist educators with maximizing their instructional practices to meet the needs of all students.

Textbook ResourcesConnectED Site - Textbook and Resources Glencoe Video Lessons Hotmath - solutions to odd problems

Comprehensive Geometry Help:Online Math Learning (Geometry) I LOVE MATHNCTM IlluminationsNew Jersey Center for Teaching & Learning (Geometry)

CalculatorFinding Your Way Around TI-83+ & TI-84+ (mathbits.com) Texas Instruments Calculator Activity ExchangeTexas Instruments Math NspiredSTEM ResourcesCasio Education for Teachers*Graphing Calculator Note: TI tutorials are available through Atomic Learning and also at the following link: Math Bits - graphing calculator steps Some activities require calculator programs and/or applications.Use the following link to access FREE software for your MAC. This will enable your computer and TI Calculator to communicate: Free TI calculator downloads

StandardsCommon Core Standards - Mathematics Common Core Standards - Mathematics Appendix A TN CoreHS Flip Book with Examples of each Standard (Designed as a resource tool to assist teachers in deepening their understanding of what each standard means in terms of what students must know and be able to do.It outlines only a sample of instructional strategies and examples. Links to conceptual categories and specific standards in the document can be accessed from page 5 Mathematics Standards for High School.)

Geometry Model Curriculum http://www.ccsstoolbox.org/http://insidemathematics.org/index.php/high-school- geometry http://www.azed.gov/azcommoncore/mathstandards/hs math/ http://learnzillion.com/common_core/math/hs http://www.livebinders.com/play/play/454480https://www.livebinders.com/play/play?id=464831 http://www.livebinders.com/play/play?id=571735North Carolina – Unpacking Common Core http://thegeometryteacher.wordpress.com/the-geometry-course/ http://math termind.blogspot.com/2012/07/common-core- geometry.html Utah Electronic School - Geometry Ohio Common Core Resources Chicago Public Schools Framework and Tasks

Mathy McMatherson Blog - Geometry in Common Core

ACT TN ACT Information & ResourcesACT College & Career Readiness Mathematics Standards

VideosMath TV VideosThe Teaching Channel Khan Academy Videos (Geometry)

TasksEdutoolbox (formerly TNCore) Tasks Inside Math Tasks Mars Tasks Dan Meyer's Three-Act Math TasksNYC tasks Illustrative Math TasksUT Dana Center SCS Math Tasks

GSE Analytic Geometry Unit 2: Right Triangle TrigonometryGSE Analytic Geometry Unit 3: Circles and Volume

NWEA MAP Resources:https://teach.mapnwea.org/assist/help_map/ApplicationHelp.htm#UsingTestResults/MAPReportsFinder.htm - Sign in and Click the Learning Continuum Tab – this resources will help as you plan for intervention, and differentiating small group instruction on the skill you are currently teaching. (Four Ways to Impact Teaching with the Learning Continuum)https://support.nwea.org/khanrit - These Khan Academy lessons are aligned to RIT scores.

Interactive ManipulativesGeoGebra – Free software for dynamic math and science learningNCTM Core Math Tools http://www.keycurriculum.com/products/sketchpad (Not free) Any activity using Geometer’s Sketchpad can also be done with any software that allows construction of figures and measurement, such as Cabri, Cabri Jr. on the TI-83 or 84 Plus,TI-92 Plus, or TI-Nspire.

Literacy ResourcesLiteracy Skills and Strategies for Content Area Teachers (Math, p. 22)Glencoe Reading & Writing in the Mathematics ClassroomGraphic Organizers (9-12) (teachervision.com)

Shelby County Schools 2016/2017Revised 2/6/17

19 of 19